Assume that historical returns and future returns are independently and identically distributed and drawn from the same distribution.

a. Calculate the

95%

confidence intervals for the expected annual return of four different investments included in the tables

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(the time period spans

92

years).

b. Assume that the values in the tables are the true expected return and volatility (i.e., estimated without error) and that these returns are normally distributed. For each investment, calculate the probability that an investor will not lose more than

5%

in the next year.

(Hint:

For each investment, you can use the function

normdist(x,mean,volatility,1)

in Excel to compute the probability that a normally distributed variable with a given mean and volatility will exceed x where x in this case is

5%.

Then subtract that probability from 100% to find the probability that an investor will not lose more than

5%.)

c. Do all the probabilities you calculated in part

(b)

make sense? If so, explain. If not, can you identify the reason?

Average Annual Returns for U.S. Small Stocks, Large Stocks (S&P 500), CorporateBonds, and Treasury Bills, 1926-2017
Investment	Average Annual Return
Small stocks	18.7%
S&P 500	12.0%
Corporate bonds	6.2%
Treasury bills	3.4%

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in order to copy its contents into a spreadsheet.)

Volatility of U.S. Small Stocks, Large Stocks (S&P 500), Corporate Bonds, and Treasury Bills, 1926-2017
Investment	Return Volatility (Standard Deviation)
Small stocks	39.2%
S&P 500	19.8%
Corporate bonds	6.4%
Treasury bills	3.1%