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I have a portfolio of 6 securities, 3 long 3 short. I need to hedge them against each other so directional exposure = 0. How would I decide how to weight each security?

Is there a model to do this?

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The keyword here is directional exposure. You first need to define what is the instrument that you do not want to have directional exposure to. Oftenwise in case of equities, this might be an equity index.

Then you would need to estimate the betas of each security against the index and set the weights in any such way that the sumproduct of all the securities' weights and betas equals zero. This way, your porftolio willhave zero directional exposure by construction.

However, the real trickery is in estimating the betas for each of the instruments. The simplest way is to just use the historical betas as an estimate for future, but there are other, more sophisticated ways to do this, and it is a whole branch of research, how to best do that.

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  • $\begingroup$ The three long assets are the exposure. I want to be delta neutral with a portfolio of the 6 assets, assuming I must hold 1/3 of each of the long assets. $\endgroup$
    – s00rz
    May 31 at 8:51
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    $\begingroup$ In that case you would estimate the other assets' beta against the returns for the porftolio of the 3 long assets. Then assign the short weights in any such way that the sumproduct of the weights and betas equals -1 (to offset the beta of +1 from the long assets). $\endgroup$
    – MGL
    May 31 at 10:08

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