Answer:
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
