The Relationship Between The Higher Moments And The Cross-section Of Stock Returns

In 1609, the first stock Exchange of the world-Amsterdam stock Exchange (AEX) founded in Amsterdam in the Netherlands. As early as in 1602 the Dutch east India company was set up, which is the first corporation can be traded in the market. Since the world's first stock exchange and the establishment of the first stock, the study about financial assets has never been interrupted. Among them, the most pioneering research is the mean-variance analysis and portfolio theory of Harry m. Markowitz (1952). Harry m. Markowitz first put forward the concept of the risk and return, and applied them into mathematical statistics on the mean-variance analysis, in order to study the portfolio composition and selection problem.Subsequently, William Sharpe (1964), Jan Mossin (1966) and John Lintner (1965) independently derived the Capital Asset Pricing Model CAPM) on the basis of the study Harry M. Markowitz (1952). Then Eugene Fama and Kenneth French (1992), Carhart (1997) are proposed Fama-French three-factor model and the Carhart four-factor model in succession to enhance the traditional capital asset pricing model yields explanatory power. Considering financial asset return's non-normal distribution, Some scholars began to study higher moments, such as Kraus and Litzenberger(1976), who developed the third moment CAPM for the first time. Subsequently, more and more scholars began to study the higher moments.Our empirical tests use moments of returns extracted from higher frequency data using the model-free methodology of Amaya, Christoffersen, Jacobs and Vasquez (2015). In this paper, research work carried out in two major areas:the market moments and the individual share's moments. On the one hand, we discuss the relationship between the market moments risk and the cross section of stock returns. First we show how to extract market higher moments from higher frequency using the method of Amaya, Christoffersen, Jacobs and Vasquez (2015) and discuss their characters. Then we explore the effect of market moments on the cross section of stock returns by sorting the cross section of stock returns into eighths based on the stock's exposure to innovations in one of the market moments and construct factor portfolios. At last, we compute the price of risk by running a series of cross-sectional regressions using the factor portfolios above. On the other hand, we also discuss the relationship between the individual moments risk and the cross section of expected stock returns and test if skewness can be a new independent driver of variation in expected return in the cross-section. There we use the similar research method above.The conclusions of empirical analysis are as following. First, stocks with high exposure to innovations in implied market skewness exhibit low returns on average, consistent with Liu, Zheng and Zhang (2012), Bo, Christoffersen and Jacobs (2013), and the risk premium approximately -9.83% per year. Moreover, the sign of the coefficient regression of the market skewness in the Fama-Macbeth regression is negative in all cases and most significant. That is, the market skewness risk factors have significant explanatory power in the cross-section of stock returns, and it can't be completely covered by the market excess return, size, book-to-market, or momentum effects. Second, little evidence exists that the market volatility, the market kurtosis and the stock returns in the cross-section are significantly related. Third, individual stock skewness and future returns in the cross-section presence significant negative relationship, consistent with Shapiro and Zhang(2010), Amaya, Christoffersen, Jacobs and Vasquez (2015). The result is significant across our research and is independent with the market excess return, size, book-to-market, or momentum effects. The result in Fama-Macbeth regression confirmed the result above again. That is, strong evidence of a reliable relation between individual stock skewness and the future returns in the cross-section exists. Fourth, the impact of individual stock volatility and individual stock kurtosis are not very significant.