Empirical analysis of optimization algorithms for portfolio allocation

Abstract

Portfolio optimization algorithms were tested using historical S&P100 data. A traditional Mean-Var algorithm is tested as well as two alternative risk methods. The alternative risk methods used the maximum drawdown (MDD) as the measure of risk rather than the standard deviation of returns. The long term performance of each portfolio produced by these algorithms was compared to various benchmarks. It was found that the algorithms often outperformed the benchmarks in real rate of return. However, when return was adjusted for risk, the algorithms generally underperformed the benchmarks. A hierarchical method involving clustering stocks before allocation was also tested, but was found to underperform allocation without clustering. MDD-minimization subject to a return constraint was found to be the only optimization algorithm that outperformed the benchmarks in each measure of performance. Closer examination revealed that this algorithm closely matched the benchmarks during periods of continuous market growth, but significantly outperformed them during periods of continuous market decline. This result supports the use of maximum drawdown as an alternative measure of risk in portfolio optimization when investors are assumed to be risk-averse.