Assume that bonds pay a real return of 2 percent. Stocks pay 22 percent half the time and -6 percent half the time. Suppose you initially have wealth of $100, and let X be your wealth after 1 year. What fraction of your wealth should you hold in stock under each of the following assumptions?
a. You want to maximize the average value of X.
b. You want to maximize the value of X when the return on stocks is -6 percent.
c. You want to be certain that X is at least $100 (that is, you don't lose any of your initial wealth). Subject to that constraint, you maximize the average value of X.