Question

Let’s say that the mean return of mutual funds in the last quarter is 2.8% with a standard deviation of 4.5%. Assume the returns are symmetrically distributed. Find the return value(s) that would separate the a. top 2.5% b. middle 99.7% c. bottom 84%

Answer 1

Solution :

mean = = 2.8% = 0.028

standard deviation = = 4.5% = 0.045

Using standard normal table,

(a)

P(Z > z) = 2.5%

1 - P(Z < z) = 0.025

P(Z < z) = 1 - 0.025 = 0.975

P(Z < 1.96) = 0.975

z = 1.96

Using z-score formula,

x = z * +

x = 1.96 * 0.045 + 0.028 = 0.1162

Return value = 11.62%

(b)

Middle 99.7% has the z values are : -2.97 and +2.97

x = -2.97 * 0.045 + 0.028 = -0.10

x = 2.97 * 0.045 + 0.028 = 0.162 = 16.2%

Return values are : 0 and 16.2%

(c)

P(Z < z) = 0.84

P(Z < 1) = 0.975

z = 1

Using z-score formula,

x = z * +

x = 1 * 0.045 + 0.028 = 0.073

Return value = 7.3%