Portfolio Performance Attribution via Shapley Value

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Portfolio Performance Attribution via Shapley Value

Nicholas Moehle
Stephen Boyd
Andrew Ang
Published on 2/11/2021
Cross-asset
Factor investing
Factor allocation
Risk management
Backtesting
Fundamental analysis
Smart beta

This paper addresses the problem of attributing portfolio performance to individual investment features, such as active strategies or factors, plus a baseline component. It highlights that traditional attribution methods can yield inconsistent results, leading to ambiguity in performance evaluation. To resolve this, the authors propose using the Shapley value from cooperative game theory, which provides a principled way to allocate performance fairly among features by considering all possible combinations and interactions. This method ensures that attributions are unique and satisfy desirable properties like efficiency and symmetry, making it a robust alternative to ad-hoc approaches.

The research discusses practical implementation by detailing both exact computational techniques for scenarios with a limited number of features and approximate methods for more complex portfolios where exact calculation is computationally intensive. By applying Shapley attribution, the paper demonstrates how investors can gain clearer insights into the contributions of each feature, enhancing decision-making and performance analysis. This approach bridges theoretical game theory with quantitative finance, offering a standardized framework that can improve transparency and accountability in investment processes.

Highlights

  • 1Introduces Shapley value as the preferred method for portfolio performance attribution
  • 2Addresses the challenge of multiple attribution methods leading to different results
  • 3Provides both exact and approximate computational methods for Shapley attribution
  • 4Applies cooperative game theory to investment feature analysis

Methods

  • M
    Shapley value from cooperative game theory
  • M
    Exact computation algorithms for attribution
  • M
    Approximate methods for practical applications
  • M
    Performance decomposition into features and baseline

Results

  • R
    Shapley value offers a fair and consistent attribution framework
  • R
    Exact methods are feasible for manageable feature sets
  • R
    Approximate methods enable application to complex portfolios
  • R
    Attribution accounts for interactions between features
0/5

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