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 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 -4.36 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 10.70 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)

Answer 1

Answer:

Explanation:

Let us follow this accordingly

a. We have that ;

Z is given as = (X-mean)/standard deviation

where X = 10, mean = 6.9 and standard deviation is 8.1 ------- for A

inputting values we have;

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%.

Hence the probability of earning more than 10% = 1-0.649 = 0.351 or 35.1%

b. At 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%.

From this, the probability of earning less than 0% = 19.71%

c. Also For B;

X = 10%, mean = 4% and standard deviation = 3.5%

inputting values gives us ;

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%.

Which makes the probability of earning more than 10% = 1-0.9568 = 0.0432 i.e 4.32%

d. Als, X = 0.

Giving us;

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 makes the probability of earning less than 10.7%.

Thus required probability gives us = 1-0.9722 = 2.78%