In this paper, we show that in a model where investors have heterogeneous preferences, the expected return of risky assets depends on the idiosyncratic coskewness beta, which measures the co-movement of the individual stock variance and the market return. We find that there is a negative (positive) relation between idiosyncratic coskewness and equity returns when idiosyncratic coskewness betas are positive (negative). Standard risk factors, such as the market, size, book-to-market, and momentum cannot explain the findings. We construct two idiosyncratic coskewness factors to capture the market-wide effect of idiosyncratic coskewness. The two idiosyncratic coskewness factors can also explain the negative and significant relation between the maximum daily return over the past one month (MAX) and expected stock returns documented in Bali, Cakici, and Whitelaw (2009). In addition, when we control for these two idiosyncratic coskewness factors, the return difference for distress-sorted portfolios found in Campbell, Hilscher, and Szilagyi (2008) becomes insignificant. Furthermore, the two idiosyncratic coskewness factors help us understand the idiosyncratic volatility puzzle found in Ang, Hodrick, Xing, and Zhang (2006). They reduce the return difference between portfolios with the smallest and largest idiosyncratic volatility by more than 60%, although the difference is still statistically significant.