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 2% 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 -2%. Then, subtract that probability from 100% to find the probability that an investor will not lose more than 2%.) 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). Confidence interval for small stocks is Lower Bound % Upper Bound % (Round to two decimal places.) (Click on the following icon in order to copy its contents into a spreadsheet.) Average Annual Returns for U.S. Small Stocks, Large Stocks (S&P 500), Corporate Bonds, and Treasury Bills, 1926-2017 Investment Small stocks S&P 500 Corporate bonds Average Annual Return 18.7% 12.0% 6.2% 3.4% Treasury bills (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 Small stocks S&P 500 Corporate bonds Treasury bills Return Volatility (Standard Deviation) 39.2% 19.8% 6.4% 3.1%