(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 are given the annual re- turns (change in value) for these investments for the years 19681988. 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 in- vestment. 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 19681988 as your estimate of expected return.

TABLE 20 Year Stocks Gold T-Bills 1968 11 11 1969 1970 14 1971 14 14 1972 19 1973 1974 1975 1976 24 22 1977 18 1978 31 1979 19 59 10 1980 33 99 11 1981 15 1982 22 11 1983 23 1984 10 1985 32 1986 19 16 1987 22 1988 17 577447865570151908656 1111 d18 11466 213592 111 6402819954152622 12 ks-94495774779352362957 111232 13-22 31 1 0-to-1- 2-St 667777777777888888888 0 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 a 999999999999999999999 111111111111111111111