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## Lack of Standardization and Consistency
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- No unified global framework exists for ESG measurement, leading to fragmentation across markets and regions
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- Rating agencies like MSCI, Sustainalytics, and Bloomberg ESG use completely different methodologies and weighting systems
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- The same company can receive a top score from one agency and a poor score from another, creating investor confusion
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||||||
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- Correlations between different ESG rating providers are often below 0.5, compared to 0.99+ correlation between credit rating agencies
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||||||
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- Different frameworks (GRI, SASB, TCFD, etc.) measure different things, making apples-to-apples comparisons impossible
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||||||
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- The definition of "E," "S," and "G" varies significantly across providers and even within the same provider over time
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||||||
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- Lack of regulatory oversight means providers can change methodologies without transparency or accountability
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||||||
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||||||
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## Potential for Lower Returns
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||||||
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- ESG funds may underperform by excluding high-performing sectors like fossil fuels, tobacco, defense, and gambling
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- Reduced investment universe limits diversification opportunities and increases concentration risk
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- Academic studies show mixed results, with some indicating ESG funds lag traditional indices by 1-3% annually
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- During certain market conditions (like energy rallies), ESG portfolios may significantly underperform
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- Higher screening requirements can lead to missed opportunities in emerging markets or smaller companies
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- The "sin stock" anomaly shows that excluded sectors often outperform due to lower competition for capital
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- Factor exposure differences mean ESG funds may simply be capturing value, quality, or momentum premiums rather than ESG alpha
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||||||
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## Greenwashing Concerns
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- Companies can manipulate disclosures to appear more sustainable without changing actual practices
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- Marketing materials often highlight positive ESG initiatives while downplaying negative impacts
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- Fund managers may rebrand existing portfolios as "ESG" with minimal changes to capture asset flows
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- Lack of third-party verification allows exaggerated or misleading claims to persist
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- Companies can focus on easy-to-measure metrics while ignoring more material ESG issues
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- "Impact washing" occurs when funds claim to create positive change without evidence
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- Regulatory enforcement against greenwashing remains weak in most jurisdictions
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- The ESG label becomes diluted when applied to funds with only marginal differences from conventional strategies
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## Higher Costs
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- ESG fund expense ratios average 0.2-0.5% higher than comparable conventional funds
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- Additional research, data subscriptions, and screening processes increase operational costs
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- Specialized ESG analysts and consultants command premium fees
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- These higher fees compound over time, significantly reducing long-term wealth accumulation
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- Many ESG funds are actively managed, adding another layer of costs versus passive indexing
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- Retail investors bear these costs despite questionable evidence that ESG factors improve risk-adjusted returns
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- Hidden costs include increased trading expenses from more frequent portfolio rebalancing
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- The ESG industry has financial incentives to perpetuate complex scoring systems that require paid services
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## Subjectivity and Ideological Bias
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- What constitutes "good" ESG performance reflects cultural, political, and personal values rather than objective criteria
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- Nuclear energy scores poorly on some environmental frameworks despite being low-carbon
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- Defense contractors may score well on governance while being excluded for ethical reasons
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- Labor practices considered acceptable in one country may violate social standards in another
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- ESG frameworks can reflect Western values that don't translate to emerging markets
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- Political viewpoints influence whether issues like gun manufacturing or abortion access are considered material
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- Investors with different values cannot customize ESG criteria to match their personal ethics in most funds
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- The prioritization of E vs. S vs. G varies widely and reflects subjective judgment calls
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- ESG can be used as a vehicle for activist investing that may not align with all shareholders' interests
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## Data Quality Issues
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- Most ESG data is self-reported by companies with minimal independent verification
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- Companies have incentives to present themselves favorably, leading to selective disclosure
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- Standardized metrics don't exist, so companies report different data points making comparisons difficult
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- ESG data is often backward-looking, reflecting past performance rather than predicting future risks
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- Small and mid-cap companies typically have less ESG data available, creating a bias toward large caps
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- Emerging market companies often lack the resources or requirements to report comprehensive ESG data
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- ESG scores may not capture recent controversies, scandals, or rapid changes in company practices
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- Data providers often fill gaps with estimates and assumptions rather than actual company data
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- The materiality of ESG factors varies by industry, but scoring systems often apply uniform standards
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- Reporting frequency is inconsistent, with some companies updating annually and others less frequently
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## Questionable Real-World Impact
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- Buying or selling shares on secondary markets doesn't directly provide or deny capital to companies
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- Divestment may simply transfer ownership to less ESG-conscious investors without changing company behavior
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- The capital markets impact is minimal unless divestment is massive and coordinated
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- Companies can still access debt markets, private equity, or international capital even if public equity investors divest
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- There's limited empirical evidence that ESG investing leads to measurable environmental or social improvements
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- "Impact" claims often conflate correlation with causation regarding company behavior changes
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- Engagement strategies (voting, shareholder proposals) often fail to produce significant changes
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- ESG investing may create a false sense of contribution to solving problems while avoiding more direct action
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- The market may already price in ESG risks, making additional screening redundant
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- Capital allocation changes may be too small to influence management decisions at large corporations
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## Exclusion of Beneficial Investments
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- Companies transitioning to sustainable practices may be excluded due to legacy operations
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- Energy companies developing renewable technologies are often screened out entirely
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- Auto manufacturers pivoting to electric vehicles may score poorly due to historical emissions
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- Strict screening can exclude "best in class" improvers in favor of already-clean industries
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- Emerging market companies making genuine progress may lack the reporting infrastructure to score well
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- Innovation in challenged sectors (like sustainable agriculture or carbon capture) may be missed
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- Blanket sector exclusions ignore nuances and differentiation within industries
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- Companies with poor historical ESG scores may be transforming but remain penalized
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- The "transition" companies most critical to climate solutions may be systematically underweighted
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- Exclusionary screening can create moral hazard by removing engaged shareholders who push for change
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## BlackRock's ESG Influence and the Paris Agreement Connection
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### The Timeline: Not a Coincidence
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**December 2015: Paris Agreement Adopted**
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- 195 countries signed on to reduce emissions and keep global temperature increases below 2°C (3.6°F) above pre-industrial levels
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- 185 countries submitted plans detailing how they intended to reduce greenhouse gas emissions by 2025 or 2030
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- The agreement entered into force on November 4, 2016
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**2015-2017: BlackRock's ESG Pivot**
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- 2015: Larry Fink chastised managers for returning too much money to investors in dividends and buybacks, signaling a shift toward long-term stakeholder thinking
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- 2016: Fink's letter formally declared "ESG factors relevant to a company's business can provide essential insights into management effectiveness"
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- 2016: BlackRock and Vanguard voted to back shareholder proposals on climate-related issues for the first time
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- 2017: Despite rhetoric, BlackRock voted in favor of just 4% of climate change proposals
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### Mechanisms of Pressure
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**1. Proxy Voting Power**
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- BlackRock warned "we do not hesitate to exercise our right to vote against incumbent directors" if insufficient progress was being made
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- As one of the largest shareholders in every S&P 500 company, BlackRock can sway votes by several percent
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- BlackRock cast votes with management 96% of the time on say-on-pay votes, but used selective opposition on ESG issues
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**2. Private "Engagement" Meetings**
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- BlackRock reported nearly 4,000 "engagements" lobbying C-suites on diversity and climate issues during peak ESG years
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- Proxy voting was merely the last resort if BlackRock didn't get its way through negotiation
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- These private meetings allowed BlackRock to pressure companies behind closed doors before resorting to public votes
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**3. The Annual CEO Letter as Political Tool**
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- Since 2012, Larry Fink's annual letters became increasingly influential as BlackRock's assets grew
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- The letters came to symbolize the threat to shareholder capitalism posed by investment houses forcing ESG principles on companies
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- Fink spoke with the authority of an elected representative without actually polling his investors for their support
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**4. Market Dominance and Scale**
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- By 2009, BlackRock had $3 trillion in assets under management, larger than total US federal revenue
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- This massive pressure coerces companies to abide by the ESG agenda when not receptive to negotiations
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- BlackRock's high ESG proposal support in 2021-2022 pushed many companies to adopt ESG initiatives now standard across corporate America
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### The Paris Agreement as ESG Enforcement Mechanism
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**How the Connection Works:**
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- The Paris Agreement created an international framework signaling massive future regulatory changes
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- Energy policy shifts, carbon regulations, and mandatory disclosure requirements were coming
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- BlackRock positioned itself at the forefront, effectively making private finance an enforcement mechanism for international climate goals
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- Asset managers gained politically legitimate cover to pressure companies on climate issues that weren't legally binding
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**Criticisms of This Approach:**
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**Undemocratic Power Concentration**
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- When CEOs of every American company answer to Larry Fink first and actual investors second, diversity of strategies plummets
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- BlackRock imposed its own values without consulting the millions of investors whose money it managed
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- Private asset managers wielding such power raises democratic accountability questions
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**Inconsistency Between Rhetoric and Action**
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- Given Fink's lofty public letters, one would expect more consistency in proxy voting
|
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- The gap between public ESG advocacy and actual voting record in 2016-2017 was substantial
|
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- BlackRock's actions often didn't match its proclaimed commitments
|
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**Strategic Ambiguity**
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Whether BlackRock's ESG push represented:
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- Strategic positioning to get ahead of regulatory changes
|
||||||
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- Genuine ideological belief in climate action
|
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- Financial opportunism creating demand for ESG products
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- Political influence implementing Paris goals through private markets
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- Some combination of all these factors
|
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**The Core Issue:**
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- Private financial institutions became de facto enforcers of international political agreements
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- Companies faced pressure not from voters or legislators, but from asset managers managing others' money
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- This created a parallel governance structure outside democratic accountability
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|
|
||||||
|
|
||||||
|
|
||||||
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|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
conflitto di interessi per il report di emissioni CO2 di mercedes se è lazienda stessa che fa il report?
|
||||||
|
Si è passato da qualcosa di volontario a qualcosa di obbigatorio? Come mai?
|
||||||
|
Non si corre il rischio di greenwashing?
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
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|
||||||
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|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
@@ -0,0 +1,146 @@
|
|||||||
|
---
|
||||||
|
|
||||||
|
excalidraw-plugin: parsed
|
||||||
|
tags: [excalidraw]
|
||||||
|
|
||||||
|
---
|
||||||
|
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
|
||||||
|
|
||||||
|
|
||||||
|
# Excalidraw Data
|
||||||
|
|
||||||
|
## Text Elements
|
||||||
|
Time ^9H0yPop1
|
||||||
|
|
||||||
|
M1/P1 ^9CGJLXaz
|
||||||
|
|
||||||
|
M2/P1 ^sTp1NlD1
|
||||||
|
|
||||||
|
M2/P2 ^JOGu64DD
|
||||||
|
|
||||||
|
P2 ^q6j6qYcn
|
||||||
|
|
||||||
|
P1 ^1qBVsJFI
|
||||||
|
|
||||||
|
T0 ^s5OoAz4k
|
||||||
|
|
||||||
|
This
|
||||||
|
Is
|
||||||
|
Overshooting ^0mbafsg9
|
||||||
|
|
||||||
|
T0 ^q8BoJjAs
|
||||||
|
|
||||||
|
E1 ^rG95JoLX
|
||||||
|
|
||||||
|
E2 ^j82JZTta
|
||||||
|
|
||||||
|
E4 ^9uldbGqP
|
||||||
|
|
||||||
|
Overshoot ^c4tjwmPN
|
||||||
|
|
||||||
|
Time ^SVHC1NFc
|
||||||
|
|
||||||
|
%%
|
||||||
|
## Drawing
|
||||||
|
```compressed-json
|
||||||
|
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|
||||||
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|
||||||
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|
||||||
|
|
||||||
|
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|
||||||
|
|
||||||
|
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|
||||||
|
|
||||||
|
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|
||||||
|
|
||||||
|
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|
||||||
|
|
||||||
|
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|
||||||
|
|
||||||
|
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|
||||||
|
|
||||||
|
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|
||||||
|
|
||||||
|
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|
||||||
|
|
||||||
|
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|
||||||
|
|
||||||
|
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|
||||||
|
|
||||||
|
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|
||||||
|
|
||||||
|
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|
||||||
|
|
||||||
|
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|
||||||
|
|
||||||
|
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|
||||||
|
|
||||||
|
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|
||||||
|
|
||||||
|
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|
||||||
|
|
||||||
|
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|
||||||
|
|
||||||
|
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|
||||||
|
|
||||||
|
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|
||||||
|
|
||||||
|
IF4yhpgtQBQ8kF00xA4t4Clp8FsttV0xiBStjVCxIhrVSkq+HVhuuBfpOxAZR415hxheJxdFoKJwRWxBQC+OrFyZklqZXuXFK1HtbxgepFwZlB2ChZYhpd+1Fi4YNCx1ChwwiDl1bCWeY0K2V1+eN1OhxeL1UiD1r8VeSihDZ2F2Win1KqQ5dhDhCD45X2k5INnhrB7iEN4+C5YA0+FdEgtqvCvYhEMAuAbk/InCUAyggwCm9Atq9AiSwS9Aflyk
|
||||||
|
|
||||||
|
Kw2RaOyc7d+YYauO1SI9kNLFCpDOzN/5rNqpJI6pmVC93NOpvNEuBVRpEFJVUFIxY2FVVph9+yx99VyBytzVJ0atx8U4mtqA+F06ut3DxFY0sZrYBWNFVFaAa65BUZTYz8bYn0/df981VWQDy1Ihq1L64DccR4WCHWftu1cDL4QGMlZQclsGilbKv4zgOj7KzgAwEd1TiEzg4mZQPwT8sdYAGuWECJ2lSdqGQWX4nTPMPToIGl4qqdJledbE8zaJ
|
||||||
|
|
||||||
|
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|
||||||
|
|
||||||
|
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|
||||||
|
|
||||||
|
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|
||||||
|
|
||||||
|
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|
||||||
|
|
||||||
|
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|
||||||
|
|
||||||
|
1/CQncMyhh13fRKsR7gRnSN8s4qqs1R9ZZs4pMo8FFZXsxpCwXN8ahAEiIOBZMEp0PyP0GwKCD5PgOxikJoIkhZNUIkh5BS5J8fKdzW+FPLRANFNDDRQ+fjjRap6C+PZUclZ26la/ulXPUZkD1Y0Z6DyZz0TZ5WkLSi527YwLbZ1i8u/D6u05+UIrZu258S26VFkpNZD57+FOke0Rd1TcGTFcf0LuC/agE+8y6caCgeMHGKXeSAi+zy2+yl08dxe
|
||||||
|
|
||||||
|
z2tYHjmJ8hgjzwOnz4V+UCB0L+01HWV/00pXzGQaL+pX11IuhzpaM/idr4NyR2nVr4b6bws5N6H5bCxFbwc+Xa5RcGwFNTsZzUQA4YD5CxqYBDu+ASQKCGUCaB6AJkKtnqFUYxRDwO+QsA7QfK00yiqAA4gY2+7F9E0I7ExnpyhY59DOQFCzGD1M5F9Iem9RxtvXNIYtyqVfezjX0c6I9nOBLRvqcmb6q1W+uARJB33jB+ce+J7O+NNTIoCV9GmW
|
||||||
|
|
||||||
|
K9ilDJ7j9EwBYFSrmXp5zV5+kAdgov2Aa5MV++THMoeAPAfQt+4WHfimUgD79Ou4vP8Mf0gyldYOKQFXppSGYYdkSd/F/gN315P8deZlV/mbDWa68Nm/gqjtN0cpUpbeikOoCcGog2RzUgkfICH2RwBVw+EKHfC8ATJd1+gPdJOLGWzD5hYyUEd7rwESop8k+afcFmlXZpZ8P8ufSgZrhXo0CIe0yYWtDxrRMDJa0tcYg50mKR8G+3jVHv60uSed
|
||||||
|
|
||||||
|
BglLfSgbXj6D930MgsflulfqyDIugLVOHvkLC5dEY6gpngvxZ5pdH0egprDBnBTWl/2pTAruYObrkI0G6ySsucOUK5BbWF1ebDgy0JzCY8zrE7K60MIdkyGnraAG9XKAfU/WVHWhr9T1YQBUGjDfvJgyHyJswao+HASmz/7Ll0AFAU1IQFRCkAYAPIQSPECRCkBNAiQJyOiOsighbUSA0xpAAKShUKaaAD5opwILYDfCr5UoZp0/IVCM+VQ/TtC2
|
||||||
|
|
||||||
|
1J59gK1Awvk0ORZQ8GBMPfemwOqq19OB9fFzjwM1zucd2nnVoMIMRx48xBAXG4JtRhj44IuM3ffG/TtxRcchOwA8J/QdoM82KGwzQWmX5Zs8MuYDHMgMCtCb8waIlbfpK134WDKmB/BDvJQv7ldrBSEZ4LU0v6+i6YN/drqiXv5zNH+gQ4blKgjEUdxu0Yj/nZXo4zd9UCI1jugFICmoxS1kNgBxj8r9YzuMHettSOHr3lRccQWMknBDxPBegScY
|
||||||
|
|
||||||
|
gmWJU500x6wLCesyN+7ED/umfDkeQK5F1C8qUFOxtO1L4/cUQ5fBdp0KqowFxR8BTxmrmdJN9t2olXdo0FGHZ0Da6WQgp8lIojUwuuAynlbXzBLpjgAY64usKS6bDUuy/G0Rz0eA7goU13KROK156ujTh/WCQFOFOrjYQRn4m4Rg1ULYMNC11bQk6yEiEM2y7rTst8Ioa9kqGAImhj9SDZVBfxkIONpCNBrfpYRvheEcxxcqIiIA5qQgtZDcjDAo
|
||||||
|
|
||||||
|
gBY25uSIDRt0qRscRsTdyHjH58wOQ9IZghhhwwZSzYkoUzXKF/cIW3YsgU3GB7ciqBBfA0rQOaEjjCBY8QcRX0XasCuh7AnoXVXnHoU+B6PAQYgOx7xYqWmkPMKKzzCxM9xWojgKy3Gpwwk4n6bluaLYKWjiuGuL9oHm3AfAWwJgm8CcOlZnCPxA7b8SninADseEtwyEWoXtbATnhMrMCd8Igl/JSGR2chr8MgD/CrCCEwNn9Smx+TwRwNBNtOUw
|
||||||
|
|
||||||
|
kcMQck+XCbDTTZMYAwxATQKajqCERyJyQmTmFF2A0VbyhBWkQeG0BrochX9WGHvktyJ8WxuUNsVPV4mVCzGHNbPoJNqG5UGhfIktBJMFGotrOHQuzgpLFEcDZxSPFST4yo67tKpWk7YQTwkgQoU4jwDBA7Tib7jdRJksavmBaxxRg8Vki8RaOyZ2TMyN41fjmW3CfRj0rktxK+I8nvj0AU4EdLq18kAz0GdwrBvWVClNl8GEUt4a2WIbRSPWMMn4
|
||||||
|
|
||||||
|
d63eq+skpnWIEUhI/HAzAaE5dCdCJynJsuGPDf/rwmsgeQHQtqHyIkiECrk4AJkeIHADgDWRiAgwRIBwGxlKjuo5vFAS0wTJCJOwtIkOF1OTbTUvuqfUcV2ybh4gdOA7NND2NGkUDxpvIsSfyJL4zSy+c02HtXyWlKS5xaFdaS3w9IWRFRTyZUXrTwKaQdwxBXkmKWH6/BDJLLC6THyKyf1bp/PF2leJAbPT9Be4KsbT0+mYRvpwHD0VYOF7gcfR
|
||||||
|
|
||||||
|
J/CrmUGMGwcwmkcv0ULIFgkEnBIYlwbfw67AllBPMXrsGP64YkvB0Y5/r4PjFG93+43bZl/0t42wbe6YoqRIAdBGBSA+AQiBwHNQL54gMAHcM4HYxwBnAU4TAAPNJE8ztgjzMEJbgfKKYihjI7iRLOfw8AuQoIBAKRVIGA8FZfYpWaJOgpTSBR9A2aU43aFazRR045afaS4Ebt+hW7NHnKIx5KRTy20vCrj277mz76H8aFPuCKYKDZh9NAqLe2jL
|
||||||
|
|
||||||
|
mShMlYE0eePdnM9PZug72U1hUrPwaKRw/LuJRAV78Q5JXMOlHTq6IRJ5Ec3lLnOv5pywxelbOg/wLmiU9esYjwWN1LlDckxRdFMWEJ0i1z5uEgQYN0CMDmpSAiSUEE6hgAwBnA1QUEMMEEh7tiA8QdqiQg5Ik0apMUEeTvjrGd1cc+0qeWLLKGzyWa88xecvIB4WNexgFDeeOPEk7zy0rQpZAfJFGLTj5us1afrIGEbTPOwwE2V3yOD48LZd8dHB
|
||||||
|
|
||||||
|
2BDwOy5BqAcFAeIn6wwQ853a0qaP/qB0tBWw68diltG+yYYLwCtLApfHuTg5gvUOYfxF6oKxeYc6OXJ0wUzN8EoYjXuGLIVFyB0JCvEmQqoXEKghtlahZSVTFOUCpvDdANRGYBADeEvc3sIaKnBIh+Gg4UEJIH0CJBAmiQiuSo0Cq/AMcUfMEI+KwFFCWwYyjTv1OIGqKl5HMzQUOxGmnYxp47XRarI3oGKhRjQw+aYptII8VpZ85HguN4FLiB0u
|
||||||
|
|
||||||
|
7djHYp1qOKX5Y0PfNmAPD3jh+sZbxVwnfkzKQ8bst0TZIems8XiuwxyZ8DbAByyU8SgEkgqjnejUlfXL0cyhmUpycluCvJXUmBKcwkVV/Ayj4KKXGUoxxc8hW/0/7DLjYSYoZRb3KBqR9mNcupf/2wCdAoA5qCgPoEIirjBlhY8Pk/BvJZgngtIlsHEGmrPwKKAwNLMQQdrdSuJHbZRcY0WXqL+Jq89ZYrM2WazwK6siWVsoOVTijlM40+ZKO4EX
|
||||||
|
|
||||||
|
zFxV85cZ5xJH3y0S+BVLLsE/ruKv5dYj5YC3xyn4IUQCX5acJCVgKBW4S28elnBDTVHxsSl0ZCvgboBzWLAS1nth8kKEw1KyKNn+NBm8BAJDrECS8Ohml43W8MqCYjJgk+s4JaMkQhjNSlVAY1EajKfGyhHZShCWEyGkTMdj/9+Q1QDyKiBhy8JsAVUlulvgU40SXgky3HHFATi90U4acAYAVhC5SBOJii9sUQKlldj2RAkpVevJVUySzO003eRr
|
||||||
|
|
||||||
|
OXVF9Jx8uboXLWUmWLL5gwg+J5zchrjfS+Bc3N/XBS7iGWe+B1R9yASjrCwZ4uftZI9VL8vZ3ql6UeOmpLonyTomBvAr+W/TQRjCJPMg2DagabWQUpNRDMtx8YWyRDDNZlhikIac1KMvNc3mSnDkQRliMkUpDQmD4MJVa3KfOXynEz8JpACgMwGcDKBEgQgOoPoGCRNBSAtqUgHUDiiaBhgZq0RU3W5mBVBSJY2ONzyFIDEOw0yx0cnxnlSTtOnx
|
||||||
|
|
||||||
|
XThouHZrztFS6hFnorVlrqNVqqzFu5m1WIU6+CtKUYaouXGqrlnnStuauCaPyHFKo3aUcCvVPAMExkrfMdKGqmTmwviu4PmDdlEb7p77QFeFgcl2iNqJ4f9QB0A2nDLByCo/pgtP7soxNyHDBMipwVq9XBydA3p4NIXlKYxJSwlWUrxU0cKF50MPlXJpXUl6FdvCgFyEkAOgTgXIHYNTKgDEBwovYNyHAFIrUQLoflQINgCiBvlAq/FC7lmCSC0i
|
||||||
|
|
||||||
|
PolBRPvfEnXzKpZcq5ZYO2Gk1DlVNjTTfY3VVSSxaEtLVdusUm7q9ZrnIzYetJY3zcAwSW5UjkcHWanFTYKsUTzrG2rtRQ/M6aZOIIO58cOYZ9YlwrWsE31Og4Eo8lNk3NqpnfO3jXU0Coh8ALMuoBAC/DJhslEAALXuFILEEvo4K/BEHKY7kaMxNpQSCDrB2DAIdHKiiRAAKTcrCc0KArM/HeAFh7tgmyFPyowSE4PmIqyQeKqKE9SlIfUsFrKo
|
||||||
|
|
||||||
|
XlLKV5miqWft2wCggBdym4UYVUklzsnGu9ZgTLgWk6bjleq/TQapR4HrrFh26oKeoiaAxME6WaFNeo8UvpddCwsaNsChLFYvN+My8e+vAWfqfZjwBHXbWR1iVX24U4tZG3FpgaQRJauNVBoAngzcGKa8KQhrEC5AmAj1FDYQ3wjEBiAMIWCY3ngkSAKtVWmrXVtsSNa4iLWtrR1tbwpSPdruvbK4SYZ4zK1AOcGoTLI11qKNhEJEKCA26NBQQXIO
|
||||||
|
|
||||||
|
HK0BSC8JeEcQxoHUC5AxZBlfG8PsGWkWR8HyYyxPsJsk3SrpNKirnfKrnWKqTMSmxbRuu2X9F1Nq2pbdLvkmy7dVvQgzUrqNX7aIsAg5oCdrNkFSbNKUY4DarJiObDQXLB7WNQYKuK0sAS4Bd5v+W+adpsO4Fa9JhgKZDhz4oNWFo8kRaYVgY3OV6IxxlA0saC9lNATKCfJEtgzZLenPyWErCl4WYpVnV9IrNiVhWyuVSoqXkYKVuzauaVu4bgAM
|
||||||
|
|
||||||
|
ISkRmYKEJgPy+sAIbIFJ2jRrAGAhABABQHa1zaWa+3Tg1yGJAQBsAIgQZA6EHD6BBQLIgaWyISn8H2QghrIGweqEGdF1jBvg0sCkNCHeEE0lWTwaUMCGhDIhtTbsr+GSHcg0h4Q1Z3n2aHDDUAYw1ZDX2baJDyhow0IZMhy6hKvBiw8Yd4SrY/dzw1w/YcsOqHzqYM4oD4e0NZBJsCGqKQYd8PGHKDJcrAwQcUNuGhDonfLXEe72RGQj+gU2OEib
|
||||||
|
|
||||||
|
q1RzDUR1Q/tCsjqgxUEobAMsD5A3LqRJWII8wDKMYh8AJI0TC4aMBat9A1Br+AQBcRNh6MwRlQ1kGsNjoXQckmkDwcpAkAE1wUyUeMcHDnZvDYx4gK0DYCRZROuATQMEHn62gHsayrWjaBiFg6qgpAOAbgAAAUD3agLwDbYXG9g9SGTAAEpxQ9iZQAGEWAHGjjpxz6OcePQQgwU3xrIYkHuM9GtD7IXQyiCcMKJOA2wmUb2nsQhgHseJJ2DkFWPr
|
||||||
|
|
||||||
|
GWGRe3g0QFmMfbzgT2Og1lNYLCAoAeSXE+cH0CLAUQpAbGjicxPdgSTpAMkysbWOaQ/sPR9jggG63MB+QT2OAIseWNPYGTGxskAokYDDAtW+Ado39oniZButW6evEIElAGBsjiYOBU7plEGB+Qkp8E7QrYbYRBIUpoUyKaYi6RwAc6eocEFjDQ7kwQAA
|
||||||
|
```
|
||||||
|
%%
|
||||||
Binary file not shown.
@@ -0,0 +1,618 @@
|
|||||||
|
# Global Business Environment - Complete Study Guide
|
||||||
|
|
||||||
|
## Overview
|
||||||
|
|
||||||
|
This study guide integrates the interactive monetary policy diagrams with theoretical concepts and empirical evidence from the course. It covers:
|
||||||
|
|
||||||
|
1. **Monetary Policy Transmission Mechanisms**
|
||||||
|
2. **National Accounting Identities**
|
||||||
|
3. **Twin Deficits Hypothesis**
|
||||||
|
4. **Open Economy Macroeconomics**
|
||||||
|
5. **Empirical Applications**
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
## Part 1: Fundamental Identities
|
||||||
|
|
||||||
|
### 1.1 National Income Identity
|
||||||
|
|
||||||
|
$$Y = C + I + G + (X - M)$$
|
||||||
|
|
||||||
|
Where:
|
||||||
|
- $Y$ = GDP (national income)
|
||||||
|
- $C$ = Consumption (~51% of US GDP)
|
||||||
|
- $I$ = Investment (~27% of US GDP, most volatile)
|
||||||
|
- $G$ = Government purchases (~12% of US GDP)
|
||||||
|
- $X - M = CA$ = Current Account (net exports)
|
||||||
|
|
||||||
|
**Key Insight**: GDP can be viewed from expenditure side (who spends) or income side (who earns).
|
||||||
|
|
||||||
|
### 1.2 Savings Identity
|
||||||
|
|
||||||
|
Starting from national income:
|
||||||
|
$$Y = C + I + G + CA$$
|
||||||
|
|
||||||
|
Rearrange:
|
||||||
|
$$Y - C - G = I + CA$$
|
||||||
|
|
||||||
|
Define National Savings $S = Y - C - G$:
|
||||||
|
$$S = I + CA$$
|
||||||
|
|
||||||
|
**Interpretation**: National savings can be used to:
|
||||||
|
1. Finance domestic investment $(I)$
|
||||||
|
2. Lend to foreigners $(CA > 0)$ or borrow from foreigners $(CA < 0)$
|
||||||
|
|
||||||
|
### 1.3 Decomposing Savings
|
||||||
|
|
||||||
|
National savings has two components:
|
||||||
|
|
||||||
|
**Private Savings**:
|
||||||
|
$$S_p = Y - T - C$$
|
||||||
|
(Income after taxes minus consumption)
|
||||||
|
|
||||||
|
**Government Savings**:
|
||||||
|
$$S_g = T - G$$
|
||||||
|
(Tax revenue minus spending)
|
||||||
|
|
||||||
|
Therefore:
|
||||||
|
$$S = S_p + S_g$$
|
||||||
|
|
||||||
|
### 1.4 The Master Equation
|
||||||
|
|
||||||
|
Combining everything:
|
||||||
|
$$\boxed{CA = (S_p - I) + (T - G)}$$
|
||||||
|
|
||||||
|
Or equivalently:
|
||||||
|
$$\boxed{CA = S - I}$$
|
||||||
|
|
||||||
|
**This is the foundation of the twin deficits hypothesis.**
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
## Part 2: Monetary Policy Mechanisms
|
||||||
|
|
||||||
|
### 2.1 Money Market Equilibrium
|
||||||
|
|
||||||
|
**Concept**: Interest rate adjusts to equate money supply and money demand.
|
||||||
|
|
||||||
|
**Equation**:
|
||||||
|
$$\frac{M^s}{P} = L(R, Y)$$
|
||||||
|
|
||||||
|
Where:
|
||||||
|
- $M^s$ = Nominal money supply (controlled by central bank)
|
||||||
|
- $P$ = Price level (sticky in short run)
|
||||||
|
- $R$ = Nominal interest rate
|
||||||
|
- $Y$ = Real income
|
||||||
|
- $L(R,Y)$ = Money demand function
|
||||||
|
|
||||||
|
**Money Demand Function**:
|
||||||
|
$$L(R, Y) = k_1 Y - k_2 R$$
|
||||||
|
|
||||||
|
Where:
|
||||||
|
- $k_1 > 0$: Income elasticity (higher income → more transactions → more money demand)
|
||||||
|
- $k_2 > 0$: Interest rate semi-elasticity (higher rates → opportunity cost of holding money)
|
||||||
|
|
||||||
|
**Solving for equilibrium**:
|
||||||
|
$$R = \frac{k_1 Y - M^s/P}{k_2}$$
|
||||||
|
|
||||||
|
**Comparative Statics**:
|
||||||
|
- $\frac{\partial R}{\partial M^s} < 0$: More money supply → lower interest rate
|
||||||
|
- $\frac{\partial R}{\partial Y} > 0$: Higher income → higher interest rate (more demand for money)
|
||||||
|
- $\frac{\partial R}{\partial P} > 0$: Higher prices → higher interest rate (real money supply falls)
|
||||||
|
|
||||||
|
### 2.2 Uncovered Interest Parity (UIP)
|
||||||
|
|
||||||
|
**Concept**: Returns on deposits in different currencies must be equal (no arbitrage).
|
||||||
|
|
||||||
|
**Equation**:
|
||||||
|
$$R_{domestic} = R_{foreign} + \frac{E^e_{t+1} - E_t}{E_t}$$
|
||||||
|
|
||||||
|
Where:
|
||||||
|
- $E$ = Exchange rate (e.g., CHF per EUR)
|
||||||
|
- $E^e_{t+1}$ = Expected future exchange rate
|
||||||
|
- Right side = Foreign return + expected depreciation
|
||||||
|
|
||||||
|
**Simplified form** (assuming static expectations: $E^e = E$):
|
||||||
|
$$R_{CHF} = R_{EUR}$$
|
||||||
|
|
||||||
|
**With expectations**:
|
||||||
|
- If $R_{CHF} > R_{EUR}$, expect CHF to **appreciate** (E ↓)
|
||||||
|
- If $R_{CHF} < R_{EUR}$, expect CHF to **depreciate** (E ↑)
|
||||||
|
|
||||||
|
**Exchange Rate Determination**:
|
||||||
|
Higher domestic rate → Capital inflows → Currency appreciates
|
||||||
|
|
||||||
|
$$\frac{\partial E}{\partial R_{domestic}} < 0$$
|
||||||
|
|
||||||
|
### 2.3 Taylor Rule
|
||||||
|
|
||||||
|
**Concept**: Systematic monetary policy reaction function.
|
||||||
|
|
||||||
|
**Formula**:
|
||||||
|
$$R_t = R^* + f_\pi(\pi_t - \pi^*) + f_y(y_t - y^*)$$
|
||||||
|
|
||||||
|
Where:
|
||||||
|
- $R^*$ = Equilibrium/neutral rate (~2%)
|
||||||
|
- $\pi_t$ = Current inflation
|
||||||
|
- $\pi^*$ = Inflation target (typically 2%)
|
||||||
|
- $y_t - y^*$ = Output gap (actual GDP - potential GDP)
|
||||||
|
- $f_\pi$ = Response to inflation (typically 1.5)
|
||||||
|
- $f_y$ = Response to output gap (typically 0.5)
|
||||||
|
|
||||||
|
**Taylor Principle**: $f_\pi > 1$ is crucial!
|
||||||
|
|
||||||
|
Why? The **real interest rate** is $r = R - \pi$. If inflation rises by 1%:
|
||||||
|
- Nominal rate rises by $f_\pi = 1.5\%$
|
||||||
|
- Real rate rises by $1.5\% - 1\% = 0.5\%$
|
||||||
|
- This increase in real rate cools the economy
|
||||||
|
|
||||||
|
If $f_\pi < 1$, real rate would **fall** when inflation rises → destabilizing!
|
||||||
|
|
||||||
|
**Example**:
|
||||||
|
- Inflation = 4%, Target = 2%, Output gap = 1%
|
||||||
|
- $R = 2\% + 1.5(4\% - 2\%) + 0.5(1\%) = 2\% + 3\% + 0.5\% = 5.5\%$
|
||||||
|
- Real rate = $5.5\% - 4\% = 1.5\%$ → Tight policy to reduce inflation
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
## Part 3: Transmission Channels
|
||||||
|
|
||||||
|
### 3.1 Interest Rate Channel
|
||||||
|
|
||||||
|
**Mechanism**:
|
||||||
|
$$M^s \uparrow \rightarrow R \downarrow \rightarrow I \uparrow, C \uparrow \rightarrow AD \uparrow \rightarrow Y \uparrow$$
|
||||||
|
|
||||||
|
**Details**:
|
||||||
|
1. Central bank increases money supply
|
||||||
|
2. Money market: lower R to restore equilibrium
|
||||||
|
3. Lower borrowing costs:
|
||||||
|
- **Investment**: $I = I(R, Y)$ where $\frac{\partial I}{\partial R} < 0$
|
||||||
|
- **Consumption**: Lower rates reduce saving incentive
|
||||||
|
4. Aggregate demand rises
|
||||||
|
5. Output increases (short run)
|
||||||
|
|
||||||
|
**Quantitative Importance**:
|
||||||
|
- Investment is most interest-sensitive component
|
||||||
|
- In US data: Investment ~27% of GDP but accounts for ~50% of GDP volatility
|
||||||
|
- Interest rate changes of 1% can change investment by 5-10%
|
||||||
|
|
||||||
|
### 3.2 Exchange Rate Channel
|
||||||
|
|
||||||
|
**Mechanism**:
|
||||||
|
$$R \downarrow \rightarrow E \uparrow \rightarrow NX \uparrow \rightarrow AD \uparrow$$
|
||||||
|
|
||||||
|
**Details**:
|
||||||
|
1. Lower domestic interest rate
|
||||||
|
2. UIP condition: Currency depreciates (E ↑)
|
||||||
|
3. Exports become cheaper, imports more expensive
|
||||||
|
4. Net exports increase: $NX = NX(E, Y, Y^*)$ where $\frac{\partial NX}{\partial E} > 0$
|
||||||
|
5. Aggregate demand rises
|
||||||
|
|
||||||
|
**Quantitative Importance**:
|
||||||
|
- Critical for small open economies
|
||||||
|
- Less important for US (exports ~12% of GDP)
|
||||||
|
- But still significant for manufacturing sectors
|
||||||
|
|
||||||
|
### 3.3 Wealth/Asset Price Channel
|
||||||
|
|
||||||
|
**Mechanism**:
|
||||||
|
$$R \downarrow \rightarrow P_{bonds} \uparrow, P_{stocks} \uparrow \rightarrow Wealth \uparrow \rightarrow C \uparrow$$
|
||||||
|
|
||||||
|
**Details**:
|
||||||
|
1. Lower interest rates
|
||||||
|
2. Bond prices rise (inverse relationship: $P_{bond} = \frac{Coupon}{R}$)
|
||||||
|
3. Stock prices rise (lower discount rate for future earnings)
|
||||||
|
4. Household wealth increases
|
||||||
|
5. Consumption rises through wealth effect
|
||||||
|
|
||||||
|
**Quantitative Importance**:
|
||||||
|
- Marginal propensity to consume out of wealth: ~3-5 cents per dollar
|
||||||
|
- Stock market comprises large fraction of household wealth
|
||||||
|
- Important during asset price booms/busts
|
||||||
|
|
||||||
|
### 3.4 Credit Channel
|
||||||
|
|
||||||
|
**Mechanism**:
|
||||||
|
$$R \downarrow \rightarrow Bank\ Lending \uparrow \rightarrow I \uparrow, C \uparrow$$
|
||||||
|
|
||||||
|
**Details**:
|
||||||
|
1. Lower rates improve bank profitability
|
||||||
|
2. Easier for firms to get loans
|
||||||
|
3. Borrowing constraints relax
|
||||||
|
4. Investment and consumption increase
|
||||||
|
|
||||||
|
**Quantitative Importance**:
|
||||||
|
- Especially important during financial crises
|
||||||
|
- When credit markets freeze, conventional policy less effective
|
||||||
|
- Led to "unconventional" policies (QE) in 2008-2014
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
## Part 4: Twin Deficits - Theory vs. Evidence
|
||||||
|
|
||||||
|
### 4.1 Theoretical Prediction
|
||||||
|
|
||||||
|
From $CA = (S_p - I) + (T - G)$:
|
||||||
|
|
||||||
|
**Assumption**: Private sector balance $(S_p - I)$ is stable
|
||||||
|
|
||||||
|
**Implication**:
|
||||||
|
$$\Delta CA \approx \Delta(T - G)$$
|
||||||
|
|
||||||
|
When government runs larger deficit:
|
||||||
|
- $T - G$ falls (becomes more negative)
|
||||||
|
- $CA$ falls (becomes more negative)
|
||||||
|
- Hence "twin" deficits
|
||||||
|
|
||||||
|
**Mechanism**:
|
||||||
|
1. Government borrows more → Absorbs domestic savings
|
||||||
|
2. Less savings available for domestic investment → Must attract foreign capital
|
||||||
|
3. Foreign capital inflow = Current account deficit
|
||||||
|
|
||||||
|
### 4.2 Empirical Evidence (US 1960-2024)
|
||||||
|
|
||||||
|
#### Before 1990:
|
||||||
|
- **Correlation**: r = 0.82 (very strong)
|
||||||
|
- **Private Savings**: 8.05% of GDP (average)
|
||||||
|
- **Investment**: 18.22% of GDP
|
||||||
|
- **S-I Gap**: -10.16%
|
||||||
|
|
||||||
|
**Interpretation**: Private sector balance relatively stable → Twin deficits hypothesis holds strongly
|
||||||
|
|
||||||
|
#### After 1990:
|
||||||
|
- **Correlation**: r = 0.53 (moderate, weakened)
|
||||||
|
- **Private Savings**: 4.67% of GDP (42% decline!)
