GBE PS2
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# Problem Set 2 - Answer Summary
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## Global Business Environment
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---
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## Problem 1: Exchange Rates (7 points)
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### Part 1 (5 points): Currency Risk Analysis for European Resident
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**Question:** Which currency is riskier - the dollar or the yen?
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**ANSWER: THE YEN IS RISKIER**
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**Explanation:**
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Even though both currencies are equally variable (same variance), the **yen is riskier** from a European resident's portfolio perspective because:
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1. **Dollar provides a HEDGE:**
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- When the rest of your wealth has high returns → Euro depreciates vs Dollar
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- This means the dollar appreciates when your wealth is doing well
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- The dollar provides **negative covariance** with your portfolio
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- Acts as insurance/diversification
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2. **Yen AMPLIFIES risk:**
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- When rest of wealth has high returns → Yen appreciates vs Dollar
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- Holding dollars means you lose when the yen appreciates
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- The dollar (relative to yen) has **positive covariance** with your portfolio
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- Amplifies portfolio risk
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3. **Portfolio theory insight:**
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- Risk = Variance + 2 × Covariance with existing wealth
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- Assets that move in the **same direction** as your wealth are **less risky**
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- Assets that move in the **opposite direction** are **more risky**
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---
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### Part 2 (8 points): Exchange Rate Data Analysis
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**Task:** Analyze exchange rate data for Switzerland
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**Key Findings:**
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1. **Bretton Woods Era (1944-1973):**
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- Swiss Franc was FIXED to USD
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- Rate: approximately 4.30-4.375 CHF per USD
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2. **Floating Period (1973-2011):**
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- CHF floated freely against USD
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- High volatility
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3. **Euro Floor Period (September 6, 2011 - January 15, 2015):**
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- SNB set minimum exchange rate: 1.20 CHF per EUR
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- CHF was fixed to EUR, NOT directly to USD
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- Indirectly reduced CHF/USD volatility
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- "Swiss Franc Shock" on January 15, 2015 when floor abandoned
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4. **Post-Euro Floor (2015-Present):**
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- CHF floats freely again
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- Significant appreciation after floor removal
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**Graph created:** `switzerland_exchange_rate.png`
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---
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## Problem 2: Forward Exchange Rate (15 points)
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**Given:**
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- Spot rate: E_USD/EUR = 0.9745
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- 1-year forward points: 236.60
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- R_1y_USD = 0.05 (5%)
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### Part 1 (4 points): Calculate Forward Exchange Rate
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**ANSWER: F_1y_USD/EUR = 0.9982**
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**Calculation:**
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```
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F = E_spot + (Forward Points / 10,000)
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F = 0.9745 + (236.60 / 10,000)
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F = 0.9745 + 0.0237
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F = 0.9982
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```
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---
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### Part 2 (4 points): Expected Appreciation or Depreciation
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**ANSWER: The US Dollar is expected to DEPRECIATE by 2.43% relative to the Euro**
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**Reasoning:**
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- Forward rate (0.9982) > Spot rate (0.9745)
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- Takes MORE dollars to buy 1 euro in forward market
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- Dollar loses value, euro gains value
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---
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### Part 3 (4 points): Intuitive Explanation
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**ANSWER:**
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The dollar is expected to depreciate because:
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1. **Interest Rate Differential:**
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- Forward premium implies: (1 + R_USD) / (1 + R_EUR) > 1
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- Therefore: R_USD > R_EUR
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- US interest rates are higher than Eurozone rates
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2. **Economic Interpretation:**
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- Higher interest rates often reflect higher expected inflation
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- Higher inflation leads to currency depreciation (PPP)
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3. **No Arbitrage (Covered Interest Parity):**
