Suppose the average return on Asset A is 6.8 percent and the standard deviation

Question

Suppose the average return on Asset A is 6.8 percent and the standard deviation is 8.8 percent and the average return and standard deviation on Asset B are 4.0 percent and 3.4 percent, respectively. Further assume that the returns are normally distributed. Use the NORMDIST function in Excel® to answer the following questions.

Suppose the average return on Asset A is 6.8 percent and the standard deviation is 8.8 percent and the average return and standard deviation on Asset B are 4.0 percent and 3.4 percent, respectively. Further assume that the returns are normally distributed. Use the NORMDIST function in Excel® to answer the following questions. a. What is the probability that in any given year, the return on Asset A will be greater than 10 percent? Less than 0 percent? (Round your answers to 2 decimal places. (e.g., 32.16)) Greater than 10 percent Less than 0 percent b. What is the probability that in any given year, the return on Asset B will be greater than 10 percent? Less than 0 percent? (Round your answers to 2 decimal places. (e.g., 32.16)) Greater than 10 percent Less than 0 percent c-1 In 1979, the return on Asset A was -4.27 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)) Probability c-2 Asset B had a return of 9.80 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)) Probability rev: 12 06 2012

Explanation / Answer

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

z = (X – µ)/

(a) z 1 = (10% – 6.8%)/8.8% = 0.3636

This z-statistic gives us the probability that the return is less than 10 percent, but we are looking for the probability the return is greater than 10 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 10 percent is 1 minus the probability of a return less than 10 percent.

Using the cumulative normal distribution table, we get:

Pr(R=10%) = 1 – Pr(R=10%) = 1 – 0.6419 35.81%

For a return less than 0 percent:

Pr(R0%) 78.01%

b)

What is the probability that in any given year, the return on Asset B will be greater than 10 percent? Less than 0 percent?

z 1 = (10% – 4%)/3.4% = 1.7647

This z-statistic gives us the probability that the return is less than 10 percent, but we are looking for the probability the return is greater than 10 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 10 percent is 1 minus the probability of a return less than 10 percent.

Using the cumulative normal distribution table, we get:

Pr(R=10%) = 1 – Pr(R=10%) = 1 – 0.9611933.88%

For a return less than 0 percent:

z 1 = (0% – 4%)/3.4% = -1.17647

Using the cumulative normal distribution table, we get:

Pr(R=0) = 1 – Pr(R=0) = 1 – 0.119703 = 88.03%

C)

The probability that the return on Asset A will be less than –4.27 percent is:

z 5 = (–4.27% – 6.8%)/8.8% = –1.25795

Pr(R=–4.27%) 10.30%

c-2

Asset B had a return of 9.80 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 = (9.8% – 4%)/3.4%= 1.705882

Pr(R=9.30%)=1-Pr(R=9.30%)1 – 0.955985=4.40%

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