Reading 50: An Introduction to Portfolio Management LOS d习题 div, interpret, between, related

honeycfa

LOS d: Compute and interpret the covariance of rates of return and show how it is related to the correlation coefficient.

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:

A) decrease.

B) remain the same.

C) increase.

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P_1,2 = 0.048/(0.026^0.5 × 0.188^0.5) = 0.69 which is lower than the original 0.79.

 

honeycfa

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) 0.00084.

C) 0.05830.

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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

honeycfa

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) 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.

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

honeycfa

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) -0.0015.

C) -0.0009.

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

honeycfa

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) 0.0022.

B) 0.0001.

C) 0.0031.

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

honeycfa

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.

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

honeycfa

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) 0.3750.

B) 0.0352.

C) 0.0264.

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

honeycfa

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.

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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.

honeycfa

A measure of how well the returns of two risky assets move together is the:

A) standard deviation.

B) covariance.

C) range.

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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. 

honeycfa

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.

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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.