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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 Tables 10.3 and 10.4 (the dates are inclusive, so the time period spans 92 years). b. Assume that the values in Tables 10.3 and 10.4 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: 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 fall below x.) c. Do the probabilities you calculated in part (b) make sense? If so, explain. If not, can you identify the reason

TABLE 10.3 Average Annual Returns for U.S. Small Stocks, Large Stocks (S&P 500), Corporate Bonds, 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%Capital Markets and the Pricing of Risk TABLE 10.4 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% Estimation Error: Using Past Returns to Predict the Future To estimate the cost of capital for an investment, we need to determine the expected return that investors will require to compensate them for that investment's risk. If the distribu- tion of past returns and the distribution of future returns are the same, we could look at the return investors expected to earn in the past on the same or similar investments, and assume they will require the same return in the future. However, there are two difficulties