Covariance Formula - How to Calculate covariance and beta


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Dear Sir,
How can I Solve the Problems? Pl. explains and solves the problems.

3. Covariance between the stocks is 0.0510. The Standard Deviation for stocks 1 & 2 are 0.2041 and 0.2944 respectively. Calculate the Correlation between the two stocks.

4. Find the covariance between two securities if the correlation coefficient between them is 0.937 and the Standard Deviation for stocks 1 & 2 are 0.303 and 0.456 respectively

6. Find the Beta of a stock if the correlation coefficient between the stock return and market return is 0.678, the variance of the stock return is 0.0456, the variance of market return is 0.0567

3 Answer(s)


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Hi!
You can solve the Question 3 as below:

The correlation coefficient, r = Covariance(1,2) /(SD1*SD2)
= 0.0510/(0.2041*0.2944)
= 0.8488 = Answer
Note: SD = Standard deviation
Pl write if you still have doubts.

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Satya
For Q. 4 use the following formula:

Covariance = Correlation coefficient* SD1*SD2*
= 0.937*0.303*0.456
= 0.1295 = Answer.
You can see that the formula in Q. 4 is just the same formula in Q.3. We've just cross multiplied the terms. So, it's better to remember any of the above formula. If any 3 quantities are given, you can find the fourth one.

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For Q. 6 you would need to use another formula as below:

Beta (β) = {r (i, m) * SDi}/ SDm,
Where r (i, m) is the correlation between the stock return ‘i’ and the market return m, SDi is the standard deviation of the stock return and SDm is the standard deviation of the market return.
Note, standard deviation is the square root of variance.
Hence Beta = 0.678 * SQRT(0.0456) / SQRT(0.0567)
= 0.608
Also, SQRT(0.0456) = 0.213542
SQRT(0.0567) = 0.238118
You need to take square root of variance to get the standard deviation. Students feed the variance values and calculate the Beta value. This is a common mistake.