Question

Renée Michaels, CFA, plans to invest $1 million in U.S. government cash equivalents for the next 90 days. Michaels’s client has authorized her to use non-U.S. government cash equivalents, but only if the currency risk is hedged to U.S. dollars by using forward currency contracts.

a. Calculate the U.S.-dollar value of the hedged investment at the end of 90 days for each of the two cash equivalents in the table below. Show all calculations.

b. Briefly explain the theory that best accounts for your results.

c. Based upon this theory, estimate the implied interest rate for a 90-day U.S. government cash equivalent.

Short answer

a. Dollar interest rate is 1.5793% which is equal to that of Yen investment

b. Interest rate parity relationship

c. Between 6.2572% to 6.3172%

Step-by-step solution

Calculation of dollar proceeds from 90 days Japanese yen

Interest rate = 7.6%

Investment = $1 million

Time = 90 days or ¼

Exchange rates = 133.05

The yen investment after exchange = $1 million x 133.05 =￥133.05 million

The yen investment after 90-day forward =￥133.05 million x[1 + (.076 / 4)]=￥135. 57795 million

Since interests are typically annualized for 360 days, for 90 days it will be divided by 4.

Selling this at the forward exchange rate of ￥133.47 = ￥135. 57795 million / ￥133.47 = $1.015793 million

Hence 90 days dollar interest rate = 1.5793%

Calculation of dollar proceeds from 90 days Swiss franc

Interest rate = 8.6%

Investment = $1 million

Time = 90 days or ¼

Exchange rates = 1.526

Hence, as above calculation, Dollar proceeds from 90 days Swiss franc

= (1 million x 1.526) x (1 + .086 / 4) / 1.5348

= $1.015643 million

This implies that the dollar interest rate is 1.5643%.

This means that it the same as of the yen investment.

Explanation of theory

The identical results in both these currencies reflect the interest rate parity relationship. This therefore asserts that the pricing relationship between interest rates, spot and forward exchange rates must make covered investments in any currency equally attractive.

Calculation of implied interest rates

Since the dollar return on default free government securities in Japan and Switzerland is 1.5793% and 1.5643% respectively. Hence the 90 days interest rate must lie between these two.

This would correspond to an annual rate between 6.2572% and 6.3172% which is less than APR in Japan or Switzerland.