Previous research indicates that returns are not normally distributed and that investors seem to care more about downside risk than total risk. Motivated by these findings and the lack of research on upside risk, we model the relation between future returns and risk measures and investigate the following questions: Are investors compensated for total risk? Is the compensation for downside risk different than the compensation for upside risk? and which measure of risk (i.e., upside, downside, or total) is most important to investors? We find that, although investors seem to be compensated for total risk, measures of downside risk, such as the lower partial moment, better explain future returns. Further, when downside and upside risk are modeled simultaneously, investors seem to care only about downside risk. Our findings are robust to the addition of control variables, including prior returns, size, book-to-market ratio of equity (B/M), and leverage. We also find evidence of short-run mean reversals in daily returns. Our findings are important because we document a positive risk-return relationship, using both total and downside risk measures; however, we find that investors are concerned more with downside risk than total risk.