Portfolio optimization for heavy-tailed assets: Extreme Risk Index vs. Markowitz

Using daily returns of the S&P500 stocks from 2001 to 2011, we perform a backtesting study of the portfolio optimization strategy based on the extreme risk index (ERI). This method uses multivariate extreme value theory to minimize the probability of large portfolio losses. With more than 400 stocks to choose from, our study applies extreme value techniques in portfolio management on a large scale. We compare the performance of this strategy with the Markowitz approach and investigate how the ERI method can be applied most effectively. Our results show that the annualized return of the ERI strategy is particularly high for assets with heavy tails. The comparison also includes maximal drawdown, transaction costs, portfolio concentration, and asset diversity in the portfolio. In addition to that we study the impact of an alternative tail index estimator.