a. To find the percentage of returns greater than 48 percent, we need to calculate the area under the bell curve to the right of 48 percent. Since we are given the average return and standard deviation, we can use the Z-score formula to calculate the Z-score for 48 percent.
Z = (x - μ) / σ
where x is the value (48 percent), μ is the mean (9 percent), and σ is the standard deviation (13 percent).
Z = (48 - 9) / 13 = 2.999
Using a Z-table or calculator, we can find that the area to the left of a Z-score of 2.999 is approximately 0.9987. To find the area to the right of 48 percent, we subtract this value from 1:
1 - 0.9987 = 0.0013
So, approximately 0.13 percent of returns were greater than 48 percent.
b. To find the percentage of returns below -4 percent, we need to calculate the area under the bell curve to the left of -4 percent. Again, we can use the Z-score formula to calculate the Z-score for -4 percent.
Z = (x - μ) / σ
where x is the value (-4 percent), μ is the mean (9 percent), and σ is the standard deviation (13 percent).
Z = (-4 - 9) / 13 = -1.3077
Using a Z-table or calculator, we can find that the area to the left of a Z-score of -1.3077 is approximately 0.0951. Therefore, approximately 9.5 percent of returns were below -4 percent.
Exercise 3-65 Algo
The historical returns on a portfolio had an average return of 9 percent and a standard deviation of 13 percent. Assume that returns on this portfolio follow a bell-shaped distribution.
a. Approximately what percentage of returns were greater than 48 percent? (Round your answer to the nearest whole percent.)
b. Approximately what percentage of returns were below −4 percent? (Round your answer to 1 decimal place.)
1 answer
1 answer