Augmented Risk Models to Mitigate Factor Alignment Problems

Volume 13, Number 3, (2015)

Anureet Saxena and Robert A. Stubbs

Construction of optimized portfolios entails a complex interaction between three key entities, namely, the risk factors, the alpha factors and the constraints. The problems that arise due to mutual misalignment between these three entities are collectively referred to as Factor Alignment Problems (FAP). Examples of FAP include risk u underestimation of optimized portfolios, undesirable exposures to factors with hidden and unaccounted systematic risk, consistent failure in achieving ex-ante performance targets, and inability to harvest high quality alphas into above-average IR. In this paper, we give a detailed analysis of FAP and discuss solution approaches based on augmenting the user risk model with a single additional factor y. For the case of unconstrained mean–variance optimization (MVO) problems, we develop a generic analytical framework to analyze the ex-post utility function of the corresponding optimal portfolios, derive a closed-form expression of the optimal factor volatility value and compare the solutions for various choices of y culminating with a closed-form expression for the optimal choice of y. Augmented risk models not only correct for risk underestimation bias of optimal portfolios but also push the ex-post efficient frontier upward thereby empowering a portfolio manager (PM) to access portfolios that lie above the traditional risk–return frontier. We corroborate our theoretical results by extensive computational experiments, and discuss market conditions under which augmented risk models are likely to be most beneficial.