The rate of return on the common stock of Flowers by Flo is expected to be 14% in a boom economy, 8% in a normal economy, and only 2% in a recessionary economy. The probabilities of these economic states are 20% for a boom, 60% for a normal economy, and 20% for a recession. What is the variance of the returns on the common stock of Flowers by Flo?

variance of the returns is 0.00144

Explanation:

Given data

boom economy = 14% = 0.14

normal economy = 8% = 0.08

recessionary economy = 2% = 0.02

boom probabilities = 20% = 0.20

normal probabilities = 60% = 0.60

recessionary probabilities = 20% = 0.20

to find out

the variance of the returns

solution

we know variance of the returns is sum of standard deviation

expected return = boom return * boom probability

expected return boom = 0.14 * 0.20 = 0.028

expected return = economy * economy probability

expected return economy = 0.08 * 0.60 = 0.048

expected return = recession * recession probability

expected return recession = 0.02 * 0.20 = 0.004

total expected return = 0.028 + 0.048 + 0.004 = 0.08

for boom economy

standard deviation = probability * (return - 0.08) ²

standard deviation = 0.20 * (0.14 - 0.08) ² = 0.00072 ... 1

for normal economy

standard deviation = probability * (economy - 0.08) ²

standard deviation = 0.60 * (0.08 - 0.08) ² = 0 ... 2

for recession economy

standard deviation = probability * (recession - 0.08) ²

standard deviation = 0.20 * (0.02 - 0.08) ² = 0.00072 ... 3

variance of the returns is sum of standard deviation

variance of the returns = 0.00072 + 0 + 0.00072

variance of the returns is 0.00144