8. HW 3 The historical returns on a portfolio had an average return of 8 percent

Question

8. HW 3

The historical returns on a portfolio had an average return of 8 percent and a standard deviation of 12 percent. Assume that returns on this portfolio follow a bell-shaped distribution.

What percentage of returns were greater than 20 percent? (Round your answer to the nearest whole percent.)

What percentage of returns were below –16 percent? (Round your answer to 1 decimal place.)

The historical returns on a portfolio had an average return of 8 percent and a standard deviation of 12 percent. Assume that returns on this portfolio follow a bell-shaped distribution.

Explanation / Answer

= 8, = 12

(a) z = (x - )/ = (20 - 8)/12 = 1

P(x > 12) = P(z > 1) = 0.1587 = 16%

(b) z = (-16 - 8)/12 = -2

P(x < -16) = P(z < -2) = 0.0228 = 2.3%

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