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 5.6 9.1 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 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

Answer 1

a.

For corporate Bond

Average return = 5.60%

Standard deviation = 9.10%

68% confident that a variable will fall within one standard deviation.

So, range of returns for a given year with probability of 68% is calculated below:

Range = mean ± 1 × Standard deviation

            = 5.60% ± (1 × 9.10%)

            = 5.60% - 9.10% and 5.60% + 9.10%

            = -3.50% and 14.70%

Range of return with 68% probability is (-3.50%) to 14.70%.

b.

95% confident that a variable will fall within 2 standard deviation.

So, range of returns for a given year with probability of 68% is calculated below:

Range = mean ± 1 × Standard deviation

            = 5.60% ± (2 × 9.10%)

            = 5.60% - 18.20% and 5.60% + 18.20%

            = -12.60% and 23.80%

Range of return with 96% probability is (-12.60%) to 23.80%.