solution

Variable Definitions:

F1 – VTSAX

F2 – VFIAX

B1 – VBTLX

S1 – MSFT

S2 – APPL

Given Investments Annual Rate of Return:

F1R = 0.147

F2R = 0.148

B1R =0.077

S1R =0.290

S2R =0.282

Maximize (F1R)(F1) + (F2R)(F2) + (B1R)(B1) + (S1R)(S1) + (S2R)(S2) – Total Annual Return

s.t.

B1 <= 0.1(F1 + F2 + B1 + S1 + S2) – Bond Mutual Fund shouldn’t exceed 10% of all investments

(S1 + S2) <= 0.2(F1 + F2 + B1 + S1 + S2) – Stocks shouldn’t exceed 20% of all investments

S2 >= 0.6(S1 + S2) – Apple stock should be at least 60% of all stock investments

Given the maximized total return : 0.1755

Build an excel model that includes these categories and add a sensitivity analysis and work to complicate the models with more constraints and more variables

– Sensitivity analysis – how robust is your solution to changes in the objective function coefficients and (especially) to changes to the right-hand sides of the constraints (i.e., what if your risk tolerance or return requirement go up or down)?

– incorporate a numerical value for the risk level of each investment. include overall model risk in your objective function or constraints. have a constraint requiring that the overall portfolio risk be below some level. determine the optimal portfolios different levels of risk tolerance,

– can you control the model to keep the overall risk below some threshold. How does the solution change if the risk level changes?

– turn this into a multi-period problem at the portfolio composition at the end of each quarter and re-optimize.