Bjs 1972 discuss another possible reason for beta

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BJS [1972] discuss another possible reason for beta factor pricing: mismeasurement of the market portfolio. If we use a market portfolio that differs randomly from the true market portfolio, stocks that seem to have low betas will on average have higher betas when we use the correct market portfolio to esti- mate them. Our betas are estimated with error (even in the final portfolio), and we select stocks that seem to have low betas. Such stocks wdl usually have posi- tive alphas using the incorrect market portfolio. The portfolio method does not eliminate this bias. Perhaps the most interesting way in which the market portfolio may be mismeasured involves our neglect of foreign stocks. World capital markets are becoming more integrated all the time. In a fully inte- grated capital market, what counts is a stock’s beta with the world market portfolio, not its beta with the issuer country market portfolio. This may cause low- beta stocks to seem consistently underpriced. If investors can buy foreign stocks without penalty, they should do so; if they cannot, stocks with low betas on their domestic market may partly substitute for foreign stocks. If this is the reason the line is flat, they may also want to emphasize stocks that have high betas with the world market portfolio. Can’t we do some tests on stock returns to sort out which of these theoretical factors is most impor- tant? I doubt that we have enough data to do that. We have lots of securities, but returns are highly correlated across securities, so these observations are far from independent. We have lots of days, but to esti- mate factor pricing what counts is the number of years for which we have data, not the number of distinct observations. If the factor prices are changing, even many years is not enough. By the time we have a reasonable estimate of how a factor was priced on average, it will be priced in a different way. Moreover, if we try to use stock returns to distinguish among these explanations, we run a heavy risk of data mining. Tests designed to distinguish may accidentally favor one explanation over another in a given period. I don’t know how to begin designing tests that escape the data mining trap. VARYING THE ANAZYSIS While the BJS study covers lots of ground, I am especially fond of the “portfolio method” we used. Nothing I have seen since 1972 leads me to believe that we can gain much by varying this method of anal- ysis. The portfolio method is simple and intuitive. We try to simulate a portfolio strategy that an investor can actually use. The strategy can use any data for constructing the portfolio each year that are available to investors at the start of that year. Thus we can incorporate into our selection method any “cross- sectional” effects that we think are important.
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