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A bond analyst is looking at historical returns for two bonds, Bond 1 and Bond 2. Bond 2’s returns are much more volatile than Bond 1. The variance of returns for Bond 1 is 0.012 and the variance of returns of Bond 2 is 0.308. The correlation between the returns of the two bonds is 0.79, and the covariance is 0.048. If the variance of Bond 1 increases to 0.026 while the variance of Bond B decreases to 0.188 and the covariance remains the same, the correlation between the two bonds will:

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?

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

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

C)	Positive covariance means that asset returns move together.

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

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?

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

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?

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

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?

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

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?

If two stocks have positive covariance, which of the following statements is TRUE?

A)	The two stocks must be in the same industry.

B)	If one stock doubles in price, the other will also double in price.

C)	The rates of return tend to move in the same direction relative to their individual means.

This is a correct description of positive covariance.

If one stock doubles in price, the other will also double in price is true if the correlation coefficient = 1. The two stocks need not be in the same industry.

This is a correct description of covariance. A positive covariance means the returns of the two securities move in the same direction. A negative covariance means that the returns of two securities move in opposite directions. A zero covariance means there is no relationship between the behaviors of two stocks. The magnitude of the covariance depends on the magnitude of the individual stock’s standard deviations and the relationship between their co-movements. The covariance is an absolute measure of movement and is measured in return units squared.

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?

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) = 0.400

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

A portfolio currently holds Randy Co. and the portfolio manager is thinking of adding either XYZ Co. or Branton Co. to the portfolio. All three stocks offer the same expected return and total risk. The covariance of returns between Randy Co. and XYZ is +0.5 and the covariance between Randy Co. and Branton Co. is -0.5. The portfolio's risk would decrease:

A)	more if she bought Branton Co.

B)	most if she put half your money in XYZ Co. and half in Branton Co.

C)	more if she bought XYZ Co.

In portfolio composition questions, return and standard deviation are the key variables. Here you are told that both returns and standard deviations are equal. Thus, you just want to pick the companies with the lowest covariance, because that would mean you picked the ones with the lowest correlation coefficient.

σ_portfolio = [W₁² σ₁² + W₂² σ₂² + 2W₁ W₂ σ₁ σ₂ r_1,2]^? where σ_Randy = Υ_Branton = σ_XYZ so you want to pick the lowest covariance which is between Randy and Branton.

Stock A has a standard deviation of 10%. Stock B has a standard deviation of 15%. The covariance between A and B is 0.0105. The correlation between A and B is:

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) = 0.0105 / (0.10 × 0.15) = 0.700

The standard deviation of the rates of return is 0.25 for Stock J and 0.30 for Stock K. The covariance between the returns of J and K is 0.025. The correlation of the rates of return between J and K is:

Cov_J,K = (r_J,K)(SD_J)(SD_K), where r = correlation coefficient and SD_x = standard deviation of stock x

Then, (r_J,K) = Cov_J,K / (SD_J × SD_K) = 0.025 / (0.25 × 0.30) = 0.333

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.

If the standard deviation of stock A is 10.6%, the standard deviation of stock B is 14.6%, and the covariance between the two is 0.015476, what is the correlation coefficient?

The formula is: (Covariance of A and B) / [(Standard deviation of A)(Standard Deviation of B)] = (Correlation Coefficient of A and B) = (0.015476) / [(0.106)(0.146)] = 1.

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?

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?

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.

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?

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