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The problem of data uncertainty has motivated the incorporation of robustoptimization in various arenas, beyond the Markowitz portfolio optimization.This work presents the extension of the robust optimization framework for theminimization of downside risk measures, such as Value-at-Risk (VaR) andConditional Value-at-Risk (CVaR). We perform an empirical study of VaR and CVaRframeworks, with respect to their robust counterparts, namely, Worst-Case VaRand Worst-Case CVaR, using the market data as well as the simulated data. Afterdiscussing the practical usefulness of the robust optimization approaches fromvarious standpoints, we infer various takeaways. The robust models in the caseof VaR and CVaR minimization exhibit superior performance with respect to theirbase versions in the cases involving higher number of stocks and simulatedsetup respectively.

Is being `Robust' beneficial?: A perspective from the Indian market