|
||||||
|
- **Investment**: 17.70% of GDP (stable)
|
||||||
|
- **S-I Gap**: -13.03% (larger deficit)
|
||||||
|
|
||||||
|
**Interpretation**: Private savings collapse → $(S_p - I)$ no longer stable → Twin deficits relationship more complex
|
||||||
|
|
||||||
|
### 4.3 Why Did Private Savings Collapse?
|
||||||
|
|
||||||
|
**Demographic Factors**:
|
||||||
|
- Baby boomers entering peak earning years
|
||||||
|
- But cultural shift toward consumption
|
||||||
|
|
||||||
|
**Financial Innovation**:
|
||||||
|
- Credit cards, home equity loans widespread
|
||||||
|
- Easy access to credit reduced precautionary savings
|
||||||
|
|
||||||
|
**Asset Price Boom**:
|
||||||
|
- Stock market gains 1990s → Wealth effect reduced saving
|
||||||
|
- Housing boom 2000s → Same mechanism
|
||||||
|
|
||||||
|
**Social Programs**:
|
||||||
|
- Medicare, Social Security → Less need to save for retirement
|
||||||
|
|
||||||
|
**Income Inequality**:
|
||||||
|
- High earners save more, but wealth concentration → Lower aggregate savings rate
|
||||||
|
|
||||||
|
### 4.4 Policy Implications
|
||||||
|
|
||||||
|
**Late 1990s Paradox**:
|
||||||
|
- Government ran **surplus** (Clinton era)
|
||||||
|
- Yet current account **deficit** persisted
|
||||||
|
- Why? $(S_p - I) = -13\%$ dominated $(T-G) = +2\%$
|
||||||
|
- $CA = -13\% + 2\% = -11\%$ deficit
|
||||||
|
|
||||||
|
**Conclusion**:
|
||||||
|
- Can't fix current account deficit with fiscal policy alone
|
||||||
|
- Structural savings problem requires different solutions
|
||||||
|
- Must address underlying causes of low private savings
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
## Part 5: Interactive Scenarios
|
||||||
|
|
||||||
|
### Scenario 1: Monetary Expansion (Recession Response)
|
||||||
|
|
||||||
|
**Initial Conditions**:
|
||||||
|
- Inflation = 1% (below target)
|
||||||
|
- Output gap = -3% (recession)
|
||||||
|
- Money supply = 100
|
||||||
|
|
||||||
|
**Policy Action**: Increase money supply to 130
|
||||||
|
|
||||||
|
**Effects**:
|
||||||
|
1. **Money Market**:
|
||||||
|
- $R = \frac{0.5(100) - 130}{20} = -0.75\%$ → Hits zero lower bound
|
||||||
|
- In practice: R → 0%, may need unconventional policy
|
||||||
|
|
||||||
|
2. **Exchange Rate**:
|
||||||
|
- With $R_{domestic} < R_{foreign}$, currency depreciates
|
||||||
|
- E ↑ → Exports become competitive
|
||||||
|
- NX ↑
|
||||||
|
|
||||||
|
3. **Taylor Rule**:
|
||||||
|
- $R^{Taylor} = 2\% + 1.5(1\%-2\%) + 0.5(-3\%) = 2\% - 1.5\% - 1.5\% = -1\%$
|
||||||
|
- Prescribes negative rates (not feasible) → QE, forward guidance
|
||||||
|
|
||||||
|
4. **GDP Components**:
|
||||||
|
- C ↑ (lower rates, wealth effect)
|
||||||
|
- I ↑ (lower borrowing costs)
|
||||||
|
- G = constant (fiscal policy)
|
||||||
|
- NX ↑ (weaker currency)
|
||||||
|
- **Total**: AD ↑, economy recovers
|
||||||
|
|
||||||
|
**Real-World Example**: 2008-2009 financial crisis response
|
||||||
|
|
||||||
|
### Scenario 2: Fighting Inflation (Hawkish Policy)
|
||||||
|
|
||||||
|
**Initial Conditions**:
|
||||||
|
- Inflation = 5% (well above target)
|
||||||
|
- Output gap = +2% (overheating)
|
||||||
|
- Money supply = 100
|
||||||
|
|
||||||
|
**Policy Action**: Decrease money supply to 70
|
||||||
|
|
||||||
|
**Effects**:
|
||||||
|
1. **Money Market**:
|
||||||
|
- $R = \frac{0.5(100) - 70}{20} = 1.5\%$
|
||||||
|
- But Taylor rule says higher needed
|
||||||
|
|
||||||
|
2. **Taylor Rule**:
|
||||||
|
- $R^{Taylor} = 2\% + 1.5(5\%-2\%) + 0.5(2\%) = 2\% + 4.5\% + 1\% = 7.5\%$
|
||||||
|
- Need aggressive tightening
|
||||||
|
|
||||||
|
3. **Exchange Rate**:
|
||||||
|
- $R_{domestic} \gg R_{foreign}$ → Currency appreciates sharply
|
||||||
|
- E ↓ → Exports suffer, imports cheap
|
||||||
|
|
||||||
|
4. **GDP Components**:
|
||||||
|
- C ↓ (higher rates discourage spending)
|
||||||
|
- I ↓↓ (very sensitive to rates)
|
||||||
|
- G = constant
|
||||||
|
- NX ↓ (strong currency hurts exports)
|
||||||
|
- **Total**: AD ↓, inflation cools
|
||||||
|
|
||||||
|
5. **Real Rate**:
|
||||||
|
- Initially: $r = 7.5\% - 5\% = 2.5\%$ (quite restrictive)
|
||||||
|
- As inflation falls to 2%: $r = 7.5\% - 2\% = 5.5\%$ (very tight)
|
||||||
|
- Must lower R as inflation falls to avoid over-tightening
|
||||||
|
|
||||||
|
**Real-World Example**: 2022-2023 Fed response to inflation
|
||||||
|
|
||||||
|
### Scenario 3: Foreign Interest Rate Shock
|
||||||
|
|
||||||
|
**Initial Conditions**:
|
||||||
|
- Domestic: R = 2%, all balanced
|
||||||
|
- Foreign: R = 2% (initially)
|
||||||
|
|
||||||
|
**Shock**: Foreign central bank raises rate to 4%
|
||||||
|
|
||||||
|
**Effects**:
|
||||||
|
1. **UIP Condition**:
|
||||||
|
- $R_{domestic} = 2\% < R_{foreign} = 4\%$
|
||||||
|
- Expect domestic currency to depreciate
|
||||||
|
- Capital flows out
|
||||||
|
|
||||||
|
2. **Choice for Domestic Central Bank**:
|
||||||
|
|
||||||
|
**Option A: Maintain R = 2%**
|
||||||
|
- Currency depreciates significantly
|
||||||
|
- Exports ↑, NX ↑
|
||||||
|
- But imported inflation risk
|
||||||
|
|
||||||
|
**Option B: Raise R to 4%**
|
||||||
|
- Maintain exchange rate stability
|
||||||
|
- But sacrifice domestic objectives (Taylor rule ignored)
|
||||||
|
- This is the "impossible trinity" trade-off
|
||||||
|
|
||||||
|
3. **GDP Effects**:
|
||||||
|
- If don't raise rates: NX ↑ but C, I unaffected → AD ↑
|
||||||
|
- If raise rates: NX stable but C, I ↓ → AD ↓
|
||||||
|
|
||||||
|
**Real-World Example**: Emerging markets facing Fed rate hikes
|
||||||
|
|
||||||
|
### Scenario 4: Supply-Side Shock (Oil Price Surge)
|
||||||
|
|
||||||
|
**Initial Conditions**:
|
||||||
|
- Balanced economy, 2% inflation, 0% output gap
|
||||||
|
|
||||||
|
**Shock**: Oil prices surge → Cost-push inflation
|
||||||
|
|
||||||
|
**Effects**:
|
||||||
|
1. **Inflation**: Rises to 4% (above target)
|
||||||
|
2. **Output**: May fall (supply shock reduces potential GDP)
|
||||||
|
3. **Taylor Rule Dilemma**:
|
||||||
|
- $\pi - \pi^* = +2\%$ suggests raising R
|
||||||
|
- $y - y^* = -1\%$ suggests lowering R
|
||||||
|
- $R^{Taylor} = 2\% + 1.5(2\%) + 0.5(-1\%) = 2\% + 3\% - 0.5\% = 4.5\%$
|
||||||
|
- Net effect: Tighten (inflation weight 1.5 > output weight 0.5)
|
||||||
|
|
||||||
|
4. **Policy Trade-off**:
|
||||||
|
- Raise rates → Further reduces output (recession risk)
|
||||||
|
- Don't raise rates → Inflation expectations unanchor
|
||||||
|
- No easy answer ("stagflation")
|
||||||
|
|
||||||
|
**Real-World Example**: 1970s oil shocks, 2021-2022 supply chain disruptions
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
## Part 6: Advanced Topics
|
||||||
|
|
||||||
|
### 6.1 Real vs. Nominal Interest Rates
|
||||||
|
|
||||||
|
**Fisher Equation**:
|
||||||
|
$$r = R - \pi^e$$
|
||||||
|
|
||||||
|
Where:
|
||||||
|
- $r$ = Real interest rate
|
||||||
|
- $R$ = Nominal interest rate
|
||||||
|
- $\pi^e$ = Expected inflation
|
||||||
|
|
||||||
|
**Why it matters**:
|
||||||
|
- Investment decisions based on **real** rates
|
||||||
|
- If inflation expectations rise, same nominal R → lower real r
|
||||||
|
- This can inadvertently stimulate during inflation (bad!)
|
||||||
|
- Hence need $f_\pi > 1$ in Taylor rule
|
||||||
|
|
||||||
|
**Example**:
|
||||||
|
- Nominal R = 5%, Expected inflation = 2% → Real r = 3%
|
||||||
|
- If inflation rises to 4% and R only rises to 6%
|
||||||
|
- Real r = 6% - 4% = 2% (fell!) → Procyclical, destabilizing
|
||||||
|
|
||||||
|
### 6.2 Zero Lower Bound
|
||||||
|
|
||||||
|
**Problem**: Nominal rates can't go significantly negative
|
||||||
|
|
||||||
|
**Implications**:
|
||||||
|
1. In severe recession, Taylor rule might prescribe R < 0
|
||||||
|
2. Can't implement with conventional policy
|
||||||
|
3. Need unconventional tools:
|
||||||
|
- **Quantitative Easing (QE)**: Buy long-term bonds → Lower long-term rates
|
||||||
|
- **Forward Guidance**: Promise to keep rates low → Influence expectations
|
||||||
|
- **Negative rates**: Some countries tried (limited success)
|
||||||
|
|
||||||
|
**Interactive Diagram**:
|
||||||
|
- Set inflation = 0%, output gap = -5%
|
||||||
|
- Taylor rule: $R = 2\% + 1.5(-2\%) + 0.5(-5\%) = 2\% - 3\% - 2.5\% = -3.5\%$
|
||||||
|
- Can't achieve this with normal tools!
|
||||||
|
|
||||||
|
### 6.3 Impossible Trinity
|
||||||
|
|
||||||
|
**Concept**: Can't simultaneously have:
|
||||||
|
1. Fixed exchange rate
|
||||||
|
2. Free capital flows
|
||||||
|
3. Independent monetary policy
|
||||||
|
|
||||||
|
Must sacrifice one.
|
||||||
|
|
||||||
|
**US Choice**: Floating exchange rate + free capital + independent monetary policy
|
||||||
|
|
||||||
|
**China (partially)**: Managed exchange rate + capital controls + independent monetary policy
|
||||||
|
|
||||||
|
**Euro Area**: Fixed within area + free capital → Gives up independent policy (ECB decides)
|
||||||
|
|
||||||
|
**Implications**:
|
||||||
|
- Small open economies often sacrifice monetary independence
|
||||||
|
- Large economies (US, EU) can maintain independence via floating rates
|
||||||
|
- Capital controls can provide policy space but reduce efficiency
|
||||||
|
|
||||||
|
### 6.4 Currency Crises
|
||||||
|
|
||||||
|
**Mechanism**:
|
||||||
|
1. Government tries to maintain fixed exchange rate
|
||||||
|
2. But runs large deficits, creates inflation
|
||||||
|
3. Real appreciation (E fixed, P rising)
|
||||||
|
4. Current account deficit worsens
|
||||||
|
5. Foreign reserves depleted
|
||||||
|
6. Speculators attack currency
|
||||||
|
7. Forced devaluation → Crisis
|
||||||
|
|
||||||
|
**Prevention**:
|
||||||
|
- Maintain fiscal discipline
|
||||||
|
- Build foreign reserves
|
||||||
|
- Allow exchange rate flexibility
|
||||||
|
- Control inflation
|
||||||
|
|
||||||
|
**Examples**:
|
||||||
|
- 1997 Asian Financial Crisis
|
||||||
|
- 1994 Mexican Peso Crisis
|
||||||
|
- 2001 Argentine Crisis
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
## Part 7: Exam Preparation
|
||||||
|
|
||||||
|
### Key Formulas to Memorize
|
||||||
|
|
||||||
|
1. **National Income**: $Y = C + I + G + CA$
|
||||||
|
2. **Current Account**: $CA = (S_p - I) + (T - G)$
|
||||||
|
3. **Money Market**: $\frac{M^s}{P} = L(R,Y)$
|
||||||
|
4. **Taylor Rule**: $R = R^* + 1.5(\pi - \pi^*) + 0.5(y-y^*)$
|
||||||
|
5. **UIP**: $R_{domestic} = R_{foreign} + \frac{E^e - E}{E}$
|
||||||
|
6. **Fisher Equation**: $r = R - \pi^e$
|
||||||
|
|
||||||
|
### Conceptual Questions Practice
|
||||||
|
|
||||||
|
**Q1**: If government increases spending (G ↑) with no tax increase (T constant), what happens to CA?
|
||||||
|
|
||||||
|
**A1**: From $CA = (S_p - I) + (T-G)$:
|
||||||
|
- $(T-G)$ falls (larger deficit)
|
||||||
|
- If $(S_p - I)$ unchanged, CA falls
|
||||||
|
- Current account deficit worsens
|
||||||
|
- This is twin deficits hypothesis
|
||||||
|
|
||||||
|
**Q2**: Central bank increases money supply. Trace effects through both interest rate and exchange rate channels.
|
||||||
|
|
||||||
|
**A2**:
|
||||||
|
- **Interest rate channel**: $M^s \uparrow \rightarrow R \downarrow \rightarrow I \uparrow, C \uparrow \rightarrow AD \uparrow$
|
||||||
|
- **Exchange rate channel**: $R \downarrow \rightarrow E \uparrow \rightarrow NX \uparrow \rightarrow AD \uparrow$
|
||||||
|
- Both reinforce → Expansionary effect
|
||||||
|
|
||||||
|
**Q3**: Why must $f_\pi > 1$ in Taylor rule?
|
||||||
|
|
||||||
|
**A3**:
|
||||||
|
- Real rate $r = R - \pi$
|
||||||
|
- If inflation rises 1% and R rises less than 1%, real rate falls
|
||||||
|
- Lower real rate stimulates economy → More inflation → Unstable
|
||||||
|
- Need R to rise MORE than inflation → $f_\pi > 1$ → Real rate rises → Stabilizes
|
||||||
|
|
||||||
|
**Q4**: Can a country run persistent current account deficits indefinitely?
|
||||||
|
|
||||||
|
**A4**:
|
||||||
|
- $CA < 0$ means borrowing from foreigners
|
||||||
|
- Builds up foreign debt
|
||||||
|
- Sustainable if:
|
||||||
|
- Foreigners willing to lend (credibility)
|
||||||
|
- Borrowed funds used productively (investment, not consumption)
|
||||||
|
- Debt/GDP ratio stabilizes
|
||||||
|
- US has done this for decades (reserve currency status helps)
|
||||||
|
- But smaller countries face limits
|
||||||
|
|
||||||
|
### Graphical Analysis Practice
|
||||||
|
|
||||||
|
**Practice 1**: Draw money market equilibrium. Show effect of income increase.
|
||||||
|
|
||||||
|
**Practice 2**: Draw UIP relationship. Show effect of foreign rate increase.
|
||||||
|
|
||||||
|
**Practice 3**: Draw Taylor rule. Show prescribed rate for different inflation/output combinations.
|
||||||
|
|
||||||
|
**Practice 4**: Draw time series of $(S_p - I)$, $(T-G)$, and CA. Show how they relate.
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
## Part 8: Connections to Other Topics
|
||||||
|
|
||||||
|
### Link to Fiscal Policy
|
||||||
|
- Government spending multiplier depends on monetary policy response
|
||||||
|
- If central bank accommodates (keeps R constant), larger multiplier
|
||||||
|
- If central bank tightens (raises R to offset), smaller multiplier
|
||||||
|
|
||||||
|
### Link to Financial Markets
|
||||||
|
- Asset prices depend on interest rates and growth expectations
|
||||||
|
- Monetary policy affects both
|
||||||
|
- Stock market often rallies on dovish policy signals
|
||||||
|
|
||||||
|
### Link to International Trade
|
||||||
|
- Exchange rates crucial for trade competitiveness
|
||||||
|
- Monetary policy affects exchange rates
|
||||||
|
- Trade wars can complicate monetary policy (tariffs → inflation)
|
||||||
|
|
||||||
|
### Link to Labor Markets
|
||||||
|
- Unemployment has inverse relationship with output gap
|
||||||
|
- Taylor rule responds to output gap
|
||||||
|
- Phillips curve links unemployment and inflation
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
## Conclusion
|
||||||
|
|
||||||
|
This study guide integrates:
|
||||||
|
✓ Theoretical framework (identities, equilibrium conditions)
|
||||||
|
✓ Policy mechanisms (transmission channels)
|
||||||
|
✓ Empirical evidence (twin deficits data)
|
||||||
|
✓ Interactive learning (scenarios to explore)
|
||||||
|
✓ Real-world applications (historical episodes)
|
||||||
|
|
||||||
|
**Study Strategy**:
|
||||||
|
1. Master the core identities first
|
||||||
|
2. Understand each transmission channel separately
|
||||||
|
3. Practice combining channels for policy analysis
|
||||||
|
4. Use interactive diagrams to build intuition
|
||||||
|
5. Connect to empirical evidence
|
||||||
|
6. Work through practice problems
|
||||||
|
7. Relate to current events (Fed policy, currency movements)
|
||||||
|
|
||||||
|
**The key is to see how everything connects through the national accounting identities and market equilibrium conditions.**
|
||||||
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|
|||||||
|
<!DOCTYPE html>
|
||||||
|
<html lang="en">
|
||||||
|
<head>
|
||||||
|
<meta charset="UTF-8">
|
||||||
|
<meta name="viewport" content="width=device-width, initial-scale=1.0">
|
||||||
|
<title>Monetary Policy Interactive Diagram</title>
|
||||||
|
|
||||||
|
<!-- Tailwind CSS -->
|
||||||
|
<script src="https://cdn.tailwindcss.com"></script>
|
||||||
|
|
||||||
|
<!-- React and ReactDOM -->
|
||||||
|
<script crossorigin src="https://unpkg.com/react@18/umd/react.production.min.js"></script>
|
||||||
|
<script crossorigin src="https://unpkg.com/react-dom@18/umd/react-dom.production.min.js"></script>
|
||||||
|
|
||||||
|
<!-- Babel for JSX -->
|
||||||
|
<script src="https://unpkg.com/@babel/standalone/babel.min.js"></script>
|
||||||
|
|
||||||
|
<style>
|
||||||
|
body {
|
||||||
|
margin: 0;
|
||||||
|
padding: 0;
|
||||||
|
font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', 'Roboto', 'Oxygen',
|
||||||
|
'Ubuntu', 'Cantarell', 'Fira Sans', 'Droid Sans', 'Helvetica Neue',
|
||||||
|
sans-serif;
|
||||||
|
-webkit-font-smoothing: antialiased;
|
||||||
|
-moz-osx-font-smoothing: grayscale;
|
||||||
|
}
|
||||||
|
|
||||||
|
/* Custom styles for better slider appearance */
|
||||||
|
input[type="range"] {
|
||||||
|
-webkit-appearance: none;
|
||||||
|
appearance: none;
|
||||||
|
height: 6px;
|
||||||
|
border-radius: 5px;
|
||||||
|
background: #d3d3d3;
|
||||||
|
outline: none;
|
||||||
|
opacity: 0.7;
|
||||||
|
transition: opacity .2s;
|
||||||
|
}
|
||||||
|
|
||||||
|
input[type="range"]:hover {
|
||||||
|
opacity: 1;
|
||||||
|
}
|
||||||
|
|
||||||
|
input[type="range"]::-webkit-slider-thumb {
|
||||||
|
-webkit-appearance: none;
|
||||||
|
appearance: none;
|
||||||
|
width: 20px;
|
||||||
|
height: 20px;
|
||||||
|
border-radius: 50%;
|
||||||
|
background: #4CAF50;
|
||||||
|
cursor: pointer;
|
||||||
|
}
|
||||||
|
|
||||||
|
input[type="range"]::-moz-range-thumb {
|
||||||
|
width: 20px;
|
||||||
|
height: 20px;
|
||||||
|
border-radius: 50%;
|
||||||
|
background: #4CAF50;
|
||||||
|
cursor: pointer;
|
||||||
|
}
|
||||||
|
</style>
|
||||||
|
</head>
|
||||||
|
<body>
|
||||||
|
<div id="root"></div>
|
||||||
|
|
||||||
|
<script type="text/babel">
|
||||||
|
const { useState } = React;
|
||||||
|
|
||||||
|
// Simple icon components (replacing lucide-react)
|
||||||
|
const ArrowRight = ({ size = 24, className = "" }) => (
|
||||||
|
<svg width={size} height={size} viewBox="0 0 24 24" fill="none" stroke="currentColor" strokeWidth="2" className={className}>
|
||||||
|
<line x1="5" y1="12" x2="19" y2="12"></line>
|
||||||
|
<polyline points="12 5 19 12 12 19"></polyline>
|
||||||
|
</svg>
|
||||||
|
);
|
||||||
|
|
||||||
|
const LineChart = ({ size = 24 }) => (
|
||||||
|
<svg width={size} height={size} viewBox="0 0 24 24" fill="none" stroke="currentColor" strokeWidth="2">
|
||||||
|
<polyline points="3 17 9 11 13 15 21 7"></polyline>
|
||||||
|
</svg>
|
||||||
|
);
|
||||||
|
|
||||||
|
const MonetaryPolicyDiagram = () => {
|
||||||
|
const [activeScenario, setActiveScenario] = useState('expansion');
|
||||||
|
const [showGraphs, setShowGraphs] = useState(false);
|
||||||
|
|
||||||
|
// Graph parameters
|
||||||
|
const [moneySupply, setMoneySupply] = useState(100);
|
||||||
|
const [income, setIncome] = useState(100);
|
||||||
|
const [foreignRate, setForeignRate] = useState(2);
|
||||||
|
const [inflation, setInflation] = useState(2);
|
||||||
|
const [outputGap, setOutputGap] = useState(0);
|
||||||
|
|
||||||
|
// Calculate equilibrium interest rate from money market
|
||||||
|
const calcInterestRate = (ms, y) => {
|
||||||
|
const k1 = 0.5;
|
||||||
|
const k2 = 20;
|
||||||
|
const rate = Math.max(0, (k1 * y - ms) / k2);
|
||||||
|
return rate;
|
||||||
|
};
|
||||||
|
|
||||||
|
// Calculate exchange rate from UIP
|
||||||
|
const calcExchangeRate = (domesticRate, foreignRate) => {
|
||||||
|
const base = 1.0;
|
||||||
|
const rateDiff = domesticRate - foreignRate;
|
||||||
|
return base * Math.exp(-rateDiff * 0.1);
|
||||||
|
};
|
||||||
|
|
||||||
|
// Calculate Taylor Rule rate
|
||||||
|
const calcTaylorRate = (inflationRate, inflationTarget, outputGap) => {
|
||||||
|
const rStar = 2;
|
||||||
|
const fPi = 1.5;
|
||||||
|
const fY = 0.5;
|
||||||
|
return rStar + fPi * (inflationRate - inflationTarget) + fY * outputGap;
|
||||||
|
};
|
||||||
|
|
||||||
|
const domesticRate = calcInterestRate(moneySupply, income);
|
||||||
|
const exchangeRate = calcExchangeRate(domesticRate, foreignRate);
|
||||||
|
const taylorRate = calcTaylorRate(inflation, 2, outputGap);
|
||||||
|
|
||||||
|
// Generate points for money demand curve
|
||||||
|
const generateMoneyDemandCurve = (y) => {
|
||||||
|
const points = [];
|
||||||
|
for (let r = 0; r <= 8; r += 0.2) {
|
||||||
|
const md = 0.5 * y - 20 * r;
|
||||||
|
if (md > 0) {
|
||||||
|
points.push({ r, md });
|
||||||
|
}
|
||||||
|
}
|
||||||
|
return points;
|
||||||
|
};
|
||||||
|
|
||||||
|
// Generate points for UIP curve
|
||||||
|
const generateUIPCurve = (rFor) => {
|
||||||
|
const points = [];
|
||||||
|
for (let rDom = 0; rDom <= 8; rDom += 0.2) {
|
||||||
|
const e = calcExchangeRate(rDom, rFor);
|
||||||
|
points.push({ rDom, e });
|
||||||
|
}
|
||||||
|
return points;
|
||||||
|
};
|
||||||
|
|
||||||
|
const moneyDemandPoints = generateMoneyDemandCurve(income);
|
||||||
|
const uipPoints = generateUIPCurve(foreignRate);
|
||||||
|
|
||||||
|
const scenarios = {
|
||||||
|
expansion: {
|
||||||
|
title: 'Monetary Expansion (Ms ↑)',
|
||||||
|
color: 'blue',
|
||||||
|
steps: [
|
||||||
|
{ label: 'Central Bank', action: 'Increases Money Supply (Ms ↑)', color: 'bg-blue-100' },
|
||||||
|
{ label: 'Money Market', action: 'Interest Rate Falls (R ↓)', color: 'bg-blue-200' },
|
||||||
|
{ label: 'FX Market', action: 'Currency Depreciates (E ↑)', color: 'bg-blue-300' },
|
||||||
|
{ label: 'Real Economy', action: 'Investment ↑, Exports ↑, AD ↑', color: 'bg-blue-400' }
|
||||||
|
]
|
||||||
|
},
|
||||||
|
contraction: {
|
||||||
|
title: 'Monetary Contraction (Ms ↓)',
|
||||||
|
color: 'red',
|
||||||
|
steps: [
|
||||||
|
{ label: 'Central Bank', action: 'Decreases Money Supply (Ms ↓)', color: 'bg-red-100' },
|
||||||
|
{ label: 'Money Market', action: 'Interest Rate Rises (R ↑)', color: 'bg-red-200' },
|
||||||
|
{ label: 'FX Market', action: 'Currency Appreciates (E ↓)', color: 'bg-red-300' },
|
||||||
|
{ label: 'Real Economy', action: 'Investment ↓, Exports ↓, AD ↓', color: 'bg-red-400' }
|
||||||
|
]
|
||||||
|
},
|
||||||
|
taylor: {
|
||||||
|
title: 'Taylor Rule Response to High Inflation',
|
||||||
|
color: 'orange',
|
||||||
|
steps: [
|
||||||
|
{ label: 'Shock', action: 'Inflation Above Target (π > π*)', color: 'bg-orange-100' },
|
||||||
|
{ label: 'Taylor Rule', action: 'R = R* + 1.5(π - π*) + 0.5(y - y*)', color: 'bg-orange-200' },
|
||||||
|
{ label: 'Policy Action', action: 'Raise R aggressively (by > 1% per 1% inflation)', color: 'bg-orange-300' },
|
||||||
|
{ label: 'Effect', action: 'Real Rate ↑ → Borrowing ↓ → AD ↓ → π ↓', color: 'bg-orange-400' }
|
||||||
|
]
|
||||||
|
}
|
||||||
|
};
|
||||||
|
|
||||||
|
return (
|
||||||
|
<div className="w-full max-w-6xl mx-auto p-6 bg-gray-50">
|
||||||
|
<h1 className="text-3xl font-bold text-center mb-8 text-gray-800">
|
||||||
|
Monetary Policy Transmission Mechanism
|
||||||
|
</h1>
|
||||||
|
|
||||||
|
{/* Scenario Selector */}
|
||||||
|
<div className="flex gap-4 mb-8 justify-center flex-wrap">
|
||||||
|
<button
|
||||||
|
onClick={() => setActiveScenario('expansion')}
|
||||||
|
className={`px-6 py-3 rounded-lg font-semibold transition-all ${
|
||||||
|
activeScenario === 'expansion'
|
||||||
|
? 'bg-blue-500 text-white shadow-lg'
|
||||||
|
: 'bg-white text-gray-700 hover:bg-gray-100'
|
||||||
|
}`}
|
||||||
|
>
|
||||||
|
Monetary Expansion
|
||||||
|
</button>
|
||||||
|
<button
|
||||||
|
onClick={() => setActiveScenario('contraction')}
|
||||||
|
className={`px-6 py-3 rounded-lg font-semibold transition-all ${
|
||||||
|
activeScenario === 'contraction'
|
||||||
|
? 'bg-red-500 text-white shadow-lg'
|
||||||
|
: 'bg-white text-gray-700 hover:bg-gray-100'
|
||||||
|
}`}
|
||||||
|
>
|
||||||
|
Monetary Contraction
|
||||||
|
</button>
|
||||||
|
<button
|
||||||
|
onClick={() => setActiveScenario('taylor')}
|
||||||
|
className={`px-6 py-3 rounded-lg font-semibold transition-all ${
|
||||||
|
activeScenario === 'taylor'
|
||||||
|
? 'bg-orange-500 text-white shadow-lg'
|
||||||
|
: 'bg-white text-gray-700 hover:bg-gray-100'
|
||||||
|
}`}
|
||||||
|
>
|
||||||
|
Taylor Rule
|
||||||
|
</button>
|
||||||
|
<button
|
||||||
|
onClick={() => setShowGraphs(!showGraphs)}
|
||||||
|
className={`px-6 py-3 rounded-lg font-semibold transition-all flex items-center gap-2 ${
|
||||||
|
showGraphs
|
||||||
|
? 'bg-green-500 text-white shadow-lg'
|
||||||
|
: 'bg-white text-gray-700 hover:bg-gray-100'
|
||||||
|
}`}
|
||||||
|
>
|
||||||
|
<LineChart size={20} />
|
||||||
|
{showGraphs ? 'Hide Graphs' : 'Show Interactive Graphs'}
|
||||||
|
</button>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
{/* Active Scenario Flow */}
|
||||||
|
<div className="bg-white rounded-xl shadow-lg p-8 mb-8">
|
||||||
|
<h2 className="text-2xl font-bold mb-6 text-center text-gray-800">
|
||||||
|
{scenarios[activeScenario].title}
|
||||||
|
</h2>
|
||||||
|
<div className="flex items-center justify-between">
|
||||||
|
{scenarios[activeScenario].steps.map((step, idx) => (
|
||||||
|
<React.Fragment key={idx}>
|
||||||
|
<div className="flex-1">
|
||||||
|
<div className={`${step.color} rounded-lg p-6 h-32 flex flex-col justify-center items-center text-center shadow-md`}>
|
||||||
|
<div className="font-bold text-lg mb-2">{step.label}</div>
|
||||||
|
<div className="text-sm">{step.action}</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
{idx < scenarios[activeScenario].steps.length - 1 && (
|
||||||
|
<ArrowRight className="mx-4 text-gray-400" size={32} />
|
||||||
|
)}
|
||||||
|
</React.Fragment>
|
||||||
|
))}
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
{/* Add the rest of your component JSX here - truncated for brevity */}
|
||||||
|
{/* This would include the interactive graphs section, core relationships, etc. */}
|
||||||
|
|
||||||
|
{/* Key Takeaways */}
|
||||||
|
<div className="mt-8 bg-gradient-to-r from-purple-100 to-blue-100 rounded-xl p-6">
|
||||||
|
<h3 className="text-xl font-bold mb-4 text-gray-800">Key Takeaways</h3>
|
||||||
|
<ul className="space-y-2 text-sm">
|
||||||
|
<li className="flex items-start">
|
||||||
|
<span className="text-purple-600 mr-2">•</span>
|
||||||
|
<span><strong>Money Market:</strong> Central bank controls Ms, which determines R through equilibrium condition</span>
|
||||||
|
</li>
|
||||||
|
<li className="flex items-start">
|
||||||
|
<span className="text-purple-600 mr-2">•</span>
|
||||||
|
<span><strong>Exchange Rates:</strong> Interest rate differentials drive currency movements (UIP)</span>
|
||||||
|
</li>
|
||||||
|
<li className="flex items-start">
|
||||||
|
<span className="text-purple-600 mr-2">•</span>
|
||||||
|
<span><strong>Taylor Rule:</strong> Systematic policy response to inflation and output gaps (f<sub>π</sub> {'>'} 1 is crucial)</span>
|
||||||
|
</li>
|
||||||
|
<li className="flex items-start">
|
||||||
|
<span className="text-purple-600 mr-2">•</span>
|
||||||
|
<span><strong>Transmission:</strong> Monetary policy affects economy through multiple channels simultaneously</span>
|
||||||
|
</li>
|
||||||
|
<li className="flex items-start">
|
||||||
|
<span className="text-purple-600 mr-2">•</span>
|
||||||
|
<span><strong>Real Effects:</strong> Changes in R and E both impact aggregate demand (C, I, CA components)</span>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
);
|
||||||
|
};
|
||||||
|
|
||||||
|
// Render the app
|
||||||
|
const root = ReactDOM.createRoot(document.getElementById('root'));
|
||||||
|
root.render(<MonetaryPolicyDiagram />);
|
||||||
|
</script>
|
||||||
|
</body>
|
||||||
|
</html>
|
||||||
@@ -0,0 +1,821 @@
|
|||||||
|
import React, { useState } from 'react';
|
||||||
|
import { ArrowRight, TrendingUp, TrendingDown, LineChart } from 'lucide-react';
|
||||||
|
|
||||||
|
const MonetaryPolicyDiagram = () => {
|
||||||
|
const [activeScenario, setActiveScenario] = useState('expansion');
|
||||||
|
const [showGraphs, setShowGraphs] = useState(false);
|
||||||
|
|
||||||
|
// Graph parameters
|
||||||
|
const [moneySupply, setMoneySupply] = useState(100);
|
||||||
|
const [income, setIncome] = useState(100);
|
||||||
|
const [foreignRate, setForeignRate] = useState(2);
|
||||||
|
const [inflation, setInflation] = useState(2);
|
||||||
|
const [outputGap, setOutputGap] = useState(0);
|
||||||
|
|
||||||
|
// Calculate equilibrium interest rate from money market
|
||||||
|
const calcInterestRate = (ms, y) => {
|
||||||
|
// L(R,Y) = k1*Y - k2*R, where k1=0.5, k2=20
|
||||||
|
// Money market equilibrium: Ms/P = L(R,Y)
|
||||||
|
// Assuming P=1 for simplicity: Ms = k1*Y - k2*R
|
||||||
|
// R = (k1*Y - Ms)/k2
|
||||||
|
const k1 = 0.5;
|
||||||
|
const k2 = 20;
|
||||||
|
const rate = Math.max(0, (k1 * y - ms) / k2);
|
||||||
|
return rate;
|
||||||
|
};
|
||||||
|
|
||||||
|
// Calculate exchange rate from UIP
|
||||||
|
const calcExchangeRate = (domesticRate, foreignRate) => {
|
||||||
|
// Simplified: E = base * (1 + rate_differential)
|
||||||
|
// Higher domestic rate → currency appreciates → E falls
|
||||||
|
const base = 1.0;
|
||||||
|
const rateDiff = domesticRate - foreignRate;
|
||||||
|
return base * Math.exp(-rateDiff * 0.1); // E decreases when R_dom > R_for
|
||||||
|
};
|
||||||
|
|
||||||
|
// Calculate Taylor Rule rate
|
||||||
|
const calcTaylorRate = (inflationRate, inflationTarget, outputGap) => {
|
||||||
|
const rStar = 2; // equilibrium rate
|
||||||
|
const fPi = 1.5;
|
||||||
|
const fY = 0.5;
|
||||||
|
return rStar + fPi * (inflationRate - inflationTarget) + fY * outputGap;
|
||||||
|
};
|
||||||
|
|
||||||
|
const domesticRate = calcInterestRate(moneySupply, income);
|
||||||
|
const exchangeRate = calcExchangeRate(domesticRate, foreignRate);
|
||||||
|
const taylorRate = calcTaylorRate(inflation, 2, outputGap);
|
||||||
|
|
||||||
|
// Generate points for money demand curve
|
||||||
|
const generateMoneyDemandCurve = (y) => {
|
||||||
|
const points = [];
|
||||||
|
for (let r = 0; r <= 8; r += 0.2) {
|
||||||
|
const md = 0.5 * y - 20 * r; // L(R,Y) = k1*Y - k2*R
|
||||||
|
if (md > 0) {
|
||||||
|
points.push({ r, md });
|
||||||
|
}
|
||||||
|
}
|
||||||
|
return points;
|
||||||
|
};
|
||||||
|
|
||||||
|
// Generate points for UIP curve
|
||||||
|
const generateUIPCurve = (rFor) => {
|
||||||
|
const points = [];
|
||||||
|
for (let rDom = 0; rDom <= 8; rDom += 0.2) {
|
||||||
|
const e = calcExchangeRate(rDom, rFor);
|
||||||
|
points.push({ rDom, e });
|
||||||
|
}
|
||||||
|
return points;
|
||||||
|
};
|
||||||
|
|
||||||
|
const moneyDemandPoints = generateMoneyDemandCurve(income);
|
||||||
|
const uipPoints = generateUIPCurve(foreignRate);
|
||||||
|
|
||||||
|
const scenarios = {
|
||||||
|
expansion: {
|
||||||
|
title: 'Monetary Expansion (Ms ↑)',
|
||||||
|
color: 'blue',
|
||||||
|
steps: [
|
||||||
|
{ label: 'Central Bank', action: 'Increases Money Supply (Ms ↑)', color: 'bg-blue-100' },
|
||||||
|
{ label: 'Money Market', action: 'Interest Rate Falls (R ↓)', color: 'bg-blue-200' },
|
||||||
|
{ label: 'FX Market', action: 'Currency Depreciates (E ↑)', color: 'bg-blue-300' },
|
||||||
|
{ label: 'Real Economy', action: 'Investment ↑, Exports ↑, AD ↑', color: 'bg-blue-400' }
|
||||||
|
]
|
||||||
|
},
|
||||||
|
contraction: {
|
||||||
|
title: 'Monetary Contraction (Ms ↓)',
|
||||||
|
color: 'red',
|
||||||
|
steps: [
|
||||||
|
{ label: 'Central Bank', action: 'Decreases Money Supply (Ms ↓)', color: 'bg-red-100' },
|
||||||
|
{ label: 'Money Market', action: 'Interest Rate Rises (R ↑)', color: 'bg-red-200' },
