Using Fama–French Factors in Forward-Looking Portfolio Risk Estimates
Summary
The document compares two proposed approaches for monthly minimum-variance stock portfolios: estimating individual variances with GARCH while using historical covariances, and modeling returns with daily Fama–French factors and regression residuals. It asks how to align factor observations and returns when estimating betas, given publication delays, and whether estimated factor covariances can support forecasts. The discussion highlights the central timing constraint: portfolio construction must use information available at the formation date, rather than future observations.
The author suggests that a factor model could combine factor covariance with residual risk, but does not settle the appropriate lag structure or estimation procedure. Nor does the text provide backtest results or establish that either proposal is superior. It also questions whether holding the recent factor covariance matrix constant amounts to forecasting future risk. These choices require point-in-time factor data, a clearly defined rebalancing schedule, and out-of-sample comparison; the document itself is a methodological question rather than a validated strategy.
Key ideas
- The proposed comparison pairs GARCH-based variance estimates with a factor-model approach for minimum-variance portfolios.
- Regression timing must respect the information actually available when the portfolio is formed.
- A factor covariance matrix and regression residuals can be used to describe return covariance under a factor model.
- Assuming recent factor covariance persists is a forecasting assumption, not a direct observation of future risk.
- The document leaves factor lags and comparative performance unresolved.
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Full text
# Fama French- typical time lag
# Fama French- typical time lag
I have daily prices of 400 stocks for the last 10 years. I have to create each month a portfolio of 20 stocks that minimizes variance with 2 approaches:
1) Estimate volatility with a GARCH(1,1) model each month using previous 6 months for the following 30 days. Then construct the covariance matrix with historical data and replace variance with that estimation (GARCH (1,1)). Finally, usign that I will have to get the min variance portfolio by minimizing that matrix.
2) On the other hand, I have the Fama and French daily factors. Using that I have to create another portfolio and compare the results with the previous one. Since the previous one is not using future data, I guess I have to do one of the following possibilities:
- run a regression of returns against lagged FF factors and then use current factors to predict future returns. Where
> $r(t)=f(FF_{t-1})$
and for
> $E \left[r_{t+1} \right]=f(FF_t)$
- run a regression of returns against same period FF factors and estimate future FF factors to estimate future returns.
> $r(t)=f(FF_{t})$
and for
> $E \left[r_{t+1} \right]=f(FF_{t+1})$
With either of those approaches, I'll get the coefficients to calculate the covariance of the returns (using the covariance of the FF plus the residuals of the regressions).
Since the Fama-French site has data with a one-month delay or more, what is the best time lag between Fama and French factors and returns to estimate betas coefficients?
Is it a common practice to estimate those factors and then applied the coefficients?
As far as I found, the typical approach is to suppose that you will have the same covariance matrix that the period where the coefficients were estimated, so actually, there's no "real" estimation of future data. It is only supposing that covariance matrix of factors will be the same as the last period. Am I right?
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.