Investigating usefulness of portfolio optimization with respect to prospect utility in financial advisory

Sammanfattning: In this paper we derive and analyze the usefulness of a prospect theory based model for selecting optimal portfolios with respect to multiple investment goals. The focus is to determine whether or not the model would be suitable for the advisory process by investigating the result given by the optimal portfolio values and proportion in risky assets in continuous time. The model is based on the framework proposed by Berkeelar et al. [1] and De Giorgi [2] and follows a two step approach. It starts by finding the optimal terminal portfolio value for each investment goal and secondly determines the optimal initial funding for each investment goal based on the optimal terminal portfolio value. We have shown that the initial funding is monotone in the long term investment goal, in other words the investor initially puts all capital in that goal and therefore neglect remaining goals. Moreover we have shown that the model, assuming evenly distributed initial capital among investment goals, results in the investor reaching the short term goal only, for median risk profile but reaching all investment goals for the extreme loss averse profile. Lastly we also point out that the model holds very high leverage in risky assets for the median risk profile and less in risky assets when the investor is considered extreme loss averse. We conclude that this model is not suitable for the financial advisory process mainly because the median risk profile does reach her long term goal.