Suppose the average return on Asset A is 6.3 percent and the standard deviation

Question

Suppose the average return on Asset A is 6.3 percent and the standard deviation is 8.3 percent and the average return and standard deviation on Asset B are 3.5 percent and 2.9 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 Asset A will be greater than 9 percent? Less than 0 percent? (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 9 percent? Less than 0 percent? (Round your answers to 2 decimal places. (e.g., 32.16))

In 1979, the return on Asset A was 4.22 percent. How likely is it that such a low return will recur at some point in the future? (Round your answer to 2 decimal places. (e.g., 32.16))

Asset B had a return of 9.30 percent in this same year. How likely is it that such a high return on T -bills will recur at some point in the future?(Round your answer to 2 decimal places. (e.g., 32.16))

Suppose the average return on Asset A is 6.3 percent and the standard deviation is 8.3 percent and the average return and standard deviation on Asset B are 3.5 percent and 2.9 percent, respectively. Further assume that the returns are normally distributed. Use the NORMDIST function in Excel® to answer the following questions.

Explanation / Answer

For each of the questions asked here, we need to use the z-statistic, which is

z = (X – µ)/

(a) z 1 = (9% – 6.3%)/8.3% = 0.3253

This z-statistic gives us the probability that the return is less than 9 percent, but we are looking for the probability the return is greater than 9 percent.

Given the symmetry of the normal distribution, and the fact that the total probability is 100 percent (or 1), the probability of a return greater than 9 percent is 1 minus the probability of a return less than 9 percent.

Using the cumulative normal distribution table, we get:

Pr(R=9%) = 1 – Pr(R=9%) = 1 – 0.6275 37.25%

For a return less than 0 percent:

Pr(R0%) 23.13%

b)

What is the probability that in any given year, the return on Asset B will be greater than 9 percent? Less than 0 percent?

z 1 = (9% – 3.5%)/2.9% = 1.8966

This z-statistic gives us the probability that the return is less than 9 percent, but we are looking for the probability the return is greater than 9 percent.

Given the symmetry of the normal distribution, and the fact that the total probability is 100 percent (or 1), the probability of a return greater than 9 percent is 1 minus the probability of a return less than 9 percent.

Using the cumulative normal distribution table, we get:

Pr(R=9%) = 1 – Pr(R=9%) = 1 – 0.9710562.89%

For a return less than 0 percent:

z 1 = (0% – 3.5%)/2.9% = -1.2069

Using the cumulative normal distribution table, we get:

Pr(R=0) = 1 – Pr(R=0) = 1 – 0.113736 = 88.62%

C)

The probability that the return on Asset A will be less than –4.22 percent is:

z 5 = (–4.22% – 6.3%)/8.3% = –1.26747

Pr(R=–4.20%) 10.25%

c-2

Asset B had a return of 9.30 percent in this same year. How likely is it that such a high return on T -bills will recur at some point in the future?

z 6 = (9.3% – 3.5%)/2.9%= 2

Pr(R=9.30%)=1-Pr(R=9.30%)1 – 0.97725=2.27%

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