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Sorry for this dumb question but what are the mathematical-finance /academic conventions for calculating portfolio weights in a long/short portfolio where the longs are fully funded by the shorts? Note that I am asking for the 'academic' conventions, I'm aware that in reality one needs to hold margin etc.

Suppose I am long USD200 of Apple, and I have shorted USD200 of Google stock. What is the portfolio weight of apple and google?

  • w_apple = 200/200 = 1 and w_google = -200/200 = -1?
  • w_apple = 200/(200 + abs(-200)) = 0.5 and w_google = -200/(200+abs(-200)) = -0.5?
  • something else?

Thanks

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The first one. Your net weight is zero. This is a self financing strategy. Think of it this way: if apple goes up by 10% and google goes down by 5% your return will be:

$r_p = 1 \times 10\% - 1 \times (-5\%)= 15\%$

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