mates is that, on average, the beta coefficients of stocks seem to move toward 1 over time. One explanation for this phenomenon is intuitive. A business enterprise usually is estab- lished to produce a specific product or service, and a new firm may be more unconven- tional than an older one in many ways, from technology to management style. As it grows, however, a firm often diversifies, first expanding to similar products and later to more di- verse operations. As the firm becomes more conventional, it starts to resemble the rest of the economy even more. Thus its beta coefficient will tend to change in the direction of 1. Another explanation for this phenomenon is statistical. We know that the average beta over all securities is 1. Thus before estimating the beta of a security our best forecast of the beta would be that it is 1. When we estimate this beta coefficient over a particular sample period, we sustain some unknown sampling error of the estimated beta. The greater the dif- ference between our beta estimate and 1, the greater is the chance that we incurred a large estimation error and that beta in a subsequent sample period will be closer to 1. The sample estimate of the beta coefficient is the best guess for the sample period. Given that beta has a tendency to evolve toward 1, however, a forecast of the future beta coefficient should adjust the sample estimate in that direction. Merrill Lynch adjusts beta estimates in a simple way.11 It takes the sample estimate of beta and averages it with 1, using weights of two-thirds and one-third: Adjusted beta 2⁄3 sample beta 1⁄3(1) For the 60 months ending in June 1994, GMs beta was estimated at .80. Note that the ad- justed beta for GM is .87, taking it a third of the way toward 1. In the absence of special information concerning GM, if our forecast for the market in- dex is 14% and T-bills pay 6%, we learn from the Merrill Lynch beta book that the CAPM forecast for the rate of return on GM stock is   E(rGM) rf adjusted beta [E(rM) rf] 6 .87 (14 6) 12.96%   The sample period regression alpha is .14%. Because GMs beta is less than 1, we know that this means that the index model alpha estimate is somewhat smaller. As in equation     11 A more sophisticated method is described in Oldrich A. Vasicek, "A Note on Using Cross-Sectional Information in Bayesian Es- timation of Security Betas," Journal of Finance 28 (1973), pp. 1233-39. III. Equilibrium In Capital Markets 10. Single−Index and Multifactor Models The McGraw−Hill Companies, 2001           CHAPTER 10 Single-Index and Multifactor Models 307