Alpha Alignment Factor: A Solution to the Underestimation of Risk for Optimized Active Portfolios

Author: Robert A. Stubbs, Dieter Vandenbussche

The underestimation of risk of optimized portfolios is a consistent criticism about risk models. 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 is not necessarily with a risk model, but is rather the interaction of expected returns, constraints, and a risk model is 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 both how pervasive the underestimation problem can be and the effectiveness of the proposed AAF in correcting the bias of the risk estimates of optimized portfolios. 

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