In this paper a discrete mixture of normal distributions is proposed to explain the observed significant kurtosis (fat tails) and significant positive skewness in the distribution of daily rates of returns for a sample of common stocks and indexes. Stationarity tests on the parameter estimates of this discrete mixture of normal distributions model revealed significant differences in the mean estimates that can explain the observed skewness and significant differences in the variance estimates that can explain the observed kurtosis. An alternative explanation for the observed fat tails is the symmetric student model. The result of a comparison between the models is that the discrete mixture of normal distributions model has substantially more descriptive validity than the student model.

Stanley J. Kon, W. Patrick Lau, Specification Test for Portfolio Regression Parameter Stationarity and the Implications for Empirical Research, The Journal of Finance, Vol. 34, No. 2, Papers and Proceedings, Thirty-Seventh Annual Meeting, American Finance Association, Chicago, Illinois, August 29-31, 1978 (May, 1979), pp. 451-465

In this paper, the portfolio and the liquidity planning problems are unified and analyzed in one model. Stochastic cash demands have a significant impact on both the composition of an individual's optimal portfolio and the pricing of capital assets in market equilibrium. The derived capital asset pricing model with cash demands and liquidation costs shows that both the market price of risk and the systematic risk of an asset are affected by the aggregate cash demands and liquidity risk. The modified model does not require that all investors hold an identical risky portfolio as implied by the Sharpe-Lintner-Mossin model. Furthermore, it provides a possible explanation for the noted discrepancies between the empirical evidence and the prediction of the traditional capital asset pricing model.