Risk Parity Portfolio Optimization under Heavy-Tailed Returns and Time-Varying Volatility

Abstract

Risk parity portfolio optimization, using expected shortfall as the risk measure, is investigated when asset returns are fat-tailed and heteroscedastic. The conditional return distribution is modeled by an elliptical multivariate generalized hyperbolic distribution, allowing for fast parameter estimation, via an expectation-maximization algorithm and a semi-closed form of the risk contributions. The efficient computation of non-Gaussian risk parity weights sidesteps the need for numerical simulations or Cornish-Fisher-type approximations. Accounting for fat-tailed returns, the risk parity allocation is less sensitive to volatility shocks, thereby generating lower portfolio turnover, in particular during market turmoils such as the global financial crisis. Although risk parity portfolios are surprisingly robust to the misuse of the Gaussian distribution, a more realistic model for conditional returns and time-varying volatilies can improve risk-adjusted returns, reduces turnover during periods of market stress and enables the use of a holistic risk model for portfolio and risk management.