Suppose the average return on Asset A is 6.9 percent and the standard deviation

Question

Suppose the average return on Asset A is 6.9 percent and the standard deviation is 8.1 percent and the average return and standard deviation on Asset B are 4.0 percent and 3.5 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 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 4.36 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 10.70 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))

Explanation / Answer

a. Z = (X-mean)/standard deviation

For A, X = 10, mean = 6.9 and standard deviation is 8.1

Thus, Z = (10-6.9)/8.1 = 0.3827

Using the NORMDIST function in excel, [NORMDIST(0.3827)] = 0.649. This is the probability of earning less than 10%. Thus the probability of earning more than 10% = 1-0.649 = 0.351 or 35.1%

b. less than 0%: X = 0,  mean = 6.9 and standard deviation is 8.1

Thus Z = (0-6.9)/8.1 = - 0.8519. Using the NORMDIST function in excel, [NORMDIST(-0.8519)] = 0.1971 or 19.71%.

Thus the probability of earning less than 0% = 19.71%

c. For B: X = 10%, mean = 4% and standard deviation = 3.5%

Thus, Z = (10-4)/3.5 = 1.7143. Using the NORMDIST function in excel, [NORMDIST(1.7143)] = 0.9568. This is the probability of earning less than 10%. Thus the probability of earning more than 10% = 1-0.9568 = 0.0432 or 4.32%

d. Now, X = 0. Thus, Z = (0-4)/3.5 = -1.1429.  Using the NORMDIST function in excel, [NORMDIST(-1.1429)] = 0.1265 or 12.65%

Thus the probability of earning less than 0% = 12.65%

e. Return on A = -4.36%

Thus z = (-4.36 - 6.9)/8.1 = -1.39. NORMDIST of -1.39 = 0.0822 or 8.22%

f. Return of B = 10.7%

Thus z = (10.7% - 4)/3.5 = 1.9143. Its NORMDIST = 0.9722

This is the probaility of earning less than 10.7%. Thus required probability = 1-0.9722 = 2.78%

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