Foreign Exchange: Notes on Nominal and Real Exchange Rates

Money, Banking, and the Economy: Foreign Exchange

Course Information

  • Date: September 17, 2025

Assignment Reminders

  • JiTT Quizzes: No quizzes next week.

  • FRED Essay 2:

    • Due: Monday, at 11:30 AM.

    • Cannot be late; Canvas will not assign a peer reviewer if submitted late.

    • Peer Review: Complete by Wednesday, 3:00 PM.

    • Credit will be lost if peer review is not completed.

  • Review Quiz 2:

    • Opens: Today (Sept 17, 2025), 3:00 PM.

    • Closes: Monday, 11:30 AM.

Midterm 1 Preparation

  • Midterm 1 Old:

    • Paper exam from before COVID-19.

    • Available: Today (Sept 17, 2025), after 3:00 PM.

    • Answer Key: Available Friday, at noon.

  • Practice Midterm 1:

    • Canvas exam from during COVID-19.

    • Available: Monday, during class.

    • Review: Video explanation of answers.

  • Midterm 1 Practice Quiz:

    • 7 Multiple Choice questions.

    • Available: Monday, at 3:00 PM.

    • Can be taken multiple times.

Lecture 7 Objectives

  • Determine the yield on foreign assets and discuss uncovered interest parity using Excel.

  • Discuss the nominal exchange rate and the market for foreign exchange in the short run.

  • Define the real exchange rate using Excel.

  • Discuss the long-run approach to foreign exchange movements.

  • Connect the bond, stock, and foreign exchange markets to analyze their interactions.

Exchange Rate Calculation Warning

  • Exchange rates can be expressed in two ways (e.g., \
    %/€ or €/\$).

  • Standard Convention (for calculations): Home price of foreign currency (e.g., \
    %/€ if you are in the U.S.).

  • Textbook Convention: Does not always follow the standard convention.

  • Exam Questions: Either system will work for answering exam questions.

  • Recommendation: Follow the slides and Brainshark videos; ignore calculations presented in the textbook.

Foreign Assets and Uncovered Interest Parity (UIP)

  • Context: Calculating dollar returns on an investment made in a foreign currency.

  • Exact Formula for Dollar Returns on a Foreign Investment: 1+i<em>$,t=(1+i€,t</em>)×E<em>t+1E</em>t1 + i<em>{\$,t}^{} = (1 + i{\text{€},t}^{</em>}) \times \frac{E<em>{t+1}}{E</em>t}

    • i$,t∗i_{\$,t}^{*}: Dollar return on foreign investment at time tt.

    • i€,t∗i_{\text{€},t}^{*}: Yield on the foreign asset (in Euros) at time tt.

    • EtE_t: Current nominal exchange rate (e.g., \
      %/€).

    • Et+1E_{t+1}: Expected nominal exchange rate in the next period.

  • Linear Approximation for Dollar Returns on a Foreign Investment: i<em>$,t≈i€,t</em>+E<em>t+1−E</em>tEti<em>{\$,t}^{} \approx i{\text{€},t}^{</em>} + \frac{E<em>{t+1} - E</em>t}{E_t}

    • This approximation simplifies the calculation by adding the foreign interest rate to the expected percentage change in the exchange rate.

  • Uncovered Interest Parity (UIP) Condition: i<em>$,t=E[i</em>$,t∗]i<em>{\$,t} = E[i</em>{\$,t}^{*}]

    • The expected dollar return on a foreign investment (the right side) should equal the return on a comparable domestic (U.S.) asset (i$,ti_{\$,t}).

    • This implies that investors are indifferent between holding domestic and foreign assets when accounting for expected exchange rate changes.

Excel Example: Investing in French Bonds

  • Scenario: You have \
    1,000 and wish to invest in French bonds.

  • Initial Conversion (at time tt):

    • Current exchange rate: E$/€,t=$1.15/€E_{\$/€,t} = \$1.15/€

    • Convert \
      1,000 to Euros: $1,000/($1.15/€)≈€869.57\$1,000 / (\$1.15/€) \approx €869.57

  • Investment in French Bonds:

    • French bond yield: i€,t∗=0.04i_{\text{€},t}^{*} = 0.04

    • Amount after one year in Euros: €869.57×(1+0.04)=€904.35€869.57 \times (1 + 0.04) = €904.35

  • Final Conversion (at time t+1t+1):

    • Expected future exchange rate: E$/€,t+1=$1.22/€E_{\$/€,t+1} = \$1.22/€

    • Amount after one year in USD: €904.35×$1.22/€≈$1,103.30€904.35 \times \$1.22/€ \approx \$1,103.30

  • Calculated Dollar Return (i$,t∗i_{\$,t}^{*}):

    • i$,t∗=($1,103.30−$1,000)/$1,000=0.1033 or 10.33%i_{\$,t}^{*} = (\$1,103.30 - \$1,000) / \$1,000 = 0.1033 \text{ or } 10.33\%

  • Approximate Dollar Return (i$,t∗i_{\$,t}^{*}):

    • i$,t∗≈0.04+($1.22−$1.15)/$1.15=0.04+0.0609≈0.1009 or 10.09%i_{\$,t}^{*} \approx 0.04 + (\$1.22 - \$1.15) / \$1.15 = 0.04 + 0.0609 \approx 0.1009 \text{ or } 10.09\%

  • UIP Implication: According to UIP, the expected returns on U.S. assets should also be approximately 10.09%10.09\% for equilibrium.

Foreign Exchange (FX) Market: Short-Run Approach

  • Determines the exchange rate in the short run.

  • Market for Euros:

    • Supply: Primarily from people who wish to sell Euros, typically Europeans (e.g., European investors buying foreign assets, European importers buying foreign goods).

    • Demand: Primarily from people who wish to buy Euros, typically non-Europeans (e.g., U.S. investors buying European assets, U.S. importers buying European goods).

  • Market for USD:

    • Supply: Primarily from people who wish to sell dollars, typically Americans.

    • Demand: Primarily from people who wish to buy dollars, typically non-Americans.

  • Relationship: The market for Euros and the market for USD are