Financial planner Minnie Margin wishes to develop a mutual fund portfolio based on the Markowitz portfolio model. She needs to determine the proportion of the portfolio to invest in each of the five mutual funds listed below so that the variance of the portfolio is minimized subject to the constraint that the expected return of the portfolio be at least 5%. Formulate the appropriate nonlinear program. Minnie assumes that the more recent returns are more likely to occur. She assumes that the probability of occurrence of scenario 1 is 40%, of scenario 2 is 30%, of scenario 3 is 20% and of scenario 4 is 10%. Annual Returns (Planning Scenarios)
Mutual Fund Year 1 Year 2 Year 3 Year 4
International Stock 22 26 4 2
Large-Cap Value 15 19 11 -5
Mid-Cap Value 17 20 -4 -1
Small-Cap Growth 23 12 3 3
Short-Term Bond 9 8 6 4
S&P 500 12 8 4 9