Covariance vs Correlation coefficient

[oatmeals2]

I've looked up a few text and tried searching online yet I can figure this out.

from a google search(might not be the best definition):
----------
Covariance is a measure of the degree to which returns on two risky assets move in tandem

Correlation is a measure that determines the degree to which two variable's movements are associated (or a measure of the dependence of two random variables)
---------

Am I missing the subtle differences?

I know that correlation coefficient ranges from:
+1 (x and y moves the same perfectly)
0 moves independently (a text mentioned 0 does not mean statisically independent)
-1 (x and y moves opposite)

I know the covariance is standardized by the denominator and does not have units.


Could someone please explain? I might be thinking about this the wrong way!

Thanks in advance.

 

[dynamic_hedger]

The correlation coefficient is the same as covariance, but has been scaled to a number between -1 and +1.

Some people make the mistake of believing that a portfolio consisting of two stocks with equal weight and a correlation of -1 will have an expected return of 0, because both stocks always move in opposite directions.

This is false. Correlation indicates direction, not magnitude. For example, if Stock A always goes up 5% when Stock B goes down 1%, the correlation is -1, but the expected return is clearly not 0.

 

[oatmeals2]

dynamic_hedger Wrote:
-------------------------------------------------------
> The correlation coefficient is the same as
> covariance, but has been scaled to a number
> between -1 and +1.
>
> Some people make the mistake of believing that a
> portfolio consisting of two stocks with equal
> weight and a correlation of -1 will have an
> expected return of 0, because both stocks always
> move in opposite directions.
>
> This is false. Correlation indicates direction,
> not magnitude. For example, if Stock A always
> goes up 5% when Stock B goes down 1%, the
> correlation is -1, but the expected return is
> clearly not 0.


Thanks hedger!

Would it be correct to say that the correlation is a better measure of direction while the covariance is a better measure of magnitude then?

 

[dynamic_hedger]

Actually, no. Compared to correlation, covariance doesn't supply any further information that's particularly meaningful.

My point is that correlation (and covariance) tell us only about the *direction* of two variables. A correlation of -1 could mean that Stock A always goes up 10% when Stock B goes down 2%. There's no need for the two percentages to be the same.

 

[jamespucyk]

Just keep in mind Covariance is to variance as correlation is to standard deviation (stdev and R are both standardized measures), just look at the equations:

Cov = E P (X-E(x))(Y-E)

R = COVxy / StdevX * StdevY

Clearly covariance is a product that is squared in magnitude, so R is more a function of the standard deviations of X and Y, if they are higher then then R will be lower and vica versa.

R is just standardized CovXY.



Edited 1 time(s). Last edit at Monday, April 17, 2006 at 09:57AM by jamespucyk.