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Is there any way to reduce Beta exposure to a single factor in the factor model?

Specifically I read somewhere that if in a single factor model, your beta, wrt to say SnP is B, you take a position of -BV in SnP to eliminate the beta component from your estimated returns. But it does not seem to add up. Can someone please explain why this would work out and if there is any other way to eliminate Beta exposure to a particular factor in the factor model.

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  • $\begingroup$ Why "it does not seem to add up"? The short position in S&P will offset the contribution from the rest of the portfolio's Beta. If your posrtfolio makes X dollars from its beta exposure the short position in S&P will lose X dollars and vice versa. (Provided you estimate of Beta holds up in the future). $\endgroup$ – Alex C Jan 30 '17 at 2:19
  • $\begingroup$ Yes the amount you make or lose is independent of beta, but for the returns we need to divide the change in net value by original value which is a function of beta now. $\endgroup$ – novice Jan 30 '17 at 2:45
  • $\begingroup$ Ah sorry I get it now, the return might be a function of beta but still independent of the return on SnP. Thanks a ton!. $\endgroup$ – novice Jan 30 '17 at 3:12

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