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I've heard in quantitative equity strategies, people backtest signals on residual returns. How does this work in practice? Do people find signals that forecast residual returns and then run the full optimization using the full covariance matrix? Or do they run portfolio optimization on the residual covariance matrix but constrain all factor exposures?

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  • $\begingroup$ Hi: When you use the term, "residual returns", I think you are referring to "idiosyncratic" return which is the return from the part of piece of the stock return that can't be modelled by factors. So, assuming that, you would still constrain using the full covariance matrix. I'm not familar with the term "residual" covariance matrix but that doesn't mean it doesn't exist. $\endgroup$
    – mark leeds
    Nov 25, 2023 at 13:30

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