A comparison of portfolios using different risk measurements

Abstract

In order to find out which risk measurement is the best indicator of efficiency in a portfolio, this study considers three different risk measurements: the meanvariance model, the mean absolute deviation model, and the downside risk model. Meanwhile short selling is also taken into account since it is an important strategy that can bring a portfolio much closer to the efficient frontier by improving a portfolio's risk-return trade-off. Therefore, six portfolio rebalancing models, including the MV model, MAD model, and the downside risk model, with/without short selling, are compared to determine which is the most efficient. All models simultaneously consider the criteria of return and risk measurement. Meanwhile, when short selling is allowed, models also consider minimizing the proportion of short selling. Therefore, multiple objective programming is employed to transform multiple objectives into a single objective in order to obtain a compromising solution. An example is used to perform simulation, and the results indicate that the MAD model, incorporated with est risk.