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

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:

python run_all_problems.py

Run Individual Problems

You can also run each problem separately:

# 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:

pip install pandas matplotlib requests numpy

Or install all at once:

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:

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.