Incremental Volatility and Related Portfolio Analytics

Abstract

In this article, the authors prove a simple formula to compute the incremental volatility, that is, 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 and to use a first-order approximation based on the gradient of the portfolio volatility. Here, the authors introduce a new exact formula that does not require recomputing the volatility of the new portfolio but exploits quantities computed previously. Using the new formula, they can easily compute the effect on the portfolio volatility of any arbitrary change in the weight of one asset as well as to determine the optimal trade, that is, the weight change that allows the maximum reduction in the portfolio volatility. A simulation exercise and an empirical analysis illustrate the clear advantage, in terms of accuracy, saving in computational time and calculation of portfolio analytics with respect to the full reevaluation and the commonly used linear approximation. Due to their striking simplicity, the new formulas provide important portfolio analytics of immediate use in the asset management industry.