September 2022
Beginner
560 pages
17h 36m
English
Content preview from Fixed Income Securities, 4th Edition
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APPENDIX TO CHAPTER 6Regression Hedging and Principal Component Analysis
A6.1 REGRESSION HEDGES AND P&L VARIANCE
This section proves that i) the regression hedge minimizes the variance of the P&L of the hedged portfolio; and ii) the volatility of the regression‐hedged portfolio equals the DV01 of the position being hedged times the standard deviation of the regression residuals.
Begin with least‐squares estimation, which finds the parameters 
and 
to minimize,
To solve this minimization, differentiate (A6.1) with respect to each of the parameters, set each result to zero, and obtain the following two equations,
(A6.2)
(A6.3)
These equations can be solved to show that,
where and are the sample averages; and the standard deviations; the covariance; and the correlation. ...
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