The Journal of finance tile of the F distribution, and for all subperiods except 1935-40 and 1946-50 the F statistics fall into the extreme right tail of the F distribution. Moreover, for the overall period and for most of the subperiods the values of Rp-r increase from lower to higher values of p. Since the twenty portfolios are formed on the basis of ranked estimates of the B risks of individual securities, these results are consistent with the positive tradeoff of risk for expected one- period percentage return hypothesized by the two-parameter model 14 And this evidence in support of a positive expected return risk tradeoff is actually quite meager relative to that in [3] and [7 In tests on common stock returns for the 1960, s, Roll [21] also finds that to a large extent, both the two-parameter model and the growth-optimal model are consistent with his data. It is well to emphasize again, however, that there is nothing anomolous in this result. It is consistent with a world of risk-averse investors and two-parameter return distributions which in addition has the are well approximated by a log utility function, 1s ers property that the market is dominated by risk-averters whose tastes for wealth V. HISTORICAL GROWTH-OPTIMAL PORTFOLIOS But this view of the world is so specific that further tests are warranted Such checks are especially desirable since the assumption of multivariate normality on which the T tests are based almost certainly does not apply to If the market is dominated by growth-optimizers, then, given complete agreement about return distributions, the market portfolio is growth-optimal Thus for any portfolio p E[In(1+ rotein(1+rot) Assuming a market that also conforms to the two-parameter model, one way to test(6) is to compute average values of observed In(1+ portfolios, and then examine whether the maximum of these averages is ob- tained with an efficient portfolio much different from M. To carry out such tests, however, we must identify the set of efficient portfolios in more concrete terms. Our models for efficient portfolios are taken from the two-parameter models of capital market equilibrium of Sharpe [23], Lintner [16], Black [2] and Vasicek [25] observed in the signs of the Yp = ip-1 of Table 1. Although it is not strong enough values of T2 and F, this pattern may provide some basis fo 15. Ro him lizes that the two-parameter and growth-optimal models are utually consistent. His reasoning, however, is based on the goodness of a quadratic approxima tion to the log utility function oint distribution of security returns is mt normal, which in turn implies that the joint distribution of portfolio returns is multi al. If portfolio returns are multivariate nor the zpt which are ratios of returns, cannot variate normal, so that sumption of the T2 tests on the znt is violated. And appar is known about the effects of nonnormality arious nonparametric methods to test the hypothes He is unable to reject the hypothesis with any of his methods, which all seem to give mparable to the t2 tests