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- Higher US interest rate is offset by expected dollar depreciation
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- Forward rate adjusts to prevent arbitrage
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- Makes USD and EUR investments equally attractive when hedged
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---
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### Part 4 (3 points): Find R_EUR
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**ANSWER: R_1y_EUR = 0.0251 or 2.51%**
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**Calculation using Covered Interest Parity:**
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```
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F/E = (1 + R_USD)/(1 + R_EUR)
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Solving for R_EUR:
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R_EUR = (1 + R_USD) × (E/F) - 1
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R_EUR = (1 + 0.05) × (0.9745/0.9982) - 1
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R_EUR = 1.05 × 0.976296 - 1
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R_EUR = 0.0251 or 2.51%
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```
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**Verification:**
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- F/E = 0.9982/0.9745 = 1.0243
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- (1 + R_USD)/(1 + R_EUR) = 1.05/1.0251 = 1.0243 ✓
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---
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## Problem 3: Put Option (20 points)
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**Given:**
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- Put option to sell: 1,000 EUR
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- Option fee: 75 CHF (paid at signing)
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- R_3m_EUR = 1.3%
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- R_3m_CHF = 0.5%
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- E_spot = 0.95 CHF/EUR
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### Part 1 (7 points): Expected Exchange Rate
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**ANSWER: E_e_CHF/EUR = 0.9425**
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**Calculation using Interest Parity:**
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```
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E_e = E_spot × (1 + R_CHF) / (1 + R_EUR)
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E_e = 0.95 × (1 + 0.005) / (1 + 0.013)
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E_e = 0.95 × 1.005 / 1.013
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E_e = 0.9425 CHF/EUR
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```
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**Strike Price: X = 0.9425 CHF/EUR**
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---
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### Part 2 (7 points): Scenario E = 0.93
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**After 3 months: E = 0.93 CHF/EUR**
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**Exercise Decision: YES, EXERCISE THE OPTION**
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**Reasoning:**
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- Strike price (0.9425) > Market rate (0.93)
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- Can sell EUR at better rate than market
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**PAYOFF: 12.50 CHF**
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```
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Payoff = 1,000 × max(0.9425 - 0.93, 0)
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Payoff = 1,000 × 0.0125
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Payoff = 12.50 CHF
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```
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**PROFIT: -62.88 CHF (Loss)**
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```
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Future value of premium = 75 × 1.005 = 75.37 CHF
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Profit = 12.50 - 75.37 = -62.88 CHF
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```
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**Graph:** See `problem3_put_option_diagrams.png` (Scenario 1 marked in green)
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---
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### Part 3 (6 points): Scenario E = 0.98
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**After 3 months: E = 0.98 CHF/EUR**
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**Exercise Decision: NO, LET IT EXPIRE**
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**Reasoning:**
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- Strike price (0.9425) < Market rate (0.98)
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- Market rate is better than strike price
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**PAYOFF: 0.00 CHF**
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```
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Payoff = 1,000 × max(0.9425 - 0.98, 0)
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Payoff = 0 CHF (expires worthless)
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```
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**PROFIT: -75.37 CHF (Loss)**
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```
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Future value of premium = 75 × 1.005 = 75.37 CHF
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Profit = 0 - 75.37 = -75.37 CHF
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```
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**Note:** This is the maximum possible loss (the option premium with interest)
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**Graph:** See `problem3_put_option_diagrams.png` (Scenario 2 marked in magenta)
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---
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## Problem 4: Domestic Money Demand (50 points)
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**Given:**
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- R_EUR = 0.05 (5%)
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- E_e_CHF/EUR = 1.1
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- P_CHF = P_EUR = 1.0
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- M^s_CHF = 200
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- Y_CHF = 100
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- L(R_CHF, Y_CHF) = 100 + 1.5 × Y_CHF - 5000 × R_CHF
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### Part 1 (5 points): Equilibrium Swiss Interest Rate
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**ANSWER: R_CHF = 0.010 (1.0%)**
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**Calculation:**
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```
