1215

The covariance of the market's returns with the stock's returns is 0.008. The standard deviation of the market's returns is 0.1 and the standard deviation of the stock's returns is 0.2. What is the correlation coefficient between the stock and market returns?

A) 0.91.

B) 0.00016.

C) 0.40.

---

Cov_A,B = (r_A,B)(SD_A)(SD_B), where r = correlation coefficient and SD_x = standard deviation of stock x

Then,  (r_A,B) = Cov_A,B / (SD_A × SD_B) = 0.008 / (0.100 × 0.200) = 0.40

Remember:  The correlation coefficient must be between -1 and 1.

1215

Which of the following statements regarding the covariance of rates of return is least accurate?

A) If the covariance is negative, the rates of return on two investments will always move in different directions relative to their means.

B) It is a measure of the degree to which two variables move together over time.

C) It is not a very useful measure of the strength of the relationship, there is absent information about the volatility of the two variables.

---

Negative covariance means rates of return will tend to move in opposite directions on average. For the returns to always move in opposite directions, they would have to be perfectly negatively correlated. Negative covariance by itself does not imply anything about the strength of the negative correlation.

1215

If the standard deviation of stock A is 13.2 percent, the standard deviation of stock B is 17.6 percent, and the covariance between the two is 0, what is the correlation coefficient?

A) +1.

B) 0.31.

C) 0.

---

Since covariance is zero, the correlation coefficient must be zero.

1215

If the standard deviation of stock A is 7.2%, the standard deviation of stock B is 5.4%, and the covariance between the two is -0.0031, what is the correlation coefficient?

A) -0.80.

B) -0.19.

C) -0.64.

---

The formula is: (Covariance of A and B)/[(Standard deviation of A)(Standard Deviation of B)] = (Correlation Coefficient of A and B) = (-0.0031)/[(0.072)(0.054)] = -0.797.

1215

If the standard deviation of returns for stock A is 0.60 and for stock B is 0.40 and the covariance between the returns of the two stocks is 0.009 what is the correlation between stocks A and B?

A) 0.0020.

B) 26.6670.

C) 0.0375.

---

Cov_A,B = (r_A,B)(SD_A)(SD_B), where r = correlation coefficient and SD_x = standard deviation of stock x

Then, (r_A,B) = Cov_A,B / (SD_A × SD_B) = 0.009 / (0.600 × 0.400) = 0.0375