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I understand the finance 101 explanation of how to minimize variance of a long-short portfolio using a covariance matrix. I also know that it doesn't really work because the covariance matrix is unstable out of sample. It has been suggested that in practice factor risks are more stable out of sample, but I don't quite understand how to use factors to minimize variance.

It has been suggested to me that this is trivial and not worth a question but I really can't find any other resources that explain in detail how to do this.

My initial thought is to measure factor exposures such as value, momentum, size, volatility, etc and try to neutralize the portfolio for them. The end result being that the factor exposures of the long side offset the factor exposures on the short side leaving me with a long portfolio that is nicely correlated to the short portfolio?

Is this correct?

If so, is there an accepted best way to choose which factor exposures to neutralize? Perhaps some factore exposures are desirable and others are not.

Any help would be greatly appreciated.

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    $\begingroup$ "I also know that it doesn't really work because the covariance matrix is unstable out of sample." I wouldn't go as far as saying that it doesn't work at all. $\endgroup$
    – Dimitri Vulis
    Commented Dec 22, 2022 at 15:18

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