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 relum 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 retum and volatility (.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 4% in the next year. (Hint: For each investment, you can use the function nordistix 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 - 4%. Then subtract that probability from 100% to find the probability that an investor will not lose more than 4%.) c. Do all the probabilities you calculated in part (b) make sense? If so, explain. If not, can you identify the reason2 a. Calculate the 95% confidence intervals for the expected annual relum 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 i Data Table Upper Bound Lower Bound % Confidence interval for S&P 500 is (Click on the following icon in order to copy its contents into a spreadsheet.) Lower Bound Upper Bound Confidence interval for corporate bonds is Lower Bound Upper Bound Confidence interval for Treasury bills is Average Annual Returns for U.S. Small Stocks, Large Stocks (S&P 500), Co 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% 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 distribute 4% in the next year. (Hint: For each inbestment, you can use the function normdistix,mean,volatility. 1) in Excel to compute the probability that a normally dis - 4%. Then subtract that probability from 100% to find the probability that an investor will not lose more than 4%.) The probability of not losing more than 4% for small stocks is%. (Round to two decimal places.) The probability of not losing more than 4% for the S&P 500 is % (Round to two decimal places.) The probability of not losing more than 4% for corporate bonds is % (Round to two decimal places.) The probability of not losing more than 4% for Treasury bills is %. (Round to two decimal places.) (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 Devia Small stocks 39.2% S&P 500 19.8% Corporate bonds 6.4% Treasury bills 3.1% 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.) Click to select your answer(s). Print Done 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 relum 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 retum and volatility (.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 4% in the next year. (Hint: For each investment, you can use the function nordistix 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 - 4%. Then subtract that probability from 100% to find the probability that an investor will not lose more than 4%.) c. Do all the probabilities you calculated in part (b) make sense? If so, explain. If not, can you identify the reason2 a. Calculate the 95% confidence intervals for the expected annual relum 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 i Data Table Upper Bound Lower Bound % Confidence interval for S&P 500 is (Click on the following icon in order to copy its contents into a spreadsheet.) Lower Bound Upper Bound Confidence interval for corporate bonds is Lower Bound Upper Bound Confidence interval for Treasury bills is Average Annual Returns for U.S. Small Stocks, Large Stocks (S&P 500), Co 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% 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 distribute 4% in the next year. (Hint: For each inbestment, you can use the function normdistix,mean,volatility. 1) in Excel to compute the probability that a normally dis - 4%. Then subtract that probability from 100% to find the probability that an investor will not lose more than 4%.) The probability of not losing more than 4% for small stocks is%. (Round to two decimal places.) The probability of not losing more than 4% for the S&P 500 is % (Round to two decimal places.) The probability of not losing more than 4% for corporate bonds is % (Round to two decimal places.) The probability of not losing more than 4% for Treasury bills is %. (Round to two decimal places.) (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 Devia Small stocks 39.2% S&P 500 19.8% Corporate bonds 6.4% Treasury bills 3.1% 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.) Click to select your answer(s). Print Done