Reading 8: Probability Concepts-LOS k 习题精选 interpret, 2011, center, border

1215

Session 2: Quantitative Methods: Basic Concepts
Reading 8: Probability Concepts

LOS k: Calculate and interpret covariance and correlation.

 

 

The covariance:

A) must be between -1 and +1.

B) can be positive or negative.

C) must be positive.

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Cov(a,b) = σ_aσ_bρ_a,b. Since ρ_a,b can be positive or negative, Cov(a,b) can be positive or negative.

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The covariance of returns on two investments over a 10-year period is 0.009. If the variance of returns for investment A is 0.020 and the variance of returns for investment B is 0.033, what is the correlation coefficient for the returns?

A) 0.350.

B) 0.444.

C) 0.687.

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The correlation coefficient is: Cov(A,B) / [(Std Dev A)(Std Dev B)] = 0.009 / [(√0.02)(√0.033)] = 0.350.

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The correlation coefficient for a series of returns on two investments is equal to 0.80. Their covariance of returns is 0.06974 . Which of the following are possible variances for the returns on the two investments?

A) 0.02 and 0.44.

B) 0.08 and 0.37.

C) 0.04 and 0.19.

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The correlation coefficient is: 0.06974 / [(Std Dev A)(Std Dev B)] = 0.8. (Std Dev A)(Std Dev B) = 0.08718. Since the standard deviation is equal to the square root of the variance, each pair of variances can be converted to standard deviations and multiplied to see if they equal 0.08718. √0.04 = 0.20 and √0.19 = 0.43589. The product of these equals 0.08718.

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Which of the following statements is least accurate regarding covariance?

A) Covariance can only apply to two variables at a time.

B) Covariance can exceed one.

C) A covariance of zero rules out any relationship.

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A covariance only measures the linear relationship. The covariance can be zero while a non-linear relationship exists. Both remaining statements are true.

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The returns on assets C and D are strongly correlated with a correlation coefficient of 0.80. The variance of returns on C is 0.0009, and the variance of returns on D is 0.0036. What is the covariance of returns on C and D?

A) 0.40110.

B) 0.00144.

C) 0.03020.

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r = Cov(C,D) / (σ_A x σ_B)
σ_A = (0.0009)^0.5 = 0.03
σ_B = (0.0036)^0.5 = 0.06
0.8(0.03)(0.06) = 0.00144

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If given the standard deviations of the returns of two assets and the correlation between the two assets, which of the following would an analyst least likely be able to derive from these?

A) Strength of the linear relationship between the two.

B) Covariance between the returns.

C) Expected returns.

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The correlations and standard deviations cannot give a measure of central tendency, such as the expected value.

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The covariance of the returns on investments X and Y is 18.17. The standard deviation of returns on X is 7%, and the standard deviation of returns on Y is 4%. What is the value of the correlation coefficient for returns on investments X and Y?

A) +0.85.

B) +0.65.

C) +0.32.

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The correlation coefficient = Cov (X,Y) / [(Std Dev. X)(Std. Dev. Y)] = 18.17 / 28 = 0.65

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With respect to the units each is measured in, which of the following is the most easily directly applicable measure of dispersion? The:

A) standard deviation.

B) covariance.

C) variance.

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The standard deviation is in the units of the random variable itself and not squared units like the variance. The covariance would be measured in the product of two units of measure.

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Given Cov(X,Y) = 1,000,000. What does this indicate about the relationship between X and Y?

A) It is strong and positive.

B) Only that it is positive.

C) It is weak and positive.

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A positive covariance indicates a positive linear relationship but nothing else. The magnitude of the covariance by itself is not informative with respect to the strength of the relationship.