The following table summarizes the average annual return and the standard deviation of returns for several types of securities over the past 75 years. ( Source: R.G. Ibbotson & Associates, Inc.)

Investment Mean Return Standard Deviation

Small-cap common stocks .170 .350

Large-cap common stocks .110 .230

Long-term bonds .080 .040

Treasury bills .035 .031

Assume annual returns in each case are approximately normally distributed around the mean rate. Using this historical information as the basis for your calculations, what is the probability of loss over the next year if you put all your money into a. Small-cap stocks? b. Large-cap stocks? c. Long-term bonds? d. Treasury bills?

a. Suppose you invest $10,000 in large-cap stocks. Using the historical performance data shown in the table, how likely is it that you will end up making more than $4400 for the year? b. Suppose you invest $10,000 in long-term bonds. How likely is it that you will end up losing at least $200 for the year? c. Suppose you invest $2000 in small-cap stocks. Determine the probability that the investment will produce a return of less than $500.

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