erm growth in a Short-Term Market as in the two-parameter model. o Thus, the first portfolio contains the securities with the lowest estimates of Bu, while the twentieth portfolio contains the securi. ties with the highest estimates of B, Let z, be the average through time of the zut. The hypothesis that the market folio is growth-optimal and thus that the pricing of assets is dominated by growth-optimizers can be rejected if the z for some portfolio or for some subset of portfolios can be shown to differ systematically from 1.0. Such a test is provided by Hotelling's T, defined in the present case as Y'S-IY where Y is the vector of Y, =Z-1, p=1,., 9, 11,..., 20, S is the 19 x 19 estimated covariance matrix of the component zut, and n is the number of months used in computing both Y and S One portfolio (we have chosen the tenth) must be omitted from the computations to avoid the singularity in S that would otherwise arise from the fact that for any t the sum of the zpt over the twenty portfolios is always very close to 20 12 Under the(in this case tenuous)assumption that the joint distribution of the zpt is multivariate normal and stationary through time, the statistic n-19 F 19(n-1) has the f distribution with degrees of freedom (DF)19 and n-19 Table 1 presents the results of the Hotelling t- tests for the overall period 1935-6/68 and for various subperiods. There are no F statistics in the table that exceed the 95 fractile of the F distribution, and the f for only one sub- period, 1956-6/68, exceeds the 90 fractile of the F distribution. In short, the vidence in Table 1 is not sufficient to reject the hypothesis that our proxy for the market portfolio is growth-optimal, and thus we cannot reject the hy hesis that the g of assets is dominated by growth-optimizers of the hypothesis E(Rp)=E(Rx), p=1, 2, 20, are presented in Table 2. 13 The results support rejection of the hy pothesis. The F statistic for the overall period 1935-6/ 68 excedes the 95 frac 10. In the two-parameter model, the risk of M is d2(RM), the variance of its one-period centage return, which can be written as 0n)=平 XiarXjM Cov(页,对)= 2xiM(2 xIM cov(郎,瓦) =∑xMov(武,x) Thus cov (R, R) is the risk of asset i in olio m in that it is the contribution of i to the le risk of M, For of this viewpoint, see [51, [7] or Fama and Miller [81, Chapter 7. isis not 11. See, for example, Morrison [19] or Anderson [1 ter that this the case. The number of securities allocated to portfolios in any given month is always less the number available 13. In this case there is no need to delete one of the portfolios from the tests since the covariance matrix of the r, is nonsingular