You can calculate the risk index of an investment by taking the absolute values of percentage changes in the value of the investment for each year and averaging them. Suppose you are trying to determine what percentage of your money you should invest in T-bills, gold, and stocks. The file P04_90.xlsx lists the annual returns (percentage changes in value) for these investments for the years 1968 through 1988. Let the risk index of a portfolio be the weighted average of the risk indices of these investments, where the weights are the fractions of the portfolio assigned to the investments.

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 0.15, and your goal is to maximize the expected return on your portfolio. Determine the maximum expected return on your portfolio, subject to the stated constraints. Use the average return earned by each investment during the years 1968 to 1988 as your estimate of expected return.