THE AMERICAN ECONOMIC REVIEW SEPTEMBER /978 enc On the basis of these assumptions we ob tain the classic CA PM formula as a special (16)(1+n)Po=Pn- case of the GCA PM suggested in this paper. In this case, equation(16)reduces to 2 TA(HR- NuoN+E nj oT ∑7|N (17)(1+r)Po=P Tk 2TACHA-IINI0T2+E N o tion induces all investors to have the same 1 nvestment strategy in risky assets,(see 2 Sharpe and Lintner, 1965a)all of them hold all the risky assets nk =n and, also N/N where T&/To and hence Nik= N Tk/To and N, N, T&/To. By substituting the last reults equation(18)we derive Equation(17)is very similar to the classic elationship of the CA PM(see equation (20)). The only two differences are: (a)no (19)(1+r)po=P1-Y he securities' risk is given as the weighted average of the risks of each investor when larger the investor's wealth(Tk), the greater his impact on price determination, and(b) or the market price of risk y, is defined some defined by Lintner(1965a). Thus, the classic (20) what differently from the well-known Y,as T0∑T CAPM may be the approximate equilib- rium model for stocks of firms which are ∑TNo*+∑No AT&T), but not for small firms whose stocks are held by a relatively small group of investors If we relax the constraint that the kth in- Since Xk Tk= To, equation(20)reduces to vestor holds only nk securities, then each the well-known equilibrium equation of the investor holds the market portfolio and traditional CA PM (see Lintner 1965a hence ,andσ2n=σ, where p.600), um and om are the expected rate of return (20)(1 r)po= pal spectively b Recall that without loss of generality we deal only with the optimal unlevered portfolio, The basic equi- Finally, I would like to emphasize the librium equation(equation (6)and hence all the other basic difference between equations(15)and deal with the levered or the unlevered portfolio. See (17). Equation(15), which I advocate, rep resents the most general form, and hence 0m3303038AN650 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 1978 Hence, (16) (1 + r)PiO = Pi, - y To ) L Tk(,k - FN2r) N 2 + Njk Tk - r) k or (17) (1 + r)PiO= Pi, nk L Tk Tk (8k - r)L, Nka,2 + E Nik -ykik JI t Z Tk (jk - r) k where Y mi E T2.jak k Equation (17) is very similar to the classic relationship of the CA PM (see equation (20')). The only two differences are: (a) now the securities' risk is given as the weighted average of the risks of each investor when the weights are Tk (gk - r), so that, the larger the investor's wealth (Tk), the greater his impact on price determination, and (b) the market price of risk y, is defined some￾what differently from the well-known y, as defined by Lintner (1965a). Thus, the classic CA PM may be the approximate equilib￾rium model for stocks of firms which are held by many investors (for example, AT&T), but not for small firms whose stocks are held by a relatively small group of investors. If we relax the constraint that the kth in￾vestor holds only nk securities, then each investor holds the market portfolio and hence6gu - r = /Im - r, and U2 = Sk, where /Im and am are the expected rate of return and variance of the market portfolio, re￾spectively. On the basis of these assumptions we ob￾tain the classic CAPM formula as a special case of the GCA PM suggested in this paper. In this case, equation (16) reduces to T 2 (18) (1 + r)pio =Pi - Y >T k LTk nk But since the relaxation of the imperfec￾tion induces all investors to have the same investment strategy in risky assets, (see Sharpe and Lintner, 1965a) all of them hold all the risky assets nk = n and, also Nik/Ni = Tk/ To and hence NTk = NiTk/ To and Njk = NJTk/ T0. By substituting the last reults in equation ( 18) we derive (19) (1 + r)p, ik =pji - = k k or (20) (1 + r)p0o = p,i - -yT k BtSince the =ro,elaxation of20) imerfcst then inuesl-knownvequilirsium haeqution samte ShrpeitindlC M Lintner 11965a, (e l fthmhl F y o ke t k basic diSernce between equation (20) run s the) wEl-nweqiiruequation of),wic avcth,ep traiinalthe CAM (see tneral f , ad ha, p. 600), ~ O . T (20') (1I r)pi = p~i, - [Ni< + Nj bSince difernc bTwee e quations20 (15)ce and (17) wel-nweqiiruequation (1) hc doate,hep tresetintsth most gseeLnnerafoman hence 6Recall that without loss of generality we deal only with the optimal unlevered portfolio. The basic equi￾librium equation (equation (6)) and hence all the other results derived from it are unchanged no matter if we deal with the levered or the unlevered portfolio. See fn. 5. 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