Risk models are often enhanced by additional latent factors deduced from alphas. The
authors conclude that an augmentation of the risk model is warranted if the alpha sources
for different assets reflect common factors missing in the risk model.
How Is This Research Useful to Practitioners?
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
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.
How Did the Authors Conduct This Research?
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.