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Suppose I have historical return data on 10 assets. How can I create a hedge portfolio that prices all these assets in a factor model?

I have chosen 3 factors: excess market return, SMB and HML from Fama-French. Now I want to have a 4th factor, and that would be the hedge portfolio, created using the historical prices of the 10 assets.

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    $\begingroup$ @AlexC I have historical returns data on 10 assets. Using this data, I want to create a hedge portfolio that would price these assets in a multi-factor model. $\endgroup$ – meta_finance Feb 6 at 23:05
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    $\begingroup$ @noob2 I have 3 factors: excess market return, SMB and HML from FF. I want to have a 4th factor and that would be the hedge portfolio. And, I have to create the hedge portfolio using the historical prices of 10 assets $\endgroup$ – meta_finance Feb 6 at 23:08
  • $\begingroup$ This question is very unclear. I'll go through it bi by bit: - 'How can I create a hedge portfolio that prices all these assets in factor model'? What do you mean with prices these assets? You already have asset prices? - "I have chosen 3 factors: ..." Do you mean that you have these factor returns available externally? Or have you estimated them from your data? Have you estimated the factor weights for each asset? Or is this your real question $\endgroup$ – Bram Feb 7 at 10:17
  • $\begingroup$ - "Now I want to have a 4th factor ...". What do you want to hedge exactly?. Hedging a portfolio consisting of weights w_i, can be done with a portfolio with weights -w_i $\endgroup$ – Bram Feb 7 at 10:18

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