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If I use every principal component to explain total variance of my portfolio, does it still make sense in portfolio optimization? Because since alpha factors try to find out and explain unexplained return by risk factors, if we explain whole part of return just by risk factors, what's the point of using alpha factors? Does this even make sense?

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  • $\begingroup$ Maybe you can clarify your terms (riskfactors, alpha factors and their connection with principal components) and state your question more clearly? $\endgroup$
    – g g
    Mar 8, 2021 at 7:33
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    $\begingroup$ Using every principal component would beat the purpose of dimensionality reduction in the first place $\endgroup$ Mar 8, 2021 at 7:38
  • $\begingroup$ For a clear definition of alpha factors and risk factors I think this link explains far better than me. quant.stackexchange.com/questions/2710/… So, briefly, risk factors are drivers of volatility and alpha factors are drivers of mean returns $\endgroup$
    – geonhwa
    Mar 8, 2021 at 8:23
  • $\begingroup$ If the number of original feature is 100, then the principal components that explain total variance also counts 100? $\endgroup$
    – geonhwa
    Mar 8, 2021 at 8:24
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    $\begingroup$ @geonhwa Yes, if you’re targeting 100% variance explaining. But in many cases you can get something like 99% with a relatively small subset of those 100 dimensions $\endgroup$ Mar 8, 2021 at 9:11

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