Financial planner Minnie Margin has a substantial number of clients who wish to own a mutual fund portfolio that matches, as a whole, the performance of the Russell 2000 index. Her task is to determine what proportion of the portfolio should be invested in each of the five mutual funds listed below so that the portfolio most closely mimics the performance of the Russell 2000 index. 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)
Min (R1 ? 20)2 + (R2 ? 22)2 + (R3 ? 8)2 + (R4 + 2)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
IS, LC, MC, SC, SB ? 0
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