Residual Return Targets and Risk Model Dependence in Alpha Forecasting

Summary

The document raises a portfolio-construction question about coordinating an alpha model with a statistical risk model. The risk model decomposes returns into factor exposures and factor returns, leaving residual returns. The proposed alpha model uses predictors to forecast next-period residual returns rather than total returns, with the aim of avoiding systematic factor exposure in the target.

The author worries that residual targets inherit the risk model’s factor choices: a sparse model may leave systematic structure for the alpha model to learn, while a larger factor set may absorb more variation. The document supplies no accepted answer, method, or empirical results, so it does not establish whether this target construction is unbiased or how the models should interact. It identifies model dependence and factor specification as issues to investigate when combining alpha forecasts with portfolio risk controls.

Key ideas

• A risk model can decompose asset returns into factor-driven and residual components.
• Forecasting residual returns aims to focus an alpha model on returns beyond the modeled systematic factors.
• The alpha target depends on the risk model’s factor selection and estimated residuals.
• Too few factors may leave systematic structure in residual returns, while additional factors change what remains unexplained.
• The document poses the model-interaction question but does not resolve it with evidence or a procedure.

Tags

# Excess Return Evaluation Bias


# Excess Return Evaluation Bias












Im currently working on a Alpha and Risk Model for constructing portfolios. From what Ive read on books and here, they are constructed in a different way and produce differents results. My Risk Model (in a statistical setting and linear world) is giving me the loadings $B$ and the factor returns $F$, so i can decompose idiosyncratic return as $\varepsilon = r - BF$. For the Alpha model, im trying to forecast the return for next period with some learning algorithm $g$, say $r_{t+1} = g(X_t)$, but since I dont want to include systematic factors on target variable, the approach would be to use excess return for that day, i.e $\varepsilon_{t + 1} = g(X_t)$.

This make sense to me, but the problem I have, is that when constructing my target variable, i need my Risk Model to produce the residuals, so maybe the excess return evaluation is biased on the results of my Risk Model and not independent of it. If i select only few factors, $g$ is learning a systematic structure and noise with selecting a lot of them.

Is this approach correctly and this 2 models interact before Portfolio Optimization or im missing something here? Thanks in advance

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