$10,000 is invested in a single asset that returns 7 percent annually for twenty-five years and $2,000 is placed in five different investments, earning returns of 100 percent, 0 percent, 5 percent, 10 percent, and 12 percent, respectively, over the twenty-year time frame. For each of the questions below, begin with the original scenario presented in the table:
a. Experiment with the return on the fifth asset. How low can the return go and still have the diversified portfolio earn a higher return than the single-asset portfolio?
b. What happens to the value of the diversified portfolio if the first two investments are both a total loss?
c. Suppose the single-asset portfolio earns a return of 8 percent annually. How does the return of the single-asset portfolio
d. Assume that Asset 1 of the diversified portfolio remains a total loss (–100% return) and asset two earns no return.
Make a table showing how sensitive the portfolio returns are to a 1-percentage-point change in the return of each of the other three assets. That is, how is the diversified portfolio’s value affected if the return on asset three is 4 percent or 6 percent? If the return on asset four is 9 percent or 11 percent? If the return on asset five is 11 percent? 13 percent? How does the total portfolio value change if each of the three asset’s returns are one percentage point lower than in the table? If they are one percentage point higher?
e. Using the sensitivity analysis of (c) and (d), explain how the two portfolios differ in their sensitivity to different returns on their assets. What are the implications of this for choosing between a single asset portfolio and a diversified portfolio?