The evaluation of investments offering non-normal return profiles like option portfolios or alternative investments is a challenging task since traditional measures like the mean-variance ones often produce inconsistent results or can be subject to manipulation. This thesis investigates the role of skewness and kurtosis in evaluating conventional and alternative investments. From the background that investors trade not only mean and variance but also higher moments, the author proposes a higher moment-based distributional risk measure, termed as the variance-equivalent risk measure, and develops a series of moment-based performance measures. Comparing these measures with conventional measures like the Sharpe Ratio, empirical testing shows that for investments with high non-normality of returns, the higher moment-based performance measures offer a significant enhancement in the performance evaluation.