You can calculate the risk index of an investment by taking the absolute values of percentage changes

Question:

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 the percentages of your money to invest in several potential investments. The file P04_90.xlsxlists the annual returns (percentage changes in value) for these investments for a 20-year period. 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 10% and 40% of the total invested. You would like the risk index of your portfolio to equal 0.16, 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 20-year period as your estimate of expected return.

Expected Return
The expected return is the profit or loss an investor anticipates on an investment that has known or anticipated rates of return (RoR). It is calculated by multiplying potential outcomes by the chances of them occurring and then totaling these... Portfolio
A portfolio is a grouping of financial assets such as stocks, bonds, commodities, currencies and cash equivalents, as well as their fund counterparts, including mutual, exchange-traded and closed funds. A portfolio can also consist of non-publicly...