Cataloged from PDF version of article.We consider the problem of optimal portfolio choice using the Conditional\ud Value-at-Risk (CVaR) and Value-at-Risk (VaR) measures for a market\ud consisting of n risky assets and a riskless asset and where short positions are\ud allowed. When the distribution of returns of risky assets is unknown but the mean\ud return vector and variance/covariance matrix of the risky assets are fixed, we derive\ud the distributionally robust portfolio rules. Then, we address uncertainty (ambiguity)\ud in the mean return vector in addition to distribution ambiguity, and derive the\ud optimal portfolio rules when the uncertainty in the return vector is modeled via an\ud ellipsoidal uncertainty set. In the presence of a riskless asset, the robust CVaR and\ud VaR measures, coupled with a minimum mean return constraint, yield simple,\ud mean-variance efficient optimal portfolio rules. In a market without the riskless\ud asset, we obtain a closed-form portfolio rule that generalizes earlier results, without\ud a minimum mean return restriction

a b s t r a c tWe consider the problem of optimal portfolio choice using the lower partial moments risk measure for a market consisting of n risky assets and a riskless asset. For when the mean return vector and variance/covariance matrix of the risky assets are specified without specifying a return distribution, we derive distributionally robust portfolio rules. We then address potential uncertainty (ambiguity) in the mean return vector as well, in addition to distribution ambiguity, and derive a closed-form portfolio rule for when the uncertainty in the return vector is modelled via an ellipsoidal uncertainty set. Our result also indicates a choice criterion for the radius of ambiguity of the ellipsoid. Using the adjustable robustness paradigm we extend the single-period results to multiple periods, and derive closed-form dynamic portfolio policies which mimic closely the single-period policy.

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