Anon

340 The Basics of financial economeTrics

x= 0 and y= 0 , respectively. The resulting sample covariance according to
equation (A.11) is then

(^) sXY, =− ...






()− ++−−





⋅⋅ 

1

3

7

6

010

1

3

11

6

0110 ()− = 0

which indicates zero correlation. Note that despite the fact that the two vari-
ables are obviously dependent, the joint occurrence of the individual values
is such that, according to the covariance, there is no relationship apparent.

correlation

If the covariance of two variables is non-zero we know that, formally, the
variables are dependent. However, the degree of correlation is not uniquely
determined.

FiGuRe A.5 Relationship between Correlation and Dependence of Bivariate Variables

cov(x,y) = 0

x,y

Dependent

cov(x,y) ≠ 0

x,y

Independent

tABle A.2 Payoff Table of the Hypothetical Variables x and y with Joint Frequencies

x

y 7/6 13/6 –5/6 –11/6

1 1/3

–2 1/6

2 1/6

–1 1/3