# P2.T5.22.14. Empirical approaches to fixed income hedging

#### David Harper CFA FRM

##### David Harper CFA FRM
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Learning objectives: Explain the drawbacks to using a DV01-neutral hedge for a bond position. Describe a regression hedge and explain how it can improve a standard DV01-neutral hedge. Calculate the regression hedge adjustment factor, beta. Calculate the face value of an offsetting position needed to carry out a regression hedge.

Questions:

22.14.1. In comparison to a yield-based DV01 hedge, which of the following is the best argument in favor of a regression hedge?

a. The regression hedge minimizes the profit and loss (P&L) variance of the hedged position
b. The regression hedge is based on economic theory and future developments rather than empirical analysis
c. The regression hedge does not require any out-of-sample test(s), which are often unreliable if the sample is small
d. The regression hedge solves for a risk-weight which qualifies as a valid risk-weighted asset (RWA) under Basel regulations

22.14.2. A market maker purchases $100.0 million in face amount of a 30-year Johnson & Johnson (JNJ) bond and hedges the interest rate risk by selling 30-year Treasury bonds. Each bond's yield and DV01 are given as the following: • JNJ bond: Yield = 3.952% and DV01 =$0.3124
• Treasury bond: Yield = 3.764% and DV01 = $0.2910 In order to increase the accuracy of the hedge, the market maker regresses (i.e., in a single-variable regression) the yield change of the JNJ bond as the dependent variable, Δy(JNJ,t), on the yield change of the Treasury bond, Δy(30,t), as the independent variable. This linear single-variable regression generates the following statistics: • Intercept, α = 0.0240 • Slope, β = 0.7150 • Coefficient of determination, R^2 = 73.4% If the market maker employs a single-variable regression hedge, which is nearest to the face amount of the Treasury bonds that will be sold? a.$15.05 million
b. $39.20 million c.$76.76 million
d. \$166.35 million

22.14.3. Erica works for a market maker who is going to hedge the purchase of Johnson & Johnson (JNJ) bonds by selling Treasury bonds. In order to compare a yield-based DV01 hedge to a regression, Erica conducts a single-variable regression; the summary results are shown below.

Erica is interested in the advisability of a yield-based DV01 hedge which assumes parallel shifts in the yields of the two bonds. Her hypothesis assumes a two-sided 95.0% confidence level. Can she accept the null hypothesis of parallel shifts in yields of the two bonds?

a. She rejects the hypothesis of parallel shifts in the yields of the two bonds because the true beta is not one
b. She accepts (i.e., cannot reject) the hypothesis of parallel shifts in the yields because the true beta might be one
c. She rejects the hypothesis of parallel shifts in the yields of the two bonds because beta the alpha is not zero
d. From a risk-return perspective, the trade is not advised because the standard error of the regression exceeds two