Generalizing the Sharpe-Lintner capital asset pricing model, Dieffenbach [4] presents a model of securities markets in a private enterprise economy in a multiperiod competitive equilibrium with uncertainty. Risk premiums on securities depend on the covariances of holding period returns with the return on the market portfolio and with a multiperiod cost-of-living index. This paper develops a quantitative theory of that relationship suitable for empirical estimation and testing. Whether the Arrow-Pratt relative risk aversion of a representative investor is greater or less than one is important in the theory; the empirical results for the United States suggest that this value exceeds one. A theoretical and empirical application of the theory to the term structure of United States Treasury securities concludes the paper. Mean observed returns are consistent with theoretical predictions for medium and long term securities, but the differences of mean observed returns among bills of different maturities exceed the theoretical predictions.