A Note on Geometric Mean Portfolio Selection and the Market Prices of Equities

Robert H. Litzenberger and A. P. Budd

Journal of Financial and Quantitative Analysis, 1971, vol. 6, issue 5, 1277-1282

Abstract: This note examines the positive implications of the Latané-Tuttle [5, 6] geometric mean portfolio selection criteria for the determination of stock prices. Recently, Mossin [9] and Lintner [10] have derived the market prices of equities under the respective assumptions that investors have quadratic and exponential utility functions. While it would be presumptuous to suggest that all investors are “long-run wealth” maximizers, this criterion has a certain amount of intuitive appeal. The geometric mean criterion is equivalent to the maximization of a Bernoulli or logarithmic utility function and displays the desirable characteristic of decreasing absolute (i.e., as the investor's wealth increases, he becomes less averse to risk). This contrasts with the exponential utility function which displays constant absolute risk aversion and the quadratic utility function which displays the undesirable characteristic of increasing absolute risk aversion. Another suggested desirable characteristic of the geometric mean criterion is that it emphasizes the avoidance of bankruptcy while maximizing the asymptotic rate of growth of wealth [4, 5] and maximizing the probability of exceeding a given wealth level within a fixed time [3]. This note analyzes the aggregate effect on stock prices of investors using the geometric mean portfolio selection criterion.

Date: 1971
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