Worst-case CVaR under a reward-penalty mechanism with applications to robust portfolio management

01 ABSTRACT

The paper introduces a reward-penalty mechanism into robust portfolio selection when the joint distribution of asset losses is uncertain, aiming to minimize worst-case CVaR. The authors first provide an explicit closed-form expression for worst-case CVaR under the reward-penalty mechanism, which generalizes results such as Jagannathan (1977), Chen et al. (2011), and Cai et al. (2024); they then solve for optimal allocations under classical and generalized mean-covariance distribution sets. Experiments on real market data indicate that the proposed models have the potential to outperform several existing related models, that incorporating downside risk helps manage risk and may achieve higher returns, and that a trade-off exists between expected return and worst-case CVaR control. The empirical findings are the authors' views and require independent verification.

02 KEY FINDINGS

1. Derives an explicit closed-form expression for worst-case CVaR under a reward-penalty mechanism, unifying and generalizing several existing models.
2. Obtains optimal portfolio allocations minimizing worst-case CVaR under both a classical mean-covariance distribution set and the generalized mean-covariance distribution set of Kang et al. (2019).
3. Real market data experiments suggest the proposed models have the potential to outperform several existing related models, and that incorporating downside risk aids risk management and may improve returns.