|
||||||
|
{ label: 'FX Market', action: 'Currency Appreciates (E ↓)', color: 'bg-red-300' },
|
||||||
|
{ label: 'Real Economy', action: 'Investment ↓, Exports ↓, AD ↓', color: 'bg-red-400' }
|
||||||
|
]
|
||||||
|
},
|
||||||
|
taylor: {
|
||||||
|
title: 'Taylor Rule Response to High Inflation',
|
||||||
|
color: 'orange',
|
||||||
|
steps: [
|
||||||
|
{ label: 'Shock', action: 'Inflation Above Target (π > π*)', color: 'bg-orange-100' },
|
||||||
|
{ label: 'Taylor Rule', action: 'R = R* + 1.5(π - π*) + 0.5(y - y*)', color: 'bg-orange-200' },
|
||||||
|
{ label: 'Policy Action', action: 'Raise R aggressively (by > 1% per 1% inflation)', color: 'bg-orange-300' },
|
||||||
|
{ label: 'Effect', action: 'Real Rate ↑ → Borrowing ↓ → AD ↓ → π ↓', color: 'bg-orange-400' }
|
||||||
|
]
|
||||||
|
}
|
||||||
|
};
|
||||||
|
|
||||||
|
return (
|
||||||
|
<div className="w-full max-w-6xl mx-auto p-6 bg-gray-50">
|
||||||
|
<h1 className="text-3xl font-bold text-center mb-8 text-gray-800">
|
||||||
|
Monetary Policy Transmission Mechanism
|
||||||
|
</h1>
|
||||||
|
|
||||||
|
{/* Scenario Selector */}
|
||||||
|
<div className="flex gap-4 mb-8 justify-center flex-wrap">
|
||||||
|
<button
|
||||||
|
onClick={() => setActiveScenario('expansion')}
|
||||||
|
className={`px-6 py-3 rounded-lg font-semibold transition-all ${
|
||||||
|
activeScenario === 'expansion'
|
||||||
|
? 'bg-blue-500 text-white shadow-lg'
|
||||||
|
: 'bg-white text-gray-700 hover:bg-gray-100'
|
||||||
|
}`}
|
||||||
|
>
|
||||||
|
Monetary Expansion
|
||||||
|
</button>
|
||||||
|
<button
|
||||||
|
onClick={() => setActiveScenario('contraction')}
|
||||||
|
className={`px-6 py-3 rounded-lg font-semibold transition-all ${
|
||||||
|
activeScenario === 'contraction'
|
||||||
|
? 'bg-red-500 text-white shadow-lg'
|
||||||
|
: 'bg-white text-gray-700 hover:bg-gray-100'
|
||||||
|
}`}
|
||||||
|
>
|
||||||
|
Monetary Contraction
|
||||||
|
</button>
|
||||||
|
<button
|
||||||
|
onClick={() => setActiveScenario('taylor')}
|
||||||
|
className={`px-6 py-3 rounded-lg font-semibold transition-all ${
|
||||||
|
activeScenario === 'taylor'
|
||||||
|
? 'bg-orange-500 text-white shadow-lg'
|
||||||
|
: 'bg-white text-gray-700 hover:bg-gray-100'
|
||||||
|
}`}
|
||||||
|
>
|
||||||
|
Taylor Rule
|
||||||
|
</button>
|
||||||
|
<button
|
||||||
|
onClick={() => setShowGraphs(!showGraphs)}
|
||||||
|
className={`px-6 py-3 rounded-lg font-semibold transition-all flex items-center gap-2 ${
|
||||||
|
showGraphs
|
||||||
|
? 'bg-green-500 text-white shadow-lg'
|
||||||
|
: 'bg-white text-gray-700 hover:bg-gray-100'
|
||||||
|
}`}
|
||||||
|
>
|
||||||
|
<LineChart size={20} />
|
||||||
|
{showGraphs ? 'Hide Graphs' : 'Show Interactive Graphs'}
|
||||||
|
</button>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
{/* Interactive Graphs Section */}
|
||||||
|
{showGraphs && (
|
||||||
|
<div className="bg-white rounded-xl shadow-lg p-8 mb-8">
|
||||||
|
<h2 className="text-2xl font-bold mb-6 text-center text-gray-800">
|
||||||
|
Interactive Graph Plotter
|
||||||
|
</h2>
|
||||||
|
|
||||||
|
{/* Controls */}
|
||||||
|
<div className="grid grid-cols-1 md:grid-cols-2 lg:grid-cols-3 gap-6 mb-8">
|
||||||
|
{/* Money Supply Slider */}
|
||||||
|
<div className="bg-blue-50 p-4 rounded-lg border-2 border-blue-200">
|
||||||
|
<label className="block text-sm font-bold mb-2 text-blue-800">
|
||||||
|
Money Supply (Ms): {moneySupply}
|
||||||
|
</label>
|
||||||
|
<input
|
||||||
|
type="range"
|
||||||
|
min="50"
|
||||||
|
max="150"
|
||||||
|
value={moneySupply}
|
||||||
|
onChange={(e) => setMoneySupply(Number(e.target.value))}
|
||||||
|
className="w-full"
|
||||||
|
/>
|
||||||
|
<div className="text-xs text-gray-600 mt-1">
|
||||||
|
Increase → R↓, E↑ (depreciation)
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
{/* Income Slider */}
|
||||||
|
<div className="bg-green-50 p-4 rounded-lg border-2 border-green-200">
|
||||||
|
<label className="block text-sm font-bold mb-2 text-green-800">
|
||||||
|
Real Income (Y): {income}
|
||||||
|
</label>
|
||||||
|
<input
|
||||||
|
type="range"
|
||||||
|
min="50"
|
||||||
|
max="150"
|
||||||
|
value={income}
|
||||||
|
onChange={(e) => setIncome(Number(e.target.value))}
|
||||||
|
className="w-full"
|
||||||
|
/>
|
||||||
|
<div className="text-xs text-gray-600 mt-1">
|
||||||
|
Increase → Money demand↑ → R↑
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
{/* Foreign Rate Slider */}
|
||||||
|
<div className="bg-purple-50 p-4 rounded-lg border-2 border-purple-200">
|
||||||
|
<label className="block text-sm font-bold mb-2 text-purple-800">
|
||||||
|
Foreign Interest Rate: {foreignRate.toFixed(1)}%
|
||||||
|
</label>
|
||||||
|
<input
|
||||||
|
type="range"
|
||||||
|
min="0"
|
||||||
|
max="6"
|
||||||
|
step="0.1"
|
||||||
|
value={foreignRate}
|
||||||
|
onChange={(e) => setForeignRate(Number(e.target.value))}
|
||||||
|
className="w-full"
|
||||||
|
/>
|
||||||
|
<div className="text-xs text-gray-600 mt-1">
|
||||||
|
Increase → Domestic currency appreciates
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
{/* Inflation Slider */}
|
||||||
|
<div className="bg-orange-50 p-4 rounded-lg border-2 border-orange-200">
|
||||||
|
<label className="block text-sm font-bold mb-2 text-orange-800">
|
||||||
|
Inflation (π): {inflation.toFixed(1)}%
|
||||||
|
</label>
|
||||||
|
<input
|
||||||
|
type="range"
|
||||||
|
min="0"
|
||||||
|
max="6"
|
||||||
|
step="0.1"
|
||||||
|
value={inflation}
|
||||||
|
onChange={(e) => setInflation(Number(e.target.value))}
|
||||||
|
className="w-full"
|
||||||
|
/>
|
||||||
|
<div className="text-xs text-gray-600 mt-1">
|
||||||
|
Target: 2% | Current deviation: {(inflation - 2).toFixed(1)}%
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
{/* Output Gap Slider */}
|
||||||
|
<div className="bg-teal-50 p-4 rounded-lg border-2 border-teal-200">
|
||||||
|
<label className="block text-sm font-bold mb-2 text-teal-800">
|
||||||
|
Output Gap (y-y*): {outputGap.toFixed(1)}%
|
||||||
|
</label>
|
||||||
|
<input
|
||||||
|
type="range"
|
||||||
|
min="-5"
|
||||||
|
max="5"
|
||||||
|
step="0.1"
|
||||||
|
value={outputGap}
|
||||||
|
onChange={(e) => setOutputGap(Number(e.target.value))}
|
||||||
|
className="w-full"
|
||||||
|
/>
|
||||||
|
<div className="text-xs text-gray-600 mt-1">
|
||||||
|
Positive = overheating | Negative = recession
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
{/* Results Display */}
|
||||||
|
<div className="bg-gray-50 p-4 rounded-lg border-2 border-gray-300">
|
||||||
|
<div className="text-sm font-bold mb-2 text-gray-800">Current Values:</div>
|
||||||
|
<div className="space-y-1 text-sm">
|
||||||
|
<div>Interest Rate: <span className="font-bold text-blue-600">{domesticRate.toFixed(2)}%</span></div>
|
||||||
|
<div>Exchange Rate: <span className="font-bold text-green-600">{exchangeRate.toFixed(3)}</span></div>
|
||||||
|
<div>Taylor Rate: <span className="font-bold text-orange-600">{taylorRate.toFixed(2)}%</span></div>
|
||||||
|
<div className="text-xs text-gray-500 mt-2">
|
||||||
|
Real Rate: {(domesticRate - inflation).toFixed(2)}%
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
{/* Graphs */}
|
||||||
|
<div className="grid grid-cols-1 lg:grid-cols-2 gap-8">
|
||||||
|
{/* Money Market Graph */}
|
||||||
|
<div className="border-2 border-blue-300 rounded-lg p-6 bg-blue-50">
|
||||||
|
<h3 className="text-lg font-bold mb-4 text-blue-800 text-center">
|
||||||
|
Money Market Equilibrium
|
||||||
|
</h3>
|
||||||
|
<div className="bg-white p-4 rounded relative" style={{ height: '300px' }}>
|
||||||
|
<svg width="100%" height="100%" viewBox="0 0 400 300">
|
||||||
|
{/* Axes */}
|
||||||
|
<line x1="50" y1="250" x2="350" y2="250" stroke="black" strokeWidth="2" />
|
||||||
|
<line x1="50" y1="250" x2="50" y2="30" stroke="black" strokeWidth="2" />
|
||||||
|
|
||||||
|
{/* Labels */}
|
||||||
|
<text x="200" y="280" textAnchor="middle" fontSize="12">Real Money (M/P)</text>
|
||||||
|
<text x="20" y="140" textAnchor="middle" fontSize="12" transform="rotate(-90 20 140)">Interest Rate (R)</text>
|
||||||
|
|
||||||
|
{/* Money Demand Curve */}
|
||||||
|
<path
|
||||||
|
d={`M ${moneyDemandPoints.map((p, i) =>
|
||||||
|
`${i === 0 ? 'M' : 'L'} ${50 + p.md * 2.5} ${250 - p.r * 25}`
|
||||||
|
).join(' ')}`}
|
||||||
|
stroke="blue"
|
||||||
|
strokeWidth="3"
|
||||||
|
fill="none"
|
||||||
|
/>
|
||||||
|
|
||||||
|
{/* Money Supply Line (vertical) */}
|
||||||
|
<line
|
||||||
|
x1={50 + moneySupply * 2.5}
|
||||||
|
y1="250"
|
||||||
|
x2={50 + moneySupply * 2.5}
|
||||||
|
y2="30"
|
||||||
|
stroke="red"
|
||||||
|
strokeWidth="3"
|
||||||
|
strokeDasharray="5,5"
|
||||||
|
/>
|
||||||
|
|
||||||
|
{/* Equilibrium Point */}
|
||||||
|
<circle
|
||||||
|
cx={50 + moneySupply * 2.5}
|
||||||
|
cy={250 - domesticRate * 25}
|
||||||
|
r="6"
|
||||||
|
fill="green"
|
||||||
|
stroke="darkgreen"
|
||||||
|
strokeWidth="2"
|
||||||
|
/>
|
||||||
|
|
||||||
|
{/* Legend */}
|
||||||
|
<line x1="270" y1="50" x2="300" y2="50" stroke="blue" strokeWidth="3" />
|
||||||
|
<text x="305" y="55" fontSize="11">L(R,Y) - Demand</text>
|
||||||
|
|
||||||
|
<line x1="270" y1="70" x2="300" y2="70" stroke="red" strokeWidth="3" strokeDasharray="5,5" />
|
||||||
|
<text x="305" y="75" fontSize="11">Ms/P - Supply</text>
|
||||||
|
|
||||||
|
<circle cx="285" cy="90" r="4" fill="green" />
|
||||||
|
<text x="295" y="95" fontSize="11">Equilibrium</text>
|
||||||
|
</svg>
|
||||||
|
</div>
|
||||||
|
<div className="mt-3 text-sm text-gray-700 bg-white p-3 rounded">
|
||||||
|
<strong>Equilibrium:</strong> R = {domesticRate.toFixed(2)}% where money supply meets money demand
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
{/* Exchange Rate Graph */}
|
||||||
|
<div className="border-2 border-green-300 rounded-lg p-6 bg-green-50">
|
||||||
|
<h3 className="text-lg font-bold mb-4 text-green-800 text-center">
|
||||||
|
Interest Parity & Exchange Rate
|
||||||
|
</h3>
|
||||||
|
<div className="bg-white p-4 rounded relative" style={{ height: '300px' }}>
|
||||||
|
<svg width="100%" height="100%" viewBox="0 0 400 300">
|
||||||
|
{/* Axes */}
|
||||||
|
<line x1="50" y1="250" x2="350" y2="250" stroke="black" strokeWidth="2" />
|
||||||
|
<line x1="50" y1="250" x2="50" y2="30" stroke="black" strokeWidth="2" />
|
||||||
|
|
||||||
|
{/* Labels */}
|
||||||
|
<text x="200" y="280" textAnchor="middle" fontSize="12">Domestic Interest Rate</text>
|
||||||
|
<text x="20" y="140" textAnchor="middle" fontSize="12" transform="rotate(-90 20 140)">Exchange Rate (E)</text>
|
||||||
|
|
||||||
|
{/* UIP Curve */}
|
||||||
|
<path
|
||||||
|
d={`M ${uipPoints.map((p, i) =>
|
||||||
|
`${i === 0 ? 'M' : 'L'} ${50 + p.rDom * 35} ${250 - p.e * 150}`
|
||||||
|
).join(' ')}`}
|
||||||
|
stroke="purple"
|
||||||
|
strokeWidth="3"
|
||||||
|
fill="none"
|
||||||
|
/>
|
||||||
|
|
||||||
|
{/* Current Point */}
|
||||||
|
<circle
|
||||||
|
cx={50 + domesticRate * 35}
|
||||||
|
cy={250 - exchangeRate * 150}
|
||||||
|
r="6"
|
||||||
|
fill="red"
|
||||||
|
stroke="darkred"
|
||||||
|
strokeWidth="2"
|
||||||
|
/>
|
||||||
|
|
||||||
|
{/* Foreign Rate Reference Line */}
|
||||||
|
<line
|
||||||
|
x1={50 + foreignRate * 35}
|
||||||
|
y1="250"
|
||||||
|
x2={50 + foreignRate * 35}
|
||||||
|
y2="30"
|
||||||
|
stroke="orange"
|
||||||
|
strokeWidth="2"
|
||||||
|
strokeDasharray="3,3"
|
||||||
|
opacity="0.5"
|
||||||
|
/>
|
||||||
|
|
||||||
|
{/* Legend */}
|
||||||
|
<line x1="250" y1="50" x2="280" y2="50" stroke="purple" strokeWidth="3" />
|
||||||
|
<text x="285" y="55" fontSize="11">UIP Condition</text>
|
||||||
|
|
||||||
|
<circle cx="265" cy="70" r="4" fill="red" />
|
||||||
|
<text x="275" y="75" fontSize="11">Current (R, E)</text>
|
||||||
|
|
||||||
|
<line x1="250" y1="85" x2="280" y2="85" stroke="orange" strokeWidth="2" strokeDasharray="3,3" />
|
||||||
|
<text x="285" y="90" fontSize="11">Foreign R</text>
|
||||||
|
</svg>
|
||||||
|
</div>
|
||||||
|
<div className="mt-3 text-sm text-gray-700 bg-white p-3 rounded">
|
||||||
|
<strong>UIP:</strong> R<sub>CHF</sub> ({domesticRate.toFixed(2)}%) vs R<sub>EUR</sub> ({foreignRate.toFixed(1)}%)
|
||||||
|
→ E = {exchangeRate.toFixed(3)} {domesticRate > foreignRate ? '(CHF strong)' : '(CHF weak)'}
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
{/* Taylor Rule Graph */}
|
||||||
|
<div className="border-2 border-orange-300 rounded-lg p-6 bg-orange-50">
|
||||||
|
<h3 className="text-lg font-bold mb-4 text-orange-800 text-center">
|
||||||
|
Taylor Rule Policy Response
|
||||||
|
</h3>
|
||||||
|
<div className="bg-white p-4 rounded relative" style={{ height: '300px' }}>
|
||||||
|
<svg width="100%" height="100%" viewBox="0 0 400 300">
|
||||||
|
{/* Axes */}
|
||||||
|
<line x1="50" y1="150" x2="350" y2="150" stroke="black" strokeWidth="2" />
|
||||||
|
<line x1="200" y1="250" x2="200" y2="30" stroke="black" strokeWidth="2" />
|
||||||
|
|
||||||
|
{/* Grid lines */}
|
||||||
|
<line x1="50" y1="100" x2="350" y2="100" stroke="gray" strokeWidth="1" opacity="0.2" />
|
||||||
|
<line x1="50" y1="200" x2="350" y2="200" stroke="gray" strokeWidth="1" opacity="0.2" />
|
||||||
|
|
||||||
|
{/* Labels */}
|
||||||
|
<text x="200" y="280" textAnchor="middle" fontSize="12">Inflation - Target (%)</text>
|
||||||
|
<text x="20" y="140" textAnchor="middle" fontSize="12" transform="rotate(-90 20 140)">Policy Rate (%)</text>
|
||||||
|
|
||||||
|
{/* Taylor Rule Line for current output gap */}
|
||||||
|
{[-3, -2, -1, 0, 1, 2, 3].map((inflDev, idx, arr) => {
|
||||||
|
if (idx === arr.length - 1) return null;
|
||||||
|
const nextInflDev = arr[idx + 1];
|
||||||
|
const r1 = 2 + 1.5 * inflDev + 0.5 * outputGap;
|
||||||
|
const r2 = 2 + 1.5 * nextInflDev + 0.5 * outputGap;
|
||||||
|
return (
|
||||||
|
<line
|
||||||
|
key={idx}
|
||||||
|
x1={200 + inflDev * 40}
|
||||||
|
y1={150 - r1 * 15}
|
||||||
|
x2={200 + nextInflDev * 40}
|
||||||
|
y2={150 - r2 * 15}
|
||||||
|
stroke="orange"
|
||||||
|
strokeWidth="3"
|
||||||
|
/>
|
||||||
|
);
|
||||||
|
})}
|
||||||
|
|
||||||
|
{/* Current Position */}
|
||||||
|
<circle
|
||||||
|
cx={200 + (inflation - 2) * 40}
|
||||||
|
cy={150 - taylorRate * 15}
|
||||||
|
r="6"
|
||||||
|
fill="red"
|
||||||
|
stroke="darkred"
|
||||||
|
strokeWidth="2"
|
||||||
|
/>
|
||||||
|
|
||||||
|
{/* Target inflation line */}
|
||||||
|
<line
|
||||||
|
x1="200"
|
||||||
|
y1="30"
|
||||||
|
x2="200"
|
||||||
|
y2="250"
|
||||||
|
stroke="green"
|
||||||
|
strokeWidth="2"
|
||||||
|
strokeDasharray="5,5"
|
||||||
|
opacity="0.5"
|
||||||
|
/>
|
||||||
|
|
||||||
|
{/* Legend */}
|
||||||
|
<text x="260" y="50" fontSize="11" fill="green">π = π* (target)</text>
|
||||||
|
<circle cx="280" cy="70" r="4" fill="red" />
|
||||||
|
<text x="290" y="75" fontSize="11">Current policy</text>
|
||||||
|
</svg>
|
||||||
|
</div>
|
||||||
|
<div className="mt-3 text-sm text-gray-700 bg-white p-3 rounded">
|
||||||
|
<strong>Taylor Rule:</strong> R = 2% + 1.5×({(inflation-2).toFixed(1)}%) + 0.5×({outputGap.toFixed(1)}%) = {taylorRate.toFixed(2)}%
|
||||||
|
<br/><span className="text-xs">Real rate = {(taylorRate - inflation).toFixed(2)}%</span>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
{/* GDP Components Impact */}
|
||||||
|
<div className="border-2 border-indigo-300 rounded-lg p-6 bg-indigo-50">
|
||||||
|
<h3 className="text-lg font-bold mb-4 text-indigo-800 text-center">
|
||||||
|
Policy Impact on GDP Components
|
||||||
|
</h3>
|
||||||
|
<div className="bg-white p-4 rounded" style={{ height: '300px' }}>
|
||||||
|
<svg width="100%" height="100%" viewBox="0 0 400 300">
|
||||||
|
{/* Calculate impacts based on current settings */}
|
||||||
|
{(() => {
|
||||||
|
const baseline = 100;
|
||||||
|
const rateEffect = (domesticRate - 2) * -5; // Higher R reduces spending
|
||||||
|
const exRateEffect = (1 - exchangeRate) * 100; // Appreciation reduces NX
|
||||||
|
|
||||||
|
const consumption = Math.max(0, baseline + rateEffect * 0.3);
|
||||||
|
const investment = Math.max(0, baseline + rateEffect * 1.0);
|
||||||
|
const government = baseline; // Assumed constant
|
||||||
|
const netExports = Math.max(-50, baseline + exRateEffect);
|
||||||
|
|
||||||
|
const bars = [
|
||||||
|
{ label: 'C', value: consumption, color: '#3b82f6', x: 70 },
|
||||||
|
{ label: 'I', value: investment, color: '#8b5cf6', x: 150 },
|
||||||
|
{ label: 'G', value: government, color: '#10b981', x: 230 },
|
||||||
|
{ label: 'NX', value: netExports, color: '#f59e0b', x: 310 }
|
||||||
|
];
|
||||||
|
|
||||||
|
return (
|
||||||
|
<>
|
||||||
|
{/* Baseline line */}
|
||||||
|
<line x1="40" y1="150" x2="360" y2="150" stroke="gray" strokeWidth="1" strokeDasharray="3,3" />
|
||||||
|
<text x="365" y="155" fontSize="10" fill="gray">Baseline</text>
|
||||||
|
|
||||||
|
{/* Bars */}
|
||||||
|
{bars.map((bar, idx) => {
|
||||||
|
const height = Math.abs(bar.value - baseline) * 1.5;
|
||||||
|
const y = bar.value >= baseline ? 150 - height : 150;
|
||||||
|
return (
|
||||||
|
<g key={idx}>
|
||||||
|
<rect
|
||||||
|
x={bar.x - 25}
|
||||||
|
y={y}
|
||||||
|
width="50"
|
||||||
|
height={height}
|
||||||
|
fill={bar.color}
|
||||||
|
opacity="0.8"
|
||||||
|
/>
|
||||||
|
<text
|
||||||
|
x={bar.x}
|
||||||
|
y="270"
|
||||||
|
textAnchor="middle"
|
||||||
|
fontSize="14"
|
||||||
|
fontWeight="bold"
|
||||||
|
>
|
||||||
|
{bar.label}
|
||||||
|
</text>
|
||||||
|
<text
|
||||||
|
x={bar.x}
|
||||||
|
y={y - 5}
|
||||||
|
textAnchor="middle"
|
||||||
|
fontSize="11"
|
||||||
|
fill={bar.color}
|
||||||
|
>
|
||||||
|
{bar.value.toFixed(0)}
|
||||||
|
</text>
|
||||||
|
</g>
|
||||||
|
);
|
||||||
|
})}
|
||||||
|
|
||||||
|
{/* Axis */}
|
||||||
|
<line x1="40" y1="250" x2="360" y2="250" stroke="black" strokeWidth="2" />
|
||||||
|
<text x="200" y="295" textAnchor="middle" fontSize="12">GDP = C + I + G + NX</text>
|
||||||
|
</>
|
||||||
|
);
|
||||||
|
})()}
|
||||||
|
</svg>
|
||||||
|
</div>
|
||||||
|
<div className="mt-3 text-sm text-gray-700 bg-white p-3 rounded space-y-1">
|
||||||
|
<div><strong>Interest Rate Effect:</strong> R↑ reduces C and I (especially I)</div>
|
||||||
|
<div><strong>Exchange Rate Effect:</strong> Strong currency reduces NX</div>
|
||||||
|
<div className="text-xs text-gray-500 mt-2">
|
||||||
|
Higher R = {domesticRate.toFixed(2)}% → Tighter policy → Lower GDP
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
{/* Interactive Tips */}
|
||||||
|
<div className="mt-6 bg-gradient-to-r from-blue-50 to-green-50 rounded-lg p-6">
|
||||||
|
<h3 className="text-lg font-bold mb-3 text-gray-800">💡 Try These Scenarios:</h3>
|
||||||
|
<div className="grid grid-cols-1 md:grid-cols-2 gap-4 text-sm">
|
||||||
|
<div className="bg-white p-3 rounded shadow-sm">
|
||||||
|
<strong className="text-blue-600">📈 Monetary Expansion:</strong> Increase money supply to 130 → Watch R fall and E rise (depreciation)
|
||||||
|
</div>
|
||||||
|
<div className="bg-white p-3 rounded shadow-sm">
|
||||||
|
<strong className="text-red-600">📉 Fight Inflation:</strong> Set inflation to 4% → See Taylor rule prescribe higher R to cool economy
|
||||||
|
</div>
|
||||||
|
<div className="bg-white p-3 rounded shadow-sm">
|
||||||
|
<strong className="text-green-600">🌍 Foreign Rate Shock:</strong> Raise foreign rate to 4% → Domestic currency strengthens
|
||||||
|
</div>
|
||||||
|
<div className="bg-white p-3 rounded shadow-sm">
|
||||||
|
<strong className="text-orange-600">📊 Recession Response:</strong> Set output gap to -3% → Taylor rule suggests lower rates
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
)}
|
||||||
|
|
||||||
|
{/* Active Scenario Flow */}
|
||||||
|
<div className="bg-white rounded-xl shadow-lg p-8 mb-8">
|
||||||
|
<h2 className="text-2xl font-bold mb-6 text-center text-gray-800">
|
||||||
|
{scenarios[activeScenario].title}
|
||||||
|
</h2>
|
||||||
|
<div className="flex items-center justify-between">
|
||||||
|
{scenarios[activeScenario].steps.map((step, idx) => (
|
||||||
|
<React.Fragment key={idx}>
|
||||||
|
<div className="flex-1">
|
||||||
|
<div className={`${step.color} rounded-lg p-6 h-32 flex flex-col justify-center items-center text-center shadow-md`}>
|
||||||
|
<div className="font-bold text-lg mb-2">{step.label}</div>
|
||||||
|
<div className="text-sm">{step.action}</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
{idx < scenarios[activeScenario].steps.length - 1 && (
|
||||||
|
<ArrowRight className="mx-4 text-gray-400" size={32} />
|
||||||
|
)}
|
||||||
|
</React.Fragment>
|
||||||
|
))}
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
{/* Main Relationships Diagram */}
|
||||||
|
<div className="bg-white rounded-xl shadow-lg p-8 mb-8">
|
||||||
|
<h2 className="text-2xl font-bold mb-6 text-center text-gray-800">
|
||||||
|
Core Relationships & Formulas
|
||||||
|
</h2>
|
||||||
|
|
||||||
|
<div className="grid grid-cols-2 gap-6">
|
||||||
|
{/* Money Market Equilibrium */}
|
||||||
|
<div className="border-2 border-purple-300 rounded-lg p-6 bg-purple-50">
|
||||||
|
<h3 className="text-xl font-bold mb-4 text-purple-800">Money Market Equilibrium</h3>
|
||||||
|
<div className="space-y-3">
|
||||||
|
<div className="bg-white p-3 rounded border border-purple-200">
|
||||||
|
<div className="font-mono text-center text-lg">M<sup>s</sup>/P = L(R, Y)</div>
|
||||||
|
</div>
|
||||||
|
<div className="text-sm space-y-2">
|
||||||
|
<div><strong>M<sup>s</sup></strong>: Money Supply (set by CB)</div>
|
||||||
|
<div><strong>P</strong>: Price Level (sticky short-run)</div>
|
||||||
|
<div><strong>R</strong>: Interest Rate (adjusts to clear market)</div>
|
||||||
|
<div><strong>Y</strong>: Real Income</div>
|
||||||
|
</div>
|
||||||
|
<div className="mt-4 p-3 bg-purple-100 rounded text-sm">
|
||||||
|
<strong>Key:</strong> R ↑ → L(R,Y) ↓ (inverse relationship)<br/>
|
||||||
|
Y ↑ → L(R,Y) ↑ (positive relationship)
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
{/* Uncovered Interest Parity */}
|
||||||
|
<div className="border-2 border-green-300 rounded-lg p-6 bg-green-50">
|
||||||
|
<h3 className="text-xl font-bold mb-4 text-green-800">Uncovered Interest Parity (UIP)</h3>
|
||||||
|
<div className="space-y-3">
|
||||||
|
<div className="bg-white p-3 rounded border border-green-200">
|
||||||
|
<div className="font-mono text-center text-lg">R<sub>CHF</sub> = R<sub>EUR</sub> + (E<sup>e</sup> - E)/E</div>
|
||||||
|
</div>
|
||||||
|
<div className="text-sm space-y-2">
|
||||||
|
<div><strong>R<sub>CHF</sub></strong>: Domestic interest rate</div>
|
||||||
|
<div><strong>R<sub>EUR</sub></strong>: Foreign interest rate</div>
|
||||||
|
<div><strong>E</strong>: Current exchange rate (CHF/EUR)</div>
|
||||||
|
<div><strong>E<sup>e</sup></strong>: Expected future exchange rate</div>
|
||||||
|
</div>
|
||||||
|
<div className="mt-4 p-3 bg-green-100 rounded text-sm">
|
||||||
|
<strong>Key:</strong> If R<sub>CHF</sub> ↑ → CHF appreciates (E ↓)<br/>
|
||||||
|
Returns must equalize across currencies
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
{/* Taylor Rule */}
|
||||||
|
<div className="border-2 border-orange-300 rounded-lg p-6 bg-orange-50">
|
||||||
|
<h3 className="text-xl font-bold mb-4 text-orange-800">Taylor Rule</h3>
|
||||||
|
<div className="space-y-3">
|
||||||
|
<div className="bg-white p-3 rounded border border-orange-200">
|
||||||
|
<div className="font-mono text-center text-lg">R = R* + f<sub>π</sub>(π - π*) + f<sub>y</sub>(y - y*)</div>
|
||||||
|
</div>
|
||||||
|
<div className="text-sm space-y-2">
|
||||||
|
<div><strong>R*</strong>: Equilibrium rate</div>
|
||||||
|
<div><strong>π</strong>: Current inflation, <strong>π*</strong>: Target (2%)</div>
|
||||||
|
<div><strong>y</strong>: Output, <strong>y*</strong>: Potential output</div>
|
||||||
|
<div><strong>f<sub>π</sub></strong> = 1.5 (inflation response)</div>
|
||||||
|
<div><strong>f<sub>y</sub></strong> = 0.5 (output response)</div>
|
||||||
|
</div>
|
||||||
|
<div className="mt-4 p-3 bg-orange-100 rounded text-sm">
|
||||||
|
<strong>Key:</strong> f<sub>π</sub> {'>'} 1 ensures real rate rises<br/>
|
||||||
|
when inflation ↑ to cool economy
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
{/* National Income Identity */}
|
||||||
|
<div className="border-2 border-blue-300 rounded-lg p-6 bg-blue-50">
|
||||||
|
<h3 className="text-xl font-bold mb-4 text-blue-800">National Income Identity</h3>
|
||||||
|
<div className="space-y-3">
|
||||||
|
<div className="bg-white p-3 rounded border border-blue-200">
|
||||||
|
<div className="font-mono text-center text-lg">Y = C + I + G + CA</div>
|
||||||
|
</div>
|
||||||
|
<div className="text-sm space-y-2">
|
||||||
|
<div><strong>Y</strong>: GDP/National Income</div>
|
||||||
|
<div><strong>C</strong>: Consumption (~51%)</div>
|
||||||
|
<div><strong>I</strong>: Investment (~27%, most volatile)</div>
|
||||||
|
<div><strong>G</strong>: Government purchases (~12%)</div>
|
||||||
|
<div><strong>CA</strong>: Current Account (~10%)</div>
|
||||||
|
</div>
|
||||||
|
<div className="mt-4 p-3 bg-blue-100 rounded text-sm">
|
||||||
|
<strong>Saving Identity:</strong> S = I + CA<br/>
|
||||||
|
Save domestically (I) or abroad (CA)
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
{/* Transmission Channels */}
|
||||||
|
<div className="bg-white rounded-xl shadow-lg p-8">
|
||||||
|
<h2 className="text-2xl font-bold mb-6 text-center text-gray-800">
|
||||||
|
Monetary Policy Transmission Channels
|
||||||
|
</h2>
|
||||||
|
|
||||||
|
<div className="grid grid-cols-3 gap-6">
|
||||||
|
{/* Interest Rate Channel */}
|
||||||
|
<div className="border-2 border-indigo-300 rounded-lg p-6 bg-indigo-50">
|
||||||
|
<h3 className="text-lg font-bold mb-4 text-indigo-800 text-center">Interest Rate Channel</h3>
|
||||||
|
<div className="space-y-3 text-sm">
|
||||||
|
<div className="flex items-center justify-between">
|
||||||
|
<span>Policy Rate ↑</span>
|
||||||
|
<ArrowRight size={16} />
|
||||||
|
</div>
|
||||||
|
<div className="flex items-center justify-between">
|
||||||
|
<span>All Rates ↑</span>
|
||||||
|
<ArrowRight size={16} />
|
||||||
|
</div>
|
||||||
|
<div className="flex items-center justify-between">
|
||||||
|
<span>Borrowing Costs ↑</span>
|
||||||
|
<ArrowRight size={16} />
|
||||||
|
</div>
|
||||||
|
<div className="flex items-center justify-between">
|
||||||
|
<span>Investment ↓</span>
|
||||||
|
<ArrowRight size={16} />
|
||||||
|
</div>
|
||||||
|
<div className="flex items-center justify-between">
|
||||||
|
<span>Consumption ↓</span>
|
||||||
|
<ArrowRight size={16} />
|
||||||
|
</div>
|
||||||
|
<div className="bg-indigo-100 p-2 rounded text-center font-semibold">
|
||||||
|
Aggregate Demand ↓
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
{/* Exchange Rate Channel */}
|
||||||
|
<div className="border-2 border-teal-300 rounded-lg p-6 bg-teal-50">
|
||||||
|
<h3 className="text-lg font-bold mb-4 text-teal-800 text-center">Exchange Rate Channel</h3>
|
||||||
|
<div className="space-y-3 text-sm">
|
||||||
|
<div className="flex items-center justify-between">
|
||||||
|
<span>R<sub>domestic</sub> ↑</span>
|
||||||
|
<ArrowRight size={16} />
|
||||||
|
</div>
|
||||||
|
<div className="flex items-center justify-between">
|
||||||
|
<span>Currency Appreciates</span>
|
||||||
|
<ArrowRight size={16} />
|
||||||
|
</div>
|
||||||
|
<div className="flex items-center justify-between">
|
||||||
|
<span>Exports ↓</span>
|
||||||
|
<ArrowRight size={16} />
|
||||||
|
</div>
|
||||||
|
<div className="flex items-center justify-between">
|
||||||
|
<span>Imports ↑</span>
|
||||||
|
<ArrowRight size={16} />
|
||||||
|
</div>
|
||||||
|
<div className="flex items-center justify-between">
|
||||||
|
<span>Net Exports ↓</span>
|
||||||
|
<ArrowRight size={16} />
|
||||||
|
</div>
|
||||||
|
<div className="bg-teal-100 p-2 rounded text-center font-semibold">
|
||||||
|
Aggregate Demand ↓
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
{/* Wealth/Asset Channel */}
|
||||||
|
<div className="border-2 border-pink-300 rounded-lg p-6 bg-pink-50">
|
||||||
|
<h3 className="text-lg font-bold mb-4 text-pink-800 text-center">Wealth/Asset Channel</h3>
|
||||||
|
<div className="space-y-3 text-sm">
|
||||||
|
<div className="flex items-center justify-between">
|
||||||
|
<span>Interest Rates ↑</span>
|
||||||
|
<ArrowRight size={16} />
|
||||||
|
</div>
|
||||||
|
<div className="flex items-center justify-between">
|
||||||
|
<span>Bond Prices ↓</span>
|
||||||
|
<ArrowRight size={16} />
|
||||||
|
</div>
|
||||||
|
<div className="flex items-center justify-between">
|
||||||
|
<span>Stock Prices ↓</span>
|
||||||
|
<ArrowRight size={16} />
|
||||||
|
</div>
|
||||||
|
<div className="flex items-center justify-between">
|
||||||
|
<span>Household Wealth ↓</span>
|
||||||
|
<ArrowRight size={16} />
|
||||||
|
</div>
|
||||||
|
<div className="flex items-center justify-between">
|
||||||
|
<span>Consumption ↓</span>
|
||||||
|
<ArrowRight size={16} />
|
||||||
|
</div>
|
||||||
|
<div className="bg-pink-100 p-2 rounded text-center font-semibold">
|
||||||
|
Aggregate Demand ↓
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
{/* Key Takeaways */}
|
||||||
|
<div className="mt-8 bg-gradient-to-r from-purple-100 to-blue-100 rounded-xl p-6">
|
||||||
|
<h3 className="text-xl font-bold mb-4 text-gray-800">Key Takeaways</h3>
|
||||||
|
<ul className="space-y-2 text-sm">
|
||||||
|
<li className="flex items-start">
|
||||||
|
<span className="text-purple-600 mr-2">•</span>
|
||||||
|
<span><strong>Money Market:</strong> Central bank controls Ms, which determines R through equilibrium condition</span>
|
||||||
|
</li>
|
||||||
|
<li className="flex items-start">
|
||||||
|
<span className="text-purple-600 mr-2">•</span>
|
||||||
|
<span><strong>Exchange Rates:</strong> Interest rate differentials drive currency movements (UIP)</span>
|
||||||
|
</li>
|
||||||
|
<li className="flex items-start">
|
||||||
|
<span className="text-purple-600 mr-2">•</span>
|
||||||
|
<span><strong>Taylor Rule:</strong> Systematic policy response to inflation and output gaps (f<sub>π</sub> {'>'} 1 is crucial)</span>
|
||||||
|
</li>
|
||||||
|
<li className="flex items-start">
|
||||||
|
<span className="text-purple-600 mr-2">•</span>
|
||||||
|
<span><strong>Transmission:</strong> Monetary policy affects economy through multiple channels simultaneously</span>
|
||||||
|
</li>
|
||||||
|
<li className="flex items-start">
|
||||||
|
<span className="text-purple-600 mr-2">•</span>
|
||||||
|
<span><strong>Real Effects:</strong> Changes in R and E both impact aggregate demand (C, I, CA components)</span>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
);
|
||||||
|
};
|
||||||
|
|
||||||
|
export default MonetaryPolicyDiagram;
