RiSK, RETURN, AND EQUILIBRIUM 6II ibrium when investors make portfolio decisions according to the two parameter model Assume again that the capital market is perfect. In additie t from the information available without cost all investors derive the same and correct assessment of the distribution of the future value of any asset or portfolio-an assumption usually called "homogeneous expe ecta tions. Finally, assume that short selling of all assets is allowed. Then Black (1972) has shown that in a market equilibrium, the so-called arket portfolio, defined by the weights total market value of all units of asset i mn≡ total market value of all assets is always efficient. Since it contains all assets in positive amounts, the market portfolio a convenient reference point for testing the expected return-risk conditions C1-C3 of the two-parameter model. And the homogeneous-expectatio aption implies a correspondence between assents of return distributions and distributions of ex post returns that is also re- quired for meaningful tests of these three hypotheses C. 4 Stochastic Model for Returns Equation(6)is in terms of expected returns. But its implications must be tested with data on period-by-period security and portfolio returns. We wish to choose a model of period-by-period returns that allows us to use observed average returns to test the expected-return conditions C1-C3, but one that is nevertheless as general as possible, We suggest the follo ing stochastic generalization of (6) Yo+Yn;+y2B2+73s1+帘t The subscript t refers to period t, so that Ri is the one-period percent- age return on security i from t-1 to t. Equation(7)allows Yot and Yit to vary stochastically from period to period. The hypothesis of condition E(Rm)-E(Rod)l in (6), is positive-that is, E(1)=E(Rmt)- E(Rm)>o The variable B2 is included in(7)to test linearity. The hypothesis of ondition Cl is E(Ye)=0, although Yet is also allowed to vary stochast- cally from period to period. Similar statements apply to the term involving Si in(7), which is meant to be some measure of the risk of security i that is not deterministically related to Bl. The hypothesis of condition C2 is E(Yar)=0, but Yat can vary stochastically through time. The disturbance n is assumed to have zero mean and to be independent of all other variables in(7). If all portfolio return distributions are to be