LO 10.2: Describe a regression hedge and explain how it can improve a standard

LO 10.2: Describe a regression hedge and explain how it can improve a standard DV01 -neutral hedge.
A regression hedge takes DV01 -style hedges and adjusts them for projected nominal yield changes compared to projected real yield changes. Least squares regression analysis, which is used for regression-based hedges, looks at the historical relationship between real and nominal yields.
The advantage of a regression framework is that it provides an estimate of a hedged portfolios volatility. An investor can gauge the expected gain in advance and compare it to historical volatility to determine whether the hedged portfolio is an attractive investment.
For example, assume a relative value trade is established whereby a trader sells a U.S. Treasury bond and buys a U.S. TIPS (which makes inflation-adjusted payments) to hedge the T-bond. The initial spread between these two securities represents the current views on inflation. Over time, changes in yields on nominal bonds and TIPS do not track one-for- one. To illustrate this hedge, assume the following data for yields and DVOls of a TIPS and a T-bond. Also assume that the trader is selling 100 million of the T-bond.
Bond TIPS T-Bond i e l Y i e l d (%) 1.325 3.475
DV01 0.084 0.068
If the trade was made DV01-neutral, which assumes that the yield on the TIPS and the nominal bond will increase/decrease by the same number of basis points, the trade will not earn a profit or sustain a loss. The calculation for the amount of TIPS to purchase to hedge the short nominal bond is as follows:
lOOMx 0.068 100
0.084 x —– 100 lOOMx 0.068 0.084
= $80.95 million
where: Fr = face amount of the real yield bond
To improve this hedge, the trader gathers yield data over time and plots a regression line, whereby the real yield is the independent variable and the nominal yield is the dependent variable. To compensate for the dispersion in the change in the nominal yield for a given change in the real yield, the trader would adjust the DV01-neutral hedge.
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Topic 10 Cross Reference to GARP Assigned Reading – Tuckman, Chapter 6
Hedge Adjustment Factor