Question

For the stocks A and B you observe the following monthly returns over the last three months:

Month	A	B
1	8.62%8.62%	1.80%1.80%
2	18.01%18.01%	7.04%7.04%
3	15.20%15.20%	10.91%10.91%

Compute the covariance and correlation between these two stocks.(rounded to four decimal places)

Select one:

a. 0.00110.0011; 0.52670.5267

b. 0.00110.0011; 0.47350.4735

c. 0.00160.0016; 0.68870.6887

d. 0.00160.0016; 0.73000.7300

e. 0.00110.0011; 0.4994

Answer 1

Let us first see the given details in the question:

Last 3 months return of stock A:

1. 8.62%
2. 18.01%
3. 15.20%

Last 3 months return of stock B:

1. 1.80%
2. 7.04%
3. 10.91%

Covariance is a statistical measure that shows whether two variables are related by measuring how the variables change in relation to each other and correlation tells how strong the relationship is.

The formula for covariance is:

Covariance= ∑(ReturnA​ − AverageA​) ∗ (ReturnB − AverageB​)​ / (Sample Size) − 1

Next, we need to calculate the average return for each stock:

• For A, it would be (8.62% + 18.01% + 15.20%) / 3 = 13.9433
• For B, it would be (1.80% + 7.04% + 10.91%) / 3 = 6.5833
• Then, we take the difference between A's return and A's average return and multiply it by the difference between B's return and B's average return.
• Finally, we divide the result by the sample size and subtract one. If it was the entire population, you could divide by the population size.

After putting the details in the formula:

Covariance= ∑(ReturnA​ − AverageA​) ∗ (ReturnB − AverageB​)​ / (Sample Size) − 1

= ∑ (25.4629+1.8573+5.4374) / 3-1

= 0.1637878

The covariance between the two is 0.1637878.

Correlation is represented by this equation:

Correlation= Covariance (A & B) / Standard Deviation (A)*Standard Deviation (B)

The Formula for Standard Deviation

Standard Deviation = ∑ [Return (A or B) - Average (A or B)] / n-1

After putting all the details in the above formula given :

Correlation is 0.743296

Therefore, the close correct option seems to be D here

I hope you find this useful