As discussed in Section 8.3, the Markowitz model uses the variance of the portfolio as the measure of risk. However, variance includes deviations both below and above the mean return. Semivariance includes only deviations below the mean and is considered by many to be a better measure of risk. (a) Develop a model that minimizes semivariance for the Hauck Financial data given in the file HauckData with a required return of 10%. Assume that the five planning scenarios in the Hauck Financial Services model are equally likely to occur. Hint: Modify model (8.10)-(8.19). Define a variable d for each scenario and let d R - R with d 0. Then make the objective function: Min 1 5 S = 1 Let FS = IB = LG = LV = proportion of portfolio invested in the foreign stock mutual fund proportion of portfolio invested in the intermediate-term bond fund proportion of portfolio invested in the large-cap growth fund proportion of portfolio invested in the large-cap value fund SG = proportion of portfolio invested in the small-cap growth fund SV = proportion of portfolio invested in the small-cap value fund R = the expected return of the portfolio Rs = the return of the portfolio in years. S Min s.t. s = R R2 R3 R4 R5 = = = = = FS + IB + LG + LV + SG + SV = RS = R s = 1 d R- d R- d3 R- dR- d5 R- R = FS, IB, LG, LV, SG, SV (b) Solve the model developed in part (a) with a required expected return of 10%. (Round your answers to three decimal places.) FS = IB = Objective value LG = LV = SG = SV = A B D E F 1 Mutual Fund Year 1 Year 2 Year 3 Year 4 Year 5 2 Foreign Stock 10.060 13.120 13.470 45.420 -21.930 3 Intermediate-Term Bond 17.640 3.250 7.510 -1.330 7.360 4 Large-Cap Growth 32.410 18.710 33.280 41.460 -23.260 5 Large-Cap Value 32.360 20.610 12.930 7.060 -5.370 6 Small-Cap Growth 33.440 19.400 3.850 58.680 -9.020 7 Small-Cap Value 24.560 25.320 -6.700 5.430 17.310