How much of the 30 year bond should she buy or sell to hedge against parallel shifts in the yield curve?

An investor holds $1m in a 10 year bond that has a basis point value (or PV01) of 5 cents. She seeks to hedge it using a 30 year bond that has a BPV of 8 cents.

How much of the 30 year bond should she buy or sell to hedge against parallel shifts in the yield curve?
A . Sell $1,600,000
B . Sell $625,000
C . Buy $1,000,000
D . Buy $1,600,000

View Answer

Answer: B

Explanation:

When hedging one fixed income security with another, the question as to how much of the hedge to buy (or sell) (ie the hedge ratio) for a given primary position is determined by their respective basis point values, which in turn are determined by their duration. Therefore, when hedging a long maturity bond with a PV01 of $3 with a short maturity bond that has a PV of $1, we will need to buy 3 times the notional value of the short maturity bond to achieve the same sensitivity to interest rates as the longer maturity bond. Additionally, we may also expect the interest rates on the hedge to move differently from the interest rates on the primary instrument being hedged, and this needs to be accounted for as well as part of the hedge ratio calculation. This is called the yield beta and is calculated as change in yield for primary position/change in yield for the hedge security.

The hedge ratio is determined both by the yield beta and the BPVs of the two securities. In this case, the yield beta is 1 (as the question speaks of a parallel shift in the yield curve, ie all rates rise or fall together), and the ratio of the BPVs is 5/8. Therefore she should sell 5/8 x 1,000,000 = $625,000 of the 30 year bond. Choice ‘b’ is the correct answer.