(A spreadsheet might be helpful on this problem.) The risk index of an investment can be obtained from return on investment (ROI) by taking the percentage of change in the value of the investment (in absolute terms) for each year, and averaging them.
Suppose you are trying to determine what percentage of your money should be invested in T-bills, gold, and stocks. In Table 20 (or File Inv68.xls) you arc given the annual returns (change in value) for these investments for the years 1968–1988. Let the risk index of a portfolio be the weighted (according to the fraction of your money assigned to each investment) average of the risk index of each individual investment. Suppose that the amount of each investment must be between 20% and 50% of the total invested. You would like the risk index of your portfolio to equal .15, and your goal is to maximize the expected return on your portfolio. Formulate an LP whose solution will maximize the expected return on your portfolio, subject to the given constraints. Use the average return earned by each investment during the years 1968–1988 as your estimate of expected return.†
table 20
Year | Stocks | Gold | T-Bills |
1968 | 11 | 11 | 5 |
1969 | −9 | 8 | 7 |
1970 | 4 | −14 | 7 |
1971 | 14 | 14 | 4 |
1972 | 19 | 44 | 4 |
1973 | −15 | 66 | 7 |
1974 | −27 | 64 | 8 |
1975 | 37 | 0 | 6 |
1976 | 24 | −22 | 5 |
1977 | −7 | 18 | 5 |
1978 | 7 | 31 | 7 |
1979 | 19 | 59 | 10 |
1980 | 33 | 99 | 11 |
1981 | −5 | −25 | 15 |
1982 | 22 | 4 | 11 |
1983 | 23 | −11 | 9 |
1984 | 6 | −15 | 10 |
1985 | 32 | −12 | 8 |
1986 | 19 | 16 | 6 |
1987 | 5 | 22 | 5 |
1988 | 17 | −2 | 6 |
†Bascd on Chandy (1987).
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