Question

If returns of S&P 500 stocks are normally distributed, what range of returns would you expect to see 95% of the time? Base your answer on the information below. Average Return Standard Deviation of returns Small Stocks 18.37% 38.79% S&P 500 11.84% 20.01% Corporate Bonds 6.47% 6.98% T-Bills 3.46% 3.14% The 95% prediction interval of the S&P500 is between % and %. (Round to two decimal places and put the lower number first.)

Answer 1

Average return of S&P 500 (u) = 11.84%

standard deviation of S&P 500 (s) = 20.01%

at 95% prediction interval, Z = 1.96

So range of return at 95% confidence level is from u - Z*s to u + Z*s

u-Z*s = 11.84-1.96*20.01 = -27.38%

u+Z*s = 11.84+1.96*20.01 = 51.06

So, 95% prediction interval of S&P 500 is between -27.38% to 51.06%