Problem 10-18 Return Distributions [LO 3] Consider the following table for the t
ID: 2754874 • Letter: P
Question
Problem 10-18 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 10.6 % 19.2 % Small-company stocks 16.4 33.0 Long-term corporate bonds 6.2 8.4 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 large-company stocks? (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 answer as a percentage rounded to 2 decimal places (e.g., 32.16).) Expected range of returns % to %
Explanation / Answer
Answer:Requirement 1:
Looking at the large-company stocks history, we see that the mean return was 11.5 percent, with a standard deviation of 20.2 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 = 11.5% ± 1(20.2%) = –8.70% to 31.7%
Answer: Requirement 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:
R ± 2 = 11.5% ± 2(20.2%) = –28.9% to 51.90%
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