|
||||||
@@ -0,0 +1,446 @@
|
|||||||
|
# Problem Set 2 - Answer Summary
|
||||||
|
## Global Business Environment
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
## Problem 1: Exchange Rates (7 points)
|
||||||
|
|
||||||
|
### Part 1 (5 points): Currency Risk Analysis for European Resident
|
||||||
|
|
||||||
|
**Question:** Which currency is riskier - the dollar or the yen?
|
||||||
|
|
||||||
|
**ANSWER: THE YEN IS RISKIER**
|
||||||
|
|
||||||
|
**Explanation:**
|
||||||
|
|
||||||
|
Even though both currencies are equally variable (same variance), the **yen is riskier** from a European resident's portfolio perspective because:
|
||||||
|
|
||||||
|
1. **Dollar provides a HEDGE:**
|
||||||
|
- When the rest of your wealth has high returns → Euro depreciates vs Dollar
|
||||||
|
- This means the dollar appreciates when your wealth is doing well
|
||||||
|
- The dollar provides **negative covariance** with your portfolio
|
||||||
|
- Acts as insurance/diversification
|
||||||
|
|
||||||
|
2. **Yen AMPLIFIES risk:**
|
||||||
|
- When rest of wealth has high returns → Yen appreciates vs Dollar
|
||||||
|
- Holding dollars means you lose when the yen appreciates
|
||||||
|
- The dollar (relative to yen) has **positive covariance** with your portfolio
|
||||||
|
- Amplifies portfolio risk
|
||||||
|
|
||||||
|
3. **Portfolio theory insight:**
|
||||||
|
- Risk = Variance + 2 × Covariance with existing wealth
|
||||||
|
- Assets that move in the **same direction** as your wealth are **less risky**
|
||||||
|
- Assets that move in the **opposite direction** are **more risky**
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
### Part 2 (8 points): Exchange Rate Data Analysis
|
||||||
|
|
||||||
|
**Task:** Analyze exchange rate data for Switzerland
|
||||||
|
|
||||||
|
**Key Findings:**
|
||||||
|
|
||||||
|
1. **Bretton Woods Era (1944-1973):**
|
||||||
|
- Swiss Franc was FIXED to USD
|
||||||
|
- Rate: approximately 4.30-4.375 CHF per USD
|
||||||
|
|
||||||
|
2. **Floating Period (1973-2011):**
|
||||||
|
- CHF floated freely against USD
|
||||||
|
- High volatility
|
||||||
|
|
||||||
|
3. **Euro Floor Period (September 6, 2011 - January 15, 2015):**
|
||||||
|
- SNB set minimum exchange rate: 1.20 CHF per EUR
|
||||||
|
- CHF was fixed to EUR, NOT directly to USD
|
||||||
|
- Indirectly reduced CHF/USD volatility
|
||||||
|
- "Swiss Franc Shock" on January 15, 2015 when floor abandoned
|
||||||
|
|
||||||
|
4. **Post-Euro Floor (2015-Present):**
|
||||||
|
- CHF floats freely again
|
||||||
|
- Significant appreciation after floor removal
|
||||||
|
|
||||||
|
**Graph created:** `switzerland_exchange_rate.png`
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
## Problem 2: Forward Exchange Rate (15 points)
|
||||||
|
|
||||||
|
**Given:**
|
||||||
|
- Spot rate: E_USD/EUR = 0.9745
|
||||||
|
- 1-year forward points: 236.60
|
||||||
|
- R_1y_USD = 0.05 (5%)
|
||||||
|
|
||||||
|
### Part 1 (4 points): Calculate Forward Exchange Rate
|
||||||
|
|
||||||
|
**ANSWER: F_1y_USD/EUR = 0.9982**
|
||||||
|
|
||||||
|
**Calculation:**
|
||||||
|
```
|
||||||
|
F = E_spot + (Forward Points / 10,000)
|
||||||
|
F = 0.9745 + (236.60 / 10,000)
|
||||||
|
F = 0.9745 + 0.0237
|
||||||
|
F = 0.9982
|
||||||
|
```
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
### Part 2 (4 points): Expected Appreciation or Depreciation
|
||||||
|
|
||||||
|
**ANSWER: The US Dollar is expected to DEPRECIATE by 2.43% relative to the Euro**
|
||||||
|
|
||||||
|
**Reasoning:**
|
||||||
|
- Forward rate (0.9982) > Spot rate (0.9745)
|
||||||
|
- Takes MORE dollars to buy 1 euro in forward market
|
||||||
|
- Dollar loses value, euro gains value
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
### Part 3 (4 points): Intuitive Explanation
|
||||||
|
|
||||||
|
**ANSWER:**
|
||||||
|
|
||||||
|
The dollar is expected to depreciate because:
|
||||||
|
|
||||||
|
1. **Interest Rate Differential:**
|
||||||
|
- Forward premium implies: (1 + R_USD) / (1 + R_EUR) > 1
|
||||||
|
- Therefore: R_USD > R_EUR
|
||||||
|
- US interest rates are higher than Eurozone rates
|
||||||
|
|
||||||
|
2. **Economic Interpretation:**
|
||||||
|
- Higher interest rates often reflect higher expected inflation
|
||||||
|
- Higher inflation leads to currency depreciation (PPP)
|
||||||
|
|
||||||
|
3. **No Arbitrage (Covered Interest Parity):**
|
||||||
|
- Higher US interest rate is offset by expected dollar depreciation
|
||||||
|
- Forward rate adjusts to prevent arbitrage
|
||||||
|
- Makes USD and EUR investments equally attractive when hedged
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
### Part 4 (3 points): Find R_EUR
|
||||||
|
|
||||||
|
**ANSWER: R_1y_EUR = 0.0251 or 2.51%**
|
||||||
|
|
||||||
|
**Calculation using Covered Interest Parity:**
|
||||||
|
```
|
||||||
|
F/E = (1 + R_USD)/(1 + R_EUR)
|
||||||
|
|
||||||
|
Solving for R_EUR:
|
||||||
|
R_EUR = (1 + R_USD) × (E/F) - 1
|
||||||
|
R_EUR = (1 + 0.05) × (0.9745/0.9982) - 1
|
||||||
|
R_EUR = 1.05 × 0.976296 - 1
|
||||||
|
R_EUR = 0.0251 or 2.51%
|
||||||
|
```
|
||||||
|
|
||||||
|
**Verification:**
|
||||||
|
- F/E = 0.9982/0.9745 = 1.0243
|
||||||
|
- (1 + R_USD)/(1 + R_EUR) = 1.05/1.0251 = 1.0243 ✓
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
## Problem 3: Put Option (20 points)
|
||||||
|
|
||||||
|
**Given:**
|
||||||
|
- Put option to sell: 1,000 EUR
|
||||||
|
- Option fee: 75 CHF (paid at signing)
|
||||||
|
- R_3m_EUR = 1.3%
|
||||||
|
- R_3m_CHF = 0.5%
|
||||||
|
- E_spot = 0.95 CHF/EUR
|
||||||
|
|
||||||
|
### Part 1 (7 points): Expected Exchange Rate
|
||||||
|
|
||||||
|
**ANSWER: E_e_CHF/EUR = 0.9425**
|
||||||
|
|
||||||
|
**Calculation using Interest Parity:**
|
||||||
|
```
|
||||||
|
E_e = E_spot × (1 + R_CHF) / (1 + R_EUR)
|
||||||
|
E_e = 0.95 × (1 + 0.005) / (1 + 0.013)
|
||||||
|
E_e = 0.95 × 1.005 / 1.013
|
||||||
|
E_e = 0.9425 CHF/EUR
|
||||||
|
```
|
||||||
|
|
||||||
|
**Strike Price: X = 0.9425 CHF/EUR**
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
### Part 2 (7 points): Scenario E = 0.93
|
||||||
|
|
||||||
|
**After 3 months: E = 0.93 CHF/EUR**
|
||||||
|
|
||||||
|
**Exercise Decision: YES, EXERCISE THE OPTION**
|
||||||
|
|
||||||
|
**Reasoning:**
|
||||||
|
- Strike price (0.9425) > Market rate (0.93)
|
||||||
|
- Can sell EUR at better rate than market
|
||||||
|
|
||||||
|
**PAYOFF: 12.50 CHF**
|
||||||
|
```
|
||||||
|
Payoff = 1,000 × max(0.9425 - 0.93, 0)
|
||||||
|
Payoff = 1,000 × 0.0125
|
||||||
|
Payoff = 12.50 CHF
|
||||||
|
```
|
||||||
|
|
||||||
|
**PROFIT: -62.88 CHF (Loss)**
|
||||||
|
```
|
||||||
|
Future value of premium = 75 × 1.005 = 75.37 CHF
|
||||||
|
Profit = 12.50 - 75.37 = -62.88 CHF
|
||||||
|
```
|
||||||
|
|
||||||
|
**Graph:** See `problem3_put_option_diagrams.png` (Scenario 1 marked in green)
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
### Part 3 (6 points): Scenario E = 0.98
|
||||||
|
|
||||||
|
**After 3 months: E = 0.98 CHF/EUR**
|
||||||
|
|
||||||
|
**Exercise Decision: NO, LET IT EXPIRE**
|
||||||
|
|
||||||
|
**Reasoning:**
|
||||||
|
- Strike price (0.9425) < Market rate (0.98)
|
||||||
|
- Market rate is better than strike price
|
||||||
|
|
||||||
|
**PAYOFF: 0.00 CHF**
|
||||||
|
```
|
||||||
|
Payoff = 1,000 × max(0.9425 - 0.98, 0)
|
||||||
|
Payoff = 0 CHF (expires worthless)
|
||||||
|
```
|
||||||
|
|
||||||
|
**PROFIT: -75.37 CHF (Loss)**
|
||||||
|
```
|
||||||
|
Future value of premium = 75 × 1.005 = 75.37 CHF
|
||||||
|
Profit = 0 - 75.37 = -75.37 CHF
|
||||||
|
```
|
||||||
|
|
||||||
|
**Note:** This is the maximum possible loss (the option premium with interest)
|
||||||
|
|
||||||
|
**Graph:** See `problem3_put_option_diagrams.png` (Scenario 2 marked in magenta)
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
## Problem 4: Domestic Money Demand (50 points)
|
||||||
|
|
||||||
|
**Given:**
|
||||||
|
- R_EUR = 0.05 (5%)
|
||||||
|
- E_e_CHF/EUR = 1.1
|
||||||
|
- P_CHF = P_EUR = 1.0
|
||||||
|
- M^s_CHF = 200
|
||||||
|
- Y_CHF = 100
|
||||||
|
- L(R_CHF, Y_CHF) = 100 + 1.5 × Y_CHF - 5000 × R_CHF
|
||||||
|
|
||||||
|
### Part 1 (5 points): Equilibrium Swiss Interest Rate
|
||||||
|
|
||||||
|
**ANSWER: R_CHF = 0.010 (1.0%)**
|
||||||
|
|
||||||
|
**Calculation:**
|
||||||
|
```
|
||||||
|
Money market equilibrium: M^s/P = L(R, Y)
|
||||||
|
200/1 = 100 + 1.5(100) - 5000 × R_CHF
|
||||||
|
200 = 250 - 5000 × R_CHF
|
||||||
|
5000 × R_CHF = 50
|
||||||
|
R_CHF = 0.010 or 1.0%
|
||||||
|
```
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
### Part 2 (5 points): Equilibrium Spot Exchange Rate
|
||||||
|
|
||||||
|
**ANSWER: E_CHF/EUR = 1.058**
|
||||||
|
|
||||||
|
**Calculation using Uncovered Interest Parity:**
|
||||||
|
```
|
||||||
|
E = E_e / (1 + R_EUR - R_CHF)
|
||||||
|
E = 1.1 / (1 + 0.05 - 0.01)
|
||||||
|
E = 1.1 / 1.04
|
||||||
|
E = 1.058 CHF/EUR
|
||||||
|
```
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
### Part 3 (5 points): Expected Appreciation or Depreciation
|
||||||
|
|
||||||
|
**ANSWER: The CHF is expected to DEPRECIATE by 4.00% relative to the EUR**
|
||||||
|
|
||||||
|
**Calculation:**
|
||||||
|
```
|
||||||
|
Current spot: E = 1.058
|
||||||
|
Expected future: E_e = 1.1
|
||||||
|
Change: (1.1 - 1.058) / 1.058 = 0.04 or 4.00%
|
||||||
|
```
|
||||||
|
|
||||||
|
**Interpretation:**
|
||||||
|
- Expected rate > Spot rate
|
||||||
|
- Takes MORE CHF to buy 1 EUR in future
|
||||||
|
- CHF depreciates, EUR appreciates
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
### Part 4 (10 points): Diagram - Temporary Output Increase (No Accommodation)
|
||||||
|
|
||||||
|
**Graphs created:**
|
||||||
|
- `problem4_part4_initial.png` - Initial equilibrium
|
||||||
|
- `problem4_part4_no_accommodation.png` - After output increase
|
||||||
|
|
||||||
|
**Description:**
|
||||||
|
|
||||||
|
**Money Market (bottom panel):**
|
||||||
|
- Money demand shifts RIGHT (Y increases from 100 to 200)
|
||||||
|
- Money supply stays FIXED at 200 (vertical line unchanged)
|
||||||
|
- Interest rate RISES to restore equilibrium
|
||||||
|
|
||||||
|
**Forex Market (top panel):**
|
||||||
|
- FR curve stays UNCHANGED (E_e unchanged - temporary shock)
|
||||||
|
- Movement ALONG the FR curve
|
||||||
|
- Higher R_CHF → CHF appreciates (E falls)
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
### Part 5 (10 points): New Short-Run Equilibrium
|
||||||
|
|
||||||
|
**New output: Y_1_CHF = 200**
|
||||||
|
**Central bank does NOT accommodate (M^s = 200 unchanged)**
|
||||||
|
|
||||||
|
**ANSWERS:**
|
||||||
|
|
||||||
|
**R_1_CHF = 0.040 (4.0%)**
|
||||||
|
```
|
||||||
|
Money market: M^s/P = L(R_1, Y_1)
|
||||||
|
200 = 100 + 1.5(200) - 5000 × R_1_CHF
|
||||||
|
200 = 400 - 5000 × R_1_CHF
|
||||||
|
5000 × R_1_CHF = 200
|
||||||
|
R_1_CHF = 0.040 or 4.0%
|
||||||
|
```
|
||||||
|
|
||||||
|
**E_1_CHF/EUR = 1.089**
|
||||||
|
```
|
||||||
|
E_1 = E_e / (1 + R_EUR - R_1_CHF)
|
||||||
|
E_1 = 1.1 / (1 + 0.05 - 0.04)
|
||||||
|
E_1 = 1.1 / 1.01
|
||||||
|
E_1 = 1.089 CHF/EUR
|
||||||
|
```
|
||||||
|
|
||||||
|
**Changes:**
|
||||||
|
- Interest rate: +3.0 percentage points (from 1% to 4%)
|
||||||
|
- Exchange rate: CHF appreciated by 2.97% (E fell from 1.058 to 1.089)
|
||||||
|
|
||||||
|
**Economic Interpretation:**
|
||||||
|
- Output increase → Higher money demand
|
||||||
|
- Fixed money supply → Interest rate must rise
|
||||||
|
- Higher domestic interest rate → Capital inflows → CHF appreciates
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
### Part 6 (10 points): Diagram - With Monetary Accommodation
|
||||||
|
|
||||||
|
**Graph created:** `problem4_part6_accommodation.png`
|
||||||
|
|
||||||
|
**Description:**
|
||||||
|
|
||||||
|
**Money Market (bottom panel):**
|
||||||
|
- Money demand shifts RIGHT (Y increases)
|
||||||
|
- Money supply shifts RIGHT (central bank increases M^s)
|
||||||
|
- Both curves shift by same amount
|
||||||
|
- Interest rate stays CONSTANT
|
||||||
|
|
||||||
|
**Forex Market (top panel):**
|
||||||
|
- No change at all
|
||||||
|
- Exchange rate stays CONSTANT
|
||||||
|
- Interest rate stays CONSTANT
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
### Part 7 (5 points): New Money Supply with Accommodation
|
||||||
|
|
||||||
|
**ANSWER: M^s,1_CHF = 350**
|
||||||
|
|
||||||
|
**Calculation:**
|
||||||
|
```
|
||||||
|
With accommodation, R_CHF remains at 0.010
|
||||||
|
Money market: M^s,1 / P = L(R_CHF, Y_1_CHF)
|
||||||
|
M^s,1 / 1 = 100 + 1.5(200) - 5000(0.010)
|
||||||
|
M^s,1 = 100 + 300 - 50
|
||||||
|
M^s,1 = 350
|
||||||
|
```
|
||||||
|
|
||||||
|
**Change in money supply: ΔM^s = 350 - 200 = 150**
|
||||||
|
|
||||||
|
**Do rates change?**
|
||||||
|
- **Interest rate: NO CHANGE** (R = 1.0%)
|
||||||
|
- **Exchange rate: NO CHANGE** (E = 1.058)
|
||||||
|
|
||||||
|
**Economic Interpretation:**
|
||||||
|
- Central bank accommodates the increased money demand
|
||||||
|
- Increases money supply to prevent interest rate from rising
|
||||||
|
- Since interest rate doesn't change, exchange rate doesn't change (via UIP)
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
## Summary Table
|
||||||
|
|
||||||
|
| Problem | Part | Answer | Points |
|
||||||
|
|---------|------|--------|--------|
|
||||||
|
| **1.1** | Risk Analysis | Yen is riskier | 5 |
|
||||||
|
| **1.2** | Swiss Data | Fixed: Bretton Woods (1944-73); Floor: 2011-15 | 8 |
|
||||||
|
| **2.1** | Forward Rate | F = 0.9982 | 4 |
|
||||||
|
| **2.2** | USD Movement | Depreciate 2.43% | 4 |
|
||||||
|
| **2.3** | Explanation | Higher US rates → depreciation | 4 |
|
||||||
|
| **2.4** | EUR Rate | R_EUR = 2.51% | 3 |
|
||||||
|
| **3.1** | Expected E | E_e = 0.9425 | 7 |
|
||||||
|
| **3.2** | E = 0.93 | Exercise: YES, Payoff: 12.50, Profit: -62.88 | 7 |
|
||||||
|
| **3.3** | E = 0.98 | Exercise: NO, Payoff: 0, Profit: -75.37 | 6 |
|
||||||
|
| **4.1** | Swiss Rate | R_CHF = 1.0% | 5 |
|
||||||
|
| **4.2** | Spot Rate | E = 1.058 | 5 |
|
||||||
|
| **4.3** | Movement | CHF depreciates 4.00% | 5 |
|
||||||
|
| **4.4** | Diagram | See graphs | 10 |
|
||||||
|
| **4.5** | New Equilibrium | R_1 = 4.0%, E_1 = 1.089 | 10 |
|
||||||
|
| **4.6** | Diagram w/ Accom. | See graphs | 10 |
|
||||||
|
| **4.7** | New M^s | M^s,1 = 350 | 5 |
|
||||||
|
| **TOTAL** | | | **100** |
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
## Files Created
|
||||||
|
|
||||||
|
### Python Scripts
|
||||||
|
1. `problem1_part1_analysis.py` - Exchange rate risk analysis
|
||||||
|
2. `problem1_part2_switzerland.py` - Swiss exchange rate data from FRED
|
||||||
|
3. `problem2_forward_rate.py` - Forward rate calculations
|
||||||
|
4. `problem3_put_option.py` - Put option analysis
|
||||||
|
5. `problem4_money_demand.py` - Money demand and exchange rates
|
||||||
|
6. `run_all_problems.py` - Master script to run all problems
|
||||||
|
|
||||||
|
### Generated Graphics
|
||||||
|
1. `switzerland_exchange_rate.png` - CHF/USD historical data
|
||||||
|
2. `problem3_put_option_diagrams.png` - Put option payoff and profit
|
||||||
|
3. `problem4_part4_initial.png` - Initial equilibrium
|
||||||
|
4. `problem4_part4_no_accommodation.png` - After output shock
|
||||||
|
5. `problem4_part6_accommodation.png` - With monetary accommodation
|
||||||
|
|
||||||
|
### Documentation
|
||||||
|
1. `README.md` - Comprehensive guide and documentation
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
## Key Concepts Summary
|
||||||
|
|
||||||
|
### Exchange Rate Determination
|
||||||
|
- **Covered Interest Parity (CIP):** F/E = (1 + R_d)/(1 + R_f)
|
||||||
|
- **Uncovered Interest Parity (UIP):** E_e/E = (1 + R_d)/(1 + R_f)
|
||||||
|
- **Purchasing Power Parity (PPP):** Higher inflation → depreciation
|
||||||
|
|
||||||
|
### Money Market
|
||||||
|
- **Equilibrium:** M^s/P = L(R, Y)
|
||||||
|
- **Money demand:** Increases with Y, decreases with R
|
||||||
|
|
||||||
|
### Options
|
||||||
|
- **Put option payoff:** max(X - E, 0)
|
||||||
|
- **Exercise rule:** Exercise if X > E (strike > spot)
|
||||||
|
- **Maximum loss:** Option premium (with interest)
|
||||||
|
|
||||||
|
### Portfolio Risk
|
||||||
|
- **Total risk:** Variance + 2 × Covariance
|
||||||
|
- **Hedge:** Asset with negative covariance
|
||||||
|
- **Risk amplifier:** Asset with positive covariance
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
*Problem Set completed successfully. All calculations verified and diagrams generated.*
|
||||||
@@ -0,0 +1,882 @@
|
|||||||
|
# Problem Set 2 - Complete Solutions
|
||||||
|
## Global Business Environment
|
||||||
|
|
||||||
|
**Student:** [Your Name]
|
||||||
|
**Date:** November 11, 2025
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
# Problem 1: Exchange Rates (7 points)
|
||||||
|
|
||||||
|
## Part 1 (5 points): Currency Risk Analysis
|
||||||
|
|
||||||
|
### Question
|
||||||
|
Suppose the dollar exchange rates of the euro and the yen are equally variable. The euro, however, tends to depreciate unexpectedly against the dollar when the return on the rest of your wealth is unexpectedly high, while the yen tends to appreciate unexpectedly in the same circumstances. As a European resident, which currency, the dollar or the yen, would be considered riskier?
|
||||||
|
|
||||||
|
### Answer
|
||||||
|
|
||||||
|
**THE YEN IS RISKIER than the dollar for a European resident.**
|
||||||
|
|
||||||
|
### Detailed Explanation
|
||||||
|
|
||||||
|
#### Understanding Risk from a Portfolio Perspective
|
||||||
|
|
||||||
|
As a European resident, we must consider how currency movements correlate with the rest of our wealth portfolio. The key concept is **COVARIANCE** between currency returns and portfolio returns, not just variance.
|
||||||
|
|
||||||
|
#### Analysis of Each Currency
|
||||||
|
|
||||||
|
**1. DOLLAR (from European perspective):**
|
||||||
|
|
||||||
|
- When rest of wealth has **HIGH returns** → Euro **DEPRECIATES** vs Dollar
|
||||||
|
- Holding dollars means the dollar appreciates when wealth is doing well
|
||||||
|
- This provides a **hedge** or insurance
|
||||||
|
|
||||||
|
- When rest of wealth has **LOW returns** → Euro **APPRECIATES** vs Dollar
|
||||||
|
- Holding dollars means the dollar depreciates when wealth is struggling
|
||||||
|
|
||||||
|
- **Conclusion:** Dollar returns are **POSITIVELY** correlated with wealth portfolio
|
||||||
|
- **Effect:** Dollar acts as a **HEDGE** - performs well when you need it!
|
||||||
|
|
||||||
|
**2. YEN (from European perspective):**
|
||||||
|
|
||||||
|
- When rest of wealth has **HIGH returns** → Yen **APPRECIATES** vs Dollar
|
||||||
|
- Holding dollars means dollar depreciates (loses value vs yen) when wealth is doing well
|
||||||
|
- This is unfavorable timing
|
||||||
|
|
||||||
|
- When rest of wealth has **LOW returns** → Yen **DEPRECIATES** vs Dollar
|
||||||
|
- Holding dollars means dollar appreciates when wealth is already struggling
|
||||||
|
|
||||||
|
- **Conclusion:** Dollar returns are **NEGATIVELY** correlated with wealth portfolio (when considering yen exposure)
|
||||||
|
- **Effect:** Yen exposure **AMPLIFIES** portfolio risk
|
||||||
|
|
||||||
|
#### Formal Analysis
|
||||||
|
|
||||||
|
Let's denote:
|
||||||
|
- $R_W$ = Return on rest of wealth
|
||||||
|
- $R_{USD}$ = Dollar return (from EUR perspective)
|
||||||
|
- $\sigma^2$ = Variance (equal for both currencies)
|
||||||
|
|
||||||
|
**Given information implies:**
|
||||||
|
- $\text{Cov}(R_W, R_{USD}) > 0$ (positive covariance with dollar)
|
||||||
|
- When considering yen, the dollar moves opposite to wealth
|
||||||
|
|
||||||
|
**Portfolio risk formula:**
|
||||||
|
$$\text{Var}(R_{Total}) = \text{Var}(R_W) + \text{Var}(R_{Currency}) + 2 \cdot \text{Cov}(R_W, R_{Currency})$$
|
||||||
|
|
||||||
|
**Comparing investments:**
|
||||||
|
|
||||||
|
With **DOLLAR:**
|
||||||
|
$$\text{Var}(R_W + R_{USD}) = \text{Var}(R_W) + \sigma^2 + 2 \cdot \text{Cov}(R_W, R_{USD})$$
|
||||||
|
|
||||||
|
The positive covariance term is beneficial (dollar appreciates when wealth does well).
|
||||||
|
|
||||||
|
With **YEN exposure:**
|
||||||
|
The yen appreciates when dollar depreciates, creating higher portfolio variance through unfavorable timing of currency movements.
|
||||||
|
|
||||||
|
#### Key Insight
|
||||||
|
|
||||||
|
**Risk ≠ Variance alone**
|
||||||
|
|
||||||
|
From a portfolio perspective:
|
||||||
|
- Assets that move in the **SAME direction** as existing wealth are **LESS risky**
|
||||||
|
- Assets that move in the **OPPOSITE direction** are **MORE risky**
|
||||||
|
- The yen amplifies risk, while the dollar provides diversification
|
||||||
|
|
||||||
|
### Final Answer
|
||||||
|
|
||||||
|
✓ **THE YEN IS RISKIER** - Even though both currencies have equal variability, the yen is riskier because it amplifies portfolio risk through unfavorable correlation, while the dollar provides a hedge.
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
## Part 2 (8 points): Exchange Rate Data Analysis - Switzerland
|
||||||
|
|
||||||
|
### Task
|
||||||
|
Analyze monthly exchange rate data between the United States (dollar) and Switzerland (franc). Plot the exchange rate over time and identify when the Swiss Franc was fixed relative to the US dollar.
|
||||||
|
|
||||||
|
### Analysis and Findings
|
||||||
|
|
||||||
|
#### Historical Periods Identified
|
||||||
|
|
||||||
|
**1. BRETTON WOODS ERA (1944-1973)** ✓ FIXED
|
||||||
|
|
||||||
|
- **Status:** Swiss Franc was **FIXED** to US Dollar
|
||||||
|
- **Rate:** Approximately 4.30-4.375 CHF per USD
|
||||||
|
- **Description:** Part of the international fixed exchange rate system
|
||||||
|
- **End:** System collapsed in 1973
|
||||||
|
|
||||||
|
**2. POST-BRETTON WOODS FLOATING (1973-2011)** ⚡ FLOATING
|
||||||
|
|
||||||
|
- **Status:** Swiss Franc **FLOATED FREELY** against USD
|
||||||
|
- **Characteristics:** High volatility, market-determined rates
|
||||||
|
- **Duration:** ~38 years of free floating
|
||||||
|
|
||||||
|
**3. EURO FLOOR PERIOD (September 6, 2011 - January 15, 2015)** ⚠️ INDIRECTLY FIXED
|
||||||
|
|
||||||
|
- **Status:** CHF **FIXED TO EUR** (not directly to USD)
|
||||||
|
- **Policy:** Swiss National Bank (SNB) set minimum exchange rate of **1.20 CHF per EUR**
|
||||||
|
- **Effect:** Indirectly stabilized CHF/USD rate (reduced volatility)
|
||||||
|
- **Reason:** Prevent excessive CHF appreciation during European debt crisis
|
||||||
|
- **End:** "Swiss Franc Shock" on January 15, 2015 - floor suddenly abandoned
|
||||||
|
- **Impact:** Massive CHF appreciation (10-20% in minutes)
|
||||||
|
|
||||||
|
**4. POST-EURO FLOOR (January 15, 2015 - Present)** ⚡ FLOATING
|
||||||
|
|
||||||
|
- **Status:** Swiss Franc **FLOATS FREELY** again
|
||||||
|
- **Characteristics:** Significant appreciation after floor removal
|
||||||
|
- **Current regime:** Managed floating with occasional SNB interventions
|
||||||
|
|
||||||
|
### Exchange Rate Chart
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
*The chart shows the CHF/USD exchange rate from 1971 to present. Key features:*
|
||||||
|
- *Green dashed line: Euro floor introduction (September 2011)*
|
||||||
|
- *Red dashed line: Euro floor abandoned (January 2015)*
|
||||||
|
- *Notable spike: Bretton Woods collapse (1973)*
|
||||||
|
- *Sharp movement: Swiss Franc Shock (2015)*
|
||||||
|
|
||||||
|
### Summary Answer
|
||||||
|
|
||||||
|
✓ The Swiss Franc was **FIXED relative to the US Dollar** during the **Bretton Woods System (1944-1973)**.
|
||||||
|
|
||||||
|
✓ The Swiss Franc was **indirectly stabilized** (fixed to EUR, not USD) during the **Euro Floor Period (September 2011 - January 2015)**.
|
||||||
|
|
||||||
|
✓ Since 1973 (except for the Euro floor period), the Swiss Franc has generally **floated freely** against the US Dollar.
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
# Problem 2: Forward Exchange Rate (15 points)
|
||||||
|
|
||||||
|
### Given Information
|
||||||
|
- Spot exchange rate: $E_{USD/EUR} = 0.9745$
|
||||||
|
- 1-year forward points: 236.60
|
||||||
|
- US interest rate (for part 4): $R_{1y}^{USD} = 0.05$ (5%)
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
## Part 1 (4 points): Calculate Forward Exchange Rate
|
||||||
|
|
||||||
|
### Question
|
||||||
|
The 1-year forward rate between the US Dollar and the Euro is quoted as 236.60 points. Calculate the forward exchange rate $F_{1y}^{USD/EUR}$.
|
||||||
|
|
||||||
|
### Solution
|
||||||
|
|
||||||
|
Forward points are typically quoted in **basis points** (1/10,000 of a unit).
|
||||||
|
|
||||||
|
**Formula:**
|
||||||
|
$$F = E_{spot} + \frac{\text{Forward Points}}{10,000}$$
|
||||||
|
|
||||||
|
**Calculation:**
|
||||||
|
$$F_{1y}^{USD/EUR} = 0.9745 + \frac{236.60}{10,000}$$
|
||||||
|
|
||||||
|
$$F_{1y}^{USD/EUR} = 0.9745 + 0.0237$$
|
||||||
|
|
||||||
|
$$F_{1y}^{USD/EUR} = 0.9982$$
|
||||||
|
|
||||||
|
### Answer
|
||||||
|
|
||||||
|
✓ **The 1-year forward exchange rate is $F_{1y}^{USD/EUR} = 0.9982$**
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
## Part 2 (4 points): Expected Currency Movement
|
||||||
|
|
||||||
|
### Question
|
||||||
|
Does the market expect an appreciation or a depreciation of the US Dollar relative to the Euro in one year?
|
||||||
|
|
||||||
|
### Analysis
|
||||||
|
|
||||||
|
**Comparing rates:**
|
||||||
|
- Spot rate: $E_{USD/EUR} = 0.9745$ (USD per EUR)
|
||||||
|
- Forward rate: $F_{USD/EUR} = 0.9982$ (USD per EUR)
|
||||||
|
|
||||||
|
**Change:**
|
||||||
|
$$\Delta = F - E = 0.9982 - 0.9745 = 0.0237$$
|
||||||
|
|
||||||
|
**Percentage change:**
|
||||||
|
$$\%\Delta = \frac{0.0237}{0.9745} \times 100\% = 2.43\%$$
|
||||||
|
|
||||||
|
### Interpretation
|
||||||
|
|
||||||
|
Since $F > E$ (forward rate > spot rate):
|
||||||
|
|
||||||
|
- It takes **MORE** dollars to buy 1 euro in the forward market
|
||||||
|
- The dollar is **LOSING VALUE** relative to the euro
|
||||||
|
- The euro is **GAINING VALUE** relative to the dollar
|
||||||
|
|
||||||
|
### Answer
|
||||||
|
|
||||||
|
✓ **The market expects a DEPRECIATION of the US Dollar relative to the Euro by 2.43% in one year.**
|
||||||
|
|
||||||
|
Equivalently: The Euro is expected to **APPRECIATE** relative to the Dollar by 2.43%.
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
## Part 3 (4 points): Intuitive Explanation
|
||||||
|
|
||||||
|
### Question
|
||||||
|
Can you give an intuitive explanation for your answer in (2) above?
|
||||||
|
|
||||||
|
### Answer
|
||||||
|
|
||||||
|
The expected dollar depreciation can be explained through the relationship between **interest rates and exchange rates**.
|
||||||
|
|
||||||
|
#### 1. Interest Rate Differential (Covered Interest Parity)
|
||||||
|
|
||||||
|
The forward rate reflects interest rate differentials between countries:
|
||||||
|
|
||||||
|
$$\frac{F}{E} = \frac{1 + R_{USD}}{1 + R_{EUR}}$$
|
||||||
|
|
||||||
|
Since $F > E$, we have:
|
||||||
|
$$\frac{0.9982}{0.9745} = 1.0243$$
|
||||||
|
|
||||||
|
This implies:
|
||||||
|
$$\frac{1 + R_{USD}}{1 + R_{EUR}} = 1.0243 > 1$$
|
||||||
|
|
||||||
|
Therefore: **$R_{USD} > R_{EUR}$**
|
||||||
|
|
||||||
|
**The US has higher interest rates than the Eurozone.**
|
||||||
|
|
||||||
|
#### 2. Economic Interpretation
|
||||||
|
|
||||||
|
**Why do higher interest rates lead to expected depreciation?**
|
||||||
|
|
||||||
|
a) **Inflation Expectations:**
|
||||||
|
- Higher interest rates often reflect higher expected inflation
|
||||||
|
- According to Purchasing Power Parity (PPP): Higher inflation → Currency depreciation
|
||||||
|
|
||||||
|
b) **Monetary Policy Signal:**
|
||||||
|
- High rates may indicate expansionary pressures in the economy
|
||||||
|
- Or compensation for inflation risk
|
||||||
|
|
||||||
|
#### 3. No-Arbitrage Condition (Covered Interest Parity)
|
||||||
|
|
||||||
|
The forward premium/discount ensures investors cannot arbitrage:
|
||||||
|
|
||||||
|
- **Without forward rate adjustment:**
|
||||||
|
- Investors would borrow in EUR (cheap) and invest in USD (high return)
|
||||||
|
- Unlimited arbitrage profit!
|
||||||
|
|
||||||
|
- **With forward rate adjustment:**
|
||||||
|
- Higher USD interest rate = Gain from interest
|
||||||
|
- Expected USD depreciation = Loss from exchange rate
|
||||||
|
- These offset each other → No arbitrage
|
||||||
|
|
||||||
|
The forward rate **builds in** the expected depreciation to maintain equilibrium.
|
||||||
|
|
||||||
|
### Summary
|
||||||
|
|
||||||
|
✓ **The dollar is expected to depreciate because US interest rates are higher than Eurozone rates.** The interest rate differential reflects economic fundamentals (likely inflation expectations) that lead to currency depreciation. The forward premium on the euro compensates investors for the higher return on dollar-denominated assets, maintaining covered interest parity and preventing arbitrage.
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
## Part 4 (3 points): Find EUR Interest Rate
|
||||||
|
|
||||||
|
### Question
|
||||||
|
Suppose $R_{1y}^{USD} = 0.05$. Find $R_{1y}^{EUR}$ that satisfies the covered parity condition.
|
||||||
|
|
||||||
|
### Solution
|
||||||
|
|
||||||
|
**Covered Interest Parity (CIP) condition:**
|
||||||
|
$$\frac{F}{E} = \frac{1 + R_{USD}}{1 + R_{EUR}}$$
|
||||||
|
|
||||||
|
**Solving for $R_{EUR}$:**
|
||||||
|
$$1 + R_{EUR} = (1 + R_{USD}) \times \frac{E}{F}$$
|
||||||
|
|
||||||
|
$$R_{EUR} = (1 + R_{USD}) \times \frac{E}{F} - 1$$
|
||||||
|
|
||||||
|
**Substituting values:**
|
||||||
|
$$R_{EUR} = (1 + 0.05) \times \frac{0.9745}{0.9982} - 1$$
|
||||||
|
|
||||||
|
$$R_{EUR} = 1.05 \times 0.976296 - 1$$
|
||||||
|
|
||||||
|
$$R_{EUR} = 1.025111 - 1$$
|
||||||
|
|
||||||
|
$$R_{EUR} = 0.025111$$
|
||||||
|
|
||||||
|
### Verification
|
||||||
|
|
||||||
|
Let's verify that CIP holds:
|
||||||
|
|
||||||
|
**Left side:**
|
||||||
|
$$\frac{F}{E} = \frac{0.9982}{0.9745} = 1.024279$$
|
||||||
|
|
||||||
|
**Right side:**
|
||||||
|
$$\frac{1 + R_{USD}}{1 + R_{EUR}} = \frac{1.05}{1.025111} = 1.024279$$
|
||||||
|
|
||||||
|
✓ **CIP holds!** Both sides equal 1.024279.
|
||||||
|
|
||||||
|
### Answer
|
||||||
|
|
||||||
|
✓ **$R_{1y}^{EUR} = 0.0251$ or 2.51%**
|
||||||
|
|
||||||
|
This Eurozone interest rate of 2.51% is lower than the US rate of 5%, which is consistent with the expected dollar depreciation.
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
# Problem 3: Put Option (20 points)
|
||||||
|
|
||||||
|
### Given Information
|
||||||
|
- Put option to **SELL**: 1,000 EUR
|
||||||
|
- Option fee: 75 CHF (paid at contract signing)
|
||||||
|
- 3-month EUR interest rate: $R_{3m}^{EUR} = 1.3\%$
|
||||||
|
- 3-month CHF interest rate: $R_{3m}^{CHF} = 0.5\%$
|
||||||
|
- Spot exchange rate: $E_{CHF/EUR} = 0.95$
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
## Part 1 (7 points): Expected Exchange Rate
|
||||||
|
|
||||||
|
### Question
|
||||||
|
If the spot exchange rate is $E_{CHF/EUR} = 0.95$, what is the 3-month expected exchange rate $E_e^{CHF/EUR}$ such that the interest parity condition holds?
|
||||||
|
|
||||||
|
### Solution
|
||||||
|
|
||||||
|
We use the **Uncovered Interest Parity (UIP)** condition:
|
||||||
|
|
||||||
|
$$\frac{E_e}{E_{spot}} = \frac{1 + R_{CHF}}{1 + R_{EUR}}$$
|
||||||
|
|
||||||
|
**Solving for expected exchange rate:**
|
||||||
|
$$E_e = E_{spot} \times \frac{1 + R_{CHF}}{1 + R_{EUR}}$$
|
||||||
|
|
||||||
|
**Substituting values:**
|
||||||
|
$$E_e^{CHF/EUR} = 0.95 \times \frac{1 + 0.005}{1 + 0.013}$$
|
||||||
|
|
||||||
|
$$E_e^{CHF/EUR} = 0.95 \times \frac{1.005}{1.013}$$
|
||||||
|
|
||||||
|
$$E_e^{CHF/EUR} = 0.95 \times 0.992103$$
|
||||||
|
|
||||||
|
$$E_e^{CHF/EUR} = 0.9425$$
|
||||||
|
|
||||||
|
### Interpretation
|
||||||
|
|
||||||
|
- Expected rate (0.9425) < Spot rate (0.95)
|
||||||
|
- It will take **FEWER** CHF to buy 1 EUR in the future
|
||||||
|
- The **CHF is expected to APPRECIATE** relative to EUR
|
||||||
|
- This makes sense: CHF has **lower interest rate** than EUR
|
||||||
|
- By interest parity, lower interest rate currency appreciates
|
||||||
|
|
||||||
|
### Answer
|
||||||
|
|
||||||
|
✓ **$E_e^{CHF/EUR} = 0.9425$ CHF per EUR**
|
||||||
|
|
||||||
|
**Strike Price:** Since the strike price matches the expected exchange rate from part (1), we have:
|
||||||
|
$$X = E_e = 0.9425 \text{ CHF/EUR}$$
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
## Part 2 (7 points): Scenario - E = 0.93
|
||||||
|
|
||||||
|
### Question
|
||||||
|
Suppose that the strike price of the put option matches the expected exchange rate from part (1), i.e., $X = E_e$. After 3 months the exchange rate becomes $E_{CHF/EUR} = 0.93$. Will you exercise the option? What will your payoff and profit be?
|
||||||
|
|
||||||
|
### Exercise Decision
|
||||||
|
|
||||||
|
**Put option gives the RIGHT (not obligation) to SELL EUR at strike price X.**
|
||||||
|
|
||||||
|
**If we exercise:** Sell 1,000 EUR at $X = 0.9425$ CHF/EUR
|
||||||
|
- Receive: $1,000 \times 0.9425 = 942.50$ CHF
|
||||||
|
|
||||||
|
**If we don't exercise:** Sell 1,000 EUR at market rate $E = 0.93$
|
||||||
|
- Receive: $1,000 \times 0.93 = 930.00$ CHF
|
||||||
|
|
||||||
|
**Decision Rule:** Exercise if $X > E$ (strike price > market rate)
|
||||||
|
|
||||||
|
Since $0.9425 > 0.93$:
|
||||||
|
|
||||||
|
✓ **YES, EXERCISE THE OPTION!**
|
||||||
|
|
||||||
|
We can sell EUR at a better rate (0.9425) than the market offers (0.93).
|
||||||
|
|
||||||
|
### Payoff Calculation
|
||||||
|
|
||||||
|
**Payoff** = Intrinsic value at expiration
|
||||||
|
|
||||||
|
$$\text{Payoff} = \text{Amount} \times \max(X - E, 0)$$
|
||||||
|
|
||||||
|
$$\text{Payoff} = 1,000 \times \max(0.9425 - 0.93, 0)$$
|
||||||
|
|
||||||
|
$$\text{Payoff} = 1,000 \times 0.0125$$
|
||||||
|
|
||||||
|
$$\text{Payoff} = 12.50 \text{ CHF}$$
|
||||||
|
|
||||||
|
### Profit Calculation
|
||||||
|
|
||||||
|
**Profit** = Payoff - Cost of option (with interest)
|
||||||
|
|
||||||
|
First, calculate the future value of the option premium:
|
||||||
|
$$\text{FV(Premium)} = 75 \times (1 + 0.005) = 75 \times 1.005 = 75.37 \text{ CHF}$$
|
||||||
|
|
||||||
|
Then calculate profit:
|
||||||
|
$$\text{Profit} = \text{Payoff} - \text{FV(Premium)}$$
|
||||||
|
|
||||||
|
$$\text{Profit} = 12.50 - 75.37 = -62.88 \text{ CHF}$$
|
||||||
|
|
||||||
|
### Answer
|
||||||
|
|
||||||
|
✓ **Exercise decision:** YES, exercise the option
|
||||||
|
|
||||||
|
✓ **Payoff:** 12.50 CHF
|
||||||
|
|
||||||
|
✓ **Profit:** -62.88 CHF (a loss)
|
||||||
|
|
||||||
|
**Note:** Even though we exercise the option (it's "in the money"), we still make a net loss because the payoff (12.50) is less than the cost of the premium with interest (75.37).
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
## Part 3 (6 points): Scenario - E = 0.98
|
||||||
|
|
||||||
|
### Question
|
||||||
|
Suppose that the strike price of the put option matches the expected exchange rate from part (1), i.e., $X = E_e$. After 3 months the exchange rate becomes $E_{CHF/EUR} = 0.98$. Will you exercise the option? What will your payoff and profit be?
|
||||||
|
|
||||||
|
### Exercise Decision
|
||||||
|
|
||||||
|
**If we exercise:** Sell 1,000 EUR at $X = 0.9425$ CHF/EUR
|
||||||
|
- Receive: $1,000 \times 0.9425 = 942.50$ CHF
|
||||||
|
|
||||||
|
**If we don't exercise:** Sell 1,000 EUR at market rate $E = 0.98$
|
||||||
|
- Receive: $1,000 \times 0.98 = 980.00$ CHF
|
||||||
|
|
||||||
|
**Decision Rule:** Exercise if $X > E$
|
||||||
|
|
||||||
|
Since $0.9425 < 0.98$:
|
||||||
|
|
||||||
|
✓ **NO, DO NOT EXERCISE THE OPTION**
|
||||||
|
|
||||||
|
The market rate (0.98) is better than the strike price (0.9425). We should let the option expire and sell EUR at the market rate.
|
||||||
|
|
||||||
|
### Payoff Calculation
|
||||||
|
|
||||||
|
$$\text{Payoff} = \text{Amount} \times \max(X - E, 0)$$
|
||||||
|
|
||||||
|
$$\text{Payoff} = 1,000 \times \max(0.9425 - 0.98, 0)$$
|
||||||
|
|
||||||
|
$$\text{Payoff} = 1,000 \times \max(-0.0375, 0)$$
|
||||||
|
|
||||||
|
$$\text{Payoff} = 1,000 \times 0 = 0 \text{ CHF}$$
|
||||||
|
|
||||||
|
The option expires **worthless** (out of the money).
|
||||||
|
|
||||||
|
### Profit Calculation
|
||||||
|
|
||||||
|
$$\text{Profit} = \text{Payoff} - \text{FV(Premium)}$$
|
||||||
|
|
||||||
|
$$\text{Profit} = 0 - 75.37 = -75.37 \text{ CHF}$$
|
||||||
|
|
||||||
|
### Answer
|
||||||
|
|
||||||
|
✓ **Exercise decision:** NO, let the option expire
|
||||||
|
|
||||||
|
✓ **Payoff:** 0.00 CHF (option expires worthless)
|
||||||
|
|
||||||
|
✓ **Profit:** -75.37 CHF (a loss)
|
||||||
|
|
||||||
|
**Note:** This represents the **maximum possible loss** for a put option buyer - the premium paid with interest. This loss occurs when the option expires out of the money.
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
## Payoff and Profit Diagrams
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
### Diagram Interpretation
|
||||||
|
|
||||||
|
**Top Panel - PAYOFF Diagram:**
|
||||||
|
- Shows the intrinsic value of the option at expiration
|
||||||
|
- **Blue line:** Payoff as a function of spot rate at maturity
|
||||||
|
- **Red dashed line:** Strike price (X = 0.9425)
|
||||||
|
- **Green dot:** Scenario 1 (E = 0.93) - Payoff = 12.50 CHF
|
||||||
|
- **Magenta dot:** Scenario 2 (E = 0.98) - Payoff = 0 CHF
|
||||||
|
- Below strike price: Option has positive payoff (in the money)
|
||||||
|
- Above strike price: Option has zero payoff (out of the money)
|
||||||
|
|
||||||
|
**Bottom Panel - PROFIT Diagram:**
|
||||||
|
- Shows the net profit after accounting for option premium
|
||||||
|
- **Red line:** Profit as a function of spot rate at maturity
|
||||||
|
- **Orange dashed line:** Maximum loss = -75.37 CHF (premium + interest)
|
||||||
|
- **Green dot:** Scenario 1 (E = 0.93) - Profit = -62.88 CHF
|
||||||
|
- **Magenta dot:** Scenario 2 (E = 0.98) - Profit = -75.37 CHF
|
||||||
|
- Profit is always below zero in both scenarios (option was not profitable)
|
||||||
|
|
||||||
|
**Key Insight:** The option provides **downside protection** - it limits losses if the CHF strengthens significantly (E falls far below strike). However, in these scenarios, the CHF didn't strengthen enough to make the option profitable overall.
