Consider the following table for the total annual returns for a given period of

Question

Consider the following table for the total annual returns for a given period of time.

What range of returns would you expect to see 68 percent of the time for long-term corporate bonds? (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  %

Series Average return Standard Deviation Large-company stocks 11.7 % 20.6 % Small-company stocks 16.4 33.0 Long-term corporate bonds 6.2 9.5 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

Explanation / Answer

Solution:

The long-term corporate bond return history, we see that the mean return was 5.8 percent, with a standard deviation of 8.9 percent. The range of returns you would expect to see 68 percent of the time is the mean plus or minus 1 standard deviation, or:

R ± 1 = 5.8% ± 1(8.9%) = –3.10% to 14.70%

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

R ± 2 = 5.8% ± 2(8.9%) = –12.00% to 23.60%

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