Summary: Assuming that a manager is loss averse we establish a delegated portfolio model with a risk constraint to research the optimal investment problem in delegated portfolio management. The delegated portfolio problem with conditional value at risk as a constraint is transformed into a stochastic optimization problem with a stochastic convex function as constraint by constructing the auxiliary function, and the existence of optimal strategies is proved. Furthermore, approximate optimal investment strategies are obtained based on a Monte Carlo penalty function algorithm constructed using a random sampling method and are proved to be almost everywhere optimal strategies for the original delegated portfolio problem when the sample number is large enough. Finally, numerical examples are given to illustrate the effectiveness of the model and the effect of loss aversion of the manager on the optimal portfolio strategies.