Question

A stock's returns have the following distribution:

Demand for the Company's Products    Probability of This Demand Occurring Rate of Return If This Demand Occurs

Weak 0.1 -22%

Below average 0.1 -8

Average 0.5 15

Above average 0.2 21

Strong 0.1 72

1.0

a. Calculate the stock's expected return. Round your answer to two decimal places. %

b. Calculate the stock's standard deviation. Do not round intermediate calculations. Round your answer to two decimal places. %

c. Calculate the stock's coefficient of variation. Round your answer to two decimal places.

Answer 1

a)

Expected return = 0.1*(-0.22) + 0.1*(-0.08) + 0.5*0.15 + 0.2*0.21 + 0.1*0.72

Expected return = -0.022 - 0.008 + 0.075 + 0.042 + 0.072

Expected return = 0.159 or 15.90%

b)

Standard deviation = [(0.1(-0.22 - 0.159)² + 0.1(-0.08 - 0.159)² + 0.5(0.5 - 0.159)² + 0.2(0.21 - 0.159)² + 0.1(0.72 - 0.159)²]^1/2

Standard deviation = [0.01436 + 0.00571 + 0.05814 + 0.00052 + 0.03147]^1/2

Standard deviation = 0.3320 or 33.20%

c)

Coefficient of variation = Standard deviation / mean

Coefficient of variation = 0.332 / 0.159

Coefficient of variation = 2.09