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Atlas/Global Business Environment /Problem Set 2/ANSWER_SUMMARY.md
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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.

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