If the economy is normal, charleston freight stock is expected to return 16.5 percent. if the economy falls into a recession, the stock's return is projected at a negative 11.6 percent. the probability of a normal economy is 80 percent while the probability of a recession is 20 percent. what is the variance of the returns on this stock?
a. 0.010346
b. 0.012634
c. 0.013420
d. 0.013927
e. 0.014315

option (B) 0.012634

Explanation:

Data provided in the question:

Expected return         Probability

         16.5%                     80%

        -11.6%                      20%

Now,

Mean return = ∑( Probability × Expected return )

= ( 0.8 × 16.5% ) + ( 0.2 × (-11.6%) )

= 13.2% - 2.32%

= 10.88%

Thus,

Variance = ∑(Probability × [ Expected return - Mean return ]² )

=  0.8 × ( 16.5% - 10.88% )² + 0.2 × ( -11.6% - 10.88% )²

= 0.8 × ( 5.62% )² + 0.2 × (-22.48%)²

= 0.8 × 0.0562² + 0.2 × 0.2248²

= 0.002526752 + 0.010107008

= 0.01263376 ≈ 0.012634

Hence,

The correct answer is option (B) 0.012634