The historical returns on a balanced portfolio have had an average return of 4% and a standard deviation of 13%. Assume that returns on this portfolio follow a normal distribution. [You may find it useful to reference the z table.]

Question

a. What percentage of returns were greater than 17%? (Round your answer to 2 decimal places.)

b. What percentage of returns were below −22%? (Round your answer to 2 decimal places.)

Answer 1

To solve this problem, we need to calculate the z-scores for 17% and -22%, and then use the z-table to find the corresponding percentages.

a. First, let's calculate the z-score for 17%:
z = (x - μ) / σ
z = (17 - 4) / 13
z = 13 / 13
z = 1

Looking up a z-score of 1 in the z-table, we find that the percentage of returns greater than 17% is approximately 0.1587, or 15.87% (rounded to 2 decimal places).

b. Next, let's calculate the z-score for -22%:
z = (x - μ) / σ
z = (-22 - 4) / 13
z = -26 / 13
z = -2

Looking up a z-score of -2 in the z-table, we find that the percentage of returns below -22% is approximately 0.0228, or 2.28% (rounded to 2 decimal places).