The most important asset pricing models consider that an investor’s utility function is completely defined by mean and variance, which requires the normality of the stock’s return distribution (or that stock returns are not skewed). However, not all stocks or markets have normal returns (e.g.: emerging markets and small public firms). The higher-order moments of stock return distributions (such as skewness and kurtosis) are valued by investors and need to be incorporated in the asset pricing models. In this article we analyse the normality and symmetry of a sample of Portuguese stocks and estimate their cost of equity (or the investors’ required return on equity) using several measures of downside risk.