SECURITY PRICES, RISK, AND MAXIMAL GAINS FROM DIVERSIFICATION *

SECURITY PRICES, RISK, AND MAXIMAL GAINS FROM DIVERSIFICATION * I. I ntroduction and G eneral S ummary of C onclusions S ections II and III of this paper set forth the simple logic which leads directly to the determination of explicit equilibrium prices of risk assets traded in competitive markets under idealized conditions. These equilibrium valuations of individual risk assets are shown to be simply, explicitly and linearly related to their respective expected returns, variances and covariances. The total risk on a given security is the sum of the variance of its own dollar return over the holding period and the combined covariance of its return with that of all other securities. This total risk on each security is “priced up” by multiplying by a “market price of dollar risk” which is common to all securities in the market. The expected dollar return on any security less this adjustment for its risk gives its certainty‐equivalent dollar return , and the market price of each security is simply the capital value of this certainty‐equivalent return using the risk‐free interest rate. In this paper, these relationships are shown to hold rigorously even when investors differ in their probability judgments and in other respects. It turns out, however, that the http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png The Journal of Finance Wiley

SECURITY PRICES, RISK, AND MAXIMAL GAINS FROM DIVERSIFICATION *

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Abstract

I. I ntroduction and G eneral S ummary of C onclusions S ections II and III of this paper set forth the simple logic which leads directly to the determination of explicit equilibrium prices of risk assets traded in competitive markets under idealized conditions. These equilibrium valuations of individual risk assets are shown to be simply, explicitly and linearly related to their respective expected returns, variances and covariances. The total risk on a given security is the sum of the variance of its own dollar return over the holding period and the combined covariance of its return with that of all other securities. This total risk on each security is “priced up” by multiplying by a “market price of dollar risk” which is common to all securities in the market. The expected dollar return on any security less this adjustment for its risk gives its certainty‐equivalent dollar return , and the market price of each security is simply the capital value of this certainty‐equivalent return using the risk‐free interest rate. In this paper, these relationships are shown to hold rigorously even when investors differ in their probability judgments and in other respects. It turns out, however, that the

Journal

The Journal of FinanceWiley

Published: Dec 1, 1965

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