October 7th, 2004, 2:07 pm
No matter the time horizon, beta is still, by definition, the ratio of the expected return on the value of a asset/portfolio versus the return of the index, or viewed another way, the statistical "delta" of your asset/portfolio to the factor of index returns.The problem, as you probably know, is that such short time horizons are not long enough to rely on the "average" used in beta which the noise around the beta will wash out, especially if you have a low R^2. If you try to compute rolling beta on such short windows, you will notice it fluctuate as wildly as stochastic vol and other highly exciting charts, which doesn't mean too well for this type of short-term "hedge".Some techniques I have used on similar problems include some representative sampling of a small selection of liquid stocks and indexes to try and get a higher R^2 to the portfolio I am trying to hedge. Even then, I generally have a horizon of 6 months or more. Some other things you might consider, but might still be long stretches, include correlation swaps, or representative sampling of a set of options. Hope this helps...