Choosing Expected Returns and Risk Estimates in Factor Models

Summary

The document explores practical estimation questions in the Fama-French family of factor models. It describes estimating a stock's factor loadings with a time-series regression, then asks how to forecast factor premiums when historical averages may not be reliable guides to future returns. It also asks whether averaging fitted stock returns offers a sound alternative.

For portfolio construction, the author asks whether volatility and correlations should come from sample estimates or from the factor model's variance decomposition, including factor risk and residual risk. The text supplies no proposed estimator, empirical comparison, or answer; it frames the trade-offs that a practitioner must address. The questions highlight that factor loadings alone do not determine expected returns, and that both factor forecasts and residual covariance assumptions matter. Its scope is limited to the estimation problem, without specifying a factor set, forecast horizon, or portfolio constraints.

Key ideas

• A factor regression estimates a stock's exposures, but expected factor returns still need to be forecast.
• Historical average returns may be noisy estimates of future factor premiums.
• Averaging fitted returns is posed as a possible stock return estimate, without evaluation.
• Portfolio risk estimates can combine factor variance with residual risk, but the text gives no method for choosing estimates.

Tags

# Expected returns and Fama-French Factor Model


# Expected returns and Fama-French Factor Model












It is my understanding that for any given stock, the sample mean of historical returns is not a good proxy for the stock's expected return. In fact, the return on a stock needs to be estimated via some sort of factor model, be it the CAPM, FF3, FF5, etc. Basically, we would run a time-series regression of the stock's returns against the factors, extract the betas, and then multiply the betas by the expected return on the factors and that would give us the expected return on the stock.

But where do we get the expected return on the factors from? In all the problems I have done in school they were always given, but now I am trying to actually do this in practice in order to optimize my portfolio and I am a bit lost. I thought about using the sample mean, but then wouldn't we have the same issue as for the individual stocks (past returns are not an indicator of future returns because returns are not IID)?

Alternatively, could we take the average of the fitted values from the factor model and use that as our proxy for the expected return on the stock?

Also, what about the standard deviation and the correlation of the stocks within in a portfolio? Do we use the sample standard deviation or do we estimate it by applying the variance operator to the factor model regression (Var[R_i] = beta^2 * Var[R_mkt] + ... + Var[epsilon])?

Any help would be much appreciated. It would also be great if you could point me to papers/articles/books that tackle these types of issues.

Thanks!

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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