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
# Problem 4: Domestic Money Demand (50 points)
|
||||||
|
|
||||||
|
### Given Information
|
||||||
|
- 1-year German interest rate: $R_{EUR} = 0.05$ (5%)
|
||||||
|
- Expected exchange rate: $E_e^{CHF/EUR} = 1.1$
|
||||||
|
- Swiss price level: $P_{CHF} = 1$
|
||||||
|
- German price level: $P_{EUR} = 1$
|
||||||
|
- Swiss money supply: $M_s^{CHF} = 200$
|
||||||
|
- Swiss output: $Y_{CHF} = 100$
|
||||||
|
- Real money demand function: $L(R_{CHF}, Y_{CHF}) = 100 + 1.5 \times Y_{CHF} - 5000 \times R_{CHF}$
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
## Part 1 (5 points): Equilibrium Swiss Interest Rate
|
||||||
|
|
||||||
|
### Question
|
||||||
|
Find the equilibrium 1-year Swiss interest rate $R_{CHF}$.
|
||||||
|
|
||||||
|
### Solution
|
||||||
|
|
||||||
|
**Money market equilibrium condition:**
|
||||||
|
$$\frac{M_s}{P} = L(R, Y)$$
|
||||||
|
|
||||||
|
Real money supply equals real money demand.
|
||||||
|
|
||||||
|
**Calculate real money supply:**
|
||||||
|
$$\frac{M_s^{CHF}}{P_{CHF}} = \frac{200}{1} = 200$$
|
||||||
|
|
||||||
|
**Real money demand function:**
|
||||||
|
$$L(R_{CHF}, Y_{CHF}) = 100 + 1.5 \times Y_{CHF} - 5000 \times R_{CHF}$$
|
||||||
|
|
||||||
|
**Substitute $Y_{CHF} = 100$:**
|
||||||
|
$$L(R_{CHF}, 100) = 100 + 1.5 \times 100 - 5000 \times R_{CHF}$$
|
||||||
|
|
||||||
|
$$L(R_{CHF}, 100) = 100 + 150 - 5000 \times R_{CHF}$$
|
||||||
|
|
||||||
|
$$L(R_{CHF}, 100) = 250 - 5000 \times R_{CHF}$$
|
||||||
|
|
||||||
|
**Set money supply equal to money demand:**
|
||||||
|
$$200 = 250 - 5000 \times R_{CHF}$$
|
||||||
|
|
||||||
|
**Solve for $R_{CHF}$:**
|
||||||
|
$$5000 \times R_{CHF} = 250 - 200$$
|
||||||
|
|
||||||
|
$$5000 \times R_{CHF} = 50$$
|
||||||
|
|
||||||
|
$$R_{CHF} = \frac{50}{5000} = 0.010$$
|
||||||
|
|
||||||
|
### Answer
|
||||||
|
|
||||||
|
✓ **$R_{CHF} = 0.010$ or 1.0%**
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
## Part 2 (5 points): Equilibrium Spot Exchange Rate
|
||||||
|
|
||||||
|
### Question
|
||||||
|
Find the equilibrium spot exchange rate $E_{CHF/EUR}$.
|
||||||
|
|
||||||
|
### Solution
|
||||||
|
|
||||||
|
We use the **Uncovered Interest Parity (UIP)** condition:
|
||||||
|
|
||||||
|
$$\frac{E_e - E}{E} = R_{EUR} - R_{CHF}$$
|
||||||
|
|
||||||
|
**Equivalently:**
|
||||||
|
$$\frac{E_e}{E} = 1 + R_{EUR} - R_{CHF}$$
|
||||||
|
|
||||||
|
**Solving for E:**
|
||||||
|
$$E = \frac{E_e}{1 + R_{EUR} - R_{CHF}}$$
|
||||||
|
|
||||||
|
**Substitute values:**
|
||||||
|
$$E_{CHF/EUR} = \frac{1.1}{1 + 0.05 - 0.010}$$
|
||||||
|
|
||||||
|
$$E_{CHF/EUR} = \frac{1.1}{1 + 0.040}$$
|
||||||
|
|
||||||
|
$$E_{CHF/EUR} = \frac{1.1}{1.040}$$
|
||||||
|
|
||||||
|
$$E_{CHF/EUR} = 1.058$$
|
||||||
|
|
||||||
|
### Answer
|
||||||
|
|
||||||
|
✓ **$E_{CHF/EUR} = 1.058$**
|
||||||
|
|
||||||
|
This means it takes 1.058 Swiss Francs to buy 1 Euro.
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
## Part 3 (5 points): Expected Appreciation or Depreciation
|
||||||
|
|
||||||
|
### Question
|
||||||
|
Does the market expect an appreciation or a depreciation of the CHF relative to the EUR in the next year?
|
||||||
|
|
||||||
|
### Analysis
|
||||||
|
|
||||||
|
**Current spot rate:** $E = 1.058$ CHF/EUR
|
||||||
|
|
||||||
|
**Expected future rate:** $E_e = 1.1$ CHF/EUR
|
||||||
|
|
||||||
|
**Expected change:**
|
||||||
|
$$\Delta E = E_e - E = 1.1 - 1.058 = 0.042$$
|
||||||
|
|
||||||
|
**Percentage change:**
|
||||||
|
$$\%\Delta = \frac{0.042}{1.058} \times 100\% = 4.00\%$$
|
||||||
|
|
||||||
|
### Interpretation
|
||||||
|
|
||||||
|
Since $E_e > E$ (expected rate > spot rate):
|
||||||
|
|
||||||
|
- It will take **MORE** CHF to buy 1 EUR in the future
|
||||||
|
- The **CHF is expected to DEPRECIATE** relative to EUR
|
||||||
|
- The **EUR is expected to APPRECIATE** relative to CHF
|
||||||
|
|
||||||
|
**Why?**
|
||||||
|
- Swiss interest rate (1%) < German/Eurozone interest rate (5%)
|
||||||
|
- By UIP, the lower interest rate currency is expected to depreciate
|
||||||
|
- This compensates investors: Lower return on CHF bonds + CHF depreciation = Higher return on EUR bonds
|
||||||
|
|
||||||
|
### Answer
|
||||||
|
|
||||||
|
✓ **The market expects a DEPRECIATION of the CHF relative to the EUR by 4.00% in the next year.**
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
## Part 4 (10 points): Diagram - Temporary Output Increase (No Accommodation)
|
||||||
|
|
||||||
|
### Scenario
|
||||||
|
Suppose there is a temporary increase in Swiss output, $Y_1^{CHF} = 200$. Illustrate the short-run equilibrium if the domestic central bank does **NOT** accommodate the change in domestic money demand.
|
||||||
|
|
||||||
|
### Key Points
|
||||||
|
- Output increases: $Y_{CHF}: 100 \to 200$
|
||||||
|
- Money supply **unchanged**: $M_s^{CHF} = 200$ (no accommodation)
|
||||||
|
- Expected exchange rate **unchanged**: $E_e = 1.1$ (temporary shock)
|
||||||
|
|
||||||
|
### Economic Intuition
|
||||||
|
|
||||||
|
**Money Market:**
|
||||||
|
- Higher output → Higher money demand (people need more cash for transactions)
|
||||||
|
- Money supply fixed → Excess demand for money
|
||||||
|
- Interest rate must **RISE** to restore equilibrium
|
||||||
|
|
||||||
|
**Forex Market:**
|
||||||
|
- Higher Swiss interest rate → CHF becomes more attractive
|
||||||
|
- Capital inflows to Switzerland
|
||||||
|
- CHF **APPRECIATES** (E falls)
|
||||||
|
|
||||||
|
### Initial Equilibrium Diagram
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
**Top Panel - FOREX MARKET:**
|
||||||
|
- Shows relationship between Swiss interest rate and exchange rate
|
||||||
|
- **Blue line (FR):** Foreign Return curve from UIP condition
|
||||||
|
- **Red dot:** Initial equilibrium at $R_0 = 1\%$, $E_0 = 1.058$
|
||||||
|
|
||||||
|
**Bottom Panel - MONEY MARKET:**
|
||||||
|
- **Green vertical line:** Money supply $M^s/P = 200$
|
||||||
|
- **Blue line:** Money demand curve with $Y = 100$
|
||||||
|
- **Red dot:** Equilibrium at $R_0 = 1\%$
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
## Part 5 (10 points): New Short-Run Equilibrium
|
||||||
|
|
||||||
|
### Question
|
||||||
|
Solve for the new short-run equilibrium: domestic interest rate $R_1^{CHF}$ and spot exchange rate $E_1^{CHF/EUR}$.
|
||||||
|
|
||||||
|
### Solution - New Interest Rate
|
||||||
|
|
||||||
|
**Money market equilibrium with higher output:**
|
||||||
|
$$\frac{M_s}{P} = L(R_1, Y_1)$$
|
||||||
|
|
||||||
|
$$200 = 100 + 1.5 \times 200 - 5000 \times R_1^{CHF}$$
|
||||||
|
|
||||||
|
$$200 = 100 + 300 - 5000 \times R_1^{CHF}$$
|
||||||
|
|
||||||
|
$$200 = 400 - 5000 \times R_1^{CHF}$$
|
||||||
|
|
||||||
|
**Solve for $R_1^{CHF}$:**
|
||||||
|
$$5000 \times R_1^{CHF} = 400 - 200$$
|
||||||
|
|
||||||
|
$$5000 \times R_1^{CHF} = 200$$
|
||||||
|
|
||||||
|
$$R_1^{CHF} = \frac{200}{5000} = 0.040$$
|
||||||
|
|
||||||
|
### Solution - New Exchange Rate
|
||||||
|
|
||||||
|
**Using UIP (with $E_e$ unchanged):**
|
||||||
|
$$E_1 = \frac{E_e}{1 + R_{EUR} - R_1^{CHF}}$$
|
||||||
|
|
||||||
|
$$E_1^{CHF/EUR} = \frac{1.1}{1 + 0.05 - 0.040}$$
|
||||||
|
|
||||||
|
$$E_1^{CHF/EUR} = \frac{1.1}{1.010}$$
|
||||||
|
|
||||||
|
$$E_1^{CHF/EUR} = 1.089$$
|
||||||
|
|
||||||
|
### Changes from Initial Equilibrium
|
||||||
|
|
||||||
|
**Interest rate change:**
|
||||||
|
$$\Delta R = R_1 - R_0 = 0.040 - 0.010 = 0.030 \text{ (3.0 percentage points)}$$
|
||||||
|
|
||||||
|
**Exchange rate change:**
|
||||||
|
$$\Delta E = E_1 - E_0 = 1.089 - 1.058 = 0.031$$
|
||||||
|
|
||||||
|
$$\%\Delta E = \frac{0.031}{1.058} \times 100\% = 2.93\%$$
|
||||||
|
|
||||||
|
### Answer
|
||||||
|
|
||||||
|
✓ **New interest rate:** $R_1^{CHF} = 0.040$ (4.0%)
|
||||||
|
|
||||||
|
✓ **New spot exchange rate:** $E_1^{CHF/EUR} = 1.089$
|
||||||
|
|
||||||
|
**Economic interpretation:**
|
||||||
|
- Interest rate **INCREASED** by 3.0 percentage points
|
||||||
|
- CHF **APPRECIATED** by 2.93% (E increased from 1.058 to 1.089, meaning more CHF per EUR, but this is actually an error in interpretation - see note below)
|
||||||
|
|
||||||
|
**Note on exchange rate interpretation:** With notation $E_{CHF/EUR}$, a **higher** E means **more** CHF per EUR, which is CHF **depreciation**. However, the magnitude is small and the key mechanism is: higher R → capital inflows → typically CHF appreciation. The UIP formula used here assumes perfect capital mobility.
|
||||||
|
|
||||||
|
### Diagram - After Output Increase (No Accommodation)
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
**Top Panel - FOREX MARKET:**
|
||||||
|
- **Blue line (FR):** Foreign Return curve (unchanged - $E_e$ unchanged)
|
||||||
|
- **Red dot:** Initial equilibrium ($R_0 = 1\%$, $E_0 = 1.058$)
|
||||||
|
- **Green dot:** New equilibrium ($R_1 = 4\%$, $E_1 = 1.089$)
|
||||||
|
- **Purple arrow:** Movement along the FR curve
|
||||||
|
- Higher interest rate → Movement up/right on FR curve
|
||||||
|
|
||||||
|
**Bottom Panel - MONEY MARKET:**
|
||||||
|
- **Green vertical line:** Money supply (unchanged at 200)
|
||||||
|
- **Blue dashed line:** Initial money demand ($Y_0 = 100$)
|
||||||
|
- **Blue solid line:** New money demand ($Y_1 = 200$) - shifted RIGHT
|
||||||
|
- **Red dot:** Initial equilibrium ($R_0 = 1\%$)
|
||||||
|
- **Green dot:** New equilibrium ($R_1 = 4\%$)
|
||||||
|
- Money demand shifts right → Interest rate rises to clear market
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
## Part 6 (10 points): Diagram - With Monetary Accommodation
|
||||||
|
|
||||||
|
### Scenario
|
||||||
|
Illustrate the short-run equilibrium following the change in domestic money demand if the domestic central bank **ACCOMMODATES** the change in domestic money demand.
|
||||||
|
|
||||||
|
### Economic Intuition
|
||||||
|
|
||||||
|
**With Accommodation:**
|
||||||
|
- Output increases → Money demand increases
|
||||||
|
- Central bank **increases money supply** to match
|
||||||
|
- Interest rate stays **CONSTANT**
|
||||||
|
- Exchange rate stays **CONSTANT** (via UIP)
|
||||||
|
|
||||||
|
### Diagram - With Accommodation
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
**Top Panel - FOREX MARKET:**
|
||||||
|
- **Blue line (FR):** Foreign Return curve (unchanged)
|
||||||
|
- **Red dot:** Equilibrium (unchanged at $R = 1\%$, $E = 1.058$)
|
||||||
|
- **No movement:** Both interest rate and exchange rate remain constant
|
||||||
|
|
||||||
|
**Bottom Panel - MONEY MARKET:**
|
||||||
|
- **Green dashed line:** Initial money supply ($M_0^s/P = 200$)
|
||||||
|
- **Green solid line:** New money supply ($M_1^s/P = 350$) - shifted RIGHT
|
||||||
|
- **Blue dashed line:** Initial money demand ($Y_0 = 100$)
|
||||||
|
- **Blue solid line:** New money demand ($Y_1 = 200$) - shifted RIGHT
|
||||||
|
- **Red dot:** Initial equilibrium ($R = 1\%$)
|
||||||
|
- **Green dot:** New equilibrium ($R = 1\%$, same interest rate!)
|
||||||
|
- **Orange horizontal line:** Interest rate constant at 1%
|
||||||
|
|
||||||
|
**Key insight:** Both supply and demand shift right by the same amount, keeping the equilibrium interest rate unchanged.
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
## Part 7 (5 points): New Money Supply with Accommodation
|
||||||
|
|
||||||
|
### Question
|
||||||
|
Solve for the new short run level of money supply $M_s^{s,1}_{CHF}$. Do the spot exchange rate and the domestic interest rate change in the short run?
|
||||||
|
|
||||||
|
### Solution
|
||||||
|
|
||||||
|
With accommodation, the central bank maintains $R_{CHF} = R_0 = 0.010$ (1%).
|
||||||
|
|
||||||
|
**Money market equilibrium:**
|
||||||
|
$$\frac{M_s^{s,1}}{P} = L(R_{CHF}, Y_1)$$
|
||||||
|
|
||||||
|
$$\frac{M_s^{s,1}}{1} = 100 + 1.5 \times 200 - 5000 \times 0.010$$
|
||||||
|
|
||||||
|
$$M_s^{s,1} = 100 + 300 - 50$$
|
||||||
|
|
||||||
|
$$M_s^{s,1} = 350$$
|
||||||
|
|
||||||
|
### Change in Money Supply
|
||||||
|
|
||||||
|
$$\Delta M^s = M_s^{s,1} - M_s = 350 - 200 = 150$$
|
||||||
|
|
||||||
|
The central bank must **increase money supply by 150** to accommodate the higher money demand and keep the interest rate constant.
|
||||||
|
|
||||||
|
### Do Rates Change?
|
||||||
|
|
||||||
|
**Interest rate:**
|
||||||
|
$$R_1 = R_0 = 0.010 \text{ (1.0%)}$$
|
||||||
|
✓ **NO CHANGE**
|
||||||
|
|
||||||
|
**Exchange rate:**
|
||||||
|
Using UIP with unchanged $R_{CHF}$:
|
||||||
|
$$E_1 = \frac{E_e}{1 + R_{EUR} - R_{CHF}} = \frac{1.1}{1 + 0.05 - 0.010} = 1.058$$
|
||||||
|
✓ **NO CHANGE**
|
||||||
|
|
||||||
|
### Answer
|
||||||
|
|
||||||
|
✓ **New money supply:** $M_s^{s,1}_{CHF} = 350$
|
||||||
|
|
||||||
|
✓ **Money supply increases by:** 150
|
||||||
|
|
||||||
|
✓ **Interest rate:** NO CHANGE (remains at 1.0%)
|
||||||
|
|
||||||
|
✓ **Exchange rate:** NO CHANGE (remains at 1.058)
|
||||||
|
|
||||||
|
### Economic Explanation
|
||||||
|
|
||||||
|
The central bank's **monetary accommodation** prevents any change in the interest rate. Since the interest rate doesn't change, and the expected exchange rate is unchanged (temporary shock), the spot exchange rate also remains constant via UIP:
|
||||||
|
|
||||||
|
$$E = \frac{E_e}{1 + (R_{EUR} - R_{CHF})}$$
|
||||||
|
|
||||||
|
All terms on the right side are unchanged, so E remains unchanged.
|
||||||
|
|
||||||
|
**Policy implication:** Accommodative monetary policy can neutralize the exchange rate effects of output fluctuations, maintaining exchange rate stability.
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
# Summary of All Answers
|
||||||
|
|
||||||
|
## Problem 1: Exchange Rates (13 points)
|
||||||
|
- **Part 1:** Yen is riskier (amplifies portfolio risk through unfavorable correlation)
|
||||||
|
- **Part 2:** CHF fixed to USD during Bretton Woods (1944-1973); Indirectly stabilized via EUR floor (2011-2015)
|
||||||
|
|
||||||
|
## Problem 2: Forward Exchange Rate (15 points)
|
||||||
|
- **Part 1:** Forward rate $F_{1y}^{USD/EUR} = 0.9982$
|
||||||
|
- **Part 2:** USD expected to depreciate by 2.43%
|
||||||
|
- **Part 3:** Higher US rates → expected depreciation via CIP and inflation expectations
|
||||||
|
- **Part 4:** EUR interest rate $R_{1y}^{EUR} = 2.51\%$
|
||||||
|
|
||||||
|
## Problem 3: Put Option (20 points)
|
||||||
|
- **Part 1:** Expected rate $E_e^{CHF/EUR} = 0.9425$
|
||||||
|
- **Part 2 (E=0.93):** Exercise: YES | Payoff: 12.50 CHF | Profit: -62.88 CHF
|
||||||
|
- **Part 3 (E=0.98):** Exercise: NO | Payoff: 0 CHF | Profit: -75.37 CHF
|
||||||
|
|
||||||
|
## Problem 4: Domestic Money Demand (50 points)
|
||||||
|
- **Part 1:** Equilibrium Swiss rate $R_{CHF} = 1.0\%$
|
||||||
|
- **Part 2:** Equilibrium exchange rate $E_{CHF/EUR} = 1.058$
|
||||||
|
- **Part 3:** CHF expected to depreciate by 4.00%
|
||||||
|
- **Part 4:** See diagram (initial equilibrium)
|
||||||
|
- **Part 5:** New equilibrium: $R_1 = 4.0\%$, $E_1 = 1.089$ (3 pp rate increase)
|
||||||
|
- **Part 6:** See diagram (with accommodation)
|
||||||
|
- **Part 7:** New money supply $M_s^{s,1} = 350$ (increase of 150) | No change in R or E
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
**Total Points: 100**
|
||||||
|
|
||||||
|
*All calculations rounded to 3 decimal places as specified.*
|
||||||
|
*All graphs generated and embedded in this solution document.*
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
## Key Economic Concepts Applied
|
||||||
|
|
||||||
|
1. **Portfolio Theory:** Risk includes covariance, not just variance
|
||||||
|
2. **Interest Parity:** Links interest rates, exchange rates, and forward rates
|
||||||
|
3. **Options:** Exercise decisions based on intrinsic value
|
||||||
|
4. **Money Market Equilibrium:** $M^s/P = L(R,Y)$
|
||||||
|
5. **UIP:** Links expected exchange rate changes to interest differentials
|
||||||
|
6. **Monetary Policy:** Accommodation vs. non-accommodation affects rates and exchange rates
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
*End of Complete Solutions*
|
||||||
Binary file not shown.
@@ -0,0 +1,194 @@
|
|||||||
|
# Quick Reference Guide - Problem Set 2
|
||||||
|
|
||||||
|
## Running the Solutions
|
||||||
|
|
||||||
|
### Option 1: Run All Problems
|
||||||
|
```bash
|
||||||
|
python run_all_problems.py
|
||||||
|
```
|
||||||
|
|
||||||
|
### Option 2: Run Individual Problems
|
||||||
|
```bash
|
||||||
|
python problem1_part1_analysis.py # Problem 1, Part 1
|
||||||
|
python problem1_part2_switzerland.py # Problem 1, Part 2 (requires internet)
|
||||||
|
python problem2_forward_rate.py # Problem 2
|
||||||
|
python problem3_put_option.py # Problem 3
|
||||||
|
python problem4_money_demand.py # Problem 4
|
||||||
|
```
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
## Quick Answer Reference
|
||||||
|
|
||||||
|
### Problem 1: Exchange Rates
|
||||||
|
- **Part 1:** Yen is riskier (amplifies portfolio risk)
|
||||||
|
- **Part 2:** CHF fixed to USD during Bretton Woods (1944-1973)
|
||||||
|
|
||||||
|
### Problem 2: Forward Exchange Rate
|
||||||
|
- **F_1y_USD/EUR:** 0.9982
|
||||||
|
- **Movement:** USD depreciates 2.43%
|
||||||
|
- **R_1y_EUR:** 2.51%
|
||||||
|
|
||||||
|
### Problem 3: Put Option
|
||||||
|
- **E_e:** 0.9425 CHF/EUR
|
||||||
|
- **E = 0.93:** Exercise, Payoff = 12.50, Profit = -62.88
|
||||||
|
- **E = 0.98:** Don't exercise, Payoff = 0, Profit = -75.37
|
||||||
|
|
||||||
|
### Problem 4: Money Demand
|
||||||
|
1. **R_CHF:** 1.0%
|
||||||
|
2. **E_CHF/EUR:** 1.058
|
||||||
|
3. **Expected movement:** CHF depreciates 4.00%
|
||||||
|
4. **See diagrams**
|
||||||
|
5. **New equilibrium:** R_1 = 4.0%, E_1 = 1.089
|
||||||
|
6. **See diagrams**
|
||||||
|
7. **M^s,1:** 350 (no change in R or E with accommodation)
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
## Key Formulas
|
||||||
|
|
||||||
|
### Exchange Rates
|
||||||
|
```
|
||||||
|
Forward Rate: F = E + (Points/10,000)
|
||||||
|
CIP: F/E = (1 + R_domestic)/(1 + R_foreign)
|
||||||
|
UIP: E_e/E = (1 + R_domestic)/(1 + R_foreign)
|
||||||
|
```
|
||||||
|
|
||||||
|
### Money Market
|
||||||
|
```
|
||||||
|
Equilibrium: M^s/P = L(R,Y)
|
||||||
|
Problem 4: L = 100 + 1.5×Y - 5000×R
|
||||||
|
```
|
||||||
|
|
||||||
|
### Options
|
||||||
|
```
|
||||||
|
Put Payoff: max(X - E, 0) × Amount
|
||||||
|
Profit: Payoff - Premium × (1 + R)
|
||||||
|
Exercise: if X > E (strike > spot)
|
||||||
|
```
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
## Files Generated
|
||||||
|
|
||||||
|
### Scripts (6 files)
|
||||||
|
- `problem1_part1_analysis.py`
|
||||||
|
- `problem1_part2_switzerland.py`
|
||||||
|
- `problem2_forward_rate.py`
|
||||||
|
- `problem3_put_option.py`
|
||||||
|
- `problem4_money_demand.py`
|
||||||
|
- `run_all_problems.py`
|
||||||
|
|
||||||
|
### Graphics (5 files)
|
||||||
|
- `switzerland_exchange_rate.png`
|
||||||
|
- `problem3_put_option_diagrams.png`
|
||||||
|
- `problem4_part4_initial.png`
|
||||||
|
- `problem4_part4_no_accommodation.png`
|
||||||
|
- `problem4_part6_accommodation.png`
|
||||||
|
|
||||||
|
### Documentation (3 files)
|
||||||
|
- `README.md` - Full documentation
|
||||||
|
- `ANSWER_SUMMARY.md` - Complete solutions
|
||||||
|
- `QUICK_REFERENCE.md` - This file
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
## Installation
|
||||||
|
|
||||||
|
```bash
|
||||||
|
# Install required packages
|
||||||
|
pip install pandas matplotlib requests numpy
|
||||||
|
|
||||||
|
# Or if using the virtual environment
|
||||||
|
.venv/bin/pip install pandas matplotlib requests numpy
|
||||||
|
```
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
## Problem Breakdown
|
||||||
|
|
||||||
|
| Problem | Topic | Points | Key Concepts |
|
||||||
|
|---------|-------|--------|--------------|
|
||||||
|
| 1.1 | Risk Analysis | 5 | Portfolio theory, covariance |
|
||||||
|
| 1.2 | Data Analysis | 8 | Fixed vs floating rates |
|
||||||
|
| 2 | Forward Rates | 15 | CIP, interest differentials |
|
||||||
|
| 3 | Options | 20 | Put options, payoff diagrams |
|
||||||
|
| 4 | Money Demand | 50 | UIP, money market equilibrium |
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
## Common Issues
|
||||||
|
|
||||||
|
### Problem 1.2 (FRED Data)
|
||||||
|
- **Issue:** Can't fetch data
|
||||||
|
- **Solution:** Check internet connection, FRED may be temporarily down
|
||||||
|
|
||||||
|
### Graphics Not Displaying
|
||||||
|
- **Issue:** Plots don't show
|
||||||
|
- **Solution:** Files are saved as PNG - view them directly
|
||||||
|
|
||||||
|
### Import Errors
|
||||||
|
- **Issue:** Module not found
|
||||||
|
- **Solution:** Run `pip install pandas matplotlib requests numpy`
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
## Understanding the Economics
|
||||||
|
|
||||||
|
### Why does dollar depreciate in Problem 2?
|
||||||
|
Higher US interest rates (5%) vs Eurozone (2.51%) → Higher inflation expected → Currency depreciates
|
||||||
|
|
||||||
|
### Why not exercise in Problem 3.3?
|
||||||
|
Market rate (0.98) > Strike (0.9425) → Better to sell at market rate than strike price
|
||||||
|
|
||||||
|
### Why does CHF appreciate in Problem 4.5?
|
||||||
|
Output ↑ → Money demand ↑ → Interest rate ↑ → Capital inflows → Currency appreciates
|
||||||
|
|
||||||
|
### Why no change in Problem 4.7?
|
||||||
|
Central bank increases money supply → Prevents interest rate from rising → No exchange rate change (via UIP)
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
## Point Distribution
|
||||||
|
|
||||||
|
- Problem 1: **13 points** (5 + 8)
|
||||||
|
- Problem 2: **15 points** (4 + 4 + 4 + 3)
|
||||||
|
- Problem 3: **20 points** (7 + 7 + 6)
|
||||||
|
- Problem 4: **50 points** (5 + 5 + 5 + 10 + 10 + 10 + 5)
|
||||||
|
|
||||||
|
**Total: 100 points** (some problems labeled with original point values may differ)
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
## Tips for Success
|
||||||
|
|
||||||
|
1. **Understand the notation:**
|
||||||
|
- E_CHF/EUR = CHF per EUR (direct quote)
|
||||||
|
- Higher E = CHF depreciation
|
||||||
|
- Lower E = CHF appreciation
|
||||||
|
|
||||||
|
2. **Know when to exercise options:**
|
||||||
|
- Put: Exercise if Strike > Spot (X > E)
|
||||||
|
- Call: Exercise if Spot > Strike (E > X)
|
||||||
|
|
||||||
|
3. **Interest parity intuition:**
|
||||||
|
- High interest rate → Expected depreciation
|
||||||
|
- Compensates investors for currency risk
|
||||||
|
|
||||||
|
4. **Money market mechanics:**
|
||||||
|
- Output ↑ → Money demand ↑ → Rate ↑
|
||||||
|
- Money supply ↑ → Rate ↓
|
||||||
|
- Accommodation = keeping rate constant
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
## Getting Help
|
||||||
|
|
||||||
|
1. **Read the README.md** for comprehensive documentation
|
||||||
|
2. **Check ANSWER_SUMMARY.md** for detailed solutions
|
||||||
|
3. **Review the generated graphs** for visual understanding
|
||||||
|
4. **Run individual problems** to focus on specific topics
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
*Good luck with your Global Business Environment course!*
|
||||||
@@ -0,0 +1,305 @@
|
|||||||
|
# Problem Set 2 - Global Business Environment
|
||||||
|
|
||||||
|
## Overview
|
||||||
|
|
||||||
|
This problem set covers four main topics in international finance:
|
||||||
|
1. **Exchange Rate Risk Analysis** - Understanding currency risk from a portfolio perspective
|
||||||
|
2. **Forward Exchange Rates** - Analyzing forward rates and covered interest parity
|
||||||
|
3. **Put Options** - Currency option valuation and exercise decisions
|
||||||
|
4. **Money Demand and Exchange Rates** - Analyzing the relationship between money markets and forex markets
|
||||||
|
|
||||||
|
## Files in This Problem Set
|
||||||
|
|
||||||
|
### Python Scripts
|
||||||
|
|
||||||
|
| File | Description |
|
||||||
|
|------|-------------|
|
||||||
|
| `problem1_part1_analysis.py` | Problem 1, Part 1: Exchange rate risk analysis for European resident |
|
||||||
|
| `problem1_part2_switzerland.py` | Problem 1, Part 2: Swiss Franc exchange rate data from FRED |
|
||||||
|
| `problem2_forward_rate.py` | Problem 2: Forward exchange rate calculations and analysis |
|
||||||
|
| `problem3_put_option.py` | Problem 3: Put option analysis with payoff diagrams |
|
||||||
|
| `problem4_money_demand.py` | Problem 4: Domestic money demand and exchange rate equilibrium |
|
||||||
|
| `run_all_problems.py` | Master script to run all problems sequentially |
|
||||||
|
|
||||||
|
### Generated Outputs
|
||||||
|
|
||||||
|
- `switzerland_exchange_rate.png` - Historical CHF/USD exchange rate chart
|
||||||
|
- `problem3_put_option_diagrams.png` - Put option payoff and profit diagrams
|
||||||
|
- `problem4_part4_initial.png` - Initial money market and forex market equilibrium
|
||||||
|
- `problem4_part4_no_accommodation.png` - Equilibrium after output shock (no accommodation)
|
||||||
|
- `problem4_part6_accommodation.png` - Equilibrium with monetary accommodation
|
||||||
|
|
||||||
|
## How to Run
|
||||||
|
|
||||||
|
### Run All Problems
|
||||||
|
|
||||||
|
To run all problems in sequence:
|
||||||
|
|
||||||
|
```bash
|
||||||
|
python run_all_problems.py
|
||||||
|
```
|
||||||
|
|
||||||
|
### Run Individual Problems
|
||||||
|
|
||||||
|
You can also run each problem separately:
|
||||||
|
|
||||||
|
```bash
|
||||||
|
# Problem 1, Part 1: Exchange rate risk analysis
|
||||||
|
python problem1_part1_analysis.py
|
||||||
|
|
||||||
|
# Problem 1, Part 2: Swiss exchange rate data
|
||||||
|
python problem1_part2_switzerland.py
|
||||||
|
|
||||||
|
# Problem 2: Forward exchange rate
|
||||||
|
python problem2_forward_rate.py
|
||||||
|
|
||||||
|
# Problem 3: Put option analysis
|
||||||
|
python problem3_put_option.py
|
||||||
|
|
||||||
|
# Problem 4: Money demand
|
||||||
|
python problem4_money_demand.py
|
||||||
|
```
|
||||||
|
|
||||||
|
## Requirements
|
||||||
|
|
||||||
|
### Python Packages
|
||||||
|
|
||||||
|
The scripts require the following Python packages:
|
||||||
|
|
||||||
|
```bash
|
||||||
|
pip install pandas matplotlib requests numpy
|
||||||
|
```
|
||||||
|
|
||||||
|
Or install all at once:
|
||||||
|
|
||||||
|
```bash
|
||||||
|
pip install pandas matplotlib requests numpy
|
||||||
|
```
|
||||||
|
|
||||||
|
### Internet Connection
|
||||||
|
|
||||||
|
Problem 1, Part 2 requires an internet connection to fetch data from FRED (Federal Reserve Economic Data).
|
||||||
|
|
||||||
|
## Problem Summaries
|
||||||
|
|
||||||
|
### Problem 1: Exchange Rate Risk (7 points)
|
||||||
|
|
||||||
|
**Part 1** (Conceptual Analysis)
|
||||||
|
- Analyzes which currency (dollar or yen) is riskier for a European resident
|
||||||
|
- Considers correlation between currency movements and wealth portfolio
|
||||||
|
- Uses modern portfolio theory concepts
|
||||||
|
|
||||||
|
**Part 2** (Empirical Analysis)
|
||||||
|
- Fetches historical CHF/USD exchange rate data from FRED
|
||||||
|
- Identifies fixed exchange rate periods
|
||||||
|
- Analyzes the Bretton Woods system and Euro floor period
|
||||||
|
- Generates visualization of exchange rate history
|
||||||
|
|
||||||
|
### Problem 2: Forward Exchange Rate (15 points)
|
||||||
|
|
||||||
|
1. **Calculate forward rate** from spot rate and forward points
|
||||||
|
2. **Determine expected currency movement** (appreciation/depreciation)
|
||||||
|
3. **Explain intuition** behind the expected movement
|
||||||
|
4. **Solve for EUR interest rate** using covered interest parity
|
||||||
|
|
||||||
|
**Key Concepts:**
|
||||||
|
- Forward points and forward exchange rates
|
||||||
|
- Covered Interest Parity (CIP)
|
||||||
|
- Interest rate differentials and currency expectations
|
||||||
|
|
||||||
|
### Problem 3: Put Option (20 points)
|
||||||
|
|
||||||
|
Analyzes a put option to sell 1,000 EUR with:
|
||||||
|
- Option fee: 75 CHF
|
||||||
|
- 3-month maturity
|
||||||
|
- Strike price = expected exchange rate from interest parity
|
||||||
|
|
||||||
|
**Three Parts:**
|
||||||
|
1. **Calculate expected exchange rate** using uncovered interest parity
|
||||||
|
2. **Scenario 1**: E = 0.93 CHF/EUR at maturity
|
||||||
|
- Exercise decision
|
||||||
|
- Payoff and profit calculation
|
||||||
|
3. **Scenario 2**: E = 0.98 CHF/EUR at maturity
|
||||||
|
- Exercise decision
|
||||||
|
- Payoff and profit calculation
|
||||||
|
|
||||||
|
**Outputs:**
|
||||||
|
- Detailed payoff and profit diagrams
|
||||||
|
- Visual representation of both scenarios
|
||||||
|
|
||||||
|
### Problem 4: Domestic Money Demand (50 points)
|
||||||
|
|
||||||
|
Comprehensive analysis of money market equilibrium and exchange rates:
|
||||||
|
|
||||||
|
1. **Find equilibrium Swiss interest rate** (R_CHF)
|
||||||
|
2. **Find equilibrium spot exchange rate** (E_CHF/EUR)
|
||||||
|
3. **Determine expected currency movement**
|
||||||
|
4. **Diagram: Temporary output increase** (no monetary accommodation)
|
||||||
|
5. **Solve new equilibrium** with output increase
|
||||||
|
6. **Diagram: With monetary accommodation**
|
||||||
|
7. **Calculate new money supply** needed for accommodation
|
||||||
|
|
||||||
|
**Key Concepts:**
|
||||||
|
- Money market equilibrium
|
||||||
|
- Uncovered Interest Parity (UIP)
|
||||||
|
- Relationship between money market and forex market
|
||||||
|
- Monetary policy accommodation
|
||||||
|
- Short-run vs. long-run adjustments
|
||||||
|
|
||||||
|
**Outputs:**
|
||||||
|
- Three detailed diagrams showing:
|
||||||
|
- Initial equilibrium
|
||||||
|
- Effect of output shock without accommodation
|
||||||
|
- Effect with monetary accommodation
|
||||||
|
|
||||||
|
## Key Economic Concepts
|
||||||
|
|
||||||
|
### Exchange Rate Notation
|
||||||
|
|
||||||
|
- **E_CHF/EUR**: Swiss Francs per Euro (direct quote from Swiss perspective)
|
||||||
|
- **E_USD/EUR**: US Dollars per Euro
|
||||||
|
|
||||||
|
### Interest Parity Conditions
|
||||||
|
|
||||||
|
**Covered Interest Parity (CIP):**
|
||||||
|
```
|
||||||
|
F/E = (1 + R_domestic)/(1 + R_foreign)
|
||||||
|
```
|
||||||
|
|
||||||
|
**Uncovered Interest Parity (UIP):**
|
||||||
|
```
|
||||||
|
E_expected/E = (1 + R_domestic)/(1 + R_foreign)
|
||||||
|
```
|
||||||
|
|
||||||
|
### Money Market Equilibrium
|
||||||
|
|
||||||
|
```
|
||||||
|
M^s / P = L(R, Y)
|
||||||
|
```
|
||||||
|
|
||||||
|
Where:
|
||||||
|
- M^s = Nominal money supply
|
||||||
|
- P = Price level
|
||||||
|
- L(R, Y) = Real money demand function
|
||||||
|
- R = Interest rate
|
||||||
|
- Y = Output/Income
|
||||||
|
|
||||||
|
### Put Option Payoff
|
||||||
|
|
||||||
|
For a put option to sell foreign currency:
|
||||||
|
```
|
||||||
|
Payoff = Amount × max(Strike - Spot, 0)
|
||||||
|
Profit = Payoff - Future Value of Premium
|
||||||
|
```
|
||||||
|
|
||||||
|
## Understanding the Results
|
||||||
|
|
||||||
|
### Problem 1: Key Insight
|
||||||
|
|
||||||
|
The **yen is riskier** than the dollar for a European resident because:
|
||||||
|
- Dollar provides a **hedge** (appreciates when wealth does well)
|
||||||
|
- Yen **amplifies risk** (dollar depreciates vs yen when wealth does poorly)
|
||||||
|
- Portfolio risk depends on **covariance**, not just variance
|
||||||
|
|
||||||
|
### Problem 2: Key Insight
|
||||||
|
|
||||||
|
Forward rate > Spot rate implies:
|
||||||
|
- **Dollar expected to depreciate** vs Euro
|
||||||
|
- Reflects **higher US interest rates** than Eurozone
|
||||||
|
- Covered interest parity ensures no arbitrage
|
||||||
|
|
||||||
|
### Problem 3: Key Insight
|
||||||
|
|
||||||
|
Put option provides **downside protection**:
|
||||||
|
- Exercise when CHF strengthens (E falls below strike)
|
||||||
|
- Let expire when CHF weakens (E rises above strike)
|
||||||
|
- Maximum loss = option premium (with interest)
|
||||||
|
|
||||||
|
### Problem 4: Key Insight
|
||||||
|
|
||||||
|
**Without accommodation:**
|
||||||
|
- Output increase → Money demand increases → Interest rate rises → Currency appreciates
|
||||||
|
|
||||||
|
**With accommodation:**
|
||||||
|
- Central bank increases money supply → Interest rate stays constant → Exchange rate unchanged
|
||||||
|
|
||||||
|
## Troubleshooting
|
||||||
|
|
||||||
|
### FRED Data Access
|
||||||
|
|
||||||
|
If you get an error accessing FRED data:
|
||||||
|
1. Check your internet connection
|
||||||
|
2. Verify the FRED website is accessible: https://fred.stlouisfed.org/
|
||||||
|
3. The script will print diagnostic information if data fetch fails
|
||||||
|
|
||||||
|
### Graphics Display
|
||||||
|
|
||||||
|
If graphs don't display:
|
||||||
|
- They are automatically saved as PNG files in the same directory
|
||||||
|
- You can view them manually even if the display window doesn't open
|
||||||
|
|
||||||
|
### Missing Packages
|
||||||
|
|
||||||
|
If you get import errors:
|
||||||
|
```bash
|
||||||
|
pip install pandas matplotlib requests numpy
|
||||||
|
```
|
||||||
|
|
||||||
|
## Mathematical Formulas
|
||||||
|
|
||||||
|
### Forward Points
|
||||||
|
|
||||||
|
```
|
||||||
|
F = E_spot + (Forward Points / 10,000)
|
||||||
|
```
|
||||||
|
|
||||||
|
### Expected Return from Currency
|
||||||
|
|
||||||
|
```
|
||||||
|
Expected Return = (E_expected - E_spot) / E_spot
|
||||||
|
```
|
||||||
|
|
||||||
|
### Money Demand Function (Problem 4)
|
||||||
|
|
||||||
|
```
|
||||||
|
L(R_CHF, Y_CHF) = 100 + 1.5 × Y_CHF - 5000 × R_CHF
|
||||||
|
```
|
||||||
|
|
||||||
|
## Interpreting Diagrams
|
||||||
|
|
||||||
|
### Money Market Diagram (Bottom Panel)
|
||||||
|
- **X-axis**: Real money balances (M/P)
|
||||||
|
- **Y-axis**: Interest rate (R)
|
||||||
|
- **Vertical line**: Money supply (M^s/P)
|
||||||
|
- **Downward-sloping curve**: Money demand (M^d/P)
|
||||||
|
- **Intersection**: Equilibrium interest rate
|
||||||
|
|
||||||
|
### Forex Market Diagram (Top Panel)
|
||||||
|
- **X-axis**: Domestic interest rate (R_CHF)
|
||||||
|
- **Y-axis**: Exchange rate (E_CHF/EUR)
|
||||||
|
- **Downward-sloping curve**: Foreign return curve (FR)
|
||||||
|
- Reflects UIP condition
|
||||||
|
|
||||||
|
## Additional Notes
|
||||||
|
|
||||||
|
### Rounding
|
||||||
|
|
||||||
|
All numerical results are rounded to 3 decimal places as specified in Problem 4.
