[3Xin4-07] Double Robustified mean-CVaR portfolio
Keywords:Portfolio Optimization, Robust Optimization, CVaR
The mean-variance portfolio has been the most widely used in practice for the purpose of portfolio construction.
However, there are two major challenges with this approach: (1) variance is a risk measure that includes upside deviations from the mean, and (2) small changes in the parameters can greatly change the optimal weights.
The first issue can be addressed by using CVaR, a risk measure that only captures downward risk. However, it is known that even small changes in the probability level, a parameter of CVaR, can significantly change the optimal weights. In addition, the instability associated with these parameter changes can deteriorate portfolio performance.
Therefore, in this study, we propose the Double Robustified mean-CVaR portfolio that solves the instability in both the mean and CVaR.
The proposed method simultaneously optimizes CVaR for multiple probability levels, as proposed in a previous study, and defines uncertainty sets for the mean parameter to perform robust optimization.
We proved that the proposed method can be formulated as a second-order cone problem. In addition, we derive an estimation error bound of the proposed method for the finite-sample case.
We confirmed through empirical analysis that the proposed method performs better than existing optimization methods.
However, there are two major challenges with this approach: (1) variance is a risk measure that includes upside deviations from the mean, and (2) small changes in the parameters can greatly change the optimal weights.
The first issue can be addressed by using CVaR, a risk measure that only captures downward risk. However, it is known that even small changes in the probability level, a parameter of CVaR, can significantly change the optimal weights. In addition, the instability associated with these parameter changes can deteriorate portfolio performance.
Therefore, in this study, we propose the Double Robustified mean-CVaR portfolio that solves the instability in both the mean and CVaR.
The proposed method simultaneously optimizes CVaR for multiple probability levels, as proposed in a previous study, and defines uncertainty sets for the mean parameter to perform robust optimization.
We proved that the proposed method can be formulated as a second-order cone problem. In addition, we derive an estimation error bound of the proposed method for the finite-sample case.
We confirmed through empirical analysis that the proposed method performs better than existing optimization methods.
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