Suppose the returns on an asset are normally distributed. The historical average

Question

Suppose the returns on an asset are normally distributed. The historical average annual return for the asset was 6.6 percent and the standard deviation was 16.5 percent. What range of returns would you expect to see 95 percent of the time? (Enter your answers for the range from lowest to highest. A negative answer should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) 95% level % to % What range would you expect to see 99 percent of the time? (Enter your answers for the range from lowest to highest. A negative answer should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) 99% level % to %

Explanation / Answer

solution=

given mean = 6.6 % standard deviation = 16.5%

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

95% level: R ± 2 = 6.6% ± 2(16.5%) =-26.4% to39.6%

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

99% level: R ± 3 = 6.6% ± 3(16.5%) =-42.9% to 56.1%

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