As mentioned before, empirical evidence shows that mean and variance alone are not sufficient to explain the return distributions. An additional factor is proposed by Kraus and Lintzenberger (1976). They propose to include the next moment, skewness, into the equation. Investors prefer portfolios that are skewed to the right to portfolios that are skewed to the left (Harvey and Siddique, 2000). As a result, higher expected returns should be required for assets that have more left skewed returns, and vice versa. Some studies have shown that investors are willing to pay for positive skewness (Omran, 2007). This has led to the three moment CAPM that includes skewness (see Elton, Gruber, Brown, & Goetzmann, 2003). The formula for the expected return in the three moment CAPM can be written as:
[3]
Where and are the slopes in the following regression:
= 1,…..n and t = 1,…T [4]
