Question

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.

1. 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.

2. 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 bond had increased to 7% and the quality yield spread narrowed to 100 basis points as you predicted. Assume a flat yield curve.

3. Show what you hedge fund’s position would be if yields on AAA bond had instead decreased to 5%, but the quality yield spread were still 100 basis points as you predicted.

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

Answer 1

All financials below are in $. Face value, FV of bonds have been assumed to be $ 1,000 which is a standard assumption for question of this kind.

Price of 2 year zero coupon bond (ZCB) = FV / (1 + S₂)²

For, AAA rated bond, S₂ = 6%; hence price of 2 year AAA rated ZCB = 1000 / (1 + 6%)² =  890.00

For, BBB rated bond, S₂ = 7.5%; hence price of 2 year BBB rated ZCB = 1000 / (1 + 7.5%)² =  865.33

Part (a)

Let's short 1 no. of AAA rated bond. Cash inflow = 890

Nos. of BBB rated bond that can be purchased = 890 / 865.33 =  1.0285

Hence, create the following portfolio:

• Short 1 no. of 2 year AAA rated ZCB
• Long 1.0285 no. of 2 year BBB rated ZCB

Part (b)

One year later,

If yields on AAA bond had increased to 7% and the quality yield spread narrowed to 100 basis points

Price of AAA rated bond = 1000 / (1 + 7%) = 934.58

Price of BBB rated bond = 1000 / (1 + 8%) = 925.93

On closing the position: We will have to pay 934.58 to close the short position on 1 no. of AAA rated ZCB and we will get 1.0285 x 925.93 =  952.32 by selling the 1.0285 no. of BBB rated ZCB.

Hence, your hedge fund’s profit = 952.32 - 934.58 = 17.74

Part (c)

if yields on AAA bond had instead decreased to 5%, but the quality yield spread were still 100 basis points

Price of AAA rated bond = 1000 / (1 + 5%) = 952.38

Price of BBB rated bond = 1000 / (1 + 6%) = 943.40

On closing the position: We will have to pay 952.38 to close the short position on 1 no. of AAA rated ZCB and we will get 1.0285 x 943.40 =  970.29 by selling the 1.0285 no. of BBB rated ZCB.

Hence, your hedge fund’s profit = 970.29 - 952.38 = 17.90

Part (d)

Your profit will reduce (decrease) if the yield spread widened instead of narrowing. In that case, Price of BBB rated ZCB will be lower than what we have found out above. Hence our inflows on selling the BBB rated ZCB will reduce and our profits would reduce (decrease).