Robust Portfolio Optimization with Respect to Spectral Risk Measures Under Correlation Uncertainty

This paper proposes a distributionally robust multi-period portfolio model with ambiguity on asset correlations with fixed individual asset return mean and variance. The correlation matrix bounds can be quantified via corresponding confidence intervals based on historical data. We employ a general class of coherent risk measures namely the spectral risk measure, which includes the popular measure conditional value-at-risk (CVaR) as a particular case, as our objective function. Specific choices of spectral risk measure permit flexibility for capturing risk preferences of different investors. A semi-analytical solution is derived for our model. The prominent stochastic dual dynamic programming (SDDP) algorithm adapted with intricate modifications is developed as a numerical method under the discrete distribution setting. In particular, our new formulation accounts for the unknown worst-case distribution in each iteration. We verify the convergence property of this algorithm under the setting of finite scenarios. Our results show that the optimal solution favours a certain degree of anti-diversification due to dependence ambiguity and exhibits its protection ability during the financial crisis period.