Quantitative Risk Management: A Practical Guide to Financial Risk, + Website

Appendix B: Stepwise Procedure for Replicating Portfolio

In Section 10.5, I laid out a simple procedure to build up a replicating portfolio by sequentially adding hedges. A more complex procedure, more closely analogous to stepwise regression, is to go back to consider earlier best-hedge assets, one at a time, to ensure that they produce a greater reduction in portfolio variance than the newest asset.

Choose the first replicating portfolio asset as the volatility-minimizing single best hedge.

That is, calculate (k) for all k. This is the best-hedge volatility for all one-asset best hedges or mirror portfolios.

Choose as the first replicating portfolio asset, 1^*, the asset k, which produces the smallest (k).

Choose the second replicating portfolio asset as that asset which, combined with the first, produces the largest reduction in portfolio variance.

That is, calculate (1^* & k) for ...