If the economy booms,RTF AB equity is expected to return 10%.If the economy goes into a recessionary period,then RTF is expected to only return 4%.The probability of a boom is 60% while the probability of a recession is 40%.What is the variance of the returns on RTF?
A).000200
B).000760
C).000864
D).001594
E).029394

Question

Quizplus · Accepted Answer

To calculate the variance, we need to use the formula: Var(RTF) = [P(boom) x (RTF boom return - expected return)²] + [P(recession) x (RTF recession return - expected return)²]

Plugging in the numbers: 
Var(RTF) = [0.60 x (0.10 - 0.07)²] + [0.40 x (0.04 - 0.07)²]
Var(RTF) = 0.60 x 0.0009 + 0.40 x 0.0009
Var(RTF) = 0.00054 + 0.00036
Var(RTF) = 0.000864

Therefore, the answer is C.

If the Economy Booms,RTF AB Equity Is Expected to Return