Question

A second version of the Markowitz portfolio model maximizes expected return subject to a constraint that the variance of the portfolio must be less than or equal to some specified amount. Consider the Hauck Financial Service data. We list the data again below along with the return of the S&P 500 Index. Hauck would like to create a portfolio using the funds listed, so that the resulting portfolio matches the return of the S&P 500 index as closely as possible. Click on the datafile logo to reference the data. Mutual Fund Year 1 Year 2 Year 3 Year 4 Year 5 Foreign Stock 10.06   13.12   13.47   45.42   -21.93   Intermediate-Term Bond 17.64   3.25   7.51   -1.33   7.36   Large-Cap Growth 32.41   18.71   33.28   41.46   -23.26   Large-Cap Value 32.36   20.61   12.93   7.06   -5.37   Small-Cap Growth 33.44   19.40   3.85   58.68   -9.02   Small-Cap Value 24.56   25.32   -6.70   5.43   17.31   S&P 500 Return 25   20   8   30   -10   (a) Develop an optimization model that will give the fraction of the portfolio to invest in each of the funds so that the return of the resulting portfolio matches as closely as possible the return of the S&P 500 Index. Hint: Minimize the sum of the squared deviations between the portfolio's return and the S&P 500 Index return for each year in the data set. 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 Ds= the difference between the portfolio return and the S&P 500 return, years If required, round your answers to two decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300) If the constant is "1" it must be entered in the box. If your answer is zero enter “0”. Min D12 + D22 + D32 + D42 + D52 s.t FS +  IB +  LG +  LV +  SG +  SV + - Select your answer -≤≥<>=Item 8 D 1 FS +  IB +  LG +  LV +  SG +  SV + - Select your answer -≤≥<>=Item 16 D 2 FS +  IB +  LG +  LV +  SG +  SV + - Select your answer -≤≥<>=Item 24 D 3 FS +  IB +  LG +  LV +  SG +  SV + - Select your answer -≤≥<>=Item 32 D 4 FS +  IB +  LG +  LV +  SG +  SV + - Select your answer -≤≥<>=Item 40 D 5 FS +  IB +  LG +  LV +  SG +  SV - Select your answer -≤≥<>=Item 47 FS, IB, LG, LV, SG, SV - Select your answer -≤≥<>=Item 49 (b) Solve the model developed in part (a). If required, round your answers to two decimal places. If your answer is zero enter “0”. FS % IB % LG % LV % SG % SV %

Answer 1

FS=30.3339%

IB=0%

LG=0%

LV=36.498%

SG=22.6551%

SV=10.513%

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