A RECENT ARTICLE in this Journal' explored the conditions for equilibrium in the market for capital assets under the assumptions that investors are riskaverters, have similar (probabilistic) beliefs about the future performance of various assets, and can borrow or lend funds at a common (pure) interest rate. Briefly, the article showed that under such conditions market prices of capital assets will adjust so that the predicted risk of each efficient portfolio's rate of return is linearly related to its predicted expected rate of return. Letting vi stand for the standard deviation of the subjective probability distribution of the rate of return on an efficient portfolio, and E1 for the expected value of the distribution, the prices of capital assets will adjust until all efficient portfolios conform to the relationship Ei =p+bbvi where p is the pure (riskless) interest rate and b (>O) is the risk-premium. An important corollary concerns the relationship among the predicted rates of return on efficient portfolios: under the assumed conditions they will be perfectly correlated.Strictly speaking, the implications of this theory cannot be tested practically, since the relationships refer to predictions concerning expected returns from assets and the associated risks. Clearly, actual results may diverge considerably from the predictions made by investors at the time they purchase assets. Moreover, investor preferences and investment opportunities presumably change over time. This poses a major problem: if the equilibrium value of p (the price of time) and b (the price of risk) change from year, it may be dangerous to use data from several years to estimate their average values. But if the results from several years are not used, how can predicted values of Et and av be estimated? In many respects the problem is similar to that of measuring demand curves. If any empirical tests are to be performed, rather stringent assumptions must be made.The remainder of this paper shows the results obtained by using ex post values of the means and standard deviations of return as surrogates for the corresponding ex ante predictions of investors. Section I provides evidence concerning the relationship between E1 and vi for the portfolios held by a

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This paper describes the advantages of using a particular model of the relationships among securities for practical applications of the Markowitz portfolio analysis technique. A computer program has been developed to take full advantage of the model: 2,000 securities can be analyzed at an extremely low cost--as little as 2% of that associated with standard quadratic programming codes. Moreover, preliminary evidence suggests that the relatively few parameters used by the model can lead to very nearly the same results obtained with much larger sets of relationships among securities. The possibility of low-cost analysis, coupled with a likelihood that a relatively small amount of information need be sacrificed make the model an attractive candidate for initial practical applications of the Markowitz technique.

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