Question

Stock A is expected to return 14 percent in a normal economy and lose 21 percent in a recession. Stock B is expected to return 11 percent in a normal economy and 5 percent in a recession. The probability of the economy being normal is 75 percent with a 25 percent probability of a recession. What is the covariance of these two securities?a) 0.007006b) 0.006563c) 0.005180d) 0.007309e) 0.006274

Answer 1

Answer:

The correct option is b) 0.006563.

Explanation:

Note: See the attached excel file for the calculation of the covariance between stocks A and B.

Covariance refers to a metric that measures the relationship between two random variables by showing the degree to which the two variables change together.

A positive covariance means that two variables move in the same direction, while a negative covariance indicates that the two variables tend to move in the opposite directions.

In the attached excel file, the following are used:

RA = Rate of Return of Stock A

RB = Rate of Return of Stock B

P = Probability

ERA = Expected return of Stock A = RA * P

ERB = Expected return of Stock B = RB * P

DA = Deviation of Stock A = RA - Sum of ERA

DB = Deviation of Stock B = RB - Sum of ERB

N = Number of observation = 2

Therefore, Covariance of Stock A and B is calculated using the covariance formula as follows:

Covariance of Stock A and B = Sum of (DA * DB) / N = 1.3125% / 2 = 0.6563%, or 0.006563

Therefore, the covariance of these two securities is 0.006563. This shows that the correct option is b) 0.006563.