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Consider a forward contract on a portfolio of zero-coupon bonds. Suppose the spot price of the underlying bond portfolio is 80.
(1)
where
• So is the currency's spot price. (This is the number of dollars one must pay today to receive one unit of the foreign currency today.)
• r is the US risk-free interest rate stated as an effective annual yield.
• d is the foreign risk-free interest rate stated as an effective annual yield.
• T is time until maturity of the forward contract (in years).
This question examines what happens if forward rates and spot rates violate the relationship stated in Eqn (1). Suppose you want to invest $1 million dollars for 2 years and observe the following (EAY) interest rates in the marketplace:
US 2-Year interest rate = 5% (EAY)
British 2-Year (risk-free) interest rate = 7% (EAY)
Each British Pound to be received immediately is worth $1.75.
The 2-Year forward rate for British Pounds is $1.85.
a) First we will calculate the proceeds from investing using the direct method. Suppose you invest the $1 million for 2 years at the 2-Year US risk-free rate. How much money will you have in 2 years?
b) Now we will calculate the proceeds from investing with the indirect method. Suppose you do the following three things today:
1. Purchase $1 million worth of British Pounds at the current spot exchange rate.
2. Invest all of these British Pounds today at the 2-Year British risk-free rate.
3. Take a short position in 2-Year British Pounds that is exactly large enough to convert the British Pounds calculated in Step 2 back into US dollars. How many US dollars will you have in 2 years?
c) In this situation would you prefer the direct 2-Year US risk-free investment or the indirect 2-Year US risk-free investment?
