If the covariance between the prices of two investments is 6

If the covariance between the prices of two investments is

600 comma 000600,000,

does this tell you that the correlation between the two is close to 1?

Choose the correct answer below.

A.

No, it only tells us that the correlation is positive.

B.

Yes

C.

No, a large covariance implies a correlation close to

minus1.

D.

No, a large covariance implies a correlation close to 0.

Solution

The covariance of (X,Y) is defined by
cov(X,Y)=E([XE(X)][YE(Y)])
and, assuming the variances are positive, the correlation of (X,Y) is defined by
cor(X,Y)=cov(X,Y)/ sd(X)sd(Y)

Correlation is a scaled version of covariance; note that the two parameters always have the same sign (positive, negative, or 0). When the sign is positive, the variables are said to be positively correlated; when the sign is negative, the variables are said to be negatively correlated; and when the sign is 0, the variables are said to be uncorrelated. Note also that correlation is dimensionless, since the numerator and denominator have the same physical units, namely the product of the units of X and Y

A.
No, it only tells us that the correlation is positive.