Robust Mean-CVaR Portfolio Optimization with Liquidity Constraints

{'en': 'Portfolio models that combine mean-CVaR objectives with robust parameter uncertainty normally treat positions as perfectly liquid. This paper adds a liquidation-horizon constraint and a position-dependent trading cost to a robust mean-CVaR model, and shows that the result is a second-order cone program. Under ellipsoidal perturbations of scenario returns, the worst-case CVaR equals the empirical CVaR plus a norm term, so no additional scenarios are needed. A rolling experiment with twenty assets and twenty replications compares four strategies. Relative to the nominal benchmark, the integrated model raises the Sharpe ratio from 0.48 to 0.68, lowers daily CVaR from 2.40% to 2.03%, and cuts the stressed liquidation cost from 145 to 45 basis points. Liquidity constraints account for most of the gain; robustness contributes mainly through lower tail risk once those constraints bind. The two frictions are partial substitutes, and ignoring either yields portfolios that are expensive to unwind.'}