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.
What will be an ideal response?
IS = proportion of portfolio invested in international stock
LC = proportion of portfolio invested in large-cap value
MC = proportion of portfolio invested in mid-cap value
SC = proportion of portfolio invested in small-cap growth
SB = proportion of portfolio invested in short-term bond
R1 = portfolio return for scenario 1 (Year 1)
R2 = portfolio return for scenario 2 (Year 2)
R3 = portfolio return for scenario 3 (Year 3)
R4 = portfolio return for scenario 4 (Year 4)
AR = expected (average) portfolio return
Min 0.25(R1 ? AR)2 + 0.25(R2 ? AR)2 + 0.25(R3 ? AR)2 + 0.25(R4 ? AR)2
22.37IS + 15.48LC + 17.42MC + 23.18SC + 9.26SB = R1
26.73IS + 19.64LC + 20.07MC + 12.36SC + 8.81SB = R2
4.86IS + 11.50LC ? 4.97MC + 3.25SC + 6.15SB = R3
2.17IS ? 5.25LC ? 1.69MC + 3.81SC + 4.04SB = R4
IS + LC + MC + SC + SB = 1
0.25R1 + 0.25R2 + 0.25R3 + 0.25R4 = AR
AR ? 5
IS, LC, MC, SC, SB ? 0
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