Portfolio Optimization for Extreme Risks with Maximum Diversification: An Empirical Analysis

Abstract

Heavy tailedness and interconnectedness widely exist in stock returns and large insurance claims, which contributes to huge losses for financial institutions. Diversification ratio (DR) measures the degree of diversification using the Value-at-Risk, which is known to capture extreme risks better than variance. The portfolio optimization strategy based on DR maximizes the effect of diversification for extreme risks. In this paper, we empirically examine the DR strategy by using more than 350 S&P 500 stocks under the assumption that the stock losses are modeled with a flexible multivariate heavy-tailed model. This assumption is verified empirically. The performance of DR strategy is compared with four benchmark strategies: equally weighted portfolio, minimum-variance portfolio, extreme risk index portfolio, and most diversified portfolio. The performance of comparison includes annualized portfolio return, modified Sharpe ratio, maximum drawdown, portfolio concentration, portfolio turnover, and the degree of diversification. DR outperforms other strategies. In particular, DR shows the highest return and maintains the highest level of diversification during the global financial crisis of 2007–2009.

Keywords

• portfolio optimization
• diversification ratio
• extreme risk
• extreme value theory