Mean-CVaR portfolio optimization with decision dependent distribution of losses under fixed dependence structure

Portfolio optimization problems include a stochastic element in the form of asset losses. Their probability distribution is generally considered to be fixed, but there are cases where this assumption does not hold. Provided that the investor’s budget is large enough relative to the size of considered companies, a significant investment can influence the loss distribution in various ways. Such a phenomenon is generally called endogenous (or decision dependent) randomness and this paper presents two underlying models dealing with such situations under the assumption of a fixed dependence structure between asset losses. Uniform enhancement model considers a positive investment effect, which is realized by a decision dependent shift of the loss distribution. Tail distortion model allows the resulting effect to be a consequence of realized market scenarios by influencing tail behavior of the loss distribution. The nature of said influence is determined by the investor’s managerial decisions. Both models are formulated as extensions of the Mean-CVaR portfolio selection problem and subsequently numerically solved. A comparison with the classical Mean-CVaR problem is presented as well in order to evaluate the effect of endogenous randomness.