Abstract
In this note we prove a simple formula to compute the Incremental Volatility, i.e. the change in the portfolio volatility due to the removal of one asset from the portfolio. The common practice adopted in the literature and in the industry is to avoid the full recalculation of the portfolio volatility, but rather to use a first order approximation based on the gradient of the portfolio volatility. Here, we introduce a new exact formula that does not require to recompute the volatility of the new portfolio, but exploits quantities computed previously. Using the new formula, we can easily compute the effect on the portfolio volatility of any arbitrary change in the weigth of one asset as well as to determine the optimal trade, i.e. the weight change that allows the maximum reduction in the portfolio volatility. Due to their striking simplicity, the new formulas provide important portfolio analytics of immediate use in the asset management industry.
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