Portfolio analysis has generally been restricted to problems in, at most, two dimensions, expected return and risk, the latter usually measured by standard deviation. In two papers Jean [2, 4] has attempted to extend the analysis to three and many dimensions by deriving risk premiums as functions of higher order moments. This paper corrects several errors in his work and derives a normative, individual pricing model for risky securities analogous to the capital market line within the framework of a perfect market.

This paper examines the pricing of convertible bonds and preferred stocks. The optimal policies for call and conversion of these securities are determined via the criterion of dominance. The techniques underlying the Black-Scholes Option Model are used to price convertible securities as contingent claims on the firm as a whole.

Using the option pricing methods developed by Black and Scholes as a general technique for contingent claims analysis, this paper examines a class of mutual funds known as Dual Purpose Funds. By constructing a simplified model for these funds under the ‘perfect hedge’ conditions of Black and Scholes, it is demonstrated that the asset value of the fund will always exceed the market value and that it is not inconsistent with market equilibrium or efficiency for the capital shares to sell at a discount. The simple model predicts price fluctuations in the seven dual funds studied quite well; however, there is a persistent downward bias in the predicted price level. Finally, refinements to the model are examined to determine the nature of the misspecification causing this bias.

This paper derives a stronger version of Huberman's recent “preference free” pricing theorem. This pricing result relates the expected return on an asset to its factor responses and the covariance structure of the residuals from a linear factor model. It must characterize any infinite asset economy in which no arbitrage opportunities are present whether or not the factor model has uncorrelated residuals. This result provides the intuition for the role of residual risk in the pricing model and eliminates some classes of arbitrage opportunities still present under Huberman's bound. Some applications to empirical tests and performance measurement are also discussed.