Learning the Shrinkage Intensity: A Data-Driven Approach for Risk-Optimized Portfolios

Gianluca De Nard & Damjan Kostovic

Journal of Financial Econometrics2026https://doi.org/10.1093/jjfinec/nbag002article
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Abstract

We introduce a new type of shrinkage estimator that is not based on asymptotic optimality, but instead learns a state-dependent shrinkage policy via supervised learning in a contextual bandit setup. The proposed estimator applies to both linear and nonlinear shrinkage and shows improved performance compared to classical shrinkage estimators. Our results demonstrate that our estimator identifies a downward bias in classical shrinkage intensity estimates derived under the i.i.d. assumption and automatically corrects for it in response to prevailing market conditions. Additionally, our data-driven approach enables more efficient implementation of risk-optimized portfolios and is well-suited for real-world investment applications, including portfolios with practical optimization constraints.

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https://doi.org/https://doi.org/10.1093/jjfinec/nbag002

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@article{gianluca2026,
  title        = {{Learning the Shrinkage Intensity: A Data-Driven Approach for Risk-Optimized Portfolios}},
  author       = {Gianluca De Nard & Damjan Kostovic},
  journal      = {Journal of Financial Econometrics},
  year         = {2026},
  doi          = {https://doi.org/https://doi.org/10.1093/jjfinec/nbag002},
}

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