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Q1. The covariance:

A)   must be between -1 and +1.

B)   can be positive or negative.

C)   must be positive.

Correct answer is B)         

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.

Q2. 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)    variance.

C)    standard deviation.

Correct answer is C)

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.

Q3. Personal Advisers, Inc., has determined four possible economic scenarios and has projected the portfolio returns for two portfolios for their client under each scenario. Personal’s economist has estimated the probability of each scenario as shown in the table below. Given this information, what is the covariance of the returns on Portfolio A and Portfolio B?

Scenario	Probability	Return on Portfolio A	Return on Portfolio B
A	15%	18%	19%
B	20%	17%	18%
C	25%	11%	10%
D	40%	7%	9%

A)   0.890223.

B)   0.002019.

C)   0.001898.

Correct answer is C)

S	P (S)	Return on Portfolio A	RA – E(RA)	Return on Portfolio B	RB – E(RB)	[RA – E(RA)] x [RB – E(RB)] x P(S)
A	15%	18%	6.35%	19%	6.45%	0.000614
B	20%	17%	5.35%	18%	5.45%	0.000583
C	25%	11%	–0.65%	10%	–2.55%	0.000041
D	40%	7%	–4.65%	9%	–3.55%	0.000660
		E(RA) =11.65%		E(RB) =12.55%		Cov(RA,RB) =0.001898

Q4. 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)  It is weak and positive.

C)  Only that it is positive.

Correct answer is C)

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.

Q5. 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.

Correct answer is C)

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