An investment advisor at Shore Financial Services wants to develop a model that can be used to allocate investment funds among four alternatives: stocks, HINT\#1 Risk Constraint: bonds, mututal funds, and cash. For the coming investment period, the company developed estimates of the annual rate of return and the associated risk for each alternative. Risk is measured Total risk is the sum of the risk for all investment alternatives. using an index between 0 and 1 , with higher risk values denoting more volatility and thus more uncertainty. For instance, if An investment advisor will meet with each client to discuss the client's investment objectives and to determine a maximum total risk value for the client. 40% of a client's funds are invested in stocks, 30% in bonds - A maximum total risk value must be at most 0.3 (a conservative investor). 20% in mutual funds, and 10% in cash Shore Financial Services specified additional guidelines that must be applied to all clients. The guidelines are as follows: the total risk for the portfolio would be - No more than 75% of the total investment may be in stocks. 0.40(0.8)+0.30(0.2)+0.2(0.3)+0.1(0.0)=0.44 - The amount invested in mutual funds must be at least as much as invested in bonds. - The amount of cash must be at least 10% of the total investment funds, but no more than 30% of the total investment funds. The objective is to determine the portion of funds allocated to each investment alternative in order to maximize the total annual return for the portfolio subject to the risk level the client is willing to tolerate. a) Define the decision variables b) Write the objective function \begin{tabular}{|l|l|} \hline Min. OR Max. & Objective Function \\ \hline maximize & \\ \hline \end{tabular} c) Write all relevant constraints for this problem Note: the table below has more rows than you need. (No need to write 12 constraints) \begin{tabular}{|c|l|} \hline Constraint Number & Constraint Equation \\ \hline 1 & \\ \hline 2 & \\ \hline 3 & \\ \hline 4 & \\ \hline 5 & \\ \hline 6 & \\ \hline 7 & \\ \hline 8 & \\ \hline 9 & \\ \hline 10 & \\ \hline 11 & \\ \hline 12 & \\ \hline \end{tabular} d) Solve this problem using Excel Solver (or IBM CPLEX) and provide the solution below \begin{tabular}{|l|l|} \hline Portion of Funds Allocated to Stocks & round to 2 decimals \\ \hline \end{tabular} \begin{tabular}{|l|l|} \hline Portion of Funds Allocated to Bonds & round to 2 decimals \\ \hline \end{tabular} Portion of Funds Allocated to Mutual Funds round to 2 decimals Portion of Funds Allocated to Cash round to 2 decimals Objective Total = round to 2 decimals An investment advisor at Shore Financial Services wants to develop a model that can be used to allocate investment funds among four alternatives: stocks, HINT\#1 Risk Constraint: bonds, mututal funds, and cash. For the coming investment period, the company developed estimates of the annual rate of return and the associated risk for each alternative. Risk is measured Total risk is the sum of the risk for all investment alternatives. using an index between 0 and 1 , with higher risk values denoting more volatility and thus more uncertainty. For instance, if An investment advisor will meet with each client to discuss the client's investment objectives and to determine a maximum total risk value for the client. 40% of a client's funds are invested in stocks, 30% in bonds - A maximum total risk value must be at most 0.3 (a conservative investor). 20% in mutual funds, and 10% in cash Shore Financial Services specified additional guidelines that must be applied to all clients. The guidelines are as follows: the total risk for the portfolio would be - No more than 75% of the total investment may be in stocks. 0.40(0.8)+0.30(0.2)+0.2(0.3)+0.1(0.0)=0.44 - The amount invested in mutual funds must be at least as much as invested in bonds. - The amount of cash must be at least 10% of the total investment funds, but no more than 30% of the total investment funds. The objective is to determine the portion of funds allocated to each investment alternative in order to maximize the total annual return for the portfolio subject to the risk level the client is willing to tolerate. a) Define the decision variables b) Write the objective function \begin{tabular}{|l|l|} \hline Min. OR Max. & Objective Function \\ \hline maximize & \\ \hline \end{tabular} c) Write all relevant constraints for this problem Note: the table below has more rows than you need. (No need to write 12 constraints) \begin{tabular}{|c|l|} \hline Constraint Number & Constraint Equation \\ \hline 1 & \\ \hline 2 & \\ \hline 3 & \\ \hline 4 & \\ \hline 5 & \\ \hline 6 & \\ \hline 7 & \\ \hline 8 & \\ \hline 9 & \\ \hline 10 & \\ \hline 11 & \\ \hline 12 & \\ \hline \end{tabular} d) Solve this problem using Excel Solver (or IBM CPLEX) and provide the solution below \begin{tabular}{|l|l|} \hline Portion of Funds Allocated to Stocks & round to 2 decimals \\ \hline \end{tabular} \begin{tabular}{|l|l|} \hline Portion of Funds Allocated to Bonds & round to 2 decimals \\ \hline \end{tabular} Portion of Funds Allocated to Mutual Funds round to 2 decimals Portion of Funds Allocated to Cash round to 2 decimals Objective Total = round to 2 decimals
