Reading 50: An Introduction to Portfolio Management - LOS standard, between, returns, stocks, white

mayanfang1

Q1. If the standard deviation of returns for stock A is 0.40 and for stock B is 0.30 and the covariance between the returns of the two stocks is 0.007 what is the correlation between stocks A and B?

A)   17.14300.

B)   0.05830.

C)   0.00084.

Q2. Which one of the following statements about correlation is FALSE?

A)   The covariance is equal to the correlation coefficient times the standard deviation of one stock times the standard deviation of the other stock.

B)   Positive covariance means that asset returns move together.

C)   If two assets have perfect negative correlation, it is impossible to reduce the portfolio's overall variance.

Q3. If the standard deviation of asset A is 3.2%, the standard deviation of asset B is 6.8%, and the correlation coefficient is –0.40, what is the covariance between A and B?

A)   -0.0021.

B)   -0.0009.

C)   -0.0015.

Q4. If the standard deviation of asset A is 12.2%, the standard deviation of asset B is 8.9%, and the correlation coefficient is 0.20, what is the covariance between A and B?

A)   0.0001.

B)   0.0022.

C)   0.0031.

Q5. Stock A has a standard deviation of 10.00. Stock B also has a standard deviation of 10.00. If the correlation coefficient between these stocks is - 1.00, what is the covariance between these two stocks?

A)   1.00.

B)   -100.00.

C)   0.00.

Q6. The correlation coefficient between stocks A and B is 0.75. The standard deviation of stock A’s returns is 16% and the standard deviation of stock B’s returns is 22%. What is the covariance between stock A and B?

A)   0.0264.

B)   0.3750.

C)   0.0352.

mayanfang1

答案和详解如下：

Q1. If the standard deviation of returns for stock A is 0.40 and for stock B is 0.30 and the covariance between the returns of the two stocks is 0.007 what is the correlation between stocks A and B?

A)   17.14300.

B)   0.05830.

C)   0.00084.

Correct answer is B)

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) = 0.007 / (0.400 × 0.300) = 0.0583

Q2. Which one of the following statements about correlation is FALSE?

A)   The covariance is equal to the correlation coefficient times the standard deviation of one stock times the standard deviation of the other stock.

B)   Positive covariance means that asset returns move together.

C)   If two assets have perfect negative correlation, it is impossible to reduce the portfolio's overall variance.

Correct answer is C)

This statement should read, "If two assets have perfect negative correlation, it is possible to reduce the portfolio's overall variance to zero."

Q3. If the standard deviation of asset A is 3.2%, the standard deviation of asset B is 6.8%, and the correlation coefficient is –0.40, what is the covariance between A and B?

A)   -0.0021.

B)   -0.0009.

C)   -0.0015.

Correct answer is B)

The formula is: (correlation)(standard deviation of A)(standard deviation of B) = (–0.40)(0.032)(0.068) = –0.00087.

Q4. If the standard deviation of asset A is 12.2%, the standard deviation of asset B is 8.9%, and the correlation coefficient is 0.20, what is the covariance between A and B?

A)   0.0001.

B)   0.0022.

C)   0.0031.

Correct answer is B)

The formula is: (correlation)(standard deviation of A)(standard deviation of B) = (0.20)(0.122)(0.089) = 0.0022.

Q5. Stock A has a standard deviation of 10.00. Stock B also has a standard deviation of 10.00. If the correlation coefficient between these stocks is - 1.00, what is the covariance between these two stocks?

A)   1.00.

B)   -100.00.

C)   0.00.

Correct answer is B)

Covariance = correlation coefficient × standard deviation_{Stock 1} × standard deviation_{Stock 2} = (- 1.00)(10.00)(10.00) = - 100.00.

Q6. The correlation coefficient between stocks A and B is 0.75. The standard deviation of stock A’s returns is 16% and the standard deviation of stock B’s returns is 22%. What is the covariance between stock A and B?

A)   0.0264.

B)   0.3750.

C)   0.0352.

Correct answer is A)

cov_1,2 = 0.75 × 0.16 × 0.22 = 0.0264 = covariance between A and B.

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