Suppose the average return on Asset A is 6.4 percent and the standard deviation

Question

Suppose the average return on Asset A is 6.4 percent and the standard deviation is 8.4 percent and the average return and standard deviation on Asset B are 3.6 percent and 3.0 percent, respectively. Further assume that the returns are normally distributed. Use the NORMDIST function in Excel® to answer the following questions.

What is the probability that in any given year, the return on Assets A will be greater than 10 percent? Less than 0 percent? (Do not round intermediate calculations and round your answers to 2 decimal places. (e.g., 32.16))

What is the probability that in any given year, the return on Asset B will be greater than 10 percent? Less than 0 percent? (Do not round intermediate calculations and round your answers to 2 decimal places. (e.g., 32.16))

In a particular year, the return on Asset A was 4.23 percent. How likely is it that such a low return will recur at some point in the future? (Do not round intermediate calculations and round your answers to 2 decimal places. (e.g., 32.16))

Asset B had a return of 9.40 percent in this same year. How likely is it that such a high return on Asset B will recur at some point in the future? (Do not round intermediate calculations and round your answers to 2 decimal places. (e.g., 32.16))

Suppose the average return on Asset A is 6.4 percent and the standard deviation is 8.4 percent and the average return and standard deviation on Asset B are 3.6 percent and 3.0 percent, respectively. Further assume that the returns are normally distributed. Use the NORMDIST function in Excel® to answer the following questions.

Explanation / Answer

Answers for given questions can be given by using Z statistic formula

Z =z = (X – µ)/

Where X = Desired Return

  µ= the mean of the distribution

= standard deviation of the distribution

the probability that in any given year, the return on Assets A will be greater than 10 percent as follows

Z=(10-6.4)/8.4

Z=.43

This z-statistic gives us the probability that the return is less than 10 percent, but we are looking for theprobability the return is greater than 10 percent. Given the symmetry of the normal distribution, and the factthat the total probability is 100 percent (or 1), the probability of a return greater than 10 percent is 1 minusthe probability of a return less than 10 percent. Using the cumulative normal distribution table, we get

=1-.666

=33.41%

Like wise,

the probability that in any given year, the return on Assets A will be less than 0 percent is 77.69%

b)the probability that in any given year, the return on Asset B will be greater than 10 percent

Z =(10-3.6)/3

Z =2.1333

the probability that in any given year, the return on Asset B will be greater than 10 percent as per cummulative normal distribution

= 1.64%

the probability that in any given year, the return on Asset B will be less than 0 percent as per cummulative normal distribution

=88.49%

C)

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