Robust Enhanced Indexation Optimization with Sparse Industry Layout Constraint

Abstract

In this paper, we investigate an enhanced indexation methodology using robust Conditional Value-at-Risk (CVaR) and group-sparse optimization. A featured difference from the existing literatures is to describe the tail risk using the worst-case CVaR of excess returns (WCVaR-ER), and the process of industry selection using a weighted $\ell_{\infty,1}$-norm constraint. We develop an accelerated alternating minimization algorithm (AMA) for solving this problem. At each iteration, this method usually alternately solves a convex cone program, which admits a closed-form solution via convex duality theory, and a projection problem onto a weighted infinity-to-one-ball, where a fixed-point iteration projection method is developed, terminating in finite number of iterations. The global convergence rates in terms of the primal and dual residuals are also provided. Empirical tests on actual data sets are presented to demonstrate the superior out-of-sample performance of our proposed strategy.

Keywords: Group-sparse optimization, Alternating minimization algorithm, Worst-case CVaR, Enhanced indexation, Out-of-sample analysis