May 28th, 2002, 4:42 pm
The main error in estimating Beta is usually nonsimultaneous quotes. The more frequently you measure, the more serious this problem. On the other hand, using a longer measurement interval throws away information that can be used to reduce sampling error. In this case you can get the best of both worlds by estimating using overlapping weekly (or any other interval) periods. Sometimes people use an autocorrelation adjustment."Adjusted" Beta can mean adjusted for many different things: capital structure, autocorrelation, events and others.Shrinkage is a general statistical technique for improving estimates. It is usually better to shrink Betas to an industry mean than to 1, although you can use 1 because you know it is the average Beta of stocks in the index weighted by index weight. The idea, in simple terms, is that your highest and lowest Betas are likely to have positive and negative respectively measurement errors.For example, suppose you want to predict a baseball player's batting average in the second half of the season, based on first half average (this was the example in Stein's famous paper). You might simply use the first half average as your prediction. But it turns out if you shrink the estimates toward the population mean, you get smaller errors. If you shrink toward position average, you do even better.