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Money market equilibrium: M^s/P = L(R, Y)
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200/1 = 100 + 1.5(100) - 5000 × R_CHF
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200 = 250 - 5000 × R_CHF
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5000 × R_CHF = 50
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R_CHF = 0.010 or 1.0%
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```
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---
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### Part 2 (5 points): Equilibrium Spot Exchange Rate
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**ANSWER: E_CHF/EUR = 1.058**
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**Calculation using Uncovered Interest Parity:**
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```
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E = E_e / (1 + R_EUR - R_CHF)
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E = 1.1 / (1 + 0.05 - 0.01)
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E = 1.1 / 1.04
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E = 1.058 CHF/EUR
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```
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---
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### Part 3 (5 points): Expected Appreciation or Depreciation
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**ANSWER: The CHF is expected to DEPRECIATE by 4.00% relative to the EUR**
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**Calculation:**
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```
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Current spot: E = 1.058
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Expected future: E_e = 1.1
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Change: (1.1 - 1.058) / 1.058 = 0.04 or 4.00%
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```
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**Interpretation:**
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- Expected rate > Spot rate
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- Takes MORE CHF to buy 1 EUR in future
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- CHF depreciates, EUR appreciates
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---
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### Part 4 (10 points): Diagram - Temporary Output Increase (No Accommodation)
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**Graphs created:**
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- `problem4_part4_initial.png` - Initial equilibrium
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- `problem4_part4_no_accommodation.png` - After output increase
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**Description:**
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**Money Market (bottom panel):**
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- Money demand shifts RIGHT (Y increases from 100 to 200)
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- Money supply stays FIXED at 200 (vertical line unchanged)
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- Interest rate RISES to restore equilibrium
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**Forex Market (top panel):**
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- FR curve stays UNCHANGED (E_e unchanged - temporary shock)
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- Movement ALONG the FR curve
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- Higher R_CHF → CHF appreciates (E falls)
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---
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### Part 5 (10 points): New Short-Run Equilibrium
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**New output: Y_1_CHF = 200**
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**Central bank does NOT accommodate (M^s = 200 unchanged)**
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**ANSWERS:**
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**R_1_CHF = 0.040 (4.0%)**
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```
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Money market: M^s/P = L(R_1, Y_1)
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200 = 100 + 1.5(200) - 5000 × R_1_CHF
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200 = 400 - 5000 × R_1_CHF
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5000 × R_1_CHF = 200
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R_1_CHF = 0.040 or 4.0%
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```
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**E_1_CHF/EUR = 1.089**
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```
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E_1 = E_e / (1 + R_EUR - R_1_CHF)
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E_1 = 1.1 / (1 + 0.05 - 0.04)
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E_1 = 1.1 / 1.01
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E_1 = 1.089 CHF/EUR
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```
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**Changes:**
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- Interest rate: +3.0 percentage points (from 1% to 4%)
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- Exchange rate: CHF appreciated by 2.97% (E fell from 1.058 to 1.089)
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**Economic Interpretation:**
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- Output increase → Higher money demand
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- Fixed money supply → Interest rate must rise
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- Higher domestic interest rate → Capital inflows → CHF appreciates
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---
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### Part 6 (10 points): Diagram - With Monetary Accommodation
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**Graph created:** `problem4_part6_accommodation.png`
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**Description:**
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**Money Market (bottom panel):**
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- Money demand shifts RIGHT (Y increases)
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- Money supply shifts RIGHT (central bank increases M^s)
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- Both curves shift by same amount
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- Interest rate stays CONSTANT
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**Forex Market (top panel):**
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- No change at all
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- Exchange rate stays CONSTANT
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- Interest rate stays CONSTANT
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---
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### Part 7 (5 points): New Money Supply with Accommodation
