Attribution Methods in Asset Pricing: Do They Account for Risk?

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Attribution Methods in Asset Pricing: Do They Account for Risk?

Dangxing Chen
Yuan Gao
Published on 7/12/2024
Equities
Machine learning
Risk management
Factor investing

This paper investigates whether popular attribution methods in machine learning, specifically Shapley value and Integrated Gradients, can accurately reflect risk in asset pricing models. The authors propose several new axioms derived from financial domain knowledge, such as Average Individual Monotonicity (AIM), Demand Individual Monotonicity (DIM), and axioms related to diminishing or increasing marginal effects. These axioms are designed to capture first-order and second-order risk sensitivities, akin to financial Greeks. Through analytical proofs and empirical examples involving coupon bonds and option pricing, the paper demonstrates that while Shapley value and Integrated Gradients satisfy some axioms, neither method satisfies all. For instance, Shapley value can violate the diminishing marginal effect axiom, and Integrated Gradients fails demand monotonicity. The findings highlight that attribution methods may provide misleading explanations in high-stakes financial applications, as they may not properly account for risk. The paper underscores the necessity of incorporating domain-specific knowledge into explainable AI to ensure that attributions are consistent with financial risk management principles.

Highlights

  • 1Proposes novel domain-specific axioms for attribution methods in asset pricing to reflect risk, including Average Individual Monotonicity (AIM), Demand Individual Monotonicity (DIM), and Diminishing/Increasing Marginal Effect axioms.
  • 2Provides a rigorous analysis of Shapley value (BShap) and Integrated Gradients (IG) against these axioms, showing that neither method satisfies all axioms.
  • 3Demonstrates through analytical and empirical examples how attribution methods can fail to capture risk, particularly in financial contexts like bond and option pricing.
  • 4Highlights the importance of incorporating domain knowledge (e.g., Greeks in finance) into explainable ML to ensure risk-sensitive explanations.

Methods

  • M
    Baseline Shapley (BShap) value for feature attribution.
  • M
    Integrated Gradients (IG) for feature attribution.
  • M
    Axiomatic analysis of attribution methods using proposed domain-specific axioms.
  • M
    Analytical and empirical examples from asset pricing (coupon bonds and option pricing) to illustrate axiom violations.

Results

  • R
    Shapley value preserves AIM and DIM but fails to preserve DME/RDME axioms in certain cases.
  • R
    Integrated Gradients preserves AIM but fails to preserve DIM and DME/RDME axioms.
  • R
    Both methods can produce attributions that do not align with risk sensitivities (e.g., positive attribution for interest rate in bond pricing when it should be negative).
  • R
    The study shows that attribution methods may not reliably reflect risks, especially when features have monotonic or convexity properties.
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