Assume the returns on an asset are normally distributed. Suppose the historical

Question

Assume the returns on an asset are normally distributed. Suppose the historical average annual return for the asset was 4.9 percent and the standard deviation was 10.4 percent. What is the probability that your return on this asset will be less than -4.9 percent in a given year? Use the NORMDIST function in Excel® to answer this question. (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Probability 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 and 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 and enter your answers as a percent rounded to 2 decimal places, e.g 32.16.) 99% level %to

Explanation / Answer

a)

NORMDIST(X,mean.standarddeviation,cumulative)

probability = NORMDIST(-4.9,4.9,10.4,TRUE) = 17.30%

b)

margin of error = z-score * standard deviation

= 1.96 * 10.4

= 20.384

lower bound = 4.9 - 20.384 = -15.48%

upper bound = 4.9 + 20.384 = 25.28%

c)

margin of error = z-score * standard deviation

= 2.58 * 10.4

= 26.832

lower bound = 4.9 - 26.832 = -21.93%

upper bound = 4.9 + 26.832 = 31.73%

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