Portfolio Optimization in a Mean-Semivariance Framework

In this paper, we demonstrate a mean-semivariance approach to measure the downside risk in optimal portfolio selections. We measure the return dispersions below the expected value of investment return. Using semivariance for measuring the downside risk is consistent with the intuitive perception of risk of investors. The mean-semivariance framework offers investors a practical guidance in asset allocations and portfolio management that aim to minimize the downside risk in investment. We use a sample of seven exchange-traded index funds (ETF) that mimic various categories of securities such as government bonds, municipal bonds, investment grade bonds, high-yield bonds, real estate bonds, mortgage backed securities (MBS), and large capitalization stocks to compare and test the differences between the optimal portfolios and asset allocations constructed out of the mean-semivariance approach and the traditional mean-variance approach. Our test results show that the mean-semivariance approach provides certain desirable benefits unavailable to a traditional mean-variance approach. Specifically, optimization under the conditions of the semivariance model produces different portfolio strategies that at least maintain and at best improve the expected return of the portfolio using traditional mean-variance model while minimizing its downside risk exposure. Our findings of the semivariance model have practical implications for both individual investors and institutional investors for asset allocations and optimal portfolio selections, as well as managing their downside risk exposure.