1. Consider a forward contract on a portfolio of zero-coupon bonds. Suppose the spot price of the underlying bond portfolio is 80. Consider an inflationary environment in which the yield on a 18-month treasury security is 6% per quarter (compounded quarterly which is somewhat more than 26% EAY).

a) What should be the forward price of the 18-month forward contract on this bond portfolio?

b) Suppose the actual forward price on the 18-month forward contract was 110. How could you make $1MM in risk-free profits today? Please state the exact positions you would have to take to make the necessary arbitrage profits.

c) Suppose you thought that interest rates would rise and that the spot price of the bond portfolio would fall over the intervening 18 months. How would that change your answer to (b)?

2. Assume markets are in equilibrium. Consider a forward contract on a portfolio of zero-coupon bonds. Suppose the spot price is 80 and the forward price on the six-month forward contract is 82.

a) Solve for the interest rate on 6-month risk-free rate? State your answer as an effective annual yield.

b) How could you use positions in the spot market and the forward market to effectively borrow $100 for 6-months risk-free at the interest rate solved for in (a)? Please state the exact positions required to effectively create the required loan.

c) How could you use positions in the spot market and the forward market to effectively lend $100 6-months risk-free at the interest rate solved for in (a)? Please state the exact positions required to effectively create the required loan.

d) Suppose the bonds in this zero-coupon bond portfolio were junk bonds which had large amounts of idiosyncratic and systematic risk. How would that change your answer to (b) and (c)? (However continue to assume the underlying bond portfolio can be traded without transactions costs and that one can short the underlying without transactions costs.)

3. Recall from Class Note 2 that the forward price for a currency forward is given by the following equation:

F = So(1 + r)^T/(1 + d)^T (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?