(Shana Salmen, Lauren McLain, Joey Ranieri, 1995)
The Situation. Our client, Mr. Louis R. McLain, Ill, CFA, is planning on starting an investment management firm and needs software to aid him in portfolio asset allocation. He requested a package that would specify the asset ``mix'' that, subject to certain assumption, would achieve a targeted return at minimum portfolio variance. He also wanted a tool to calculate the terminal wealth distribution given that portfolio's return and variance. This tool also needed to provide graphical support to aid investors in visualizing the potential return per dollar invested.
Method of Analysis. We needed a non-linear programming model that could handle quadratic equations and multiple constraints to minimize the portfolio variance, so we chose to develop the model in GAMS. The minimal cost of the PC-based GAMS software package made it attractive to our client, even though it does not have a user-friendly interface. For the terminal wealth distribution tool, we chose Microsoft Excel due to it's ease of use and popularity. It produces outstanding graphs that can be easily changed from one type to another (i.e. line graph to bar chart).
Findings. After developing a working model, Mr. McLain provided us with asset class and portfolio information to test the GAMS model and Excel spreadsheet. Our results showed that the first seven portfolio target returns yielded infeasible solutions because the constraints were violated. The other nine portfolio target returns yielded feasible solutions while adhering to all constraints. The model successfully allocated the appropriate percentage of assets to the different classes while minimizing overall portfolio variance. This information was fed into the spreadsheet which calculated the terminal wealth distribution for specific time horizons. The results of the spreadsheet show that greater returns are more likely over longer investment horizons.