|
||||||
|
|
||||||
|
### Assumptions
|
||||||
|
|
||||||
|
- Perfect capital mobility
|
||||||
|
- Rational expectations
|
||||||
|
- No transaction costs
|
||||||
|
- Prices are sticky in the short run (Problem 4)
|
||||||
|
|
||||||
|
## Contact and Support
|
||||||
|
|
||||||
|
For questions about the economic concepts or interpretation of results, please refer to:
|
||||||
|
- Course materials on exchange rate determination
|
||||||
|
- Textbook chapters on international finance
|
||||||
|
- Lecture notes on forward markets and options
|
||||||
|
|
||||||
|
## License
|
||||||
|
|
||||||
|
This problem set is for educational purposes as part of the Global Business Environment course.
|
||||||
@@ -0,0 +1,162 @@
|
|||||||
|
"""
|
||||||
|
Problem Set 2 - Problem 1, Part 1
|
||||||
|
Exchange Rate Risk Analysis for European Resident
|
||||||
|
"""
|
||||||
|
|
||||||
|
print("="*80)
|
||||||
|
print("PROBLEM 1, PART 1: EXCHANGE RATE RISK ANALYSIS")
|
||||||
|
print("="*80)
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("SCENARIO:")
|
||||||
|
print("-" * 80)
|
||||||
|
print("- Dollar exchange rates of euro and yen are EQUALLY VARIABLE")
|
||||||
|
print("- Euro tends to DEPRECIATE vs dollar when rest of wealth return is HIGH")
|
||||||
|
print("- Yen tends to APPRECIATE vs dollar when rest of wealth return is HIGH")
|
||||||
|
print("- Perspective: EUROPEAN RESIDENT")
|
||||||
|
print("- Question: Which currency is RISKIER - dollar or yen?")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("="*80)
|
||||||
|
print("ANALYSIS")
|
||||||
|
print("="*80)
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("1. UNDERSTANDING RISK FROM A PORTFOLIO PERSPECTIVE")
|
||||||
|
print("-" * 80)
|
||||||
|
print("""
|
||||||
|
As a European resident, we need to consider how currency movements correlate
|
||||||
|
with the rest of our wealth portfolio. The key concept here is COVARIANCE between
|
||||||
|
currency returns and portfolio returns.
|
||||||
|
|
||||||
|
Risk is not just about volatility (variance) - it's about how an asset moves
|
||||||
|
relative to your other wealth.
|
||||||
|
""")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("2. CORRELATION WITH WEALTH PORTFOLIO")
|
||||||
|
print("-" * 80)
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("EURO vs DOLLAR (from European perspective):")
|
||||||
|
print(" • When rest of wealth has unexpectedly HIGH returns → Euro DEPRECIATES vs Dollar")
|
||||||
|
print(" → Holding dollars means: Good wealth times = Dollar appreciates (good!)")
|
||||||
|
print(" • When rest of wealth has unexpectedly LOW returns → Euro APPRECIATES vs Dollar")
|
||||||
|
print(" → Holding dollars means: Bad wealth times = Dollar depreciates (bad!)")
|
||||||
|
print()
|
||||||
|
print(" ⇒ Dollar returns are POSITIVELY correlated with wealth portfolio")
|
||||||
|
print(" ⇒ Dollar acts as a HEDGE - it performs well when you need it!")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("YEN vs DOLLAR (from European perspective):")
|
||||||
|
print(" • When rest of wealth has unexpectedly HIGH returns → Yen APPRECIATES vs Dollar")
|
||||||
|
print(" → Holding dollars means: Good wealth times = Dollar depreciates (bad!)")
|
||||||
|
print(" • When rest of wealth has unexpectedly LOW returns → Yen DEPRECIATES vs Dollar")
|
||||||
|
print(" → Holding dollars means: Bad wealth times = Dollar appreciates (good!)")
|
||||||
|
print()
|
||||||
|
print(" ⇒ Dollar returns are NEGATIVELY correlated with wealth portfolio")
|
||||||
|
print(" ⇒ Dollar amplifies risk - loses value when your wealth is already doing poorly!")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("3. WHICH CURRENCY IS RISKIER?")
|
||||||
|
print("-" * 80)
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("From a European resident's perspective:")
|
||||||
|
print()
|
||||||
|
print(" YEN is RISKIER than DOLLAR")
|
||||||
|
print()
|
||||||
|
print("Reasoning:")
|
||||||
|
print(" • Both currencies have equal variance (equally variable)")
|
||||||
|
print(" • But COVARIANCE with wealth portfolio differs:")
|
||||||
|
print()
|
||||||
|
print(" - DOLLAR: Provides NEGATIVE covariance (hedge)")
|
||||||
|
print(" → When EUR/USD moves such that dollar strengthens during good times,")
|
||||||
|
print(" this is helpful as a diversification/insurance")
|
||||||
|
print()
|
||||||
|
print(" - YEN: Provides POSITIVE covariance (amplifies risk)")
|
||||||
|
print(" → When EUR/JPY moves such that yen appreciates during good times,")
|
||||||
|
print(" holding dollars (yen depreciates vs dollar) means you lose")
|
||||||
|
print(" on currency when your wealth is already vulnerable")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("="*80)
|
||||||
|
print("FORMAL ANALYSIS")
|
||||||
|
print("="*80)
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("Let's denote:")
|
||||||
|
print(" • R_W = Return on rest of wealth")
|
||||||
|
print(" • R_USD = Dollar return (from EUR perspective)")
|
||||||
|
print(" • R_YEN = Yen return (from EUR perspective)")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("Given information:")
|
||||||
|
print(" • Var(R_USD) = Var(R_YEN) = σ² (equal variability)")
|
||||||
|
print(" • When R_W is HIGH: EUR depreciates vs USD → R_USD is HIGH (positive correlation)")
|
||||||
|
print(" • When R_W is HIGH: YEN appreciates vs USD → R_USD is LOW (negative correlation)")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("Therefore:")
|
||||||
|
print(" • Cov(R_W, R_USD) > 0 (positive covariance)")
|
||||||
|
print(" • Cov(R_W, R_YEN) < 0 (negative covariance)")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("Portfolio risk including currency exposure:")
|
||||||
|
print(" Var(R_Total) = Var(R_W) + Var(R_Currency) + 2·Cov(R_W, R_Currency)")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("Comparing dollar vs yen investment:")
|
||||||
|
print()
|
||||||
|
print(" With DOLLAR:")
|
||||||
|
print(" Var(R_W + R_USD) = Var(R_W) + σ² + 2·Cov(R_W, R_USD)")
|
||||||
|
print(" = Var(R_W) + σ² + 2·(positive)")
|
||||||
|
print()
|
||||||
|
print(" With YEN (holding dollars):")
|
||||||
|
print(" Since yen appreciates when dollar depreciates, holding dollars means")
|
||||||
|
print(" exposure to yen risk in opposite direction")
|
||||||
|
print(" This creates HIGHER total portfolio variance")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("="*80)
|
||||||
|
print("ANSWER")
|
||||||
|
print("="*80)
|
||||||
|
print()
|
||||||
|
print("For a EUROPEAN RESIDENT:")
|
||||||
|
print()
|
||||||
|
print(" THE YEN IS RISKIER THAN THE DOLLAR")
|
||||||
|
print()
|
||||||
|
print("Even though both currencies are equally variable, the yen is riskier because:")
|
||||||
|
print()
|
||||||
|
print("1. The dollar provides a HEDGE against portfolio risk")
|
||||||
|
print(" (appreciates when your wealth does well)")
|
||||||
|
print()
|
||||||
|
print("2. The yen AMPLIFIES portfolio risk")
|
||||||
|
print(" (the dollar depreciates against yen when your wealth does poorly)")
|
||||||
|
print()
|
||||||
|
print("3. From a portfolio perspective, assets that move in the SAME direction")
|
||||||
|
print(" as your existing wealth are LESS risky than assets that move in the")
|
||||||
|
print(" OPPOSITE direction")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("="*80)
|
||||||
|
print("ADDITIONAL CONSIDERATIONS")
|
||||||
|
print("="*80)
|
||||||
|
print()
|
||||||
|
print("Ambiguities and assumptions:")
|
||||||
|
print()
|
||||||
|
print("1. We interpret 'rest of your wealth' as the European resident's non-currency")
|
||||||
|
print(" wealth portfolio (stocks, bonds, real estate, etc.)")
|
||||||
|
print()
|
||||||
|
print("2. We assume the question asks about holding dollars vs holding yen")
|
||||||
|
print(" (or equivalently, being exposed to dollar vs yen exchange rate risk)")
|
||||||
|
print()
|
||||||
|
print("3. We use modern portfolio theory framework where risk is measured by")
|
||||||
|
print(" contribution to total portfolio variance")
|
||||||
|
print()
|
||||||
|
print("4. Alternative interpretation: If the question asks which currency is riskier")
|
||||||
|
print(" to SHORT, the answer would be reversed - but the standard interpretation")
|
||||||
|
print(" is which currency is riskier to HOLD")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("="*80)
|
||||||
@@ -0,0 +1,171 @@
|
|||||||
|
"""
|
||||||
|
Problem Set 2 - Problem 1, Part 2, Question e)
|
||||||
|
Exchange Rate Analysis: Switzerland (CHF) vs US Dollar (USD)
|
||||||
|
"""
|
||||||
|
|
||||||
|
import pandas as pd
|
||||||
|
import matplotlib.pyplot as plt
|
||||||
|
import requests
|
||||||
|
from datetime import datetime
|
||||||
|
|
||||||
|
# FRED API endpoint for Swiss Franc to USD exchange rate
|
||||||
|
# FRED series: DEXSZUS (Switzerland / U.S. Foreign Exchange Rate)
|
||||||
|
# This is Swiss Francs per U.S. Dollar
|
||||||
|
|
||||||
|
def fetch_fred_data(series_id):
|
||||||
|
"""Fetch monthly exchange rate data from FRED"""
|
||||||
|
url = f"https://fred.stlouisfed.org/graph/fredgraph.csv?id={series_id}"
|
||||||
|
|
||||||
|
try:
|
||||||
|
df = pd.read_csv(url)
|
||||||
|
print(f"Columns found: {df.columns.tolist()}")
|
||||||
|
print(f"First few rows:\n{df.head()}")
|
||||||
|
|
||||||
|
# The first column should be DATE
|
||||||
|
date_col = df.columns[0]
|
||||||
|
value_col = df.columns[1]
|
||||||
|
|
||||||
|
df = df.rename(columns={date_col: 'DATE', value_col: 'Exchange_Rate'})
|
||||||
|
df['DATE'] = pd.to_datetime(df['DATE'])
|
||||||
|
|
||||||
|
# Remove missing values (marked as '.')
|
||||||
|
df = df[df['Exchange_Rate'] != '.']
|
||||||
|
df['Exchange_Rate'] = pd.to_numeric(df['Exchange_Rate'], errors='coerce')
|
||||||
|
df = df.dropna()
|
||||||
|
return df
|
||||||
|
except Exception as e:
|
||||||
|
print(f"Error fetching data: {e}")
|
||||||
|
import traceback
|
||||||
|
traceback.print_exc()
|
||||||
|
return None
|
||||||
|
|
||||||
|
def plot_exchange_rate(df, country_name):
|
||||||
|
"""Plot exchange rate over time"""
|
||||||
|
plt.figure(figsize=(14, 8))
|
||||||
|
plt.plot(df['DATE'], df['Exchange_Rate'], linewidth=1.5, color='#d62728')
|
||||||
|
plt.xlabel('Date', fontsize=12)
|
||||||
|
plt.ylabel('Swiss Francs per US Dollar', fontsize=12)
|
||||||
|
plt.title(f'Switzerland (CHF) / US Dollar Exchange Rate\nMonthly Data from FRED', fontsize=14, fontweight='bold')
|
||||||
|
plt.grid(True, alpha=0.3)
|
||||||
|
|
||||||
|
# Add annotations for key events
|
||||||
|
# Euro floor: September 2011 - January 2015 (CHF was pegged at 1.20 per EUR)
|
||||||
|
plt.axvline(x=pd.to_datetime('2011-09-06'), color='green', linestyle='--', alpha=0.7, linewidth=2)
|
||||||
|
plt.axvline(x=pd.to_datetime('2015-01-15'), color='red', linestyle='--', alpha=0.7, linewidth=2)
|
||||||
|
|
||||||
|
plt.text(pd.to_datetime('2011-09-06'), plt.ylim()[1]*0.95,
|
||||||
|
'Euro Floor\nIntroduced\n(Sep 2011)',
|
||||||
|
rotation=0, verticalalignment='top', fontsize=9, color='green')
|
||||||
|
plt.text(pd.to_datetime('2015-01-15'), plt.ylim()[1]*0.95,
|
||||||
|
'Euro Floor\nAbandoned\n(Jan 2015)',
|
||||||
|
rotation=0, verticalalignment='top', fontsize=9, color='red')
|
||||||
|
|
||||||
|
plt.tight_layout()
|
||||||
|
plt.savefig('/home/quinta/Documents/Atlas/Global Business Environment /Problem Set 2/switzerland_exchange_rate.png', dpi=300, bbox_inches='tight')
|
||||||
|
print("Plot saved as 'switzerland_exchange_rate.png'")
|
||||||
|
plt.show()
|
||||||
|
|
||||||
|
def analyze_fixed_periods(df):
|
||||||
|
"""Analyze periods when the currency might have been fixed"""
|
||||||
|
print("\n" + "="*80)
|
||||||
|
print("ANALYSIS: When was the Swiss Franc Fixed Relative to the US Dollar?")
|
||||||
|
print("="*80)
|
||||||
|
|
||||||
|
# Calculate rolling standard deviation to identify stable periods
|
||||||
|
df['Rolling_Std'] = df['Exchange_Rate'].rolling(window=12).std()
|
||||||
|
|
||||||
|
print("\nKey Observations:")
|
||||||
|
print("-" * 80)
|
||||||
|
|
||||||
|
# Historical context
|
||||||
|
print("\n1. BRETTON WOODS ERA (1944-1973):")
|
||||||
|
bretton_woods = df[(df['DATE'] >= '1944-01-01') & (df['DATE'] <= '1973-12-31')]
|
||||||
|
if not bretton_woods.empty:
|
||||||
|
print(f" - Period: 1944-1973")
|
||||||
|
print(f" - Average rate: {bretton_woods['Exchange_Rate'].mean():.4f} CHF/USD")
|
||||||
|
print(f" - Standard deviation: {bretton_woods['Exchange_Rate'].std():.4f}")
|
||||||
|
print(f" - The Swiss Franc was part of the Bretton Woods fixed exchange rate system")
|
||||||
|
print(f" - Fixed at 4.375 CHF per USD (1945-1949), then adjusted to ~4.30 (1949-1973)")
|
||||||
|
|
||||||
|
print("\n2. POST-BRETTON WOODS FLOATING (1973-2011):")
|
||||||
|
floating = df[(df['DATE'] >= '1973-01-01') & (df['DATE'] <= '2011-09-01')]
|
||||||
|
if not floating.empty:
|
||||||
|
print(f" - Period: 1973-2011")
|
||||||
|
print(f" - Average rate: {floating['Exchange_Rate'].mean():.4f} CHF/USD")
|
||||||
|
print(f" - Standard deviation: {floating['Exchange_Rate'].std():.4f}")
|
||||||
|
print(f" - Swiss Franc floated freely, showing significant volatility")
|
||||||
|
|
||||||
|
print("\n3. EURO FLOOR PERIOD (September 2011 - January 2015):")
|
||||||
|
euro_floor = df[(df['DATE'] >= '2011-09-06') & (df['DATE'] <= '2015-01-15')]
|
||||||
|
if not euro_floor.empty:
|
||||||
|
print(f" - Period: September 6, 2011 - January 15, 2015")
|
||||||
|
print(f" - Average rate: {euro_floor['Exchange_Rate'].mean():.4f} CHF/USD")
|
||||||
|
print(f" - Standard deviation: {euro_floor['Exchange_Rate'].std():.4f}")
|
||||||
|
print(f" - Swiss National Bank (SNB) set minimum exchange rate of 1.20 CHF per EUR")
|
||||||
|
print(f" - This indirectly affected CHF/USD rate (reduced volatility)")
|
||||||
|
print(f" - Not directly fixed to USD, but to EUR")
|
||||||
|
|
||||||
|
print("\n4. POST-EURO FLOOR (January 2015 - Present):")
|
||||||
|
post_floor = df[df['DATE'] >= '2015-01-15']
|
||||||
|
if not post_floor.empty:
|
||||||
|
print(f" - Period: January 15, 2015 - Present")
|
||||||
|
print(f" - Average rate: {post_floor['Exchange_Rate'].mean():.4f} CHF/USD")
|
||||||
|
print(f" - Standard deviation: {post_floor['Exchange_Rate'].std():.4f}")
|
||||||
|
print(f" - Swiss Franc floats freely again")
|
||||||
|
print(f" - Significant appreciation immediately after floor removal")
|
||||||
|
|
||||||
|
print("\n" + "="*80)
|
||||||
|
print("CONCLUSION:")
|
||||||
|
print("="*80)
|
||||||
|
print("""
|
||||||
|
The Swiss Franc was FIXED relative to the US Dollar during:
|
||||||
|
1. BRETTON WOODS SYSTEM (1944-1973): Directly fixed to USD
|
||||||
|
- Official fixed exchange rate system
|
||||||
|
- Rate: approximately 4.30-4.375 CHF per USD
|
||||||
|
|
||||||
|
The Swiss Franc was INDIRECTLY STABILIZED (but not fixed to USD) during:
|
||||||
|
2. EURO FLOOR PERIOD (September 2011 - January 2015): Fixed to EUR, not USD
|
||||||
|
- SNB maintained a floor of 1.20 CHF per EUR
|
||||||
|
- This reduced CHF/USD volatility but CHF/USD was not directly fixed
|
||||||
|
- Abandoned on January 15, 2015 ("Swiss Franc Shock")
|
||||||
|
|
||||||
|
Since 1973 (except for the Euro floor period), the Swiss Franc has generally
|
||||||
|
floated freely against the US Dollar.
|
||||||
|
""")
|
||||||
|
print("="*80)
|
||||||
|
|
||||||
|
def main():
|
||||||
|
print("Fetching Swiss Franc exchange rate data from FRED...")
|
||||||
|
print("FRED Series: DEXSZUS (Swiss Francs per US Dollar)")
|
||||||
|
print("-" * 80)
|
||||||
|
|
||||||
|
# Fetch data
|
||||||
|
df = fetch_fred_data('DEXSZUS')
|
||||||
|
|
||||||
|
if df is not None:
|
||||||
|
print(f"\nData retrieved successfully!")
|
||||||
|
print(f"Date range: {df['DATE'].min().date()} to {df['DATE'].max().date()}")
|
||||||
|
print(f"Number of observations: {len(df)}")
|
||||||
|
print(f"\nFirst few observations:")
|
||||||
|
print(df.head())
|
||||||
|
print(f"\nLast few observations:")
|
||||||
|
print(df.tail())
|
||||||
|
|
||||||
|
# Analyze fixed periods
|
||||||
|
analyze_fixed_periods(df)
|
||||||
|
|
||||||
|
# Plot
|
||||||
|
print("\nGenerating plot...")
|
||||||
|
plot_exchange_rate(df, "Switzerland")
|
||||||
|
|
||||||
|
# Summary statistics
|
||||||
|
print("\n" + "="*80)
|
||||||
|
print("SUMMARY STATISTICS")
|
||||||
|
print("="*80)
|
||||||
|
print(df['Exchange_Rate'].describe())
|
||||||
|
|
||||||
|
else:
|
||||||
|
print("Failed to fetch data. Please check your internet connection.")
|
||||||
|
|
||||||
|
if __name__ == "__main__":
|
||||||
|
main()
|
||||||
@@ -0,0 +1,207 @@
|
|||||||
|
"""
|
||||||
|
Problem Set 2 - Problem 2
|
||||||
|
Forward Exchange Rate Analysis
|
||||||
|
"""
|
||||||
|
|
||||||
|
print("="*80)
|
||||||
|
print("PROBLEM 2: FORWARD EXCHANGE RATE ANALYSIS")
|
||||||
|
print("="*80)
|
||||||
|
print()
|
||||||
|
|
||||||
|
# Given data
|
||||||
|
spot_rate = 0.9745 # E_USD/EUR
|
||||||
|
forward_points = 236.60
|
||||||
|
|
||||||
|
print("GIVEN INFORMATION:")
|
||||||
|
print("-" * 80)
|
||||||
|
print(f"Spot Exchange Rate (E_USD/EUR): {spot_rate}")
|
||||||
|
print(f"1-Year Forward Points: {forward_points}")
|
||||||
|
print()
|
||||||
|
|
||||||
|
# Part 1: Calculate forward exchange rate
|
||||||
|
print("="*80)
|
||||||
|
print("PART 1: CALCULATE FORWARD EXCHANGE RATE")
|
||||||
|
print("="*80)
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("Forward points are typically quoted in basis points (1/10,000)")
|
||||||
|
print("Formula: F = E_spot + (Forward Points / 10,000)")
|
||||||
|
print()
|
||||||
|
|
||||||
|
forward_rate = spot_rate + (forward_points / 10000)
|
||||||
|
|
||||||
|
print(f"Calculation:")
|
||||||
|
print(f"F_1y_USD/EUR = {spot_rate} + ({forward_points} / 10,000)")
|
||||||
|
print(f"F_1y_USD/EUR = {spot_rate} + {forward_points/10000:.4f}")
|
||||||
|
print(f"F_1y_USD/EUR = {forward_rate:.4f}")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print(f"✓ ANSWER: The 1-year forward rate is F_1y_USD/EUR = {forward_rate:.4f}")
|
||||||
|
print()
|
||||||
|
|
||||||
|
# Part 2: Expected appreciation or depreciation
|
||||||
|
print("="*80)
|
||||||
|
print("PART 2: EXPECTED APPRECIATION OR DEPRECIATION")
|
||||||
|
print("="*80)
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("Comparing spot and forward rates:")
|
||||||
|
print(f" • Spot rate: E_USD/EUR = {spot_rate:.4f} (USD per EUR)")
|
||||||
|
print(f" • Forward rate: F_USD/EUR = {forward_rate:.4f} (USD per EUR)")
|
||||||
|
print()
|
||||||
|
|
||||||
|
difference = forward_rate - spot_rate
|
||||||
|
pct_change = (difference / spot_rate) * 100
|
||||||
|
|
||||||
|
print(f"Change: {forward_rate:.4f} - {spot_rate:.4f} = {difference:.4f}")
|
||||||
|
print(f"Percentage change: {pct_change:.2f}%")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("Interpretation:")
|
||||||
|
print(f" Since F > E (forward rate > spot rate):")
|
||||||
|
print(f" • It takes MORE dollars to buy 1 euro in the forward market")
|
||||||
|
print(f" • The dollar is expected to DEPRECIATE relative to the euro")
|
||||||
|
print(f" • Equivalently, the euro is expected to APPRECIATE relative to the dollar")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print(f"✓ ANSWER: The market expects a DEPRECIATION of the US Dollar")
|
||||||
|
print(f" relative to the Euro in one year.")
|
||||||
|
print(f" (The dollar loses value; the euro gains value)")
|
||||||
|
print()
|
||||||
|
|
||||||
|
# Part 3: Intuitive explanation
|
||||||
|
print("="*80)
|
||||||
|
print("PART 3: INTUITIVE EXPLANATION")
|
||||||
|
print("="*80)
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("Why does the market expect the dollar to depreciate?")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("The forward rate reflects INTEREST RATE DIFFERENTIALS between countries.")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("1. COVERED INTEREST PARITY (CIP):")
|
||||||
|
print(" The forward rate adjusts to eliminate arbitrage opportunities between")
|
||||||
|
print(" investing in USD vs EUR after accounting for exchange rate risk.")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print(" Formula: F/E = (1 + R_USD)/(1 + R_EUR)")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("2. INTERPRETATION:")
|
||||||
|
print(" Since F > E, we have:")
|
||||||
|
print(f" {forward_rate:.4f}/{spot_rate:.4f} = {forward_rate/spot_rate:.4f}")
|
||||||
|
print()
|
||||||
|
|
||||||
|
implied_ratio = forward_rate / spot_rate
|
||||||
|
|
||||||
|
print(f" This means: (1 + R_USD)/(1 + R_EUR) = {implied_ratio:.4f}")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print(" Rearranging: 1 + R_USD = {:.4f} × (1 + R_EUR)".format(implied_ratio))
|
||||||
|
print()
|
||||||
|
|
||||||
|
print(" If the ratio > 1, then R_USD > R_EUR")
|
||||||
|
print(" → US interest rates are HIGHER than Eurozone interest rates")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("3. INTUITIVE EXPLANATION:")
|
||||||
|
print()
|
||||||
|
print(" • The US has higher interest rates than the Eurozone")
|
||||||
|
print(" • Higher interest rates typically indicate:")
|
||||||
|
print(" - Expectations of higher inflation in the US")
|
||||||
|
print(" - Or tighter monetary policy")
|
||||||
|
print(" - Or higher risk premium")
|
||||||
|
print()
|
||||||
|
print(" • According to Purchasing Power Parity (PPP):")
|
||||||
|
print(" Higher inflation → Currency depreciation")
|
||||||
|
print()
|
||||||
|
print(" • Covered Interest Parity ensures that investors can't arbitrage:")
|
||||||
|
print(" - The higher US interest rate is offset by expected dollar depreciation")
|
||||||
|
print(" - This makes USD and EUR investments equally attractive (when hedged)")
|
||||||
|
print()
|
||||||
|
print(" • The forward rate builds in this expected depreciation")
|
||||||
|
print(" - Investors demand more dollars per euro in the forward market")
|
||||||
|
print(" - This compensates for the expected loss in dollar value")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print(f"✓ ANSWER: The dollar is expected to depreciate because US interest rates")
|
||||||
|
print(f" are higher than Eurozone rates. The interest rate differential")
|
||||||
|
print(f" typically reflects inflation differentials or other economic factors")
|
||||||
|
print(f" that lead to currency depreciation. The forward premium on the euro")
|
||||||
|
print(f" compensates investors for the higher return on dollar-denominated")
|
||||||
|
print(f" assets, maintaining covered interest parity.")
|
||||||
|
print()
|
||||||
|
|
||||||
|
# Part 4: Find EUR interest rate
|
||||||
|
print("="*80)
|
||||||
|
print("PART 4: FIND R_EUR USING COVERED INTEREST PARITY")
|
||||||
|
print("="*80)
|
||||||
|
print()
|
||||||
|
|
||||||
|
R_USD = 0.05
|
||||||
|
|
||||||
|
print(f"Given: R_1y_USD = {R_USD:.4f} (5%)")
|
||||||
|
print(f" E_USD/EUR = {spot_rate:.4f}")
|
||||||
|
print(f" F_1y_USD/EUR = {forward_rate:.4f}")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("Covered Interest Parity Condition:")
|
||||||
|
print(" F/E = (1 + R_USD)/(1 + R_EUR)")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("Solving for R_EUR:")
|
||||||
|
print(" 1 + R_EUR = (1 + R_USD) × (E/F)")
|
||||||
|
print(" R_EUR = (1 + R_USD) × (E/F) - 1")
|
||||||
|
print()
|
||||||
|
|
||||||
|
R_EUR = (1 + R_USD) * (spot_rate / forward_rate) - 1
|
||||||
|
|
||||||
|
print(f"Calculation:")
|
||||||
|
print(f" R_EUR = (1 + {R_USD}) × ({spot_rate:.4f}/{forward_rate:.4f}) - 1")
|
||||||
|
print(f" R_EUR = {1 + R_USD:.4f} × {spot_rate/forward_rate:.6f} - 1")
|
||||||
|
print(f" R_EUR = {(1 + R_USD) * (spot_rate / forward_rate):.6f} - 1")
|
||||||
|
print(f" R_EUR = {R_EUR:.6f}")
|
||||||
|
print()
|
||||||
|
|
||||||
|
R_EUR_pct = R_EUR * 100
|
||||||
|
|
||||||
|
print(f"✓ ANSWER: R_1y_EUR = {R_EUR:.4f} or {R_EUR_pct:.2f}%")
|
||||||
|
print()
|
||||||
|
|
||||||
|
# Verification
|
||||||
|
print("VERIFICATION:")
|
||||||
|
print("Checking covered interest parity:")
|
||||||
|
print()
|
||||||
|
|
||||||
|
lhs = forward_rate / spot_rate
|
||||||
|
rhs = (1 + R_USD) / (1 + R_EUR)
|
||||||
|
|
||||||
|
print(f" Left side: F/E = {forward_rate:.4f}/{spot_rate:.4f} = {lhs:.6f}")
|
||||||
|
print(f" Right side: (1 + R_USD)/(1 + R_EUR) = {1+R_USD:.4f}/{1+R_EUR:.6f} = {rhs:.6f}")
|
||||||
|
print()
|
||||||
|
|
||||||
|
if abs(lhs - rhs) < 0.0001:
|
||||||
|
print("✓ Covered Interest Parity HOLDS! ✓")
|
||||||
|
else:
|
||||||
|
print(f" Difference: {abs(lhs - rhs):.8f}")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("="*80)
|
||||||
|
print("SUMMARY OF ANSWERS")
|
||||||
|
print("="*80)
|
||||||
|
print()
|
||||||
|
print(f"1. Forward Exchange Rate: F_1y_USD/EUR = {forward_rate:.4f}")
|
||||||
|
print()
|
||||||
|
print(f"2. Expected Movement: The US Dollar is expected to DEPRECIATE")
|
||||||
|
print(f" relative to the Euro by {pct_change:.2f}%")
|
||||||
|
print()
|
||||||
|
print(f"3. Intuitive Explanation: Higher US interest rates (compared to")
|
||||||
|
print(f" Eurozone) imply expected dollar depreciation. The forward premium")
|
||||||
|
print(f" compensates for the interest rate differential via covered interest parity.")
|
||||||
|
print()
|
||||||
|
print(f"4. Eurozone Interest Rate: R_1y_EUR = {R_EUR:.4f} ({R_EUR_pct:.2f}%)")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("="*80)
|
||||||
@@ -0,0 +1,326 @@
|
|||||||
|
"""
|
||||||
|
Problem Set 2 - Problem 3
|
||||||
|
Put Option Analysis
|
||||||
|
"""
|
||||||
|
|
||||||
|
import numpy as np
|
||||||
|
import matplotlib.pyplot as plt
|
||||||
|
|
||||||
|
print("="*80)
|
||||||
|
print("PROBLEM 3: PUT OPTION ANALYSIS")
|
||||||
|
print("="*80)
|
||||||
|
print()
|
||||||
|
|
||||||
|
# Given data
|
||||||
|
amount_eur = 1000 # EUR
|
||||||
|
option_fee_chf = 75 # CHF
|
||||||
|
R_3m_EUR = 0.013 # 1.3%
|
||||||
|
R_3m_CHF = 0.005 # 0.5%
|
||||||
|
E_spot = 0.95 # CHF/EUR
|
||||||
|
|
||||||
|
print("GIVEN INFORMATION:")
|
||||||
|
print("-" * 80)
|
||||||
|
print(f"Put option to SELL: {amount_eur:,} EUR")
|
||||||
|
print(f"Option fee: {option_fee_chf} CHF (paid at signing)")
|
||||||
|
print(f"3-month EUR interest rate: R_3m_EUR = {R_3m_EUR:.3f} ({R_3m_EUR*100:.1f}%)")
|
||||||
|
print(f"3-month CHF interest rate: R_3m_CHF = {R_3m_CHF:.3f} ({R_3m_CHF*100:.1f}%)")
|
||||||
|
print(f"Spot exchange rate: E_CHF/EUR = {E_spot:.2f}")
|
||||||
|
print()
|
||||||
|
|
||||||
|
# Part 1: Calculate expected exchange rate
|
||||||
|
print("="*80)
|
||||||
|
print("PART 1: EXPECTED EXCHANGE RATE FROM INTEREST PARITY")
|
||||||
|
print("="*80)
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("Interest Parity Condition (Uncovered Interest Parity):")
|
||||||
|
print(" E_e / E_spot = (1 + R_CHF) / (1 + R_EUR)")
|
||||||
|
print()
|
||||||
|
print("Solving for expected exchange rate E_e:")
|
||||||
|
print(" E_e = E_spot × (1 + R_CHF) / (1 + R_EUR)")
|
||||||
|
print()
|
||||||
|
|
||||||
|
E_expected = E_spot * (1 + R_3m_CHF) / (1 + R_3m_EUR)
|
||||||
|
|
||||||
|
print(f"Calculation:")
|
||||||
|
print(f" E_e = {E_spot:.2f} × (1 + {R_3m_CHF:.3f}) / (1 + {R_3m_EUR:.3f})")
|
||||||
|
print(f" E_e = {E_spot:.2f} × {1 + R_3m_CHF:.4f} / {1 + R_3m_EUR:.4f}")
|
||||||
|
print(f" E_e = {E_spot:.2f} × {(1 + R_3m_CHF) / (1 + R_3m_EUR):.6f}")
|
||||||
|
print(f" E_e = {E_expected:.6f}")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print(f"✓ ANSWER: E_e_CHF/EUR = {E_expected:.4f} CHF per EUR")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("Interpretation:")
|
||||||
|
print(f" • The expected exchange rate ({E_expected:.4f}) is LOWER than spot ({E_spot:.2f})")
|
||||||
|
print(f" • This means the CHF is expected to APPRECIATE relative to EUR")
|
||||||
|
print(f" • This makes sense: CHF has lower interest rate than EUR")
|
||||||
|
print(f" • By interest parity, lower interest rate currency appreciates")
|
||||||
|
print()
|
||||||
|
|
||||||
|
# Strike price equals expected exchange rate
|
||||||
|
X = E_expected
|
||||||
|
|
||||||
|
print(f"Strike Price: X = E_e = {X:.4f} CHF/EUR")
|
||||||
|
print()
|
||||||
|
|
||||||
|
# Part 2: Exercise decision when E = 0.93
|
||||||
|
print("="*80)
|
||||||
|
print("PART 2: SCENARIO WITH E_CHF/EUR = 0.93 AFTER 3 MONTHS")
|
||||||
|
print("="*80)
|
||||||
|
print()
|
||||||
|
|
||||||
|
E_future_1 = 0.93
|
||||||
|
|
||||||
|
print(f"After 3 months: E_CHF/EUR = {E_future_1:.2f}")
|
||||||
|
print(f"Strike price: X = {X:.4f}")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("EXERCISE DECISION:")
|
||||||
|
print("-" * 80)
|
||||||
|
print()
|
||||||
|
print("Put option gives the RIGHT (not obligation) to SELL EUR at strike price X")
|
||||||
|
print()
|
||||||
|
print(f" • If we exercise: Sell 1,000 EUR at X = {X:.4f} CHF/EUR")
|
||||||
|
print(f" → Receive: {amount_eur:,} × {X:.4f} = {amount_eur * X:.2f} CHF")
|
||||||
|
print()
|
||||||
|
print(f" • If we don't exercise: Sell 1,000 EUR at market rate E = {E_future_1:.2f}")
|
||||||
|
print(f" → Receive: {amount_eur:,} × {E_future_1:.2f} = {amount_eur * E_future_1:.2f} CHF")
|
||||||
|
print()
|
||||||
|
|
||||||
|
if X > E_future_1:
|
||||||
|
exercise_1 = True
|
||||||
|
print(f"Since X ({X:.4f}) > E ({E_future_1:.2f}), we SHOULD EXERCISE the option!")
|
||||||
|
print(f"We can sell EUR at a better rate than the market offers.")
|
||||||
|
else:
|
||||||
|
exercise_1 = False
|
||||||
|
print(f"Since X ({X:.4f}) ≤ E ({E_future_1:.2f}), we should NOT exercise.")
|
||||||
|
print(f"The market rate is better than the strike price.")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("PAYOFF AND PROFIT:")
|
||||||
|
print("-" * 80)
|
||||||
|
print()
|
||||||
|
|
||||||
|
if exercise_1:
|
||||||
|
payoff_1 = amount_eur * (X - E_future_1)
|
||||||
|
print("Payoff (intrinsic value at expiration):")
|
||||||
|
print(f" Payoff = Amount × max(X - E, 0)")
|
||||||
|
print(f" Payoff = {amount_eur:,} × max({X:.4f} - {E_future_1:.2f}, 0)")
|
||||||
|
print(f" Payoff = {amount_eur:,} × {X - E_future_1:.4f}")
|
||||||
|
print(f" Payoff = {payoff_1:.2f} CHF")
|
||||||
|
else:
|
||||||
|
payoff_1 = 0
|
||||||
|
print("Payoff (intrinsic value at expiration):")
|
||||||
|
print(f" Payoff = Amount × max(X - E, 0)")
|
||||||
|
print(f" Payoff = {amount_eur:,} × max({X:.4f} - {E_future_1:.2f}, 0)")
|
||||||
|
print(f" Payoff = 0 CHF (option expires worthless)")
|
||||||
|
|
||||||
|
print()
|
||||||
|
|
||||||
|
# Calculate profit (accounting for option premium with interest)
|
||||||
|
option_cost_future = option_fee_chf * (1 + R_3m_CHF)
|
||||||
|
profit_1 = payoff_1 - option_cost_future
|
||||||
|
|
||||||
|
print("Profit (payoff minus cost of option with interest):")
|
||||||
|
print(f" Option fee paid upfront: {option_fee_chf} CHF")
|
||||||
|
print(f" Future value of option fee: {option_fee_chf} × (1 + {R_3m_CHF:.3f}) = {option_cost_future:.2f} CHF")
|
||||||
|
print(f" Profit = Payoff - FV(Option Fee)")
|
||||||
|
print(f" Profit = {payoff_1:.2f} - {option_cost_future:.2f}")
|
||||||
|
print(f" Profit = {profit_1:.2f} CHF")
|
||||||
|
print()
|
||||||
|
|
||||||
|
if profit_1 > 0:
|
||||||
|
print(f"✓ The option generates a POSITIVE profit of {profit_1:.2f} CHF")
|
||||||
|
elif profit_1 < 0:
|
||||||
|
print(f"✗ The option generates a NEGATIVE profit (loss) of {abs(profit_1):.2f} CHF")
|
||||||
|
else:
|
||||||
|
print("○ The option breaks even (zero profit)")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print(f"✓ ANSWER PART 2:")
|
||||||
|
print(f" • Exercise decision: {'YES, exercise the option' if exercise_1 else 'NO, let it expire'}")
|
||||||
|
print(f" • Payoff: {payoff_1:.2f} CHF")
|
||||||
|
print(f" • Profit: {profit_1:.2f} CHF")
|
||||||
|
print()
|
||||||
|
|
||||||
|
# Part 3: Exercise decision when E = 0.98
|
||||||
|
print("="*80)
|
||||||
|
print("PART 3: SCENARIO WITH E_CHF/EUR = 0.98 AFTER 3 MONTHS")
|
||||||
|
print("="*80)
|
||||||
|
print()
|
||||||
|
|
||||||
|
E_future_2 = 0.98
|
||||||
|
|
||||||
|
print(f"After 3 months: E_CHF/EUR = {E_future_2:.2f}")
|
||||||
|
print(f"Strike price: X = {X:.4f}")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("EXERCISE DECISION:")
|
||||||
|
print("-" * 80)
|
||||||
|
print()
|
||||||
|
print("Put option gives the RIGHT (not obligation) to SELL EUR at strike price X")
|
||||||
|
print()
|
||||||
|
print(f" • If we exercise: Sell 1,000 EUR at X = {X:.4f} CHF/EUR")
|
||||||
|
print(f" → Receive: {amount_eur:,} × {X:.4f} = {amount_eur * X:.2f} CHF")
|
||||||
|
print()
|
||||||
|
print(f" • If we don't exercise: Sell 1,000 EUR at market rate E = {E_future_2:.2f}")
|
||||||
|
print(f" → Receive: {amount_eur:,} × {E_future_2:.2f} = {amount_eur * E_future_2:.2f} CHF")
|
||||||
|
print()
|
||||||
|
|
||||||
|
if X > E_future_2:
|
||||||
|
exercise_2 = True
|
||||||
|
print(f"Since X ({X:.4f}) > E ({E_future_2:.2f}), we SHOULD EXERCISE the option!")
|
||||||
|
print(f"We can sell EUR at a better rate than the market offers.")
|
||||||
|
else:
|
||||||
|
exercise_2 = False
|
||||||
|
print(f"Since X ({X:.4f}) ≤ E ({E_future_2:.2f}), we should NOT exercise.")
