Bruno’s stock should return 14 percent in a boom, 11 percent in a normal economy, and 4 percent in a recession. the probabilities of a boom, normal economy, and recession are 8 percent, 90 percent, and 2 percent, respectively. what is the variance of the returns on this stock?
a. 0.011387
b. 0.000169
c. 0.001506
d. 0.001538
e. 0.011561

option (b)  variance of the returns is 0.000169

Explanation:

Given data

boom return = 14% = 0.14

normal economy = 11% = 0.11

recession = 4% = 0.04

boom probability = 8% = 0.08

normal economy  probability = 90 %  = 0.90

recession  probability = 2 % = 0.02

to find out

the variance of the returns on this stock

solution

we know variance of the returns is sum of standard deviation

expected return = boom return × boom probability

expected return boom = 0.14 × 0.08 = 0.0112

expected return = economy × economy probability

expected return economy  = 0.11 × 0.9 = 0.099

expected return = recession × recession probability

expected return recession = 0.04 × 0.02 = 0.0008

total expected return = 0.0112 + 0.099 + 0.0008 = 0.111

for boom

standard deviation = probability × (return - 0.111)²

standard deviation = 0.08 × (0.14 - 0.111)²   = 0.00006728    1

for normal economy

standard deviation = probability × (economy - 0.111)²

standard deviation = 0.90 × (0.11 - 0.111)²   = 0.00000090    2

for recession

standard deviation = probability × (recession - 0.111)²

standard deviation = 0.02 × (0.04 - 0.111)²   = 0.00010082    3

variance of the returns is sum of standard deviation

variance of the returns = 0.00006728 + 0.00000090 + 0.00010082

variance of the returns is 0.000169

answer; ///(d); determining who competes most closely   with whom evaluating whether industry driving forces and competitive pressure favor some strategic groups and hurt others, and ascertaining whether the profit potential of different strategic groups varies due to the strengths and weaknesses in each groups respective market positions;