Reading 52: Portfolio Risk and Return: Part I-LOS c 习题精选 2011, interpret, returns, center, style

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Session 12: Portfolio Management
Reading 52: Portfolio Risk and Return: Part I

LOS c: Calculate and interpret the mean, variance, and covariance (or correlation) of asset returns based on historical data.

 

 

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) remain the same.

B) increase.

C) decrease.

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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.

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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.

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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) = 0.009 / (0.600 × 0.400) = 0.0375

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

A) covariance.

B) standard deviation.

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. 

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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) = 0.40

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

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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.

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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.

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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.

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

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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.

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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.

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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.

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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) -100.00.

B) 1.00.

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.

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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.

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