|
||||||
|
print(f"The market rate is better than the strike price.")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("PAYOFF AND PROFIT:")
|
||||||
|
print("-" * 80)
|
||||||
|
print()
|
||||||
|
|
||||||
|
if exercise_2:
|
||||||
|
payoff_2 = amount_eur * (X - E_future_2)
|
||||||
|
print("Payoff (intrinsic value at expiration):")
|
||||||
|
print(f" Payoff = Amount × max(X - E, 0)")
|
||||||
|
print(f" Payoff = {amount_eur:,} × max({X:.4f} - {E_future_2:.2f}, 0)")
|
||||||
|
print(f" Payoff = {amount_eur:,} × {X - E_future_2:.4f}")
|
||||||
|
print(f" Payoff = {payoff_2:.2f} CHF")
|
||||||
|
else:
|
||||||
|
payoff_2 = 0
|
||||||
|
print("Payoff (intrinsic value at expiration):")
|
||||||
|
print(f" Payoff = Amount × max(X - E, 0)")
|
||||||
|
print(f" Payoff = {amount_eur:,} × max({X:.4f} - {E_future_2:.2f}, 0)")
|
||||||
|
print(f" Payoff = 0 CHF (option expires worthless)")
|
||||||
|
|
||||||
|
print()
|
||||||
|
|
||||||
|
profit_2 = payoff_2 - option_cost_future
|
||||||
|
|
||||||
|
print("Profit (payoff minus cost of option with interest):")
|
||||||
|
print(f" Option fee paid upfront: {option_fee_chf} CHF")
|
||||||
|
print(f" Future value of option fee: {option_fee_chf} × (1 + {R_3m_CHF:.3f}) = {option_cost_future:.2f} CHF")
|
||||||
|
print(f" Profit = Payoff - FV(Option Fee)")
|
||||||
|
print(f" Profit = {payoff_2:.2f} - {option_cost_future:.2f}")
|
||||||
|
print(f" Profit = {profit_2:.2f} CHF")
|
||||||
|
print()
|
||||||
|
|
||||||
|
if profit_2 > 0:
|
||||||
|
print(f"✓ The option generates a POSITIVE profit of {profit_2:.2f} CHF")
|
||||||
|
elif profit_2 < 0:
|
||||||
|
print(f"✗ The option generates a NEGATIVE profit (loss) of {abs(profit_2):.2f} CHF")
|
||||||
|
else:
|
||||||
|
print("○ The option breaks even (zero profit)")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print(f"✓ ANSWER PART 3:")
|
||||||
|
print(f" • Exercise decision: {'YES, exercise the option' if exercise_2 else 'NO, let it expire'}")
|
||||||
|
print(f" • Payoff: {payoff_2:.2f} CHF")
|
||||||
|
print(f" • Profit: {profit_2:.2f} CHF")
|
||||||
|
print()
|
||||||
|
|
||||||
|
# Create graphs
|
||||||
|
print("="*80)
|
||||||
|
print("GENERATING PAYOFF AND PROFIT DIAGRAMS")
|
||||||
|
print("="*80)
|
||||||
|
print()
|
||||||
|
|
||||||
|
# Generate exchange rate range
|
||||||
|
E_range = np.linspace(0.85, 1.05, 200)
|
||||||
|
|
||||||
|
# Calculate payoff and profit for each exchange rate
|
||||||
|
payoffs = amount_eur * np.maximum(X - E_range, 0)
|
||||||
|
profits = payoffs - option_cost_future
|
||||||
|
|
||||||
|
# Create figure with two subplots
|
||||||
|
fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(12, 10))
|
||||||
|
|
||||||
|
# Plot 1: Payoff diagram
|
||||||
|
ax1.plot(E_range, payoffs, 'b-', linewidth=2.5, label='Payoff')
|
||||||
|
ax1.axhline(y=0, color='k', linestyle='-', linewidth=0.5)
|
||||||
|
ax1.axvline(x=X, color='r', linestyle='--', linewidth=1.5, alpha=0.7, label=f'Strike Price (X = {X:.4f})')
|
||||||
|
|
||||||
|
# Mark the two scenarios on payoff diagram
|
||||||
|
ax1.plot(E_future_1, payoff_1, 'go', markersize=12, label=f'Scenario 1: E = {E_future_1:.2f}', zorder=5)
|
||||||
|
ax1.plot(E_future_2, payoff_2, 'mo', markersize=12, label=f'Scenario 2: E = {E_future_2:.2f}', zorder=5)
|
||||||
|
|
||||||
|
# Add annotations
|
||||||
|
ax1.annotate(f'Payoff = {payoff_1:.2f} CHF',
|
||||||
|
xy=(E_future_1, payoff_1), xytext=(E_future_1-0.03, payoff_1+50),
|
||||||
|
fontsize=10, ha='right',
|
||||||
|
bbox=dict(boxstyle='round,pad=0.5', facecolor='green', alpha=0.3),
|
||||||
|
arrowprops=dict(arrowstyle='->', connectionstyle='arc3,rad=0', color='green'))
|
||||||
|
|
||||||
|
ax1.annotate(f'Payoff = {payoff_2:.2f} CHF',
|
||||||
|
xy=(E_future_2, payoff_2), xytext=(E_future_2+0.03, payoff_2+50),
|
||||||
|
fontsize=10, ha='left',
|
||||||
|
bbox=dict(boxstyle='round,pad=0.5', facecolor='magenta', alpha=0.3),
|
||||||
|
arrowprops=dict(arrowstyle='->', connectionstyle='arc3,rad=0', color='magenta'))
|
||||||
|
|
||||||
|
ax1.set_xlabel('Spot Exchange Rate at Maturity (E_CHF/EUR)', fontsize=11, fontweight='bold')
|
||||||
|
ax1.set_ylabel('Payoff (CHF)', fontsize=11, fontweight='bold')
|
||||||
|
ax1.set_title('Put Option PAYOFF Diagram\n(Intrinsic Value at Expiration)', fontsize=13, fontweight='bold')
|
||||||
|
ax1.grid(True, alpha=0.3)
|
||||||
|
ax1.legend(loc='upper right', fontsize=10)
|
||||||
|
ax1.set_xlim([0.85, 1.05])
|
||||||
|
|
||||||
|
# Plot 2: Profit diagram
|
||||||
|
ax2.plot(E_range, profits, 'r-', linewidth=2.5, label='Profit')
|
||||||
|
ax2.axhline(y=0, color='k', linestyle='-', linewidth=0.5)
|
||||||
|
ax2.axvline(x=X, color='r', linestyle='--', linewidth=1.5, alpha=0.7, label=f'Strike Price (X = {X:.4f})')
|
||||||
|
ax2.axhline(y=-option_cost_future, color='orange', linestyle=':', linewidth=2,
|
||||||
|
label=f'Maximum Loss = -{option_cost_future:.2f} CHF')
|
||||||
|
|
||||||
|
# Mark the two scenarios on profit diagram
|
||||||
|
ax2.plot(E_future_1, profit_1, 'go', markersize=12, label=f'Scenario 1: E = {E_future_1:.2f}', zorder=5)
|
||||||
|
ax2.plot(E_future_2, profit_2, 'mo', markersize=12, label=f'Scenario 2: E = {E_future_2:.2f}', zorder=5)
|
||||||
|
|
||||||
|
# Add annotations
|
||||||
|
ax2.annotate(f'Profit = {profit_1:.2f} CHF',
|
||||||
|
xy=(E_future_1, profit_1), xytext=(E_future_1-0.03, profit_1+20),
|
||||||
|
fontsize=10, ha='right',
|
||||||
|
bbox=dict(boxstyle='round,pad=0.5', facecolor='green', alpha=0.3),
|
||||||
|
arrowprops=dict(arrowstyle='->', connectionstyle='arc3,rad=0', color='green'))
|
||||||
|
|
||||||
|
ax2.annotate(f'Profit = {profit_2:.2f} CHF',
|
||||||
|
xy=(E_future_2, profit_2), xytext=(E_future_2+0.03, profit_2-30),
|
||||||
|
fontsize=10, ha='left',
|
||||||
|
bbox=dict(boxstyle='round,pad=0.5', facecolor='magenta', alpha=0.3),
|
||||||
|
arrowprops=dict(arrowstyle='->', connectionstyle='arc3,rad=0', color='magenta'))
|
||||||
|
|
||||||
|
ax2.set_xlabel('Spot Exchange Rate at Maturity (E_CHF/EUR)', fontsize=11, fontweight='bold')
|
||||||
|
ax2.set_ylabel('Profit (CHF)', fontsize=11, fontweight='bold')
|
||||||
|
ax2.set_title('Put Option PROFIT Diagram\n(Payoff - Cost of Option)', fontsize=13, fontweight='bold')
|
||||||
|
ax2.grid(True, alpha=0.3)
|
||||||
|
ax2.legend(loc='upper right', fontsize=10)
|
||||||
|
ax2.set_xlim([0.85, 1.05])
|
||||||
|
|
||||||
|
plt.tight_layout()
|
||||||
|
plt.savefig('/home/quinta/Documents/Atlas/Global Business Environment /Problem Set 2/problem3_put_option_diagrams.png',
|
||||||
|
dpi=300, bbox_inches='tight')
|
||||||
|
print("✓ Graphs saved as 'problem3_put_option_diagrams.png'")
|
||||||
|
plt.show()
|
||||||
|
|
||||||
|
print()
|
||||||
|
print("="*80)
|
||||||
|
print("SUMMARY OF ALL ANSWERS")
|
||||||
|
print("="*80)
|
||||||
|
print()
|
||||||
|
print(f"PART 1: Expected Exchange Rate")
|
||||||
|
print(f" E_e_CHF/EUR = {E_expected:.4f}")
|
||||||
|
print()
|
||||||
|
print(f"PART 2: Scenario E = {E_future_1:.2f}")
|
||||||
|
print(f" • Exercise: {'YES' if exercise_1 else 'NO'}")
|
||||||
|
print(f" • Payoff: {payoff_1:.2f} CHF")
|
||||||
|
print(f" • Profit: {profit_1:.2f} CHF")
|
||||||
|
print()
|
||||||
|
print(f"PART 3: Scenario E = {E_future_2:.2f}")
|
||||||
|
print(f" • Exercise: {'YES' if exercise_2 else 'NO'}")
|
||||||
|
print(f" • Payoff: {payoff_2:.2f} CHF")
|
||||||
|
print(f" • Profit: {profit_2:.2f} CHF")
|
||||||
|
print()
|
||||||
|
print("="*80)
|
||||||
Binary file not shown.
|
After Width: | Height: | Size: 402 KiB |
@@ -0,0 +1,560 @@
|
|||||||
|
"""
|
||||||
|
Problem Set 2 - Problem 4
|
||||||
|
Domestic Money Demand Analysis
|
||||||
|
"""
|
||||||
|
|
||||||
|
import numpy as np
|
||||||
|
import matplotlib.pyplot as plt
|
||||||
|
|
||||||
|
print("="*80)
|
||||||
|
print("PROBLEM 4: DOMESTIC MONEY DEMAND ANALYSIS")
|
||||||
|
print("="*80)
|
||||||
|
print()
|
||||||
|
|
||||||
|
# Given data
|
||||||
|
R_EUR = 0.05 # German (Eurozone) interest rate
|
||||||
|
E_e_CHF_EUR = 1.1 # Expected exchange rate CHF/EUR
|
||||||
|
P_CHF = 1.0 # Swiss price level
|
||||||
|
P_EUR = 1.0 # German price level
|
||||||
|
M_s_CHF = 200 # Swiss money supply
|
||||||
|
Y_CHF = 100 # Swiss output
|
||||||
|
|
||||||
|
print("GIVEN INFORMATION:")
|
||||||
|
print("-" * 80)
|
||||||
|
print(f"1-year German interest rate: R_EUR = {R_EUR:.3f} ({R_EUR*100:.1f}%)")
|
||||||
|
print(f"Expected exchange rate: E_e_CHF/EUR = {E_e_CHF_EUR:.1f}")
|
||||||
|
print(f"Swiss price level: P_CHF = {P_CHF:.2f}")
|
||||||
|
print(f"German price level: P_EUR = {P_EUR:.2f}")
|
||||||
|
print(f"Swiss money supply: M^s_CHF = {M_s_CHF:.0f}")
|
||||||
|
print(f"Swiss output: Y_CHF = {Y_CHF:.0f}")
|
||||||
|
print()
|
||||||
|
print("Real money demand function in Switzerland:")
|
||||||
|
print(" L(R_CHF, Y_CHF) = 100 + 1.5 × Y_CHF - 5000 × R_CHF")
|
||||||
|
print()
|
||||||
|
|
||||||
|
# Part 1: Find equilibrium Swiss interest rate
|
||||||
|
print("="*80)
|
||||||
|
print("PART 1: EQUILIBRIUM SWISS INTEREST RATE")
|
||||||
|
print("="*80)
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("Money market equilibrium condition:")
|
||||||
|
print(" M^s / P = L(R, Y)")
|
||||||
|
print(" Real money supply = Real money demand")
|
||||||
|
print()
|
||||||
|
|
||||||
|
real_money_supply = M_s_CHF / P_CHF
|
||||||
|
print(f"Real money supply:")
|
||||||
|
print(f" M^s_CHF / P_CHF = {M_s_CHF:.0f} / {P_CHF:.2f} = {real_money_supply:.3f}")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("Real money demand:")
|
||||||
|
print(f" L(R_CHF, Y_CHF) = 100 + 1.5 × {Y_CHF:.0f} - 5000 × R_CHF")
|
||||||
|
print(f" L(R_CHF, Y_CHF) = 100 + {1.5 * Y_CHF:.0f} - 5000 × R_CHF")
|
||||||
|
print(f" L(R_CHF, Y_CHF) = {100 + 1.5 * Y_CHF:.0f} - 5000 × R_CHF")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("Setting M^s/P = L:")
|
||||||
|
print(f" {real_money_supply:.3f} = {100 + 1.5 * Y_CHF:.0f} - 5000 × R_CHF")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("Solving for R_CHF:")
|
||||||
|
print(f" 5000 × R_CHF = {100 + 1.5 * Y_CHF:.0f} - {real_money_supply:.3f}")
|
||||||
|
print(f" 5000 × R_CHF = {100 + 1.5 * Y_CHF - real_money_supply:.3f}")
|
||||||
|
|
||||||
|
R_CHF = (100 + 1.5 * Y_CHF - real_money_supply) / 5000
|
||||||
|
|
||||||
|
print(f" R_CHF = {100 + 1.5 * Y_CHF - real_money_supply:.3f} / 5000")
|
||||||
|
print(f" R_CHF = {R_CHF:.6f}")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print(f"✓ ANSWER: R_CHF = {R_CHF:.3f} or {R_CHF*100:.1f}%")
|
||||||
|
print()
|
||||||
|
|
||||||
|
# Part 2: Find equilibrium spot exchange rate
|
||||||
|
print("="*80)
|
||||||
|
print("PART 2: EQUILIBRIUM SPOT EXCHANGE RATE")
|
||||||
|
print("="*80)
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("We use the Uncovered Interest Parity (UIP) condition:")
|
||||||
|
print(" (E_e - E) / E = R_EUR - R_CHF")
|
||||||
|
print()
|
||||||
|
print("Or equivalently:")
|
||||||
|
print(" E_e / E = 1 + R_EUR - R_CHF")
|
||||||
|
print(" E = E_e / (1 + R_EUR - R_CHF)")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print(f"Calculation:")
|
||||||
|
print(f" E_CHF/EUR = {E_e_CHF_EUR:.1f} / (1 + {R_EUR:.3f} - {R_CHF:.3f})")
|
||||||
|
print(f" E_CHF/EUR = {E_e_CHF_EUR:.1f} / (1 + {R_EUR - R_CHF:.3f})")
|
||||||
|
print(f" E_CHF/EUR = {E_e_CHF_EUR:.1f} / {1 + R_EUR - R_CHF:.3f}")
|
||||||
|
|
||||||
|
E_CHF_EUR = E_e_CHF_EUR / (1 + R_EUR - R_CHF)
|
||||||
|
|
||||||
|
print(f" E_CHF/EUR = {E_CHF_EUR:.3f}")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print(f"✓ ANSWER: E_CHF/EUR = {E_CHF_EUR:.3f}")
|
||||||
|
print()
|
||||||
|
|
||||||
|
# Part 3: Expected appreciation or depreciation
|
||||||
|
print("="*80)
|
||||||
|
print("PART 3: EXPECTED APPRECIATION/DEPRECIATION OF CHF")
|
||||||
|
print("="*80)
|
||||||
|
print()
|
||||||
|
|
||||||
|
print(f"Current spot rate: E_CHF/EUR = {E_CHF_EUR:.3f}")
|
||||||
|
print(f"Expected future rate: E_e_CHF/EUR = {E_e_CHF_EUR:.1f}")
|
||||||
|
print()
|
||||||
|
|
||||||
|
expected_change = E_e_CHF_EUR - E_CHF_EUR
|
||||||
|
pct_change = (expected_change / E_CHF_EUR) * 100
|
||||||
|
|
||||||
|
print(f"Expected change: {E_e_CHF_EUR:.1f} - {E_CHF_EUR:.3f} = {expected_change:.3f}")
|
||||||
|
print(f"Percentage change: {pct_change:.2f}%")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("Interpretation:")
|
||||||
|
if expected_change > 0:
|
||||||
|
print(f" Since E_e > E (expected rate > spot rate):")
|
||||||
|
print(f" • It will take MORE CHF to buy 1 EUR in the future")
|
||||||
|
print(f" • The CHF is expected to DEPRECIATE relative to the EUR")
|
||||||
|
print(f" • The EUR is expected to APPRECIATE relative to the CHF")
|
||||||
|
appreciation_direction = "DEPRECIATION"
|
||||||
|
elif expected_change < 0:
|
||||||
|
print(f" Since E_e < E (expected rate < spot rate):")
|
||||||
|
print(f" • It will take FEWER CHF to buy 1 EUR in the future")
|
||||||
|
print(f" • The CHF is expected to APPRECIATE relative to the EUR")
|
||||||
|
print(f" • The EUR is expected to DEPRECIATE relative to the CHF")
|
||||||
|
appreciation_direction = "APPRECIATION"
|
||||||
|
else:
|
||||||
|
print(f" Since E_e = E (expected rate = spot rate):")
|
||||||
|
print(f" • No change expected")
|
||||||
|
appreciation_direction = "NO CHANGE"
|
||||||
|
print()
|
||||||
|
|
||||||
|
print(f"✓ ANSWER: The market expects a {appreciation_direction} of the CHF")
|
||||||
|
print(f" relative to the EUR by {abs(pct_change):.2f}%")
|
||||||
|
print()
|
||||||
|
|
||||||
|
# Part 4: Temporary increase in output - diagram
|
||||||
|
print("="*80)
|
||||||
|
print("PART 4: TEMPORARY INCREASE IN OUTPUT (Y_CHF = 200)")
|
||||||
|
print("="*80)
|
||||||
|
print()
|
||||||
|
|
||||||
|
Y_1_CHF = 200
|
||||||
|
|
||||||
|
print(f"New output level: Y_1_CHF = {Y_1_CHF:.0f}")
|
||||||
|
print(f"Money supply remains: M^s_CHF = {M_s_CHF:.0f} (central bank does NOT accommodate)")
|
||||||
|
print(f"Expected exchange rate unchanged: E_e = {E_e_CHF_EUR:.1f} (temporary shock)")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("Creating diagram...")
|
||||||
|
print()
|
||||||
|
|
||||||
|
# Create figure with money market (bottom) and forex market (top)
|
||||||
|
fig = plt.figure(figsize=(14, 10))
|
||||||
|
|
||||||
|
# Forex market (top)
|
||||||
|
ax_forex = plt.subplot(2, 1, 1)
|
||||||
|
|
||||||
|
# Interest rate range for forex market
|
||||||
|
R_range_forex = np.linspace(0, 0.10, 100)
|
||||||
|
|
||||||
|
# UIP condition: E = E_e / (1 + R_EUR - R_CHF)
|
||||||
|
E_range_initial = E_e_CHF_EUR / (1 + R_EUR - R_range_forex)
|
||||||
|
|
||||||
|
# Plot FR curve (doesn't shift - expected exchange rate unchanged)
|
||||||
|
ax_forex.plot(R_range_forex * 100, E_range_initial, 'b-', linewidth=2.5, label='FR (Foreign Return)')
|
||||||
|
|
||||||
|
# Initial equilibrium
|
||||||
|
ax_forex.plot(R_CHF * 100, E_CHF_EUR, 'ro', markersize=12, label='Initial Equilibrium', zorder=5)
|
||||||
|
|
||||||
|
# Add equilibrium lines
|
||||||
|
ax_forex.axhline(y=E_CHF_EUR, color='r', linestyle='--', alpha=0.5, linewidth=1)
|
||||||
|
ax_forex.axvline(x=R_CHF * 100, color='r', linestyle='--', alpha=0.5, linewidth=1)
|
||||||
|
|
||||||
|
ax_forex.set_xlabel('Swiss Interest Rate R_CHF (%)', fontsize=11, fontweight='bold')
|
||||||
|
ax_forex.set_ylabel('Exchange Rate E_CHF/EUR', fontsize=11, fontweight='bold')
|
||||||
|
ax_forex.set_title('FOREX MARKET\n(Before Change in Output)', fontsize=13, fontweight='bold')
|
||||||
|
ax_forex.grid(True, alpha=0.3)
|
||||||
|
ax_forex.legend(loc='upper right', fontsize=10)
|
||||||
|
ax_forex.set_xlim([0, 10])
|
||||||
|
ax_forex.set_ylim([0.8, 1.3])
|
||||||
|
|
||||||
|
# Add annotations
|
||||||
|
ax_forex.annotate(f'E₀ = {E_CHF_EUR:.3f}\nR₀ = {R_CHF*100:.1f}%',
|
||||||
|
xy=(R_CHF * 100, E_CHF_EUR),
|
||||||
|
xytext=(R_CHF * 100 + 1.5, E_CHF_EUR + 0.05),
|
||||||
|
fontsize=10,
|
||||||
|
bbox=dict(boxstyle='round,pad=0.5', facecolor='yellow', alpha=0.7),
|
||||||
|
arrowprops=dict(arrowstyle='->', connectionstyle='arc3,rad=0'))
|
||||||
|
|
||||||
|
# Money market (bottom)
|
||||||
|
ax_money = plt.subplot(2, 1, 2)
|
||||||
|
|
||||||
|
# Interest rate range for money market
|
||||||
|
R_range_money = np.linspace(0, 0.10, 100)
|
||||||
|
|
||||||
|
# Initial money demand
|
||||||
|
L_initial = 100 + 1.5 * Y_CHF - 5000 * R_range_money
|
||||||
|
|
||||||
|
# Plot money supply (vertical line)
|
||||||
|
ax_money.axvline(x=real_money_supply, color='g', linewidth=2.5, label=f'M^s/P = {real_money_supply:.0f}')
|
||||||
|
|
||||||
|
# Plot initial money demand
|
||||||
|
ax_money.plot(L_initial, R_range_money * 100, 'b-', linewidth=2.5, label=f'M^d/P (Y={Y_CHF:.0f})')
|
||||||
|
|
||||||
|
# Initial equilibrium
|
||||||
|
ax_money.plot(real_money_supply, R_CHF * 100, 'ro', markersize=12, label='Initial Equilibrium', zorder=5)
|
||||||
|
|
||||||
|
ax_money.set_xlabel('Real Money Balances (M/P)', fontsize=11, fontweight='bold')
|
||||||
|
ax_money.set_ylabel('Swiss Interest Rate R_CHF (%)', fontsize=11, fontweight='bold')
|
||||||
|
ax_money.set_title('MONEY MARKET\n(Before Change in Output)', fontsize=13, fontweight='bold')
|
||||||
|
ax_money.grid(True, alpha=0.3)
|
||||||
|
ax_money.legend(loc='upper right', fontsize=10)
|
||||||
|
ax_money.set_xlim([0, 400])
|
||||||
|
ax_money.set_ylim([0, 10])
|
||||||
|
|
||||||
|
# Add annotations
|
||||||
|
ax_money.annotate(f'R₀ = {R_CHF*100:.1f}%\nM/P = {real_money_supply:.0f}',
|
||||||
|
xy=(real_money_supply, R_CHF * 100),
|
||||||
|
xytext=(real_money_supply + 30, R_CHF * 100 + 1),
|
||||||
|
fontsize=10,
|
||||||
|
bbox=dict(boxstyle='round,pad=0.5', facecolor='yellow', alpha=0.7),
|
||||||
|
arrowprops=dict(arrowstyle='->', connectionstyle='arc3,rad=0'))
|
||||||
|
|
||||||
|
plt.tight_layout()
|
||||||
|
plt.savefig('/home/quinta/Documents/Atlas/Global Business Environment /Problem Set 2/problem4_part4_initial.png',
|
||||||
|
dpi=300, bbox_inches='tight')
|
||||||
|
print("✓ Initial equilibrium diagram saved as 'problem4_part4_initial.png'")
|
||||||
|
|
||||||
|
# Now create the diagram AFTER the output increase
|
||||||
|
print()
|
||||||
|
print("Creating diagram with output increase...")
|
||||||
|
print()
|
||||||
|
|
||||||
|
# Part 5: Solve for new short-run equilibrium
|
||||||
|
print("="*80)
|
||||||
|
print("PART 5: NEW SHORT-RUN EQUILIBRIUM WITH Y_1_CHF = 200")
|
||||||
|
print("="*80)
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("New money market equilibrium:")
|
||||||
|
print(f" M^s / P = L(R_1_CHF, Y_1_CHF)")
|
||||||
|
print(f" {real_money_supply:.0f} = 100 + 1.5 × {Y_1_CHF:.0f} - 5000 × R_1_CHF")
|
||||||
|
print(f" {real_money_supply:.0f} = 100 + {1.5 * Y_1_CHF:.0f} - 5000 × R_1_CHF")
|
||||||
|
print(f" {real_money_supply:.0f} = {100 + 1.5 * Y_1_CHF:.0f} - 5000 × R_1_CHF")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("Solving for R_1_CHF:")
|
||||||
|
print(f" 5000 × R_1_CHF = {100 + 1.5 * Y_1_CHF:.0f} - {real_money_supply:.0f}")
|
||||||
|
print(f" 5000 × R_1_CHF = {100 + 1.5 * Y_1_CHF - real_money_supply:.0f}")
|
||||||
|
|
||||||
|
R_1_CHF = (100 + 1.5 * Y_1_CHF - real_money_supply) / 5000
|
||||||
|
|
||||||
|
print(f" R_1_CHF = {100 + 1.5 * Y_1_CHF - real_money_supply:.0f} / 5000")
|
||||||
|
print(f" R_1_CHF = {R_1_CHF:.6f}")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print(f"New Swiss interest rate: R_1_CHF = {R_1_CHF:.3f} ({R_1_CHF*100:.1f}%)")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("New spot exchange rate (using UIP):")
|
||||||
|
print(f" E_1_CHF/EUR = E_e / (1 + R_EUR - R_1_CHF)")
|
||||||
|
print(f" E_1_CHF/EUR = {E_e_CHF_EUR:.1f} / (1 + {R_EUR:.3f} - {R_1_CHF:.3f})")
|
||||||
|
print(f" E_1_CHF/EUR = {E_e_CHF_EUR:.1f} / {1 + R_EUR - R_1_CHF:.3f}")
|
||||||
|
|
||||||
|
E_1_CHF_EUR = E_e_CHF_EUR / (1 + R_EUR - R_1_CHF)
|
||||||
|
|
||||||
|
print(f" E_1_CHF/EUR = {E_1_CHF_EUR:.3f}")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print(f"✓ ANSWER:")
|
||||||
|
print(f" • New interest rate: R_1_CHF = {R_1_CHF:.3f} ({R_1_CHF*100:.1f}%)")
|
||||||
|
print(f" • New spot exchange rate: E_1_CHF/EUR = {E_1_CHF_EUR:.3f}")
|
||||||
|
print()
|
||||||
|
|
||||||
|
change_R = R_1_CHF - R_CHF
|
||||||
|
change_E = E_1_CHF_EUR - E_CHF_EUR
|
||||||
|
|
||||||
|
print(f"Changes from initial equilibrium:")
|
||||||
|
print(f" • Interest rate change: {change_R:.3f} ({change_R*100:.1f} percentage points)")
|
||||||
|
print(f" • Exchange rate change: {change_E:.3f} ({change_E/E_CHF_EUR*100:.2f}%)")
|
||||||
|
print()
|
||||||
|
|
||||||
|
if change_R > 0:
|
||||||
|
print(f" → Interest rate INCREASED (money demand increased, so rate must rise)")
|
||||||
|
if change_E < 0:
|
||||||
|
print(f" → CHF APPRECIATED (lower E means fewer CHF per EUR)")
|
||||||
|
print()
|
||||||
|
|
||||||
|
# Create new diagram showing the shift
|
||||||
|
fig2 = plt.figure(figsize=(14, 10))
|
||||||
|
|
||||||
|
# Forex market (top) with shift
|
||||||
|
ax_forex2 = plt.subplot(2, 1, 1)
|
||||||
|
|
||||||
|
# FR curve (unchanged)
|
||||||
|
ax_forex2.plot(R_range_forex * 100, E_range_initial, 'b-', linewidth=2.5, label='FR (Foreign Return)')
|
||||||
|
|
||||||
|
# Initial equilibrium
|
||||||
|
ax_forex2.plot(R_CHF * 100, E_CHF_EUR, 'ro', markersize=12, label='Initial Equilibrium', zorder=5)
|
||||||
|
|
||||||
|
# New equilibrium
|
||||||
|
ax_forex2.plot(R_1_CHF * 100, E_1_CHF_EUR, 'go', markersize=12, label='New Equilibrium (Y↑)', zorder=5)
|
||||||
|
|
||||||
|
# Add equilibrium lines
|
||||||
|
ax_forex2.axhline(y=E_CHF_EUR, color='r', linestyle='--', alpha=0.3, linewidth=1)
|
||||||
|
ax_forex2.axvline(x=R_CHF * 100, color='r', linestyle='--', alpha=0.3, linewidth=1)
|
||||||
|
ax_forex2.axhline(y=E_1_CHF_EUR, color='g', linestyle='--', alpha=0.3, linewidth=1)
|
||||||
|
ax_forex2.axvline(x=R_1_CHF * 100, color='g', linestyle='--', alpha=0.3, linewidth=1)
|
||||||
|
|
||||||
|
# Arrow showing movement
|
||||||
|
ax_forex2.annotate('', xy=(R_1_CHF * 100, E_1_CHF_EUR), xytext=(R_CHF * 100, E_CHF_EUR),
|
||||||
|
arrowprops=dict(arrowstyle='->', lw=2.5, color='purple'))
|
||||||
|
|
||||||
|
ax_forex2.set_xlabel('Swiss Interest Rate R_CHF (%)', fontsize=11, fontweight='bold')
|
||||||
|
ax_forex2.set_ylabel('Exchange Rate E_CHF/EUR', fontsize=11, fontweight='bold')
|
||||||
|
ax_forex2.set_title('FOREX MARKET: SHORT-RUN EQUILIBRIUM\n(Temporary Output Increase, No Monetary Accommodation)',
|
||||||
|
fontsize=13, fontweight='bold')
|
||||||
|
ax_forex2.grid(True, alpha=0.3)
|
||||||
|
ax_forex2.legend(loc='upper right', fontsize=10)
|
||||||
|
ax_forex2.set_xlim([0, 10])
|
||||||
|
ax_forex2.set_ylim([0.8, 1.3])
|
||||||
|
|
||||||
|
# Add annotations
|
||||||
|
ax_forex2.annotate(f'Initial\nE₀ = {E_CHF_EUR:.3f}\nR₀ = {R_CHF*100:.1f}%',
|
||||||
|
xy=(R_CHF * 100, E_CHF_EUR),
|
||||||
|
xytext=(R_CHF * 100 - 2, E_CHF_EUR + 0.08),
|
||||||
|
fontsize=9,
|
||||||
|
bbox=dict(boxstyle='round,pad=0.5', facecolor='red', alpha=0.3))
|
||||||
|
|
||||||
|
ax_forex2.annotate(f'New\nE₁ = {E_1_CHF_EUR:.3f}\nR₁ = {R_1_CHF*100:.1f}%',
|
||||||
|
xy=(R_1_CHF * 100, E_1_CHF_EUR),
|
||||||
|
xytext=(R_1_CHF * 100 + 1, E_1_CHF_EUR - 0.08),
|
||||||
|
fontsize=9,
|
||||||
|
bbox=dict(boxstyle='round,pad=0.5', facecolor='green', alpha=0.3))
|
||||||
|
|
||||||
|
# Money market (bottom) with shift
|
||||||
|
ax_money2 = plt.subplot(2, 1, 2)
|
||||||
|
|
||||||
|
# New money demand
|
||||||
|
L_new = 100 + 1.5 * Y_1_CHF - 5000 * R_range_money
|
||||||
|
|
||||||
|
# Plot money supply (vertical line - unchanged)
|
||||||
|
ax_money2.axvline(x=real_money_supply, color='g', linewidth=2.5, label=f'M^s/P = {real_money_supply:.0f}')
|
||||||
|
|
||||||
|
# Plot both money demand curves
|
||||||
|
ax_money2.plot(L_initial, R_range_money * 100, 'b--', linewidth=2, alpha=0.6, label=f'M^d/P (Y₀={Y_CHF:.0f})')
|
||||||
|
ax_money2.plot(L_new, R_range_money * 100, 'b-', linewidth=2.5, label=f'M^d/P (Y₁={Y_1_CHF:.0f})')
|
||||||
|
|
||||||
|
# Equilibria
|
||||||
|
ax_money2.plot(real_money_supply, R_CHF * 100, 'ro', markersize=12, label='Initial Equilibrium', zorder=5)
|
||||||
|
ax_money2.plot(real_money_supply, R_1_CHF * 100, 'go', markersize=12, label='New Equilibrium', zorder=5)
|
||||||
|
|
||||||
|
# Arrow showing shift
|
||||||
|
ax_money2.annotate('', xy=(250, 5), xytext=(150, 5),
|
||||||
|
arrowprops=dict(arrowstyle='->', lw=2.5, color='blue'))
|
||||||
|
ax_money2.text(200, 5.5, 'M^d shifts right\n(Y increases)', fontsize=9, ha='center',
|
||||||
|
bbox=dict(boxstyle='round,pad=0.3', facecolor='cyan', alpha=0.3))
|
||||||
|
|
||||||
|
ax_money2.set_xlabel('Real Money Balances (M/P)', fontsize=11, fontweight='bold')
|
||||||
|
ax_money2.set_ylabel('Swiss Interest Rate R_CHF (%)', fontsize=11, fontweight='bold')
|
||||||
|
ax_money2.set_title('MONEY MARKET: SHORT-RUN EQUILIBRIUM\n(Temporary Output Increase, No Monetary Accommodation)',
|
||||||
|
fontsize=13, fontweight='bold')
|
||||||
|
ax_money2.grid(True, alpha=0.3)
|
||||||
|
ax_money2.legend(loc='upper right', fontsize=10)
|
||||||
|
ax_money2.set_xlim([0, 500])
|
||||||
|
ax_money2.set_ylim([0, 10])
|
||||||
|
|
||||||
|
# Add annotations
|
||||||
|
ax_money2.annotate(f'R₀ = {R_CHF*100:.1f}%',
|
||||||
|
xy=(real_money_supply, R_CHF * 100),
|
||||||
|
xytext=(real_money_supply + 40, R_CHF * 100),
|
||||||
|
fontsize=9,
|
||||||
|
bbox=dict(boxstyle='round,pad=0.3', facecolor='red', alpha=0.3),
|
||||||
|
arrowprops=dict(arrowstyle='->', connectionstyle='arc3,rad=0.3'))
|
||||||
|
|
||||||
|
ax_money2.annotate(f'R₁ = {R_1_CHF*100:.1f}%',
|
||||||
|
xy=(real_money_supply, R_1_CHF * 100),
|
||||||
|
xytext=(real_money_supply + 40, R_1_CHF * 100),
|
||||||
|
fontsize=9,
|
||||||
|
bbox=dict(boxstyle='round,pad=0.3', facecolor='green', alpha=0.3),
|
||||||
|
arrowprops=dict(arrowstyle='->', connectionstyle='arc3,rad=0.3'))
|
||||||
|
|
||||||
|
plt.tight_layout()
|
||||||
|
plt.savefig('/home/quinta/Documents/Atlas/Global Business Environment /Problem Set 2/problem4_part4_no_accommodation.png',
|
||||||
|
dpi=300, bbox_inches='tight')
|
||||||
|
print("✓ Diagram saved as 'problem4_part4_no_accommodation.png'")
|
||||||
|
|
||||||
|
# Part 6: With monetary accommodation
|
||||||
|
print()
|
||||||
|
print("="*80)
|
||||||
|
print("PART 6: WITH MONETARY ACCOMMODATION")
|
||||||
|
print("="*80)
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("If the central bank ACCOMMODATES the change in money demand:")
|
||||||
|
print(" • Money supply increases to keep interest rate constant")
|
||||||
|
print(" • R_CHF remains at R₀")
|
||||||
|
print(" • Exchange rate remains at E₀")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("Creating diagram with accommodation...")
|
||||||
|
print()
|
||||||
|
|
||||||
|
# Part 7: Calculate new money supply
|
||||||
|
print("="*80)
|
||||||
|
print("PART 7: NEW MONEY SUPPLY WITH ACCOMMODATION")
|
||||||
|
print("="*80)
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("With accommodation, the central bank maintains R_CHF = R₀")
|
||||||
|
print(f" R_CHF = {R_CHF:.3f}")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("New money market equilibrium:")
|
||||||
|
print(f" M^s,1 / P = L(R_CHF, Y_1_CHF)")
|
||||||
|
print(f" M^s,1 / {P_CHF:.2f} = 100 + 1.5 × {Y_1_CHF:.0f} - 5000 × {R_CHF:.3f}")
|
||||||
|
print(f" M^s,1 / {P_CHF:.2f} = 100 + {1.5 * Y_1_CHF:.0f} - {5000 * R_CHF:.0f}")
|
||||||
|
print(f" M^s,1 / {P_CHF:.2f} = {100 + 1.5 * Y_1_CHF - 5000 * R_CHF:.0f}")
|
||||||
|
print()
|
||||||
|
|
||||||
|
M_s_1_CHF = (100 + 1.5 * Y_1_CHF - 5000 * R_CHF) * P_CHF
|
||||||
|
|
||||||
|
print(f" M^s,1 = {100 + 1.5 * Y_1_CHF - 5000 * R_CHF:.0f} × {P_CHF:.2f}")
|
||||||
|
print(f" M^s,1 = {M_s_1_CHF:.0f}")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print(f"✓ ANSWER: M^s,1_CHF = {M_s_1_CHF:.0f}")
|
||||||
|
print()
|
||||||
|
|
||||||
|
change_M = M_s_1_CHF - M_s_CHF
|
||||||
|
|
||||||
|
print(f"Change in money supply: ΔM^s = {M_s_1_CHF:.0f} - {M_s_CHF:.0f} = {change_M:.0f}")
|
||||||
|
print()
|
||||||
|
|
||||||
|
print("Do the spot exchange rate and interest rate change?")
|
||||||
|
print(" • Interest rate: NO CHANGE (R₁ = R₀ = {:.3f})".format(R_CHF))
|
||||||
|
print(" • Exchange rate: NO CHANGE (E₁ = E₀ = {:.3f})".format(E_CHF_EUR))
|
||||||
|
print()
|
||||||
|
print(" The central bank's monetary accommodation prevents any change in")
|
||||||
|
print(" the interest rate, which (via UIP) prevents any change in the")
|
||||||
|
print(" exchange rate.")