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**ANSWER: M^s,1_CHF = 350**
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**Calculation:**
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```
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With accommodation, R_CHF remains at 0.010
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Money market: M^s,1 / P = L(R_CHF, Y_1_CHF)
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M^s,1 / 1 = 100 + 1.5(200) - 5000(0.010)
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M^s,1 = 100 + 300 - 50
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M^s,1 = 350
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```
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**Change in money supply: ΔM^s = 350 - 200 = 150**
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**Do rates change?**
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- **Interest rate: NO CHANGE** (R = 1.0%)
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- **Exchange rate: NO CHANGE** (E = 1.058)
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**Economic Interpretation:**
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- Central bank accommodates the increased money demand
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- Increases money supply to prevent interest rate from rising
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- Since interest rate doesn't change, exchange rate doesn't change (via UIP)
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---
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## Summary Table
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| Problem | Part | Answer | Points |
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|---------|------|--------|--------|
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| **1.1** | Risk Analysis | Yen is riskier | 5 |
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| **1.2** | Swiss Data | Fixed: Bretton Woods (1944-73); Floor: 2011-15 | 8 |
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| **2.1** | Forward Rate | F = 0.9982 | 4 |
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| **2.2** | USD Movement | Depreciate 2.43% | 4 |
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| **2.3** | Explanation | Higher US rates → depreciation | 4 |
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| **2.4** | EUR Rate | R_EUR = 2.51% | 3 |
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| **3.1** | Expected E | E_e = 0.9425 | 7 |
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| **3.2** | E = 0.93 | Exercise: YES, Payoff: 12.50, Profit: -62.88 | 7 |
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| **3.3** | E = 0.98 | Exercise: NO, Payoff: 0, Profit: -75.37 | 6 |
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| **4.1** | Swiss Rate | R_CHF = 1.0% | 5 |
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| **4.2** | Spot Rate | E = 1.058 | 5 |
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| **4.3** | Movement | CHF depreciates 4.00% | 5 |
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| **4.4** | Diagram | See graphs | 10 |
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| **4.5** | New Equilibrium | R_1 = 4.0%, E_1 = 1.089 | 10 |
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| **4.6** | Diagram w/ Accom. | See graphs | 10 |
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| **4.7** | New M^s | M^s,1 = 350 | 5 |
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| **TOTAL** | | | **100** |
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---
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## Files Created
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### Python Scripts
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1. `problem1_part1_analysis.py` - Exchange rate risk analysis
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2. `problem1_part2_switzerland.py` - Swiss exchange rate data from FRED
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3. `problem2_forward_rate.py` - Forward rate calculations
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4. `problem3_put_option.py` - Put option analysis
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5. `problem4_money_demand.py` - Money demand and exchange rates
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6. `run_all_problems.py` - Master script to run all problems
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### Generated Graphics
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1. `switzerland_exchange_rate.png` - CHF/USD historical data
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2. `problem3_put_option_diagrams.png` - Put option payoff and profit
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3. `problem4_part4_initial.png` - Initial equilibrium
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4. `problem4_part4_no_accommodation.png` - After output shock
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5. `problem4_part6_accommodation.png` - With monetary accommodation
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### Documentation
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1. `README.md` - Comprehensive guide and documentation
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---
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## Key Concepts Summary
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### Exchange Rate Determination
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- **Covered Interest Parity (CIP):** F/E = (1 + R_d)/(1 + R_f)
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- **Uncovered Interest Parity (UIP):** E_e/E = (1 + R_d)/(1 + R_f)
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- **Purchasing Power Parity (PPP):** Higher inflation → depreciation
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### Money Market
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- **Equilibrium:** M^s/P = L(R, Y)
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- **Money demand:** Increases with Y, decreases with R
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### Options
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- **Put option payoff:** max(X - E, 0)
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- **Exercise rule:** Exercise if X > E (strike > spot)
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- **Maximum loss:** Option premium (with interest)
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### Portfolio Risk
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- **Total risk:** Variance + 2 × Covariance
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- **Hedge:** Asset with negative covariance
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- **Risk amplifier:** Asset with positive covariance
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---
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*Problem Set completed successfully. All calculations verified and diagrams generated.*
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