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Dynamic Portfolio Optimization Using Information from a Crisis Indicator

Author

Listed:
  • Victor Gonzalo

    (Department of Mathematics, Technical University of Munich, 85748 Munich, Germany)

  • Markus Wahl

    (Department of Mathematics, Technical University of Munich, 85748 Munich, Germany)

  • Rudi Zagst

    (Department of Mathematics, Technical University of Munich, 85748 Munich, Germany)

Abstract

Investors face the challenge of how to incorporate economic and financial forecasts into their investment strategy, especially in times of financial crisis. To model this situation, we consider a financial market consisting of a risk-free asset with a constant interest rate as well as a risky asset whose drift and volatility is influenced by a stochastic process indicating the probability of potential market downturns. We use a dynamic portfolio optimization approach in continuous time to maximize the expected utility of terminal wealth and solve the corresponding HJB equations for the general class of HARA utility functions. The resulting optimal strategy can be obtained in closed form. It corresponds to a CPPI strategy with a stochastic multiplier that depends on the information from the crisis indicator. In addition to the theoretical results, a performance analysis of the derived strategy is implemented. The specified model is fitted using historic market data and the performance is compared to the optimal portfolio strategy obtained in a Black–Scholes framework without crisis information. The new strategy clearly dominates the BS-based CPPI strategy with respect to the Sharpe Ratio and Adjusted Sharpe Ratio.

Suggested Citation

  • Victor Gonzalo & Markus Wahl & Rudi Zagst, 2025. "Dynamic Portfolio Optimization Using Information from a Crisis Indicator," Mathematics, MDPI, vol. 13(16), pages 1-36, August.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:16:p:2664-:d:1727754
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    References listed on IDEAS

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    1. Johannes Hauptmann & Anja Hoppenkamps & Aleksey Min & Franz Ramsauer & Rudi Zagst, 2014. "Forecasting market turbulence using regime-switching models," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 28(2), pages 139-164, May.
    2. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    3. Gabriel Frahm, 2018. "An Intersection–Union Test for the Sharpe Ratio," Risks, MDPI, vol. 6(2), pages 1-13, April.
    4. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    5. Arsalane Chouaib Guidoum & Kamal Boukhetala, 2020. "Performing Parallel Monte Carlo and Moment Equations Methods for Itô and Stratonovich Stochastic Differential Systems: R Package Sim.DiffProc," Post-Print hal-03188407, HAL.
    6. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    7. Jakub Trybuła & Dariusz Zawisza, 2019. "Continuous-Time Portfolio Choice Under Monotone Mean-Variance Preferences—Stochastic Factor Case," Mathematics of Operations Research, INFORMS, vol. 44(3), pages 966-987, August.
    8. Luz Rocío Sotomayor & Abel Cadenillas, 2009. "Explicit Solutions Of Consumption‐Investment Problems In Financial Markets With Regime Switching," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 251-279, April.
    9. Jan Kallsen & Johannes Muhle-Karbe, 2010. "Utility Maximization In Affine Stochastic Volatility Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(03), pages 459-477.
    10. Jun Liu, 2007. "Portfolio Selection in Stochastic Environments," The Review of Financial Studies, Society for Financial Studies, vol. 20(1), pages 1-39, January.
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