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. (there's no given standard deviation by that i can find in the question).

Click on the datafile logo to reference the data.

Mutual Fund	Year 1	Year 2	Year 3	Year 4	Year 5
Foreign Stock	10.060	13.120	13.470	45.420	-21.930
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
Large-Cap Value	32.360	20.610	12.930	7.060	-5.370
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
S&P 500 Return	25.000	20.000	8.000	30.000	-10.000

(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)

Min D1^2 + D2^2 + D3^2 + D4^2 + D5^2s.t

_FS+ _IB+ _LG+ _LV+ _SG+ _SV+ - Select your answer -??<>=Item 8D1

_FS+ _IB+ _LG+ _LV+ _SG+ _SV+ - Select your answer -??<>=Item 16D2

_FS+ _IB+ _LG+ _LV+ _SG+ _SV+ - Select your answer -??<>=Item 24D3

FS+ IB+ LG+ LV+ SG+ SV+ - Select your answer -??<>=Item 32D4

FS+ IB+ LG+ LV+ SG+ SV+ - Select your answer -??<>=Item 40D5

FS+ IB+ LG+ LV+ SG+ SV- Select your answer -??<>=Item 47

1FS, IB, LG, LV, SG, SV- Select your answer -??<>=Item 480

(b)

Solve the model developed in part (a).

If required, round your answers to two decimal places.

FS	%
IB	%
LG	%
LV	%
SG	%
SV	%