The Effect of Kurtosis on the Cross-Section of Stock Returns

Abstract

In this study, I show an effect of the statistical fourth moment on stock returns. In the mean–variance framework, rational investors follow two strategies: optimize the mean–variance of return and diversify the portfolio. Regarding the first approach, investors intend to generate the maximum level of return while facing a constant level of risk (or, the standard deviation) of return. It is possible that firm specific risk can be concentrated in the portfolio. However, diversification of the assets can eliminate that (idiosyncratic) risk from the portfolio. After a long period of time, in a diversified portfolio the shape of the return distribution appears to be peaked around the average value of the return compared with that of the typical shape of the return distribution. If investors have a preference for skewness in their returns, they also can produce peakedness in the shape of the distribution. The statistical fourth moment (kurtosis) measures the magnitude of peakedness of the distribution. As the kurtosis of the distribution increases the distribution will appear more peaked. I find evidence that kurtosis positively and significantly predicts future stock returns over the period 1981–2011. The effect remains after controlling for other factors in multivariate regressions. Introduction A number of studies state that investors who are undiversified commonly hold a few numbers of assets that result in failure to eliminate idiosyncratic risk (see Kelly, 1995; and Goetzmannand and Kumar, 2004). Under standard portfolio theory, those investors capture the same amount of expected returns as those who have a large number of assets. The former type of investors face higher risk than the latter type of investors. Mitton and Vorkink (2007) mention that if investors show under–diversification in their portfolios, they are likely to earn extreme positive returns while experiencing a high value of skewness. Conine and Tamarkin (1981) provide a similar argument in a different way–investors try to avoid diversification in their portfolios when investors realize they are earning extremely large returns. Therefore, in the mean–variance–skewness framework, investors with a preference for skewness may obtain an efficient portfolio. However, in the mean–variance–skewness framework, stocks that provide extremely large returns ultimately result in portfolio returns that are positively skewed (i.e. skewed to the right). A very low probability is associated with the extreme return above the mean for a positively skewed distribution.