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 s for each scenario and let d s R R s with d s 0 Then make the objective function Min 1 5 5 s 1 d s 2 Let FS proportion of portfolio invested in the foreign stock mutual fund IB proportion of portfolio invested in the intermediate term bond fund LG proportion of portfolio invested in the large cap growth fund LV 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 R s the return of the portfolio in year s Min 1 5 5 s 1 d s 2 s t R 1 R 2 R 3 R 4 R 5 FS IB LG LV SG SV 5 R s s 1 R d 1 R d 2 R d 3 R d 4 R d 5 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 LG LV SG SV Objective value AutoSave OFF A A FC HauckData Q Search (Cmd Ctrl U) Home Insert Draw Page Layout Formulas Data Review View Comments Share Times New Roman 12 AA ab Wrap Text v General Paste BIUV A Merge Center v v 00 80 Conditional Format Cell Insert Delete Format Sort Find Add ins Formatting as Table Styles Filter Select B14 X V fx B C D E F G H K M N O P Q R S U V Mutual Fund Year 1 Year 2 Year 3 Year 4 Year 5 2 Foreign Stock 10 060 13 120 13 470 4 45 420 21 930 3 Intermediate Term Bond 17 640 3 250 7 510 1 330 7 360 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 Small Cap Value 24 560 25 320 6 700 5 430 17 310 00 Data Ready Accessibility Good to go 110

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Question: 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

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 variabled_sfor each scenario and let

d_sRR_s

with

d_s0.

Then make the objective function:

Min

5

s= 1

d_s².

Let

FS	=	proportion of portfolio invested in the foreign stock mutual fund
IB	=	proportion of portfolio invested in the intermediate-term bond fund
LG	=	proportion of portfolio invested in the large-cap growth fund
LV	=	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
R_s	=	the return of the portfolio in years.

Min

5

s= 1

d_s²

s.t.

R₁

R₂

R₃

R₄

R₅

FS+IB+LG+LV+SG+SV=

5	R_s

s= 1

d₁R

d₂R

d₃R

d₄R

d₅R

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.)

=Objective value

AutoSave OFF A A FC ... HauckData Q Search (Cmd + Ctrl + U) Home Insert Draw Page Layout Formulas Data Review View Comments Share Times New Roman 12 AA ab Wrap Text v General Paste BIUV A Merge Center v v % " 00 -80 Conditional Format Cell Insert Delete Format Sort Find Add-ins Formatting as Table Styles Filter Select B14 X V fx B C D E F G H K M N O P Q R S U V Mutual Fund Year 1 Year 2 Year 3 Year 4 Year 5 2 Foreign Stock 10.060 13.120 13.470 4 45.420 21.930 3 Intermediate-Term Bond 17.640 3.250 7.510 -1.330 7.360 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 Small-Cap Value 24.560 25.320 -6.700 5.430 17.310 00 Data + Ready Accessibility: Good to go 110%

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