Investment Portfolio Optimization: Sensitivity Analysis

Impact of Minimum CD & Treasury Bond Investment

Question: If the amount invested in CDs and treasury bonds is at least $5,000 plus 1.2 times the amount invested in municipal bonds and growth stocks, what is the new optimal solution and Optimal Feasible Value (OFV)?

Answer: Since the allowable increase is greater than $5,000 and this is a binding constraint, you must re-solve the problem to obtain the new optimal solution. The new OFV can be estimated using the shadow price: New OFV ≈ Old OFV + 5000 * (-0.0295).

Adding a GIC Investment Alternative

Question: If there is another investment alternative in Guaranteed Investment Certificates (GICs) with a Return on Investment (ROI) of 10%, what is the new optimal solution and OFV?

Answer: Introducing a new investment alternative (GICs) adds a new variable to the model. Therefore, the entire problem must be re-solved to determine the new optimal solution and OFV.

Removing Max CD Investment Constraint

Question: If the constraint on the maximum amount invested in Certificates of Deposit (CDs) is removed, what is the new optimal solution and OFV?

Answer: As this is a non-binding constraint, removing it does not affect the current optimal solution or the OFV.

Adjusting Investment Ratio Constraint

Question: If the ratio of the amount invested in CDs and treasury bills to the amount invested in municipal bonds and growth stocks should be at least 1.5:1, what is the new optimal solution and OFV?

Answer: This change modifies the Left-Hand Side (LHS) of an existing constraint. Consequently, the problem needs to be re-solved to find the new optimal solution and OFV.

Reduced Total Investment Funds

Question: If Kathleen discovers she made a calculation error and only has $69,500 to invest (originally $70,000), what is the new optimal solution and OFV?

Answer: This involves multiple changes, including a $500 decrease in the Right-Hand Side (RHS) of a binding constraint (total funds). We can check the validity of using shadow prices with the 100% rule for simultaneous RHS changes. Assuming the calculation is (500 / Allowable Decrease 1) + (100 / Allowable Change 2) + (150 / Allowable Change 3) = (500/∞) + (100/∞) + (150/17181.82), the sum is less than 1. While this suggests shadow prices might be valid for estimation, the safest approach is to re-solve the problem. The estimated OFV change using shadow prices might be calculated as: New OFV ≈ 6618.18 – 500*(0.094545455) – 100*(0) – 150*(0). However, re-solving provides the definitive new optimal solution and OFV.

Adding Constraint on MB & TB Investment

Question: If the amount invested in municipal bonds (MB) and treasury bills (TB) together is not more than 60% of the total available funds, is the current solution still optimal? What is the optimal solution and OFV?

Answer: This adds a new constraint: MB + TB ≤ 0.60 * Total Funds. Assuming total funds are $70,000, this means MB + TB ≤ $42,000. If the current optimal solution already satisfies this new constraint, then the optimal solution and OFV remain unchanged.

Adding Multiple Non-Binding Constraints

Question: If the total amount invested in Treasury Bills (TB) and CDs is at least $35,000, and the amount invested in Municipal Bonds (MB) is not more than $1,000, what is the OFV and optimal solution?

Answer: Both proposed changes introduce constraints: (1) TB + CDs ≥ $35,000 and (2) MB ≤ $1,000. If these are non-binding constraints (meaning the current optimal solution already satisfies them) and the changes are within allowable limits, the optimal solution and OFV remain unchanged.