Reading 8: Probability Concepts-LOS k习题精选 2010, interpret, border, center

bmaggie

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) must be positive.

C) can be positive or negative.

bmaggie

The covariance:

A) must be between -1 and +1.

B) must be positive.

C) can be positive or negative.

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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.

bmaggie

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

A) covariance.

B) standard deviation.

C) variance.

bmaggie

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

A) covariance.

B) standard deviation.

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.

bmaggie

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.

bmaggie

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.

bmaggie

Which of the following statements is least accurate regarding covariance?

A) A covariance of zero rules out any relationship.

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

C) Covariance can exceed one.

bmaggie

Which of the following statements is least accurate regarding covariance?

A) A covariance of zero rules out any relationship.

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

C) Covariance can exceed one.

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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.

bmaggie

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.

bmaggie

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