Problem 10-24 Using Return Distributions Suppose the returns on an asset are nor

Question

Problem 10-24 Using Return Distributions Suppose the returns on an asset are normally distributed. Suppose the historical average annual return for the asset was 5.7 percent and the standard deviation was 18.3 percent. What is the probability that your return on this asset will be less than –4.1 percent in a given year? Use the NORMDIST function in Excel® to answer this question. (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Probability 29.61 %

What range of returns would you expect to see 95 percent of the time? (Enter your answers for the range from lowest to highest. Negative amounts should be indicated by a minus sign. Do not round intermediate calculations and round your final answers 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. Negative amounts should be indicated by a minus sign. Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16))

99% level % to %

Explanation / Answer

Answer: 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 = 5.7% ± 2(18.3%)

= –30.90% to 42.30%

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= ± 2 = 5.7% ± 3(18.3%)

= –49.20% to 60.60%

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