Portfolio risk allocation through Shapley value

TL;DR

This paper proposes using the Shapley value from cooperative game theory to allocate risk among non-orthogonal risk factors in portfolios, providing a natural interpretation of each factor's contribution to overall risk.

Contribution

It introduces a novel application of Shapley value for risk allocation in complex portfolios, including derivatives and enterprise risk measures, with explicit formulas and algorithms.

Findings

Shapley value effectively allocates risk among non-orthogonal factors.

Explicit formulas and algorithms are derived for practical computation.

Application to derivatives and enterprise risk measures demonstrates versatility.

Abstract

We argue that using the Shapley value of cooperative game theory as the scheme for risk allocation among non-orthogonal risk factors is a natural way of interpreting the contribution made by each of such factors to overall portfolio risk. We discuss a Shapley value scheme for allocating risk to non-orthogonal greeks in a portfolio of derivatives. Such a situation arises, for example, when using a stochastic volatility model to capture option volatility smile. We also show that Shapley value allows for a natural method of interpreting components of enterprise risk measures such as VaR and ES. For all applications discussed, we derive explicit formulas and / or numerical algorithms to calculate the allocations.