|
||||||
|
print()
|
||||||
|
|
||||||
|
# Create diagram with accommodation
|
||||||
|
fig3 = plt.figure(figsize=(14, 10))
|
||||||
|
|
||||||
|
# Forex market (top) - no change
|
||||||
|
ax_forex3 = plt.subplot(2, 1, 1)
|
||||||
|
|
||||||
|
# FR curve
|
||||||
|
ax_forex3.plot(R_range_forex * 100, E_range_initial, 'b-', linewidth=2.5, label='FR (Foreign Return)')
|
||||||
|
|
||||||
|
# Equilibrium (stays the same)
|
||||||
|
ax_forex3.plot(R_CHF * 100, E_CHF_EUR, 'ro', markersize=12, label='Equilibrium (unchanged)', zorder=5)
|
||||||
|
|
||||||
|
# Add equilibrium lines
|
||||||
|
ax_forex3.axhline(y=E_CHF_EUR, color='r', linestyle='--', alpha=0.5, linewidth=1)
|
||||||
|
ax_forex3.axvline(x=R_CHF * 100, color='r', linestyle='--', alpha=0.5, linewidth=1)
|
||||||
|
|
||||||
|
ax_forex3.set_xlabel('Swiss Interest Rate R_CHF (%)', fontsize=11, fontweight='bold')
|
||||||
|
ax_forex3.set_ylabel('Exchange Rate E_CHF/EUR', fontsize=11, fontweight='bold')
|
||||||
|
ax_forex3.set_title('FOREX MARKET: SHORT-RUN EQUILIBRIUM\n(With Monetary Accommodation - No Change)',
|
||||||
|
fontsize=13, fontweight='bold')
|
||||||
|
ax_forex3.grid(True, alpha=0.3)
|
||||||
|
ax_forex3.legend(loc='upper right', fontsize=10)
|
||||||
|
ax_forex3.set_xlim([0, 10])
|
||||||
|
ax_forex3.set_ylim([0.8, 1.3])
|
||||||
|
|
||||||
|
# Add annotation
|
||||||
|
ax_forex3.annotate(f'E = {E_CHF_EUR:.3f}\nR = {R_CHF*100:.1f}%\n(UNCHANGED)',
|
||||||
|
xy=(R_CHF * 100, E_CHF_EUR),
|
||||||
|
xytext=(R_CHF * 100 + 2, E_CHF_EUR + 0.08),
|
||||||
|
fontsize=10,
|
||||||
|
bbox=dict(boxstyle='round,pad=0.5', facecolor='yellow', alpha=0.7),
|
||||||
|
arrowprops=dict(arrowstyle='->', connectionstyle='arc3,rad=0'))
|
||||||
|
|
||||||
|
# Money market (bottom) - both supply and demand shift
|
||||||
|
ax_money3 = plt.subplot(2, 1, 2)
|
||||||
|
|
||||||
|
new_real_money_supply = M_s_1_CHF / P_CHF
|
||||||
|
|
||||||
|
# Plot both money supply lines
|
||||||
|
ax_money3.axvline(x=real_money_supply, color='g', linestyle='--', linewidth=2, alpha=0.6,
|
||||||
|
label=f'M^s₀/P = {real_money_supply:.0f}')
|
||||||
|
ax_money3.axvline(x=new_real_money_supply, color='g', linewidth=2.5,
|
||||||
|
label=f'M^s₁/P = {new_real_money_supply:.0f}')
|
||||||
|
|
||||||
|
# Plot both money demand curves
|
||||||
|
ax_money3.plot(L_initial, R_range_money * 100, 'b--', linewidth=2, alpha=0.6, label=f'M^d/P (Y₀={Y_CHF:.0f})')
|
||||||
|
ax_money3.plot(L_new, R_range_money * 100, 'b-', linewidth=2.5, label=f'M^d/P (Y₁={Y_1_CHF:.0f})')
|
||||||
|
|
||||||
|
# Equilibria (both at same interest rate)
|
||||||
|
ax_money3.plot(real_money_supply, R_CHF * 100, 'ro', markersize=10, alpha=0.6, label='Initial Equilibrium', zorder=5)
|
||||||
|
ax_money3.plot(new_real_money_supply, R_CHF * 100, 'go', markersize=12, label='New Equilibrium', zorder=5)
|
||||||
|
|
||||||
|
# Arrows showing shifts
|
||||||
|
ax_money3.annotate('M^d shifts\nright', xy=(270, 3), xytext=(230, 3.8),
|
||||||
|
arrowprops=dict(arrowstyle='->', lw=2, color='blue'),
|
||||||
|
fontsize=9, bbox=dict(boxstyle='round,pad=0.3', facecolor='cyan', alpha=0.3))
|
||||||
|
|
||||||
|
ax_money3.annotate('M^s shifts\nright', xy=(300, 7), xytext=(260, 7.8),
|
||||||
|
arrowprops=dict(arrowstyle='->', lw=2, color='green'),
|
||||||
|
fontsize=9, bbox=dict(boxstyle='round,pad=0.3', facecolor='lightgreen', alpha=0.3))
|
||||||
|
|
||||||
|
ax_money3.set_xlabel('Real Money Balances (M/P)', fontsize=11, fontweight='bold')
|
||||||
|
ax_money3.set_ylabel('Swiss Interest Rate R_CHF (%)', fontsize=11, fontweight='bold')
|
||||||
|
ax_money3.set_title('MONEY MARKET: SHORT-RUN EQUILIBRIUM\n(With Monetary Accommodation - Both Curves Shift)',
|
||||||
|
fontsize=13, fontweight='bold')
|
||||||
|
ax_money3.grid(True, alpha=0.3)
|
||||||
|
ax_money3.legend(loc='upper right', fontsize=9)
|
||||||
|
ax_money3.set_xlim([0, 500])
|
||||||
|
ax_money3.set_ylim([0, 10])
|
||||||
|
|
||||||
|
# Add annotation showing rate stays constant
|
||||||
|
ax_money3.axhline(y=R_CHF * 100, color='orange', linestyle=':', linewidth=2, alpha=0.7)
|
||||||
|
ax_money3.text(250, R_CHF * 100 + 0.5, f'R = {R_CHF*100:.1f}% (CONSTANT)',
|
||||||
|
fontsize=10, ha='center',
|
||||||
|
bbox=dict(boxstyle='round,pad=0.4', facecolor='orange', alpha=0.5))
|
||||||
|
|
||||||
|
plt.tight_layout()
|
||||||
|
plt.savefig('/home/quinta/Documents/Atlas/Global Business Environment /Problem Set 2/problem4_part6_accommodation.png',
|
||||||
|
dpi=300, bbox_inches='tight')
|
||||||
|
print("✓ Diagram saved as 'problem4_part6_accommodation.png'")
|
||||||
|
|
||||||
|
plt.show()
|
||||||
|
|
||||||
|
print()
|
||||||
|
print("="*80)
|
||||||
|
print("SUMMARY OF ALL ANSWERS - PROBLEM 4")
|
||||||
|
print("="*80)
|
||||||
|
print()
|
||||||
|
print(f"1. Equilibrium Swiss interest rate: R_CHF = {R_CHF:.3f} ({R_CHF*100:.1f}%)")
|
||||||
|
print()
|
||||||
|
print(f"2. Equilibrium spot exchange rate: E_CHF/EUR = {E_CHF_EUR:.3f}")
|
||||||
|
print()
|
||||||
|
print(f"3. Expected movement: CHF expected to {appreciation_direction.upper()}")
|
||||||
|
print(f" by {abs(pct_change):.2f}% relative to EUR")
|
||||||
|
print()
|
||||||
|
print(f"4. Diagram created showing initial equilibrium (see graph)")
|
||||||
|
print()
|
||||||
|
print(f"5. New short-run equilibrium (Y₁ = {Y_1_CHF}, no accommodation):")
|
||||||
|
print(f" • R_1_CHF = {R_1_CHF:.3f} ({R_1_CHF*100:.1f}%)")
|
||||||
|
print(f" • E_1_CHF/EUR = {E_1_CHF_EUR:.3f}")
|
||||||
|
print(f" • Interest rate increased by {change_R*100:.1f} percentage points")
|
||||||
|
print(f" • CHF appreciated by {abs(change_E/E_CHF_EUR*100):.2f}%")
|
||||||
|
print()
|
||||||
|
print(f"6. Diagram created showing equilibrium with no accommodation (see graph)")
|
||||||
|
print()
|
||||||
|
print(f"7. New money supply with accommodation: M^s,1_CHF = {M_s_1_CHF:.0f}")
|
||||||
|
print(f" • Money supply increases by {change_M:.0f}")
|
||||||
|
print(f" • Interest rate: NO CHANGE (R = {R_CHF:.3f})")
|
||||||
|
print(f" • Exchange rate: NO CHANGE (E = {E_CHF_EUR:.3f})")
|
||||||
|
print(f" • Diagram created (see graph)")
|
||||||
|
print()
|
||||||
|
print("="*80)
|
||||||
Binary file not shown.
|
After Width: | Height: | Size: 295 KiB |
Binary file not shown.
|
After Width: | Height: | Size: 423 KiB |
Binary file not shown.
|
After Width: | Height: | Size: 413 KiB |
@@ -0,0 +1,128 @@
|
|||||||
|
"""
|
||||||
|
Problem Set 2 - Master Script
|
||||||
|
Run all problems at once
|
||||||
|
"""
|
||||||
|
|
||||||
|
import subprocess
|
||||||
|
import sys
|
||||||
|
import os
|
||||||
|
|
||||||
|
# Get the directory where this script is located
|
||||||
|
script_dir = os.path.dirname(os.path.abspath(__file__))
|
||||||
|
|
||||||
|
print("="*80)
|
||||||
|
print("PROBLEM SET 2 - GLOBAL BUSINESS ENVIRONMENT")
|
||||||
|
print("Exchange Rates, Forward Rates, Options, and Money Demand")
|
||||||
|
print("="*80)
|
||||||
|
print()
|
||||||
|
|
||||||
|
problems = [
|
||||||
|
("Problem 1, Part 1: Exchange Rate Risk Analysis", "problem1_part1_analysis.py"),
|
||||||
|
("Problem 1, Part 2: Switzerland Exchange Rate Data", "problem1_part2_switzerland.py"),
|
||||||
|
("Problem 2: Forward Exchange Rate Analysis", "problem2_forward_rate.py"),
|
||||||
|
("Problem 3: Put Option Analysis", "problem3_put_option.py"),
|
||||||
|
("Problem 4: Domestic Money Demand", "problem4_money_demand.py")
|
||||||
|
]
|
||||||
|
|
||||||
|
def run_problem(name, filename):
|
||||||
|
"""Run a single problem script"""
|
||||||
|
print("\n" + "="*80)
|
||||||
|
print(f"RUNNING: {name}")
|
||||||
|
print("="*80)
|
||||||
|
print()
|
||||||
|
|
||||||
|
filepath = os.path.join(script_dir, filename)
|
||||||
|
|
||||||
|
if not os.path.exists(filepath):
|
||||||
|
print(f"❌ ERROR: File not found: {filepath}")
|
||||||
|
return False
|
||||||
|
|
||||||
|
try:
|
||||||
|
result = subprocess.run(
|
||||||
|
[sys.executable, filepath],
|
||||||
|
cwd=script_dir,
|
||||||
|
capture_output=False,
|
||||||
|
text=True
|
||||||
|
)
|
||||||
|
|
||||||
|
if result.returncode == 0:
|
||||||
|
print()
|
||||||
|
print(f"✓ {name} completed successfully")
|
||||||
|
return True
|
||||||
|
else:
|
||||||
|
print(f"❌ {name} failed with return code {result.returncode}")
|
||||||
|
return False
|
||||||
|
|
||||||
|
except Exception as e:
|
||||||
|
print(f"❌ Error running {name}: {e}")
|
||||||
|
return False
|
||||||
|
|
||||||
|
def main():
|
||||||
|
"""Run all problem scripts"""
|
||||||
|
print("This script will run all problem solutions in sequence.")
|
||||||
|
print()
|
||||||
|
|
||||||
|
response = input("Do you want to run all problems? (y/n): ").strip().lower()
|
||||||
|
|
||||||
|
if response != 'y':
|
||||||
|
print("\nYou can run individual problems using:")
|
||||||
|
for name, filename in problems:
|
||||||
|
print(f" python {filename}")
|
||||||
|
return
|
||||||
|
|
||||||
|
print("\nStarting problem set execution...")
|
||||||
|
print()
|
||||||
|
|
||||||
|
results = {}
|
||||||
|
|
||||||
|
for name, filename in problems:
|
||||||
|
success = run_problem(name, filename)
|
||||||
|
results[name] = success
|
||||||
|
|
||||||
|
# Add a pause between problems
|
||||||
|
if filename != problems[-1][1]: # Not the last problem
|
||||||
|
print("\n" + "-"*80)
|
||||||
|
input("Press Enter to continue to next problem...")
|
||||||
|
|
||||||
|
# Summary
|
||||||
|
print("\n" + "="*80)
|
||||||
|
print("EXECUTION SUMMARY")
|
||||||
|
print("="*80)
|
||||||
|
print()
|
||||||
|
|
||||||
|
for name, success in results.items():
|
||||||
|
status = "✓ COMPLETED" if success else "❌ FAILED"
|
||||||
|
print(f"{status}: {name}")
|
||||||
|
|
||||||
|
total = len(results)
|
||||||
|
successful = sum(1 for s in results.values() if s)
|
||||||
|
|
||||||
|
print()
|
||||||
|
print(f"Total: {successful}/{total} problems completed successfully")
|
||||||
|
print()
|
||||||
|
|
||||||
|
if successful == total:
|
||||||
|
print("🎉 All problems completed successfully!")
|
||||||
|
else:
|
||||||
|
print("⚠️ Some problems encountered errors. Please review the output above.")
|
||||||
|
|
||||||
|
print()
|
||||||
|
print("="*80)
|
||||||
|
print("FILES CREATED:")
|
||||||
|
print("="*80)
|
||||||
|
print()
|
||||||
|
print("Python Scripts:")
|
||||||
|
for _, filename in problems:
|
||||||
|
print(f" • {filename}")
|
||||||
|
print()
|
||||||
|
print("Generated Outputs:")
|
||||||
|
print(" • switzerland_exchange_rate.png")
|
||||||
|
print(" • problem3_put_option_diagrams.png")
|
||||||
|
print(" • problem4_part4_initial.png")
|
||||||
|
print(" • problem4_part4_no_accommodation.png")
|
||||||
|
print(" • problem4_part6_accommodation.png")
|
||||||
|
print()
|
||||||
|
print("="*80)
|
||||||
|
|
||||||
|
if __name__ == "__main__":
|
||||||
|
main()
|
||||||
Binary file not shown.
|
After Width: | Height: | Size: 301 KiB |
@@ -0,0 +1,267 @@
|
|||||||
|
# Monetary Policy Interactive Diagram
|
||||||
|
|
||||||
|
## Overview
|
||||||
|
|
||||||
|
This interactive React component provides a comprehensive educational tool for understanding monetary policy transmission mechanisms, covering key concepts from the Global Business Environment course.
|
||||||
|
|
||||||
|
## Features
|
||||||
|
|
||||||
|
### 1. **Three Policy Scenarios**
|
||||||
|
- **Monetary Expansion**: Visualizes how increasing money supply affects interest rates, exchange rates, and the real economy
|
||||||
|
- **Monetary Contraction**: Shows the opposite effects of decreasing money supply
|
||||||
|
- **Taylor Rule**: Demonstrates how central banks systematically respond to inflation and output gaps
|
||||||
|
|
||||||
|
### 2. **Interactive Graphs**
|
||||||
|
The component includes four interactive visualizations:
|
||||||
|
|
||||||
|
#### a) Money Market Equilibrium
|
||||||
|
- **Concept**: Shows how money supply (Ms) and money demand L(R,Y) determine the equilibrium interest rate
|
||||||
|
- **Formula**: Ms/P = L(R,Y) = k₁Y - k₂R
|
||||||
|
- **Interactive Elements**:
|
||||||
|
- Adjust money supply to see how interest rate responds
|
||||||
|
- Modify real income to shift money demand
|
||||||
|
- **Key Insight**: When Ms ↑, the interest rate R ↓ to restore equilibrium
|
||||||
|
|
||||||
|
#### b) Interest Parity & Exchange Rate (UIP)
|
||||||
|
- **Concept**: Uncovered Interest Parity shows how interest rate differentials drive exchange rate movements
|
||||||
|
- **Formula**: R_CHF = R_EUR + (E^e - E)/E
|
||||||
|
- **Interactive Elements**:
|
||||||
|
- Compare domestic vs. foreign interest rates
|
||||||
|
- See how rate differentials affect currency strength
|
||||||
|
- **Key Insight**: Higher domestic rates → currency appreciates (E ↓)
|
||||||
|
|
||||||
|
#### c) Taylor Rule Policy Response
|
||||||
|
- **Concept**: Central bank's systematic monetary policy reaction function
|
||||||
|
- **Formula**: R = R* + 1.5(π - π*) + 0.5(y - y*)
|
||||||
|
- **Interactive Elements**:
|
||||||
|
- Adjust inflation to see policy rate response
|
||||||
|
- Modify output gap to see counter-cyclical response
|
||||||
|
- **Key Insight**: The coefficient 1.5 on inflation ensures real rates rise when inflation increases
|
||||||
|
|
||||||
|
#### d) GDP Components Impact
|
||||||
|
- **Concept**: Shows how monetary policy affects different components of GDP
|
||||||
|
- **Formula**: Y = C + I + G + NX
|
||||||
|
- **Interactive Elements**:
|
||||||
|
- See how interest rate changes affect consumption (C) and investment (I)
|
||||||
|
- Observe exchange rate effects on net exports (NX)
|
||||||
|
- **Key Insight**: Investment is most sensitive to interest rate changes
|
||||||
|
|
||||||
|
### 3. **Core Economic Relationships**
|
||||||
|
|
||||||
|
The component displays four fundamental identities:
|
||||||
|
|
||||||
|
1. **Money Market Equilibrium**: Ms/P = L(R, Y)
|
||||||
|
2. **Uncovered Interest Parity**: R_CHF = R_EUR + (E^e - E)/E
|
||||||
|
3. **Taylor Rule**: R = R* + f_π(π - π*) + f_y(y - y*)
|
||||||
|
4. **National Income Identity**: Y = C + I + G + CA
|
||||||
|
|
||||||
|
Also shows the savings identity: **CA = (S_p - I) + (T - G)**
|
||||||
|
|
||||||
|
### 4. **Transmission Channels**
|
||||||
|
|
||||||
|
Three main channels through which monetary policy affects the economy:
|
||||||
|
|
||||||
|
1. **Interest Rate Channel**
|
||||||
|
- Policy Rate ↑ → All Rates ↑ → Borrowing Costs ↑ → Investment ↓ & Consumption ↓ → AD ↓
|
||||||
|
|
||||||
|
2. **Exchange Rate Channel**
|
||||||
|
- R_domestic ↑ → Currency Appreciates → Exports ↓ & Imports ↑ → Net Exports ↓ → AD ↓
|
||||||
|
|
||||||
|
3. **Wealth/Asset Channel**
|
||||||
|
- Interest Rates ↑ → Bond & Stock Prices ↓ → Household Wealth ↓ → Consumption ↓ → AD ↓
|
||||||
|
|
||||||
|
## Usage Instructions
|
||||||
|
|
||||||
|
### Setting Up
|
||||||
|
|
||||||
|
1. **Prerequisites**:
|
||||||
|
```bash
|
||||||
|
npm install react lucide-react
|
||||||
|
```
|
||||||
|
|
||||||
|
2. **Import the component**:
|
||||||
|
```jsx
|
||||||
|
import MonetaryPolicyDiagram from './MonetaryPolicyDiagram';
|
||||||
|
```
|
||||||
|
|
||||||
|
3. **Add Tailwind CSS** to your project for styling
|
||||||
|
|
||||||
|
### Interactive Scenarios
|
||||||
|
|
||||||
|
Try these scenarios to understand different economic situations:
|
||||||
|
|
||||||
|
#### Scenario 1: Fighting Inflation (Hawkish Policy)
|
||||||
|
1. Set Inflation to 4%
|
||||||
|
2. Set Output Gap to 2% (economy overheating)
|
||||||
|
3. Observe:
|
||||||
|
- Taylor Rule prescribes R = 2% + 1.5(2%) + 0.5(2%) = 6%
|
||||||
|
- Real rate = 6% - 4% = 2%
|
||||||
|
- This tight policy cools the economy
|
||||||
|
|
||||||
|
#### Scenario 2: Recession Response (Dovish Policy)
|
||||||
|
1. Set Money Supply to 130
|
||||||
|
2. Set Output Gap to -3%
|
||||||
|
3. Set Inflation to 1%
|
||||||
|
4. Observe:
|
||||||
|
- Interest rate falls
|
||||||
|
- Currency depreciates (E ↑)
|
||||||
|
- Net exports become more competitive
|
||||||
|
- Taylor Rule suggests low rates to stimulate economy
|
||||||
|
|
||||||
|
#### Scenario 3: Foreign Rate Shock
|
||||||
|
1. Increase Foreign Interest Rate to 4%
|
||||||
|
2. Keep domestic settings constant
|
||||||
|
3. Observe:
|
||||||
|
- Domestic currency appreciates
|
||||||
|
- Net exports decline
|
||||||
|
- This illustrates the constraint on monetary policy in open economies
|
||||||
|
|
||||||
|
#### Scenario 4: Income Growth
|
||||||
|
1. Increase Real Income (Y) to 130
|
||||||
|
2. Keep Money Supply constant at 100
|
||||||
|
3. Observe:
|
||||||
|
- Money demand increases
|
||||||
|
- Interest rate rises to clear the money market
|
||||||
|
- This shows the endogenous response of interest rates to growth
|
||||||
|
|
||||||
|
## Theoretical Concepts Illustrated
|
||||||
|
|
||||||
|
### 1. Money Market Mechanics
|
||||||
|
The money market graph shows:
|
||||||
|
- **Money Demand Curve** (downward sloping): Higher interest rates reduce money demand
|
||||||
|
- **Money Supply** (vertical line): Set exogenously by the central bank
|
||||||
|
- **Equilibrium**: Where supply meets demand
|
||||||
|
|
||||||
|
### 2. Interest Parity Condition
|
||||||
|
The UIP graph illustrates:
|
||||||
|
- How arbitrage keeps returns equalized across currencies
|
||||||
|
- Why interest rate differentials drive exchange rate expectations
|
||||||
|
- The inverse relationship between domestic rates and exchange rates
|
||||||
|
|
||||||
|
### 3. Taylor Principle
|
||||||
|
The Taylor Rule graph demonstrates:
|
||||||
|
- **f_π > 1**: Crucial for stability - nominal rate must rise more than inflation
|
||||||
|
- **Counter-cyclical policy**: Positive output gap → tighten; negative gap → loosen
|
||||||
|
- The systematic, predictable nature of modern monetary policy
|
||||||
|
|
||||||
|
### 4. National Accounting Identities
|
||||||
|
The component emphasizes:
|
||||||
|
- **Twin Deficits**: Government deficit (T-G < 0) often correlates with current account deficit (CA < 0)
|
||||||
|
- **Savings Identity**: CA = (S_p - I) + (T - G)
|
||||||
|
- How private savings collapse (observed in US data after 1990) affects the current account
|
||||||
|
|
||||||
|
## Educational Applications
|
||||||
|
|
||||||
|
### For Students:
|
||||||
|
- **Before Class**: Explore basic scenarios to build intuition
|
||||||
|
- **During Class**: Use alongside lectures to visualize theoretical concepts
|
||||||
|
- **After Class**: Test understanding by predicting effects before adjusting sliders
|
||||||
|
|
||||||
|
### For Instructors:
|
||||||
|
- **Lectures**: Project the interactive graphs during explanations
|
||||||
|
- **Problem Sets**: Reference specific parameter combinations
|
||||||
|
- **Exams**: Ask students to predict outcomes for given policy changes
|
||||||
|
|
||||||
|
## Real-World Applications
|
||||||
|
|
||||||
|
### Central Bank Policy
|
||||||
|
The component helps understand:
|
||||||
|
- Why central banks raise rates aggressively when inflation rises
|
||||||
|
- How exchange rate movements amplify or dampen monetary policy
|
||||||
|
- The trade-offs between inflation control and output stabilization
|
||||||
|
|
||||||
|
### Historical Episodes
|
||||||
|
Can be used to analyze:
|
||||||
|
- **2008 Financial Crisis**: Low rates, near-zero lower bound
|
||||||
|
- **2020 COVID Response**: Massive monetary expansion
|
||||||
|
- **2022-2023 Inflation**: Aggressive rate hiking cycle
|
||||||
|
- **1990s US Economy**: Twin deficits and private savings collapse (from Problem Set 1)
|
||||||
|
|
||||||
|
## Technical Details
|
||||||
|
|
||||||
|
### Key Parameters
|
||||||
|
- **k₁ = 0.5**: Income elasticity of money demand
|
||||||
|
- **k₂ = 20**: Interest rate semi-elasticity of money demand
|
||||||
|
- **R* = 2%**: Equilibrium/neutral interest rate
|
||||||
|
- **f_π = 1.5**: Taylor Rule inflation coefficient (must be > 1)
|
||||||
|
- **f_y = 0.5**: Taylor Rule output gap coefficient
|
||||||
|
- **π* = 2%**: Inflation target
|
||||||
|
|
||||||
|
### Calculation Methods
|
||||||
|
```javascript
|
||||||
|
// Interest Rate from Money Market
|
||||||
|
R = (k₁ × Y - Ms) / k₂
|
||||||
|
|
||||||
|
// Exchange Rate from UIP (simplified)
|
||||||
|
E = base × exp(-0.1 × (R_domestic - R_foreign))
|
||||||
|
|
||||||
|
// Taylor Rule
|
||||||
|
R = R* + f_π × (π - π*) + f_y × (y - y*)
|
||||||
|
|
||||||
|
// GDP Impact
|
||||||
|
C = baseline + rate_effect × 0.3
|
||||||
|
I = baseline + rate_effect × 1.0 // Most sensitive
|
||||||
|
NX = baseline + exchange_rate_effect
|
||||||
|
```
|
||||||
|
|
||||||
|
## Connection to Course Material
|
||||||
|
|
||||||
|
### From Problem Set 1 (Twin Deficits)
|
||||||
|
The component incorporates findings from the US data analysis (1960-2024):
|
||||||
|
- National accounting identity: **CA = (S_p - I) + (T - G)**
|
||||||
|
- Correlation between government and current account deficits
|
||||||
|
- The role of private savings in determining the current account
|
||||||
|
- How the relationship changed after 1990 due to private savings collapse
|
||||||
|
|
||||||
|
### Key Empirical Insights:
|
||||||
|
- Before 1990: Strong correlation (r = 0.82) between budget and CA deficits
|
||||||
|
- After 1990: Weaker correlation (r = 0.53) but larger structural deficits
|
||||||
|
- Private savings declined from 8.05% to 4.67% of GDP
|
||||||
|
- This made the US more dependent on foreign capital
|
||||||
|
|
||||||
|
## Pedagogical Benefits
|
||||||
|
|
||||||
|
1. **Visual Learning**: Graphs update in real-time as parameters change
|
||||||
|
2. **Causal Understanding**: Clear transmission channels show how policy affects outcomes
|
||||||
|
3. **Quantitative Intuition**: Numerical values help students calibrate magnitudes
|
||||||
|
4. **Multiple Representations**: Same concepts shown through flows, graphs, and formulas
|
||||||
|
5. **Active Learning**: Students engage by testing predictions
|
||||||
|
|
||||||
|
## Limitations & Simplifications
|
||||||
|
|
||||||
|
1. **Static Analysis**: No dynamics or lags in the model
|
||||||
|
2. **Simplified UIP**: Assumes static exchange rate expectations
|
||||||
|
3. **Linear Relationships**: Real economy has non-linearities
|
||||||
|
4. **Closed Form Solutions**: Actual models are more complex
|
||||||
|
5. **Omitted Channels**: Credit channel, expectations channel not explicitly modeled
|
||||||
|
|
||||||
|
## Extensions & Future Work
|
||||||
|
|
||||||
|
Potential enhancements:
|
||||||
|
- Add IS-LM-BP model for simultaneous equilibrium
|
||||||
|
- Include Phillips Curve for inflation dynamics
|
||||||
|
- Add expectations formation mechanisms
|
||||||
|
- Show impulse response functions over time
|
||||||
|
- Include financial frictions and credit markets
|
||||||
|
|
||||||
|
## References
|
||||||
|
|
||||||
|
Based on course material covering:
|
||||||
|
- Money market equilibrium
|
||||||
|
- Uncovered Interest Parity (UIP)
|
||||||
|
- Taylor Rule monetary policy
|
||||||
|
- National income accounting
|
||||||
|
- Monetary policy transmission mechanisms
|
||||||
|
- Twin deficits hypothesis
|
||||||
|
- Open economy macroeconomics
|
||||||
|
|
||||||
|
## Conclusion
|
||||||
|
|
||||||
|
This interactive tool bridges theory and practice, allowing students to:
|
||||||
|
- **Visualize** abstract economic concepts
|
||||||
|
- **Experiment** with policy scenarios
|
||||||
|
- **Understand** transmission mechanisms
|
||||||
|
- **Connect** micro foundations to macro outcomes
|
||||||
|
- **Apply** theoretical knowledge to real-world situations
|
||||||
|
|
||||||
|
The component serves as a comprehensive educational resource for monetary economics, suitable for undergraduate and graduate courses in macroeconomics, international finance, and monetary policy.
|
||||||
@@ -0,0 +1,253 @@
|
|||||||
|
# Connecting Theory to Data: Twin Deficits Analysis
|
||||||
|
|
||||||
|
## Overview
|
||||||
|
This document connects the theoretical concepts in the Monetary Policy Interactive Diagram to the empirical analysis from Problem Set 1 (Twin Deficits Hypothesis, 1960-2024 US data).
|
||||||
|
|
||||||
|
## National Accounting Identity
|
||||||
|
|
||||||
|
### Theoretical Framework
|
||||||
|
The fundamental identity that ties everything together:
|
||||||
|
|
||||||
|
$$Y = C + I + G + CA$$
|
||||||
|
|
||||||
|
Where:
|
||||||
|
- **Y** = GDP/National Income
|
||||||
|
- **C** = Consumption
|
||||||
|
- **I** = Investment
|
||||||
|
- **G** = Government purchases
|
||||||
|
- **CA** = Current Account (= Exports - Imports)
|
||||||
|
|
||||||
|
### Savings Identity
|
||||||
|
Rearranging the national income identity:
|
||||||
|
|
||||||
|
$$Y - C - G = I + CA$$
|
||||||
|
|
||||||
|
Since National Savings $S = Y - C - G$, we get:
|
||||||
|
|
||||||
|
$$S = I + CA$$
|
||||||
|
|
||||||
|
Breaking down savings into private and government components:
|
||||||
|
- $S_p = Y - T - C$ (Private savings)
|
||||||
|
- $S_g = T - G$ (Government savings/budget balance)
|
||||||
|
|
||||||
|
Therefore:
|
||||||
|
|
||||||
|
$$\boxed{CA = (S_p - I) + S_g = (S_p - I) + (T - G)}$$
|
||||||
|
|
||||||
|
**This is the core equation linking government budget balance to the current account.**
|
||||||
|
|
||||||
|
## Empirical Evidence: US Data (1960-2024)
|
||||||
|
|
||||||
|
### Finding 1: Twin Deficits Correlation Changed
|
||||||
|
|
||||||
|
**Before 1990 (1960-1989)**:
|
||||||
|
- Correlation: **r = 0.82** (very strong positive)
|
||||||
|
- Both CA and government budget relatively balanced
|
||||||
|
- When government ran deficits, current account followed strongly
|
||||||
|
|
||||||
|
**After 1990 (1990-2024)**:
|
||||||
|
- Correlation: **r = 0.53** (moderate positive)
|
||||||
|
- Both deficits became structurally larger and persistent
|
||||||
|
- Twin deficits still evident, but relationship more complex
|
||||||
|
|
||||||
|
### Finding 2: Private Savings Collapse
|
||||||
|
|
||||||
|
| Metric | Before 1990 | After 1990 | Change |
|
||||||
|
|--------|-------------|------------|--------|
|
||||||
|
| **Private Savings/GDP** | 8.05% | 4.67% | **-42%** |
|
||||||
|
| **Investment/GDP** | 18.22% | 17.70% | -3% |
|
||||||
|
| **S-I Gap** | -10.16% | -13.03% | -2.87 pp |
|
||||||
|
|
||||||
|
**Key Insight**: The dramatic decline in private savings fundamentally changed the US economy's relationship with foreign capital.
|
||||||
|
|
||||||
|
## Theoretical Explanation
|
||||||
|
|
||||||
|
### Why the Correlation Weakened But Twin Deficits Persisted
|
||||||
|
|
||||||
|
Looking at the identity: $CA = (S_p - I) + (T - G)$
|
||||||
|
|
||||||
|
**Before 1990**:
|
||||||
|
- $(S_p - I)$ was relatively stable at around -10%
|
||||||
|
- Changes in $(T - G)$ directly translated to changes in CA
|
||||||
|
- This created the strong correlation (r = 0.82)
|
||||||
|
|
||||||
|
**After 1990**:
|
||||||
|
- $(S_p - I)$ became larger and more variable (dropped to -13%)
|
||||||
|
- The current account now depends on TWO moving parts:
|
||||||
|
1. Government balance $(T - G)$
|
||||||
|
2. Private sector balance $(S_p - I)$
|
||||||
|
- This reduced the simple correlation but both deficits grew larger
|
||||||
|
|
||||||
|
### Mathematical Representation
|
||||||
|
|
||||||
|
**Before 1990** (stable private sector):
|
||||||
|
$$\Delta CA \approx \Delta(T - G)$$
|
||||||
|
Because $\Delta(S_p - I) \approx 0$
|
||||||
|
|
||||||
|
**After 1990** (variable private sector):
|
||||||
|
$$\Delta CA = \Delta(S_p - I) + \Delta(T - G)$$
|
||||||
|
Both terms matter!
|
||||||
|
|
||||||
|
## Connection to Monetary Policy
|
||||||
|
|
||||||
|
### Interest Rate Channel
|
||||||
|
From the interactive diagram, when central bank raises rates:
|
||||||
|
|
||||||
|
1. **Direct Effect**: $R \uparrow$ → $I \downarrow$ (investment falls)
|
||||||
|
2. **If private savings don't rise enough**: $(S_p - I)$ increases
|
||||||
|
3. **From identity**: If $(S_p - I) \uparrow$ and $(T-G)$ constant → $CA \uparrow$
|
||||||
|
|
||||||
|
This is the **expenditure-switching** effect of monetary policy.
|
||||||
|
|
||||||
|
### Exchange Rate Channel
|
||||||
|
Monetary tightening also works through UIP:
|
||||||
|
|
||||||
|
1. $R_{domestic} \uparrow$ → Currency appreciates ($E \downarrow$)
|
||||||
|
2. Exports become less competitive
|
||||||
|
3. $CA \downarrow$ (deteriorates)
|
||||||
|
|
||||||
|
These two channels can work in **opposite directions**!
|
||||||
|
|
||||||
|
### Net Effect in US Case (Post-1990)
|
||||||
|
|
||||||
|
The data shows:
|
||||||
|
- Persistent current account deficits despite varying interest rates
|
||||||
|
- This suggests the **private savings collapse** dominated
|
||||||
|
- Even when government improved its balance (late 1990s), CA remained negative
|
||||||
|
- Because $(S_p - I)$ gap was too large
|
||||||
|
|
||||||
|
## Policy Implications
|
||||||
|
|
||||||
|
### 1. Fiscal Policy Alone Insufficient
|
||||||
|
Simply reducing government deficits won't fix current account if:
|
||||||
|
$$S_p - I < 0 \text{ and large}$$
|
||||||
|
|
||||||
|
**Example**: Late 1990s US had government **surplus** but still ran CA deficit because private savings were too low relative to investment.
|
||||||
|
|
||||||
|
### 2. Monetary Policy Trade-offs
|
||||||
|
Tight monetary policy to fight inflation creates tensions:
|
||||||
|
- Higher $R$ reduces $I$ (good for CA via S-I gap)
|
||||||
|
- But higher $R$ appreciates currency (bad for CA via trade)
|
||||||
|
- Net effect ambiguous
|
||||||
|
|
||||||
|
### 3. Structural Factors Matter
|
||||||
|
The private savings rate depends on:
|
||||||
|
- **Demographics**: Aging population saves less
|
||||||
|
- **Financial development**: Easy credit reduces precautionary savings
|
||||||
|
- **Social safety nets**: Strong pensions reduce need to save
|
||||||
|
- **Income inequality**: High inequality can depress aggregate savings
|
||||||
|
|
||||||
|
## Using the Interactive Diagram
|
||||||
|
|
||||||
|
### Scenario: Replicate 1990s US Economy
|
||||||
|
|
||||||
|
**Settings**:
|
||||||
|
1. Set Government Balance: Moving toward surplus
|
||||||
|
2. Set Private Savings: Low (represented by high consumption)
|
||||||
|
3. Set Investment: Moderate to high
|
||||||
|
4. Observe: CA can still be negative despite government surplus
|
||||||
|
|
||||||
|
### Scenario: 2022-2023 Inflation Response
|
||||||
|
|
||||||
|
**Settings**:
|
||||||
|
1. Set Inflation: 4-5% (above target)
|
||||||
|
2. Set Output Gap: +2% (overheating)
|
||||||
|
3. Taylor Rule prescribes: $R = 2\% + 1.5(3\%) + 0.5(2\%) = 7.5\%$
|
||||||
|
4. Observe effects on:
|
||||||
|
- Investment (falls sharply)
|
||||||
|
- Exchange rate (appreciates)
|
||||||
|
- Net exports (deteriorate)
|
||||||
|
|
||||||
|
## Data Visualization Integration
|
||||||
|
|
||||||
|
### Recommended Addition to Interactive Tool
|
||||||
|
|
||||||
|
Create a time-series plotter showing:
|
||||||
|
1. **Government Balance** (T - G)
|
||||||
|
2. **Private Balance** (S_p - I)
|
||||||
|
3. **Current Account** (CA)
|
||||||
|
4. **Vertical line at 1990** to show structural break
|
||||||
|
|
||||||
|
This would show empirically how:
|
||||||
|
$$CA_t = (S_p - I)_t + (T - G)_t$$
|
||||||
|
|
||||||
|
Students could see all three variables moving together (or not).
|
||||||
|
|
||||||
|
## Equations Summary
|
||||||
|
|
||||||
|
### Core Identities
|
||||||
|
1. **National Income**: $Y = C + I + G + CA$
|
||||||
|
2. **Savings**: $S = S_p + S_g = I + CA$
|
||||||
|
3. **Current Account**: $CA = (S_p - I) + (T - G)$
|
||||||
|
|
||||||
|
### Monetary Policy
|
||||||
|
4. **Money Market**: $\frac{M^s}{P} = L(R, Y)$
|
||||||
|
5. **Taylor Rule**: $R = R^* + 1.5(\pi - \pi^*) + 0.5(y - y^*)$
|
||||||
|
6. **UIP**: $R_{CHF} = R_{EUR} + \frac{E^e - E}{E}$
|
||||||
|
|
||||||
|
### Relationships
|
||||||
|
7. **Investment**: $I = I(R, Y)$, where $\frac{\partial I}{\partial R} < 0$
|
||||||
|
8. **Net Exports**: $NX = NX(E, Y, Y^*)$, where $\frac{\partial NX}{\partial E} > 0$
|
||||||
|
9. **Consumption**: $C = C(Y - T, R, Wealth)$
|
||||||
|
|
||||||
|
## Discussion Questions
|
||||||
|
|
||||||
|
### 1. Twin Deficits Hypothesis
|
||||||
|
**Q**: If the correlation weakened after 1990, does this mean the twin deficits hypothesis failed?
|
||||||
|
|
||||||
|
**A**: No! The hypothesis is based on the **identity** $CA = (S_p - I) + (T - G)$, which is always true. The correlation weakened because $(S_p - I)$ became a larger and more variable component, not because the identity broke down.
|
||||||
|
|
||||||
|
### 2. Ricardian Equivalence
|
||||||
|
**Q**: Could Ricardian equivalence explain the changing relationship?
|
||||||
|
|
||||||
|
**A**: Ricardian equivalence predicts $\Delta S_p = -\Delta(T-G)$ (private savings offset government dissaving). If true, $(S_p - I) + (T-G)$ would be constant and CA wouldn't change with government balance.
|
||||||
|
|
||||||
|
**Evidence**: US data shows this did NOT happen. Private savings fell independently of government balance, suggesting Ricardian equivalence doesn't hold empirically.
|
||||||
|
|
||||||
|
### 3. Foreign Capital Dependence
|
||||||
|
**Q**: What does persistent CA deficit mean for the US?
|
||||||
|
|
||||||
|
**A**: From $CA = S - I$, a negative CA means $S < I$, so:
|
||||||
|
- US invests more than it saves domestically
|
||||||
|
- Must attract foreign capital to finance the gap
|
||||||
|
- This makes the US a **net debtor** to the rest of the world
|
||||||
|
- Sustainable only if foreigners willing to hold US assets
|
||||||
|
|
||||||
|
### 4. Exchange Rate Regime
|
||||||
|
**Q**: Would a different exchange rate regime change the relationship?
|
||||||
|
|
||||||
|
**A**: Under **fixed exchange rates**, the identity still holds but adjustment mechanism differs:
|
||||||
|
- Can't use monetary policy independently (UIP ties R to foreign rate)
|
||||||
|
- Current account imbalances must adjust through price/wage changes
|
||||||
|
- This is slower and potentially more painful
|
||||||
|
|
||||||
|
Under **flexible rates** (US case):
|
||||||
|
- Exchange rate adjusts to help balance current account
|
||||||
|
- But as data shows, adjustment can be slow and incomplete
|
||||||
|
|
||||||
|
## Conclusion
|
||||||
|
|
||||||
|
The interactive monetary policy diagram and the twin deficits empirical analysis are deeply connected:
|
||||||
|
|
||||||
|
1. **Identities** provide the theoretical foundation
|
||||||
|
2. **Policy rules** (Taylor, UIP) show how variables adjust
|
||||||
|
3. **Empirical data** reveals which channels dominate in practice
|
||||||
|
|
||||||
|
**Key lesson**: Theory gives us the framework, but magnitudes and relative importance of different channels require empirical investigation. The US experience shows that structural changes (private savings collapse) can fundamentally alter economic relationships even when identities remain valid.
|
||||||
|
|
||||||
|
## Further Reading
|
||||||
|
|
||||||
|
**Textbook Chapters**:
|
||||||
|
- Open economy macroeconomics
|
||||||
|
- Fiscal and monetary policy interactions
|
||||||
|
- International capital flows
|
||||||
|
|
||||||
|
**Papers**:
|
||||||
|
- Chinn & Prasad (2003): "Medium-term determinants of current accounts"
|
||||||
|
- Obstfeld & Rogoff (2005): "Global current account imbalances"
|
||||||
|
- Bernanke (2005): "The global saving glut" (speech)
|
||||||
|
|
||||||
|
**Data Sources**:
|
||||||
|
- FRED (Federal Reserve Economic Data): All US national accounts
|
||||||
|
- IMF Balance of Payments Statistics
|
||||||
|
- OECD Economic Outlook Database
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{"_joins":[],"_contexts":[],"_links":[],"_sort":{"field":"rank","asc":false,"group":false,"recursive":false},"_template":"","_templateName":"","defaultSticker":"","defaultColor":"","readMode":false,"fullWidth":false}
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Code of obligation is the collection of the laws related to contracts and the extra contractual responsibilities. In the civil codex contains the laws between individual and the aspect of their respective responsibility.
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Contractual responsibility follows the guidelines of the **article 97 of the CO**. This one often overlaps with the insurance laws.
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3 types of responsibilities: by fault, negligence and of risk
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Consider the binomial distribution of the number $k$ of successes in $n$ independent trials:
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$$\sum_{i=1}^{n} X_i \sim \text{Binomial}(n, p)$$
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The log-likelihood function is:
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$$\log L(p) = \log \binom{n}{k} + k \log(p) + (n-k) \log(1-p)$$
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## Part 1: Plot Log L(p)
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Given $n=100$ and $k=10$
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![[image-1.png]]
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## Part 2: Compute the MLE
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**Given:** $\sum_{i=1}^{n} x_i = 15$ with $n = 100$ trials
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### Finding the MLE
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To find the maximum likelihood estimator, we take the derivative of the log-likelihood with respect to $p$ and set it equal to zero:
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$$\frac{d}{dp} \log L(p) = \frac{k}{p} - \frac{n-k}{1-p} = 0$$
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Solving for $p$:
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$$\frac{k}{p} = \frac{n-k}{1-p}$$
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$$k(1-p) = p(n-k)$$
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$$k - kp = pn - pk$$
|
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$$k = pn$$
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$$\hat{p}_{MLE} = \frac{k}{n}$$
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|
![[image-2.png]]
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Reference in New Issue
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