Optimal Portfolios with Traditional and Alternative Investments: An Empirical Investigation

Abstract

This article empirically investigates the diversification effects on a traditional portfolio by introducing alternative investments (hedge funds, managed futures, real estate, private equities, and commodities). The authors analyze two portfolios: the one with the lowest risk (Minimum Risk Portfolio, or MRP) and the one with the highest (modified) Sharpe Ratio (Maximum Relative Performance Portfolio, or MRPP) for the period April 1999 to April 2009. This article is the first attempt to incorporate a variety of risk measures (Volatility, Value at Risk, and Conditional Value at Risk) as the objective function for portfolio optimization and for different estimates for the expected return (historical estimates, robust Bayes-Stein estimates, Capital Asset Pricing Model (CAPM) estimates, and Black-Litterman estimates). Furthermore, the alternative risk measures are additionally modified for the skewness and the kurtosis: modified VaR and modified CVaR. The influences of the higher moments on asset allocation are also examined in connection with different risk measures and various estimators for expected returns.