Estimating skewness persistence in market returns

Recent researches on stock market volatility have found considerable empirical evidence for the persistence of variance in stock market returns. The ARCH and unit root models in different versions analysed by Engle and Bollerslev (1986), Schwert (1989) and Nelson (1991) have usually discussed the conditional variance process as a function of lagged variance, where the skewness of the return distributions has no impact. Yet skewness preference by investors has been empirically documented by a number of researchers. Thus Kraus and Litzenberger (1976) applied the capital asset pricing model in a generalized form to allow for the effect of systematic market skewness on monthly excess returns for 20 portfolios for January 1936 to June 1970 constructed from the New York Stock Exchange (NYSE) stocks and found the regression coefficients of both beta and gamma parameters to be statistically significant. They also found that the higher beta portfolios tend to have more than proportionately higher gammas, where betas reflect the effect of variance and gammas the effect of skewness. This provides a partial explanation for the common empirical finding that the slope of the capital market line is lower than predicted by the traditional mean variance theory. That is, investors have an aversion to increases in market beta as a direct measure of systematic standard deviation and have a preference for increases in beta as a surrogate for proportionally greater increases in systematic positive skewness. More recently Friend and Westerfield (1980), Homaifar and Graddy (1988) and Falk and Levy (1989) found that in the long run, where the market is positively skewed, the marginal rate of substitution of the mean return for skewness is negative, indicating a preference for positive systematic skewness. A second reason for testing whether there is skewness persistence in a return process is the fact that the residuals