Journal of Banking and Finance 7 (1983) 31--44. North-Holland Publishing Company THE PRICING OF CAPITAL ASSETS IN A MULTIPERIOD WORLD Marshall E. BLUME* The University of Pennsylvania Philadelphia PA 19104 USA Received March 1981, final version received September 1982 This paper proposes a general framework for the pricing of capital assets in a multiperiod world. Under quite general conditions, the analysis shows that the equilibrium expected nominal return on any asset can always be expressed as the sum of the risk-free rate and various risk premiums. The first risk premium is identical to the usual risk premium in the Sharpe-Lintner- Mossin capital asset pricing model. The mathem atical forms of all the remaining risk prem iums are identical even though each individual risk premium may be present for a different reason. I Introduction Recent empirical tests of the traditional capital asset pricing model of Sharpe, Lintner and Mossin have found that this model is not fully consistent with observed returns on common stock? Partly in resPonse, various authors have developed alternative pricing models. For instance, in a multiperiod world, Merton 1973) postulates a changing investment opportunity set as a function of a stochastic interest rate. In another early extension, Mayers 1972) allows for human capital. Many other extensions have been proposed, but any attempt to review everyone would require an article in itself. The purpose of this paper is to propose a general framework in which to interpret these various extensions and by implication to demonstrate their conceptual similarities. Specifically, the expected nominal return on any asset in equilibrium can be viewed as the sum of the nominal risk-free asset, and four basic kinds of premiums. The first premium is the one common to the traditional capital asset pricing model and is associated with the usual beta coefficient of that model. The remaining three types of premiums are associated respectively with: a) state variables which condition the evaluation of end-of-period nominal wealth, b) departures of the joint probability distribution of end-of-period random variables from normality, *The author would like to thank Professors Eugene Fama, Andre Farber, Irwin Friend, E. Han Kim, Stuart M. Turnbull, and Randolph Westerfield for their helpful comments. The financial support of the Rodney L. White Center for Financial R esearch is gratefully acknowledged. 1For example, see Blume and Friend (1973) or Fama and MacBeth (1973). 0378-4266/83/ 03.00