Question

11. After studying Iris Hamson’s credit analysis, George Davies is considering whether he can increase the holding period return on Yucatan Resort’s excess cash holdings (which are held in pesos) by investing those cash holdings in the Mexican bond market. Although Davies would be investing in a peso-denominated bond, the investment goal is to achieve the highest holding period return, measured in U.S. dollars, on the investment.

Davies finds the higher yield on the Mexican one-year bond, which is considered to be free of credit risk, to be attractive but he is concerned that depreciation of the peso will reduce the holding period return, measured in U.S. dollars. Hamson has prepared selected economic and financial data, given in Exhibit 3-1, to help Davies make the decision.

Selected Economic and Financial Data for U.S. and Mexico

Expected U.S. Inflation Rate                                                             2.0% per year

Expected Mexican Inflation Rate                                          6.0% per year

U.S. One-year Treasury Bond Yield                                                  2.5%

Mexican One-year Bond Yield                                                           6.5%

Nominal Exchange Rates

Spot                                                                                       9.5000 Pesos = U.S. $ 1.00

One-year Forward                                                                9.8707 Pesos = U.S. $ 1.00

Hamson recommends buying the Mexican one-year bond and hedging the foreign currency exposure using the one-year forward exchange rate. She concludes: “This transaction will result in a U.S. dollar holding period return that is equal to the holding period return of the U.S. one-year bond.”

1. Calculate the U.S. dollar holding period return that would result from the transaction recommended by Hamson. Show your calculations. State whether Hamson’s conclusion about the U.S. dollar holding period return resulting from the transaction is correct or incorrect. After conducting his own analysis of the U.S. and Mexican economies, Davies expects that both the U.S. inflation rate and the real exchange rate will remain constant over the coming year. Because of favorable political developments in Mexico, however, he expects that the Mexican inflation rate (in annual terms) will fall from 6.0 percent to 3.0 percent before the end of the year. As a result, Davies decides to invest Yucatan Resorts’ cash holdings in the Mexican one-year bond but not to hedge the currency exposure.
2. Calculate the expected exchange rate (pesos per dollar) one year from now. Show your calculations. Note: Your calculations should assume that Davies is correct in his expectations about the real exchange rate and the Mexican and U.S. inflation rates.
3. Calculate the expected U.S. dollar holding period return on the Mexican one-year bond. Show your calculations. Note: Your calculations should assume that Davies is correct in his expectations about the real exchange rate and the Mexican and U.S. inflation rates.

Answer 1

ANSWER:

a.       The U.S. dollar holding period return that would result from the transaction recommended by Hamson is 2.5%. The investor can buy “x” amount of pesos at the (indirect) spot exchange rate, invest these “x” pesos in the Mexican bond market and have “x × (1 + Y_MEX)” pesos in one year, and convert these pesos back into dollars using the (indirect) forward exchange rate. Interest rate parity asserts that the two holding period returns must be equal, which can be represented by the formula:

(1 + Y_US) = Spot × (1 + Y_MEX) × (1 / Forward)

      where “Spot” and “Forward” are in indirect terms. The left side of the equation represents the holding period return for a U.S. dollar-denominated bond. If interest rate parity holds, the “Y_US” term also corresponds to the U.S. dollar holding period return for the currency-hedged Mexican one-year bond. The right side of the equation is the holding period return, in dollar terms, for a currency-hedged peso-denominated bond.

Solving for Y_US:

(1 + Y_US) = 9.5000 × (1 + 0.065) × (1 / 9.8707)

(1 + Y_US) = 9.5000 × 1.065 × 0.1013

(1 + Y_US) = 1.0249

Y_US = 1.0249 – 1.0000 = 0.0249 = 2.5%

Thus Y_US = 2.5%, which is the same yield as on the one-year U.S. bond. Hamson’s conclusion about the U.S. dollar holding period return is correct.

b.      The expected exchange rate one year from now is 9.5931. The rate can be calculated by using the formula:

(1 + %Δ R_US) = (1 + %Δ S_US) × [(1 + %Δ P_US) / (1 + %Δ P_MEX)]

     = (S₁ / S₀) × [(1 + %Δ P_US) / (1 + %Δ P_MEX)]

where R_US is the real U.S. dollar exchange rate, S_i is the nominal spot exchange rate in period i, and %Δ P is the inflation rate. Note that the currency quotes are in indirect form. Solving for S₁ (the expected exchange rate one year from now):

(1 + 0.0000) = (S₁ / 9.5000) × [(1 + 0.02) / (1 + 0.03)]

1.0000 = (S₁ / 9.5000) × 0.9903

1.0098 = S₁ / 9.5000

S₁ = 9.5931

c.       The expected U.S. dollar holding period return on the Mexican one-year bond is 5.47%. The return can be calculated as shown below, using the formula in Part A and the current spot exchange rate and expected one-year spot exchange rate calculated in Part B.

Holding period return = [(1 + Y_MEX) × (1 + %Δ peso’s value)] – 1

   = [(1 + YMEX) × (S0 / S1)] – 1

   = [(1 + 0.065) × (9.5000 / 9.5931)] – 1

   = (1.065 × 0.9903) – 1

   = 5.47%