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

TL;DR

This study evaluates the extreme risk index (ERI) for portfolio optimization using large-scale data of S&P 500 stocks, demonstrating its superior performance over traditional methods in managing heavy-tailed assets.

Contribution

First large-scale application of multivariate extreme value theory in portfolio management, comparing ERI with standard strategies on extensive real-world data.

Findings

ERI outperforms minimum variance and equal-weighted portfolios on heavy-tailed assets.

ERI reduces large portfolio losses and improves risk-adjusted returns.

Alternative tail index estimators impact ERI's effectiveness.

Abstract

Using daily returns of the S&P 500 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 seems to be the first application of extreme value techniques in portfolio management on a large scale. The primary aim of our investigation is the potential of ERI in practice. The performance of this strategy is benchmarked against the minimum variance portfolio and the equally weighted portfolio. These fundamental strategies are important benchmarks for large-scale applications. Our comparison includes annualized portfolio returns, maximal drawdowns, transaction costs, portfolio concentration, and asset diversity in the portfolio. In addition to that we study the impact of an alternative tail index estimator. Our results show that the ERI strategy significantly outperforms both the minimum-variance portfolio and the equally weighted portfolio on assets with heavy tails.