Consider the following table for the total annual returns for a given period of
ID: 2766333 • Letter: C
Question
Consider the following table for the total annual returns for a given period of time. Series Average return Standard Deviation Large-company stocks 11.7 % 20.6 % Small-company stocks 16.4 33.0 Long-term corporate bonds 6.1 8.8 Long-term government bonds 6.1 9.4 Intermediate-term government bonds 5.6 5.7 U.S. Treasury bills 3.8 3.1 Inflation 3.1 4.2 What range of returns would you expect to see 95 percent of the time for long-term corporate bonds? (Negative amount 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. Enter your answers as a percentage rounded to 2 decimal places (e.g., 32.16).) Requirement 2: What about 99 percent of the time? (Negative amount 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. Enter your answers as a percentage rounded to 2 decimal places (e.g., 32.16).)
Explanation / Answer
R ± 2 = 6.1% ± 2(8.8%) = –11.5% to 23.7%
Looking at the long-term corporate bond return history, we see that the mean return was 6.1 percent, with a standard deviation of 18.8 percent. The range of returns you would expect to see 95 percent of the time is the mean plus or minus 2 standard deviations.
R ± 3 = 6.1% ± 3(8.8%) = –20.3% to 32.5%
The range of returns you would expect to see 99 percent of the time is the mean plus or minus 3 standard deviations.