Neutralizing a Portfolio’s Fama–French Factor Exposure
Summary
The document explains a way to remove a portfolio’s estimated exposure to a Fama–French factor. First, regress the portfolio’s excess returns on the chosen factor to estimate its beta. Then combine the portfolio with a short position in the factor proportional to that beta. The resulting return is described as the portfolio’s alpha plus its regression residual, making it uncorrelated with that factor under the model.
The discussion uses HML as an example and says the hedged portfolio’s expected return is its alpha, with risk measured by the residual’s standard deviation. A second answer agrees that factor returns can be traded as long–short portfolios and that regression betas can set hedge amounts. The treatment assumes a valid beta estimate and factor returns that can be traded as described. It does not address estimation error, transaction costs, rebalancing, or neutrality to multiple factors at once.
Key ideas
- Estimate a portfolio’s exposure to a chosen factor with a time-series regression.
- Offset the estimated exposure by taking a short position in the factor portfolio.
- Under the regression model, the hedged return consists of alpha and residual returns.
- The explanation assumes the estimated beta is suitable for sizing the hedge.
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Full text
# How to make a portfolio neutral to a Fama-French factor?
# How to make a portfolio neutral to a Fama-French factor?
I have quintiles of 58 companies each that I have performed a CAPM regression with. I now wish to try and make these quintile portfolios neutral to Fama-French factors and was hoping for some insight as to whether or not I am doing this correctly.
To this end, does this seem to make any sense? First, I will take the monthly factors from the Fama-French library and regress each factor I want to use against my quintile portfolio excess returns. This will give me the betas of my quintiles to the factors regressed against. After, I will use these betas by subtracting from my five quintiles' monthly returns by the returns calculated for the risk factors multiplied by the betas calculated for those factors.
This might sound like a load of nonsense, and it may well be, because I can't find anywhere online that suggests this and I would appreciate any help.
Thank you!
## Answer by phdstudent (score 2)
https://quant.stackexchange.com/a/82120
Let's be more formal about this.
You have a portfolio $p$, with returns $r_{p,t}$. There is also a fama-french factor, let's pick HML, with return $HML_t$.
You want to make the portfolio neutral to a fama-french factor. I am not sure what you mean by neutral, but I am going to assume that you mean uncorrelated with that factor.
You can run the regression:
$$r_{p,t} - r_f = \alpha_p + \beta^{HML} HML_t + \epsilon_t$$
and you obtain an estimate $\hat{\beta}^{HML}$.
Now if you go long \$1 of portfolio $p$ and short $\\\$\hat{\beta}^{HML}$ of HML, you get a portfolio with return:
$$r_{new} = r_{p,t} - r_f - \beta^{HML} HML_t = \alpha_p + \epsilon_t$$
By definitions this portfolio is uncorrelated with the value factor of fama-french. This portfolio $r_{new}$ has expected return $\alpha_p$ and standard deviation $\sigma_\epsilon$.
## Answer by KaiSqDist (score 0)
https://quant.stackexchange.com/a/79732
> After, I will use these betas by subtracting from my five quintiles' monthly returns by the returns calculated for the risk factors multiplied by the betas calculated for those factors.
I believe you are right.
As the Fama-French factor modelling use-case illustrates how factor returns themselves are the returns of a long-short portfolio (consisting of long and short the top and bottom percentiles of a universe of assets exposed to that particular factor, say volatility), you can use your betas (that are deduced in time series regressions) to compute the amount of the portfolios (that represent the factors) to trade and make your portfolio factor-neutral.
I understand that this question is quite long ago, but I recently started reading up on this, albeit more on the Rosenberg cross-sectional stuff.
Happy to talk about the Fama-French variants as well.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.