An estimation-free, robust conditional value-at-risk allocation model

Carlos Jabbour, Javier F. Peña, Juan C. Vera, Luis F. Zuluaga

Abstract

ABSTRACT

We propose a novel optimization model for risk-averse investors to obtain robust solutions for portfolio allocation problems. Unlike related models in the literature, no historical data or statistical estimation techniques are used to compute the parameters of the model. Instead, the parameters are directly obtained from current prices of options on the assets being considered. Furthermore, the model only requires the solution of a linear program. To find a robust portfolio, we minimize the portfolio’s worst case conditional value-at-risk over all asset return distributions that replicate the current option prices. The model addresses the main practical limitations associated with classical portfolio allocation techniques, namely, the high sensitivity to model parameters and the difficulty to obtain accurate parameters’ estimates. These characteristics, together with their linear programming formulation and the use of a coherent downside measure of risk, should be appealing to practitioners. We provide numerical experiments to illustrate the characteristics of the model.