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Problem 13-17 A second version of the Markowitz portfolio model maximizes expected return subject to a constraint that the variance of the portfolio must be
Problem 13-17
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 | 19.4 | 3.85 | 58.68 | -9.02 |
Small-Cap Value | 24.56 | 25.32 | -6.7 | 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. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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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) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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(b) | Solve the model developed in part (a). | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
If required, round your answers to two decimal places. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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