THE AMERICAN ECONOMIC REVIEW SEPTEMBER 978 run a time-series regression trary to the expected results from the CAPM Rt=a;+β1Rnt+ea since, if the CA PM is cor find that y2=0. Moreover, in most cases and estimate the systematic risk B, of each the contribution of Se, to the coefficient of asset i(where R and Rmt are the rates of re- correlation is even more important than the urn of the ith asset and the market port- contribution of the systematic risk, B folio, respectively, in year t). In the second In this paper I try to narrow the gap be- step, in order to examine the validity of the tween the theoretical model and the em CA PM, we run a cross-section regression irical findings by deriving a new version of R the Ca PM in which investors are assumed to hold in their portfolios some given num- R, is the average return on the ith ber of securities. obviously, investors' port- risky asset, B, is the estimate of the ith asset folios differ in the proportions of risky as stematic risk take s sets and even in the types of risky assets egression, and u, is a residual term. If the that they hold This, of course, is consistent CA PM is valid one should obtain(see equa- with investors' behavior as established in tion (I))in equilibrium, Yo =0 and y,- previous empirical research. I denote the Rm-r, where Yo and f, are the regression modified model as GCA PM (general capital coefficients estimated by(1), and Rm is the asset pricing model), since the CAPM average observed rate of return on the mar ket portfolio( for example, average rate of return on Standard and Poor's ind these conditions is given in Section Il. In Unfortunately, in virtually all empirical the third section I show that the modified research, ' it emerges that fo is significantly model explains the discrepancy between the positive and y is much below Rm-r. For theoretical results of the CAPM and the rates of return of individual stocks the cor- empirical findings mentioned above. Some elation coefficient of (1)is very low if one empirical results are presented which con employs monthly rates of return, and only firm that the systematic risk 8, plays no role 20-25 percent with annual rates of return in explaining price behavior, once the vari- Finally, in virtually all empirical studies, ance is taken into account, (Section IV) formulation(3)increases the correlation co- Concluding remarks are given in Section V efficient (3)R-r=0+;6,+2S I. Equilibrium in an Imperfect Market The CAPM where i stands for the ith security and s William Sharpe and Lintner(1965a)have e residual variance around the time-series shown that if there is no constraint on the regression(2), 1. e, the variance of the re- number of securities to be included in the siduals eit. In this formulation the estimate investors' portfolio, all investors will hold Y, happens to be significantly positive, con- some combination of m, the market port folio of risky assets, and the riskless asset See Fisher Black. Michael Jensen ron bearing interest rate r(see Figure 1) rton Now, suppose that, as a result of transac- Mill emphasize that the low correlation is obtained tion costs, indivisibility of investment,or and scho when equation(I')is regressed using ck. even the cost of keeping track of the new n order to minimize the measurement errors, it is financial development of all securities, the mon to use in(I')portfolios rather than individual kth investor decides to invest only in nk ks. This portfolio technique increases the correla possible errors, individual stocks show in spite of the securities. Under this constraint he will tion coefficient dramatically. Howe have some interior efficient set (of risky the CAPM defines equilibrium prices of individual sets), say, A'B, and the investor will divide his portfolio between some risky portfolio k 0m3303038AN644 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 1978 run a time-series regression, (2) Rit ai j + 3iRmt + eit and estimate the systematic risk f3 of each asset i (where Rit and Rmt are the rates of re￾turn of the ith asset and the market port￾folio, respectively, in year t). In the second step, in order to examine the validity of the CA PM, we run a cross-section regression, (1') Ri-r = 'Yo + zlyli + Ui where Ri is the average return on the ith risky asset, fi is the estimate of the ith asset systematic risk, taken from the time-series regression, and ui is a residual term. If the CAPM is valid one should obtain (see equa￾tion (1)) in equilibrium, j0 = 0 and j' = Rm - r, where ' and 7 are the regression coefficients estimated by (1'), and Rm is the average observed rate of return on the mar￾ket portfolio (for example, average rate of return on Standard and Poor's index). Unfortunately, in virtually all empirical research,3 it emerges that 'o is significantly positive and j, is much below Rm - r. For rates of return of individual stocks the cor￾relation coefficient of (1') is very low if one employs monthly rates of return, and only 20-25 percent with annual rates of return.4 Finally, in virtually all empirical studies, formulation (3) increases the correlation co￾efficient, (3) Ri- r = To+ j lOi+ 72Sei where i stands for the ith security and S2. is the residual variance around the time-series regression (2), i.e., the variance of the re￾siduals eit. In this formulation the estimate y2 happens to be significantly positive, con￾trary to the expected results from the CA PM since, if the CAPM is correct, one should find that 72 = 0- Moreover, in most cases, the contribution of S2. to the coefficient of correlation is even more important than the contribution of the systematic risk, /3. In this paper I try to narrow the gap be￾tween the theoretical model and the em￾pirical findings by deriving a new version of the CA PM in which investors are assumed to hold in their portfolios some given num￾ber of securities. Obviously, investors' port￾folios differ in the proportions of risky as￾sets and even in the types of risky assets that they hold. This, of course, is consistent with investors' behavior as established in previous empirical research. I denote the modified model as GCA PM (general capital asset pricing model), since the CA PM emerges as a special case. The derivation of the GCAPM under these conditions is given in Section II. In the third section I show that the modified model explains the discrepancy between the theoretical results of the CAPM and the empirical findings mentioned above. Some empirical results are presented which con￾firm that the systematic risk fi plays no role in explaining price behavior, once the vari￾ance is taken into account, (Section IV). Concluding remarks are given in Section V. I. Equilibrium in an Imperfect Market: The GCA PM William Sharpe and Lintner (1965a) have shown that, if there is no constraint on the number of securities to be included in the investors' portfolio, all investors will hold some combination of m, the market port￾folio of risky assets, and the riskless asset bearing interest rate r (see Figure 1). Now, suppose that, as a result of transac￾tion costs, indivisibility of investment, or even the cost of keeping track of the new financial development of all securities, the kth investor decides to invest only in nk securities. Under this constraint he will have some interior efficient set (of risky as￾sets), say, A 'B', and the investor will divide his portfolio between some risky portfolio k 3See Fisher Black, Michael Jensen, and Myron Scholes; George Douglas; Lintner (1965b); Merton Miller and Scholes. 4I emphasize that the low correlation is obtained when equation (1') is regressed using individual stock. In order to minimize the measurement errors, it is common to use in (I') portfolios rather than individual stocks. This portfolio technique increases the correla￾tion coefficient dramatically. However, in spite of the possible errors, individual stocks should be used since the CA PM defines equilibrium prices of individual stocks. This content downloaded from 202.115.118.13 on Wed, 11 Sep 2013 03:07:38 AM All use subject to JSTOR Terms and Conditions