Reading 8: Probability Concepts - LOS j ～ Q6-10

答案和详解如下：

6、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)   variance.

C)   covariance.

D)   kurtosis.

The correct answer was A)

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. Kurtosis is not a measure of dispersion.

7、The covariance:

A)   can be positive or negative.

B)   must be between -1 and +1.

C)   must be positive.

D)   must be less than +1.

The correct answer was A)

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.

8、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)   0.03 and 0.28.

C)   0.04 and 0.19.

D)   0.08 and 0.37.

The correct answer was C)

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.

9、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)   0.444.

B)   0.687.

C)   0.350.

D)   0.785.

The correct answer was C)

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

10、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)   +0.32.

B)   +0.85.

C)   +0.65.

D)   +2.59.

The correct answer was C)    

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