Reference dependence, loss aversion, and risk seeking for losses together comprise the preference-based component of prospect theory that sets its value function apart from the standard risk-aversion model. Using an elasticity analysis, we show that this distinctive preference component serves to underpin negative-feedback trading propensities, but cannot manifest itself in behavior directly or holistically at the individual-choice level. We then propose and demonstrate that the market interaction between prospect-theory investors and regular CRRA investors allows this preference component to dominate in equilibrium behavior and hence helps to reestablish the intuitive link between prospect-theory preferences and negative-feedback trading patterns. In the model, the interaction also reconciles the contrarian behavior of prospect-theory investors with asymmetric volatility and short-term return reversal. The results suggest that prospect-theory preferences can lead investors to behave endogenously as contrarian noise traders in the market interaction process.

As the skewed return distribution is a prominent feature in nonlinear portfolio selection problems which involve derivative assets with nonlinear payoff structures, Value-at-Risk (VaR) is particularly suitable to serve as a risk measure in nonlinear portfolio selection. Unfortunately, the nonlinear portfolio selection formulation using VaR risk measure is in general a computationally intractable optimization problem. We investigate in this paper nonlinear portfolio selection models using approximate parametric Value-at-Risk. More specifically, we use first-order and second-order approximations of VaR for constructing portfolio selection models, and show that the portfolio selection models based on Delta-only, Delta–Gamma-normal and worst-case Delta–Gamma VaR approximations can be reformulated as second-order cone programs, which are polynomially solvable using interior-point methods. Our simulation and empirical results suggest that the model using Delta–Gamma-normal VaR approximation performs the best in terms of a balance between approximation accuracy and computational efficiency.