Optimizing the manager structure in a downside risk framework

To decide the investment policy of a pension fund, a plan sponsor first conducts an asset allocation study and then he/she hires active managers to add active return to the portfolio. In order to seek active return, a plan sponsor must necessarily accept risk. But how much risk does the plan sponsor have to take, and how many managers does he/she have to hire? This problem that a plan sponsor often is faced with is a manager selection problem. A lot of methods to decide the manager structure have been proposed, however, in the most cases the returns of the active funds are assumed to be normally distributed. In this study I empirically show that the returns of actively managed funds are not normally distributed and it is impossible for a plan sponsor to optimize the manager structure by using the standard mean variance model. To accurately capture the risk of the funds, I use the target semi-deviation as a measure of risk. In my framework, shortfall below the return of policy asset mix is recognized as risk, and manager's active alpha is adjusted by the target semi-deviation. I also propose a method to decompose a portfolio's target semi-deviation for converting the optimal manager structure into the optimal risk allocation.