Robust Portfolio Optimization Under High-Dimensional Heavy-Tailed Time Series

• Activity Number: 341
• Type: Contributed
• Date/Time: Tuesday, August 5, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Risk Analysis
• Author(s): Huitong Qiu*+ and Fang Han and Brian Scott Caffo and Han Liu
• Companies: Johns Hopkins University and Johns Hopkins University and Johns Hopkins University and Princeton University
• Keywords: robust estimator ; portfolio risk minimization ; weak dependence

Abstract

In portfolio optimization, estimating the covariance matrix (or the scatter matrix, which is a matrix proportional to the covariance matrix) of stock returns is the key step. In this paper, we propose a new robust portfolio optimization strategy by resorting to a quantile based scatter matrix estimator. Computationally, the proposed robust portfolio optimization method is as efficient as its Gaussian-based alternative. Theoretically, by exploiting the quantile-based statistics, we show that the actual portfolio risk approximates the oracle risk with parametric rate even under very heavy-tailed distributions and a stationary time series with weak dependence. The rate of convergence is set in a double asymptotic framework where the portfolio size may scale exponentially with sample size. The empirical effectiveness of the proposed estimator is demonstrated in both synthetic and real data. The experiments visualize that the proposed method can significantly stabilize portfolio risk under highly volatile stock returns, and effectively avoid extremal losses.