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I have a portfolio of weights $\mathbf{x}$ where some positions in $\mathbf{x}$ are short s.t. $\Sigma_i x_i=0$ (dollar neutral).

The standard way to estimate the volatility contribution per asset is by using $\mathbf{x}'\Sigma$ where $\Sigma$ is the covariance matrix of asset returns. From this, I would look at the asset with the largest vol-contribution and increase (decrease) its position to increase (decrease) my portfolio volatility to target a specific volatility.

This works in a long only portfolio where $x_i > 0 \, \forall i$, however it can yield negative values in a long-short portfolio. How would I use / interpret the form $\mathbf{x}'\Sigma$ in terms of volatility contribution per asset to adjust weights in a long-short portfolio to target volatility?

I found this post quite useful in giving some background, but I am confused as to the difference in "marginal risk contribution" and "sensitivity of the portfolio volatility with respect to an assets volatility", especially in how it relates to a long-short portfolio.

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  • $\begingroup$ my hunch is: in theory an asset could yield negative values because by going short it is cancelling risks from other assets $\endgroup$ Commented Nov 15, 2023 at 14:40

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