Modeling asset returns with skewness, kurtosis, and outliers

Abstract

This chapter uses an exponential generalized beta distribution of the second kind (EGB2) to model the returns on 30 Dow Jones industrial stocks. The model accounts for stock return characteristics, including fat tails, peakedness (leptokurtosis), skewness, clustered conditional variance, and leverage effect. The evidence suggests that the error assumption based on the EGB2 distribution is capable of taking care of skewness, kurtosis, and peakedness and therefore is also capable of making good predictions on extreme values. The goodness-of-fit statistic provides supporting evidence in favor of EGB2 distribution in modeling stock returns. This chapter also finds evidence that the leverage effect is diminished when higher moments are considered. The EGB2 distribution used in this chapter is a four-parameter distribution. It has a closed-form density function and its higher-order moments are finite and explicitly expressed by its parameters. The EGB2 distribution nests many widely used distributions such as normal distribution, log-normal distribution, Weibull distribution, and standard logistic distribution.