The alpha alignment factor: a solution to the underestimation of risk for optimized active portfolios

Anureet Saxena and Robert A. Stubbs

Abstract

ABSTRACT

A common criticism of risk models is that they have a tendency to underestimate the risk associated with optimized portfolios. Quantitative portfolio managers have historically used a variety of ad hoc techniques to overcome this issue in their investment processes. In this paper, we construct a theory explaining why risk models underestimate the risk of optimized portfolios. We show that the problem does not necessarily lie solely with the risk model, but is instead due to the interaction of expected returns, constraints and a risk model in an optimizer. We develop an optimization technique that incorporates a dynamic alpha alignment factor (AAF) into the factor risk model during the optimization process. Using actual portfolio manager backtests, we illustrate how pervasive the underestimation problem can be and we show the effectiveness of the proposed AAF in correcting the bias of the risk estimates of optimized portfolios.