In this paper, we develop a Capital Asset Pricing Model (CAPM) using a mean-lower partial moment framework. We explicitly derive formulae for the equilibrium values of risky assets that hold for arbitrary probability distributions. We show that when the probability distributions and portfolio returns are either normal, stable (with the same characteristic exponent between 1 and 2 and the same skewness parameter, not necessarily zero), or Student-t distributions, our CAPM reduces to the traditional mean-scale CAPM's. Consequently, since the traditional equilibrium models are special cases of our model, the mean-lower partial moment framework is guaranteed to do at least as well in explaining market data. As an application of our theory, we derive an acceptance criterion for capital investment projects and note that corporate finance theory results developed, for example, in the well-known mean- variance framework carry over to the mean-lower partial moment framework.

This paper develops optimal portfolio choice and market equilibrium when investors behave according to a generalized lexicographic safety-first rule. We show that the mutual fund separation property holds for the optimal portfolio choice of a risk-averse safety-first investor. We also derive an explicit valuation formula for the equilibrium value of assets. The valuation formula reduces to the well-known two-parameter capital asset pricing model (CAPM) when investors approximate the tail of the portfolio distribution using Tchebychev's inequality or when the assets have normal or stable Paretian distributions. This shows the robustness of the CAPM to safety-first investors under traditional distributional assumptions. In addition, we indicate how additional information about the portfolio distribution can be incorporated to the safety-first valuation formula to obtain alternative empirically testable models.

The option pricing model developed by Black and Scholes and extended by Merton gives rise to partial differential equations governing the value of an option. When the underlying stock pays no dividends – and in some very restrictive cases when it does – a closed form solution to the differential equation subject to the appropriate boundary conditions, has been obtained. But, in some relevant cases such as the one in which the stock pays discrete dividends, no closed form solution has been found. This paper shows how to solve these equations by numerical methods. In addition, the optimal strategy for exercising American options is derived. A numerical illustration of the procedure is also presented.

This paper analyzes the optimal portfolio choice problem when security returns have a joint multivariate normal distribution with unknown parameters. For the case of limited, but sufficient (sample plus prior) information, we show that for a general family of conjugate priors, the optimal portfolio choice is obtained by the use of a mean-variance analysis that differs from traditional mean-variance analysis due to estimation risk. We also consider two illustrative cases of insufficient sample information and minimal prior information and show that in these cases it is asymptotically optimal for an investor to limit diversification to a subset of the securities. These theoretical results corroborate observed investor behavior in capital markets.

This paper develops a new distribution theory for common stock returns. The model is composed of a calendar time diffusion process and a jump process where the magnitudes of the jumps may be autocorrelated. Empirical tests are performed on a month of transactions returns for twenty New York Stock Exchange securities. The data analysis supports the validity of the proposed theory.

Savings bonds, retractable bonds and callable bonds are each equivalent to a straight bond with an option. Neglecting default risk the value of these contingent claims depends upon the riskless interest rate. This paper employs the option pricing framework to value these bonds, under the assumptions that the interest rate follows a Gauss-Wiener process and that the pure expectations hypothesis holds.