Portfolio optimization with serially correlated, skewed and fat tailed index returns

This paper finds that mean-variance portfolio optimization of stocks, bonds, hedge funds, real estate investment trusts and commodities is sufficiently exact to optimize the investor’s utility. We approximate the expected utility using a Taylor series expansion including terms involving third and fourth order moments. The empirical findings for monthly data from August 1994–August 2009 suggest that the incorporation of skewness and kurtosis cause no noticeable change in the optimal portfolio allocation. However, the serial correlations of smoothed returns of hedge funds and real estate investment trusts indeed cause major changes in optimal portfolio allocation. Consequently, attention needs to be drawn to significant serial correlation and not to potential deviations from normality due to skewed and fat-tailed return distributions. The out-of-sample analysis using a moving window gives evidence that the optimal portfolio weight differ significantly considering serial correlation. The optimization using smoothed returns leads to the highest terminal wealth after 10 years. The highest utility is reached with smoothed as well as shrinked returns, while using unsmoothed as well as shrinked returns leads to an out-of-sample disaster. These findings have practical implications for investors who are willing to diversify their portfolios with hedge funds and real estate investment trusts.