Direct Data-Driven Portfolio Optimization with Guaranteed Shortfall Probability

This paper proposes a novel methodology for optimal allocation of a portfolio of risky financial assets. Most existing methods that aim at compromising between portfolio performance (e.g., expected return) and its risk (e.g., volatility or shortfall probability) need some statistical model of the asset returns. This means that: ({\em i}) one needs to make rather strong assumptions on the market for eliciting a return distribution, and ({\em ii}) the parameters of this distribution need be somehow estimated, which is quite a critical aspect, since optimal portfolios will then depend on the way parameters are estimated. Here we propose instead a direct, data-driven, route to portfolio optimization that avoids both of the mentioned issues: the optimal portfolios are computed directly from historical data, by solving a sequence of convex optimization problems (typically, linear programs). Much more importantly, the resulting portfolios are theoretically backed by a guarantee that their expected shortfall is no larger than an a-priori assigned level. This result is here obtained assuming efficiency of the market, under no hypotheses on the shape of the joint distribution of the asset returns, which can remain unknown and need not be estimate

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. © 2013 Elsevier B.V. All rights reserved