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Risk‐sensitive benchmarked asset management with expert forecasts

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  • Mark H.A. Davis
  • Sébastien Lleo

Abstract

We propose a continuous‐time model in which investors use expert forecasts to construct a benchmark‐outperforming portfolio in two steps. The estimation step takes the form of a Kalman filter. The control step derives the optimal investment policy in closed form and establishes that the value function is the unique classical solution to the Hamilton‐Jacobi‐Bellman partial differential equation. We show that the optimal investment policy generates a continuum of investment strategies, from passive benchmark replication to fully active bets in the Kelly portfolio. However, our model warns against over‐betting on financial markets. Moreover, we find that the Kelly portfolio performs both security selection and factor tilt. A simulation study with market data confirms that factor choice is critical at every stage of the investment process. Finally, debiasing is equally crucial. Portfolios with debiased expert forecasts outperform portfolios with biased forecasts.

Suggested Citation

  • Mark H.A. Davis & Sébastien Lleo, 2021. "Risk‐sensitive benchmarked asset management with expert forecasts," Mathematical Finance, Wiley Blackwell, vol. 31(4), pages 1162-1189, October.
    • Handle: RePEc:bla:mathfi:v:31:y:2021:i:4:p:1162-1189
    DOI: 10.1111/mafi.12310
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    References listed on IDEAS

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    Cited by:

    1. Jan Obłój & Thaleia Zariphopoulou, 2021. "In memoriam: Mark H. A. Davis and his contributions to mathematical finance," Mathematical Finance, Wiley Blackwell, vol. 31(4), pages 1099-1110, October.
    2. Lleo, Sébastien & Runggaldier, Wolfgang J., 2024. "On the separation of estimation and control in risk-sensitive investment problems under incomplete observation," European Journal of Operational Research, Elsevier, vol. 316(1), pages 200-214.
    3. Kexin Chen & Hoi Ying Wong, 2022. "Duality in optimal consumption--investment problems with alternative data," Papers 2210.08422, arXiv.org, revised Jul 2023.
    4. Christoph Knochenhauer & Alexander Merkel & Yufei Zhang, 2024. "Optimal Investment with Costly Expert Opinions," Papers 2409.11569, arXiv.org.
    5. Marcin Pitera & {L}ukasz Stettner, 2022. "Discrete-time risk sensitive portfolio optimization with proportional transaction costs," Papers 2201.02828, arXiv.org.
    6. S'ebastien Lleo & Wolfgang J. Runggaldier, 2023. "On the Separation of Estimation and Control in Risk-Sensitive Investment Problems under Incomplete Observation," Papers 2304.08910, arXiv.org, revised Nov 2023.

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