227k views
3 votes
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

User Htz
by
8.2k points

1 Answer

3 votes

Answer:

option (B) 0.012634

Step-by-step 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

User Rosann
by
7.7k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.