Question

Consider the following table for the total annual returns for a given period of time. Series Large-company stocks Small-company stocks Long-term corporate bonds Long-term government bonds Intermediate-term government bonds U.S. Treasury bills Inflation Average return 10.9% 16.4 6.2 6.1 Standard Deviation 21.2% 33.0 8.4 9.4 5.7 3.1 4.2. اي اسيا ني ܗ ܗ ܝ What range of returns would you expect to see 68 percent of the time for large-company stocks? (A negative answer should be indicated by a minus sign. Input your answers from lowest to highest to receive credit for your answers. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) Expected range of returns % to What about 95 percent of the time? (A negative answer should be indicated by a minus sign. Input your answers from lowest to highest to receive credit for your answers. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) Expected range of returns % to

Answer 1

Confidence intervals for a normal distribution are :

68% of values fall within 1 standard deviation of the mean (-1s <= X <= 1s)

95% of values fall within 1.96 or 2 standard deviations of the mean (-1.96s <= X <= 1.96s)

1) Looking at the large company stocks' return history, we see that the mean return was 10.9%, with a standard deviation of 21.2%. The range of returns we would expect to see 68% of the time is the mean plus or minus 1 standard deviation, or:

Return ± 1 Standard Deviation = 10.9% ± 1(21.2%) = –10.3% to 32.1%

2) The range of returns you would expect to see 95 percent of the time is the mean plus or minus 2 standard deviations, or:

Return ± 2 Standard Deviation = 10.9% ± 2(21.2%) = -31.5% to 53.3%