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Portfolio risk allocation through Shapley value

Author

Listed:
  • Patrick S. Hagan

    (Gorilla Science, Baruch College, One Bernard Baruch Way, New York, NY 10010, USA)

  • Andrew Lesniewski

    (Department of Mathematics, Baruch College, One Bernard Baruch Way, New York, NY 10010, USA)

  • Georgios E. Skoufis

    (Santander Corporate & Investment Banking, 2 Triton Square, Regents Place, London NW1 3AN, UK)

  • Diana E. Woodward

    (Gorilla Science, Baruch College, One Bernard Baruch Way, New York, NY 10010, USA)

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.

Suggested Citation

  • Patrick S. Hagan & Andrew Lesniewski & Georgios E. Skoufis & Diana E. Woodward, 2025. "Portfolio risk allocation through Shapley value," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 12(02), pages 1-18, June.
    • Handle: RePEc:wsi:ijfexx:v:12:y:2025:i:02:n:s2424786323500044
    DOI: 10.1142/S2424786323500044
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