Estimating Fund Alpha with Multi-Factor Regression

Summary

The document presents a proposed way to estimate historical alpha for a set of fund returns. The approach regresses each fund’s returns on excess returns for selected underlying exposures, interprets the fitted coefficients as factor betas, and treats average residual returns as alpha. Stepwise regression is mentioned as the method for selecting or fitting the factors.

This is a question about whether that procedure correctly represents a multi-factor asset-pricing model; the document provides no answer or empirical evidence. It therefore serves mainly as a prompt to examine model specification and interpretation. A regression intercept or mean residual is conditional on the chosen factors, sample, and estimation method, and the factor coefficients should not automatically be treated as CAPM betas when multiple exposures are included. The proposed calculation alone does not establish persistent manager skill or risk-adjusted performance.

Key ideas

• The proposed method regresses fund returns on excess returns for selected exposures.
• It interprets the fitted factor coefficients as exposures and average residual returns as alpha.
• Stepwise regression is part of the question’s proposed factor-selection procedure.
• The document does not resolve whether this specification is valid or provide supporting evidence.
• Estimated alpha depends on the factors, sample, and regression choices.

Tags

# Is this methodology to calculate Alpha using multi-factor regression model correct?


# Is this methodology to calculate Alpha using multi-factor regression model correct?












I am trying to find out Historical Alphas of a bunch of fund returns ${F_i}$ by Using Regression Model$(stepwise)$ with regressors as its underlying exposure-returns(risk-free rate subtracted) i.e. $$ \mathrm{E_i = X_i-R_f} $$ $$ \mathrm{F_i} = {a_i + \beta_{1i}E_{1}+\beta_{2i}E_{2}...} $$

Here, I assume that this regression model is representative of a Multi-factor CAPM model and the obtained ${\beta_i}$ are the CAPM-${\beta}$ i.e. systemic risk of ${F_i}$ w.r.t. ${E_i}$.

Then, I use these models to calculate average historical ${\alpha_i}$ which is excess return for fund ${F_i}$ using below formula.

$$ \mathrm{\alpha_i} = avg({F_i - F_i^{estimated})} $$

Is this simplistic approach correct, if not, what is the correct way?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.