# LO 10.5: Calculate the face value o f multiple offsetting swap positions needed to

LO 10.5: Calculate the face value o f multiple offsetting swap positions needed to carry out a two-variable regression hedge.
Regression hedging can also be conducted with two independent variables. For example, assume a trader in euro interest rate swaps buys/receives the fixed rate in a relatively illiquid 20-year swap and wishes to hedge this interest rate exposure. In this case, a regression hedge with swaps of different maturities would be appropriate. Since it may be impractical to hedge this position by immediately selling 20-year swaps, the trader may choose to sell a combination of 10- and 30-year swaps.
The trader is thus relying on a two-variable regression model to approximate the relationship between changes in 20-year swap rates and changes in 10- and 30-year swap rates. The following regression equation describes this relationship:
Ayt20 = ol + (310Ayt10 + (330Ayt30 + et
Similar to the single-variable regression hedge, this hedge of the 20-year euro swap can be expressed in terms of risk weights, which are the beta coefficients in the above equation:
(F10 xD V O l10) (F20 x DVO l20)
(- F 30x DVQ130) (F20x DV0120)
change in 10-year swap rate, 3
change in 30-year swap rate, 3
The trader next does an initial regression analysis using data on changes in the 10-, 20-, and 30-year euro swap rates for a five-year time period. Assume the regression output is as follows:
Number of observations R-squared Standard error
1281 99.8% 0.14
Regression Coefficients Alpha Change in 10-year swap rate Change in 30-year swap rate
Value -0.0014 0.2221 0.7765
Standard Error
0.0040 0.0034 0.0037
Given these regression results and an illiquid 20-year swap, the trader would hedge 22.21% of the 20-year swap DV01 with a 10-year swap and 77.65% of the 20-year swap DV01 with a 30-year swap. Because these weights sum to approximately one, the regression hedge DV01 will be very close to the 20-year swap DV01.
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2018 Kaplan, Inc.
Topic 10 Cross Reference to GARP Assigned Reading – Tuckman, Chapter 6
The two-variable approach will provide a better hedge (in terms of R-squared) compared to a single-variable approach. However, regression hedging is not an exact science. There are several cases in which simply doing a one-security DV01 hedge, or a two-variable hedge with arbitrary risk weights, is not appropriate (e.g., hedging during a financial crisis).
Level and Change Regressions