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 (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 3% 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 - 3%. Then subtract that probability from 100% to find the probability that an investor will not lose more than 3%.) c. Do all the probabilities you calculated in part (b) make sense? If so, explain. If not, can you identify the reason? a. Calculate the 95% confidence intervals for the expected annual return of four different investments included in the tables (the dates are inclusive, so the time period spans 92 years). Lower Bound Upper Bound Confidence interval for small stocks is % (Round to two decimal places.) Upper Bound Lower Bound % Confidence interval for S&P 500 is % (Round to two decimal places.) Upper Bound Lower Bound % Confidence interval for corporate bonds is (Round to two decimal places.) Lower Bound Upper Bound Confidence interval for Treasury bills is (Round to two decimal places.) 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 3% in the next year. (Hint: For each inbestment, 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 - 3%.. Then subtract that probability from 100% to find the probability that an investor will not lose more than 3%.) The probability of not losing more than 3% for small stocks is %. (Round to two decimal places.) The probability of not losing more than 3% for the S&P 500 is %. (Round to two decimal places.) The probability of not losing more than 3% for corporate bonds is %. (Round to two decimal places.) The probability of not losing more than 3% for Treasury bills is %. (Round to two decimal places.) c. Do all the probabilities you calculated in part (b) make sense? If so, explain. If not, can you identify the reason? (Select the best choice below.) O A. Yes. All these investments involve risk, and so you expect to lose money some of the time. B. No. You cannot lose money on Treasury bills. The problem is that the returns on Treasury bills are not normally distributed. O C. No. The probability that you can have a return on the S&P less than 3% is not nearly as high as 77.56%. The problem is that the return of the S&P 500 is not normally distributed. D. No. The probability that you can have a return on small stocks less than 3% is not nearly as high as 71.01%. The problem is that the return of small stocks are not normally distributed. 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% Click on the following icon 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%