# LO 10.4: Calculate the face value o f an offsetting position needed to carry out a

LO 10.4: Calculate the face value o f an offsetting position needed to carry out a regression hedge.
Defining FR and FN as the face amounts of the real and nominal bonds, respectively, and their corresponding DVOls as DV01^ and DV01^, a DV01 hedge is adjusted by the hedge adjustment factor, or beta, as follows:
FR = FN x
PV01N DV01r
X(3
Now that we have determined the variability between the nominal and real yields, the hedge can be adjusted by the hedge adjustment factor of 1.0198:
xl.0198
$82.55 million \ / .068 0.084 V0 / lOOMx This regression hedge approach suggests that for every$ 100 million sold in T-bonds, we should buy \$82.55 million in TIPS. This will account for hedging not only the size of the underlying instrument, but also differences between nominal and real yields over time.
Note that in our example, the beta was close to one, so the resulting regression hedge did not change much from the DV01-neutral hedge. The regression hedge approach assumes that the hedge coefficient, (3, is constant over time. This of course is not always the case, so it is best to estimate the coefficient over different time periods and make comparisons.
Two other factors should be also considered in our analysis: (1) the R-squared (i.e., the coefficient of determination), and (2) the standard error of the regression (SER). The
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Topic 10 Cross Reference to GARP Assigned Reading – Tuckman, Chapter 6
R-squared gives the percentage of variation in nominal yields that is explained by real yields. The standard error of the regression is the standard deviation of the realized error terms in the regression.
Two-Variable Regression Hedge