Problem 10-17 Return Distributions [LO 3] Consider the following table for the t

Question

Problem 10-17 Return Distributions [LO 3] 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 6.3 9.6 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 Requirement 1: 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).) Expected range of returns % to % 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).) Expected range of returns % to %

Explanation / Answer

1)

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

Where range of return of long term government bond

Mean = 6.1

Standard deviation = 9.4

95% level: R ± 2

= 6.1% ± 2(9.4%)

= –12.70% to 24.90%

2:

The range of returns you would expect to see 99 percent of the time is the mean plus or minus 3 standard deviations, or:

99% level: R ± 3

= 6.1% ± 3(9.4%)

= –22.10% to 34.3

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