Optimal Portfolios with Traditional and Alternative Investments: An Empirical Investigation

This paper empirically investigates the diversification effects on a traditional portfolio by introducing alternative investments (hedge funds, managed futures, real estate, private equities and commodities). This paper 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 the portfolio optimization and different estimates for the expected return (historical estimates, robust Bayes–Stein estimates, 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). In this manner, the influences of the higher moments on the asset allocation can also be examined in connection with different risk measures and various estimators for expected returns. Formulation of the Problem The last months especially have shown that investors’ confidence in capital markets has suffered drastically. The turbulence on capital markets was accompanied by enormous breaks in prices. Therefore, private as well as institutional investors looked for alternative investments, to which less attention had been paid until then. The amount of alternative investments, which include hedge funds, managed futures, real estate, private equities and commodities, has already increased by over 13 percent on average in Europe (JP Morgan Asset Management [2007]). Therefore, capital assets have to be chosen, weighted and combined in the right way to achieve preferably high returns on investments by taking low risks at the same time. This can be carried out by an asset allocation of different types of investments. Investors who do not want to take high risks try to choose their investments in such a way that, in the case of a loss on stock markets, as it happened e.g. in the actual subprime crisis, their portfolio remains widely unaffected. To find out how such astonishing events affect different investments, the three worst months of the international stock markets of the last ten years are pulled up and analyzed. During this period, the world stock markets registered the strongest losses in October 2008 with -20.71%