Delta-Gamma Component VaR: Non-Linear Risk Decomposition for any Type of Funds

Abstract

This article develops an analytical methodology for decomposing non-linear portfolio risk not only by instrument, but also by fund managers or sub-portfolios for one single manager. Furthermore the approach may be used by quantitative portfolio managers for risk decomposition by factors under a factor investing strategy. We refer to this approach as ``Delta-Gamma Component Value-at-Risk'' (DG CVaR) as it decomposes VaR using an analytic approximation. The approach is well suited to funds holding any asset class or instrument type together with options. This decomposition approach is additive under non-linear portfolio returns, fully captures the correlations between instrument returns, and thus is well suited for decomposing risk by instrument, manager, sub-portfolio, or factor, modulo the limitations of VaR. We provide an example from a representative CTA portfolio that demonstrates superiority of the decomposition approach over other common practices for risk decomposition. The core methodology is implemented in R and made available to readers. The source can be found at https://github.com/mfrdixon/RiskDecomposition.