Asset Pricing In Multiperiod Securities Markets

The paper provides an intertemporal version of the capital asset pricing model (CAPM) of Sharpe and Lintner. Although we allow for general changes in the investment opportunity set and for general risk-averse preferences, there are conditions under which two mutual funds are sufficient to generate all optimal portfolios. In particular, we require that the Riesz claim, which represents the date O pricing functional for the marketed claims, should lie in a scalar Brownian information set. Then we obtain an instantaneous counterpart to the CAPM pricing formula: a linear relationship between the conditional mean returns on the securities and conditional covariances with the return on the market portfolio. Our use of option pricing techniques requires continuous trading but does not require continuous consumption. In addition, we consider a large economy with a factor structure, as in Ross' arbitrage pricing theory. The dividends are assumed to have an approximate factor structure, with the factor components lying in the information set generated by an N-dimensional Brownian motion, and with the covariance matrices of the idiosyncratic components having uniformly bounded eigenvalues. We obtain an N-factor version of the pricing formula and relate the factors to the gains processes {price change plus accumulated dividends) for well-diversified portfolios. An approximate factor structure for dividends implies an approximate factor structure for the gains processes of the securities. Furthermore, the assumption_that per.capita supply is well diversified can motivate our condition that the Riesz claim lies in an N-dimensional Brownian information set.