Multiperiod Portfolio Selection and Capital Asset Pricing

The purpose of this paper is to derive a simple capital asset pricing model in a multiperiod setting based on a microeconomic model of multiperiod portfolio selection. Capital asset pricing theory has been developed by Sharpe [1964], Lintner [1965] and Mossin [1966] in a oneperiod context using the microeconomic model of portfolio selection advanced by Markowitz [1959]. The first multiperiod models intended an extension of Markowitz’s results to several periods; the first of these models work with a utility function defined cawealth at the planning horizon (e.g. Smith [1967], Mossin [1968], Chen, Jen and Zionts [1971]). A somewhat newer approach that is more in the tradition of microeconomic theory, uses utility functions defined on the vector of present and future consumption streams (e.g. Hakansson [1969], Samuelson [1969], Fama [197o] and in a continuous time framework Merton [1971]). Usually, these approaches make a profit by the assumption of additive utility or of serial independence of subsequent rates of return on every risky asset (for a more detailed discussion of the literature see Long [1972, pp. 146–15o]).