6I6 JOURNAL OF POLITICAL ECONOMY is, they are recomputed from monthly returns for 1930 through 1935 1936,or1937 As a measure of the non-B risk of security i we use s(ei), the standard deviation of the least-squares residuals eit from the so-called market model Rit=ar+Brmt+eit The standard deviation s(ei)is a measure of non-B risk in the following sense. One view of risk, antithetic to that of portfolio theory says that e risk of a security is measured by the total dispersion of its return distribution. Given a market dominated by risk averters, this model would predict that a security s expected return is related to its total return dis persion rather than just to the contribution of the security to the dispersion in the return on an efficient portfolio. If B,= cov(Ri, Rm)/o2(Rm),then in( 8)cov( EL, Rm)=0, and 2(R)=B2o(Rn)+G2(C)+21c0v(Rm,) Thus, from (9),one can say that s(ei) is an estimate of that part of the dispersion of the distribution of the return on security i that is not directl related toβ The month-by-month returns on the 20 portfolios, with equal weighting of individual securities each month, are also computed for the 4-year period 1935-38. For each month t of this period, the following cross- sectional regression-the empirical analog of equation(7)-is =5o+分1Ant-1+分B2p:-1+935n:=1(2)+ p=1,2,,20 The independent variable B, t-1 is the average of the B: for securities in ortfolio p discussed above; Bi. t-1 is the average of the squared values of these Bi(and is thus somewhat mislabeled); and Sp,t-1()is likewise the average of s(el) for securities in portfolio p. The s(e are computed from data for the same period as the component B of B, .t-1, and like thes they are updated annuall The regression equation(10)is(7)averaged across the securities in a portfolio, with estimates Bp. -1, B=,, t-1, and p t-1(2,)used as explanatory variables, and with least sults ir stomates of the stochastic coefficients Yot,?1t, et, and Yst. The results from(10)-the time series of month-by month values of the regression coefficients %ot, Y1t, i2t, and %at for the 4-year period 1935-38--are the inputs for our tests of the two-parameter odel for this period. To get results for other periods, the steps described hose accustomed to the portfolio viewpoint, this alternative model may m so naive that it should be classified as a straw man. but it is the model of risk luidity preference”and“ market seg e term structure of interest rates and by the Keynesian "normal backwardation of commodity futures markets. For a discussion of the issues with respect to hese markets, see Roll(1970)and K. Miller(1971)
riSK, RETURN, AND EQUILIBRIUM above are repeated. That is, 7 years of data are used to form portfolios the next 5 years are used to compute initial values of the independen variables in(10); and then the risk-return regressions of (10)are month by month for the following 4-year period The nine different portfolio formation periods (all except the first years in length), initial 5-year estimation periods, and testing periods(al but the last 4 years in length)are shown in table 1. The choice of 4-year testing periods is a balance of computation costs against the desire to reform portfolios frequently. The choice of 7-year portfolio formation Bp t-1 and 5, t-1(e,)in the risk-return regressions reflects a desire to bal ance the statistical power obtained with a large sample from a stationary process against potential problems caused by any nonconstancy of the pi The choices here are in line with the results of Gonedes(1973). His esults also led us to require that to be included in a portfolio a security available in the first month of a testing period must also have data for all 5 years of the preceding estimation period and for at least 4 years of the portfolio formation period. The total number of securities available in the first month of each testing period and the number of securities meeting the data requirement are shown in table 1 Table 2 shows the values of the 20 portfolios B, t-1 and their standard errors s(Bp, t-1) for four of the nine 5-year estimation periods. Also shown are: r(Rp, Rm), the coefficient of determination between Rpt and Rnt tion of the portfolio residuals from the market model of (8), not to be confused with Sp, t-1(2i), the average for individual securities, which is also shown. The B, t-1 and Sp,t-1(()are the independent variables in the risk turn regressions of (10) for the first month of the 4-year testing period following the four estimation periods shown. Under the assumptions that for a given security the disturbances ej (8)are serially independent, independent of Rmt, and identically distrib gh time, the standard error of B; is /no(r where n is the number of months used to compute B.Likewise 0(-1)=-0(G) no(ru) Thus, the fact that in table 2, s(E,) is gener the order of one -third to one-seventh 5,, t-1(21) implies that s(Bpt-1) is one-third to one-seventh