It is common practice to revise forecasted returns on the basis of changes in the risk model. Recent trends suggest that risk models are adjusted and augmented on the basis of latent factors influencing the alpha portion of forecasted returns. Adding missing factors could provide valuable information for portfolio construction.

Mean–variance optimization is an important aspect of portfolio construction. In the optimization process, alpha is the “extra” return over the expected asset return commensurate with the risk taken, which is attributable to the portfolio manager’s special insights. Alphas may be accompanied by missing factors, however, requiring augmentation of the risk model to include the source of risk for the extra-return alpha.

In their study, the authors use cases to show that portfolio construction can be improved through risk model adjustments. They caution, however, that one should not add missing factors to the risk model without considering their commonality with the model.

The authors consider four scenarios. In the base case, there are no additional factors and no alpha. The second scenario involves pure alphas and no additional risk factors. The third scenario covers alphas with an additional source of systematic risk. The fourth scenario involves an additional risk factor and no alpha.

By studying the case in which a common factor that underlies alpha signals is not fully reflected in the risk model, the authors find that augmenting the risk model in such a case provides better information for portfolio construction. Another case in the study involves alphas that are truly smart betas—extra returns are not associated with extra risk taking. In this case, adjusting the risk model for sources of smart betas can result in a misspecification of the model, leading to losses for the portfolio manager.

The authors examine the inconsistency of the risk model compared with the alpha sources and the resulting errors in asset allocation. Using different scenarios, they show that in some cases, adjustments to the risk model lead to improvements in portfolio construction, whereas in other cases, risk model adjustments lead to suboptimal portfolios.

In a segmentation/smart beta world, unconstrained borrowing investors earn a smart beta premium by overweighting value stocks and underweighting growth stocks. This smart beta premium is not compensation for any risk taken. The authors show convincingly that changes in the risk model in such cases are unwarranted. They also show that when a factor is missing from the risk model—which is the risk exposure to earn the extra-return alpha—augmenting the risk model helps with efficient portfolio construction.

A sound economic rationale for the generation of alpha and beta can be a good basis for deciding whether a risk model adjustment is needed. In practice, however, there is enough uncertainty to know the exact reasons for the generation of alphas or smart betas. The robustness of this study should be checked by including various constraints—active weight constraints, turnover constraints, and trading costs—to gain additional insights into the risk–return paradigm in portfolio construction.