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I have a portfolio of long/short positions in stocks. I would like to calculate the portfolio correlation. Should I somehow account for the short position while calculating the portfolio correlation? I am using formula a) from here.

Would be grateful for help!

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If you follow the methodology on the page you point to, you will take these correlations into account because it will be in the sign of the weights $w_i$:

For instance, the first method: $$C := {2\sum_i \sum_{j> i} w_i \rho_{i,j} w_j \over 1 - \sum_i w_i^2}$$

Say you have only two stocks in the portfolio correlated at 0.5:

  1. Say $w_i=w_j=1/2$, $$C^+={1/4 \over 1 - 1/2}$$

  2. And now say $w_i=-w_j=1/2$, $$C^-=-{1/4 \over 1 - 1/2}=-C^+$$

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  • $\begingroup$ Thanks for your answer. I see your point, but what would happen if the portfolio consisted of, for example, cfd positions? So basically you profit from the stock going down but the amount of your investment, thus the weight, is not negative. $\endgroup$ – abu Jun 25 '18 at 21:50
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    $\begingroup$ You should not mix leverage and portfolio characteristics. The weight of the stock is negative if you bet on downward moves, and positive if you bet on upward ones; see it as a convention. The way you finance the portfolio is aother story. $\endgroup$ – lehalle Jun 26 '18 at 21:22

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