Portfolio optimization: The Downside risk framework versus the Mean-Variance framework

The tradeoff between risk and return is a topic that most investors consider carefully before an investment decision is made. Markowitz’s pioneer work on portfolio selection using the mean-variance framework has entailed a great extent of research in this field. One research is the Sharpe ratio, which is a measure of a financial performance using variance as a risk measure. The shortcoming of variance is that it puts equal weights on positive and negative returns. Investors’ attitudes towards risk are different but in general investors are more concerned about the downside risk rather than the upside risk. This study has thus constructed a new ratio with similar interpretation as for the Sharpe ratio. The new ratio introduced referred to as the downside risk ratio, uses the downside risk measure expected shortfall as the risk measure instead of variance. To find out if there are any differences in asset allocation using different risk measure an actual performance of four stock market indexes will be evaluated using both the Sharpe ratio strategy and the downside risk ratio strategy. Optimal weights for both a portfolio with two indexes (total of six portfolios) and a portfolio containing all the indexes are found. Finally, both strategies the Sharpe ratio and the downside risk ratio will be assessed in terms of whether there are any differences in constructing a portfolio using either a variance or an expected shortfall as a risk measure.