Factor Investing: A Decomposition of Returns into Risk and Mispricing

Objective:

This study examines the role of the underlying nature of factor returns in the context of factor-based investing. Higher returns from investment factors or financial anomalies may arise either from exposure to greater risk or from mispricing that stem from market inefficiencies, behavioral biases, and cognitive mistakes made by investors. A review of the literature reveals that, for many investment factors, there is no definitive answer as to whether their returns are driven by risk or by mispricing—leaving the question open to further investigation. Meanwhile, most factor investing strategies have been developed within a risk-based interpretative framework. This research addresses whether differentiating and accounting for the nature of factor returns can influence the performance of factor investing strategies. More specifically, the goal is to evaluate the dual interpretations—risk-based and mispricing-based—for several widely used investment factors, and to determine whether incorporating mispricing-based interpretations alongside risk-based ones can enhance factor return predictability and ultimately improve investment performance.



Method:

The study introduces a novel perspective in which factor returns are allowed to simultaneously reflect both risk and mispricing components—unlike traditional views that attribute returns solely to one or the other. Given the lack of developed behavioral multi-factor models in Iran’s capital market, the study utilizes U.S. market data and focuses on well-established investment factors in that context. First, a common mispricing factor is constructed using behavioral components drawn from existing behavioral asset pricing models. Next, the risk and mispricing characteristics of each investment factor are quantified monthly using the beta from the CAPM (to reflect risk exposure) and the beta relative to the mispricing factor (to capture mispricing). These characteristics are then assigned to each factor on a monthly basis. In the final stage, the parametric optimization model of Brandt et al. (2009) is employed to assess whether using both risk and mispricing characteristics—alongside predictors of market risk conditions and behavioral sentiment—can enhance the performance of factor investing strategies. Performance outcomes from different optimization scenarios are compared with those of a standard equal-weight strategy.



Findings:

In the section analyzing mispricing characteristics of different investment factors, the results indicate that the short legs of the value and momentum factors are more exposed to mispricing than their long legs. Conversely, in the size factor, the long side shows greater mispricing exposure. The findings for value and size align with expectations: the short leg of the value factor typically includes growth stocks, which are more speculative and therefore more prone to mispricing. Similarly, the size factor's long leg includes small-cap stocks, whose smaller size makes them more susceptible to speculative behavior, explaining their higher mispricing risk.

However, when risk and mispricing characteristics are used alone in optimization strategies, they do not lead to performance improvement and underperform even relative to equal-weight strategies. In contrast, when these characteristics are combined with predictors of market-wide risk and behavioral sentiment, the performance of factor investing improves significantly—both in terms of mean return and Sharpe ratio—surpassing the results of single-factor models and equal-weighted approaches.



Conclusion:

The results demonstrate that decomposing factor returns into risk and mispricing components provides a more nuanced understanding of factor behavior over time. Incorporating both characteristics, along with market-level predictive variables for risk and sentiment, can enhance the effectiveness of factor-based investment strategies. Overall, the findings suggest that moving beyond a purely risk-based interpretation of factor returns and embracing a dual-component view can contribute meaningfully to the development of the factor investing literature.