Suppose you are a strategist for a hedge fund. Your research indicates that the quality spread for BBB bonds and AAA bonds is 150 basis points in periods of economic slowdown and only 100 bp in periods of economic expansion.

Currently, the economy is in a recession, and one- and two-year zero coupon bonds for AAA and BBB bonds are trading at 6% and 7.5%. Leading economic indicators, though, strongly point to the economy hitting its trough relatively soon and then expanding over the next year.

a. Given the economic growth forecast, construct a quality spread for your hedge fund formed by going short in one of the bonds with the proceeds used to purchase the other. Assume perfect divisibility.

b. Show what your hedge fund’s profit or loss could be if you closed your position a year later and the economy were growing and yields on AAA bonds had increased to7%and the quality yield spread narrowed to 100 basis points as you predicted. Assume a flat yield curve and annual compounding.

c. Show what your hedge fund’s position would be if yields on AAA bonds had instead decreased to 5%, but the quality yield spread was still 100 BP as you predicted.

d. What would happen to your profit or loss if the yield spread widened instead of narrowed?