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Mean semi-deviation from a target and robust portfolio choice under distribution and mean return ambiguity
Cataloged from PDF version of article.We 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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