UNCERTAINTY AND RELATIVE RATES OF RETURN ON SECURITIES: A THEORETICAL AND EMPIRICAL ANALYSIS*

Abstract

s of Doctoral Dissertations 1023 The index is therefore then relatively low. The probability distribution conditional on the state of the world of future commodity prices and security returns describes the consumption-investment opportunity set for an individual. The dependence of this set on the state of the world determines the dependence of the single period utility and the index on the state of the world. The expected return on a security is then the sum of three terms: first, the return on a riskless security; second, the Arrow-Pratt relative risk aversion of the representative individual multiplied by the covariance of the return with the return on the market portfolio; third, one minus this relative risk aversion multiplied by the covariance of the return with the cost-of-living index of the representative individual. The Sharpe-Lintner result is just this finding without the third term. The formula is useful for empirical work, since one can express the cost-of-living index as a function of observable variables. Whether the relative risk aversion is greater or less than one is clearly important. A discussion of how one might test the model and estimate the unknown parameters follows the theoretical development. Using a likelihood ratio test involving monthly post World War II returns on common stock, one always accepts the null hypothesis that the theory is valid; but the power of the test is low. Estimating the relative risk aversion of the representative individual from observed security returns, one finds great uncertainty in the estimate; but the results indicate a relative risk aversion exceeding one. The model provides a quantitative theory of the term structure of interest rates. Many investigators conclude that expected returns need not be independent of maturity, but they do not present an explicit quantitative theory of the determinants of the differentials. The Sharpe-Lintner equation also does not yield such a theory, since in general it is valid only if the future consumption-investment opportunity' set is independent of the state of world. In particular there must be no uncertainty about future interest rates, and the equation therefore does not provide any theory beyond the traditional certainty theory. Using the theory, one can compute predicted expected returns as a function of maturity. For post World War II data a comparison of the predicted and observed means of United States Treasury securities supports the theory except for short term bills. For them transactions costs may perhaps explain the disparity. A three asset-short term bonds, long term bonds, and stock-theoretical model of portfolio choice concludes the thesis. The results together with empirical regularities associated with the preferred habitat theory of portfolio choice implies a relative risk aversion exceeding one for the representative individual. This content downloaded from 207.46.13.121 on Wed, 05 Jul 2017 18:02:13 UTC All use subject to http://about.jstor.org/terms