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Thecodont

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Schweser had a question where you needed to calculte the significance of correlation. The started from covarriance and varrince of x and y. This is a no sweat problem until they gave me a varriance covarriance “matrix” that looked like this
X Y
X 50.4 20.2
Y 20.2 36.5
I still can not see how you are supposed to figure out wich one is varriance and covarriance. Any thoughts?
 
covariance is 20.2 since they are same for both in matrix
 
Oh, I see we have three dif variables. varriance would be unique for each asset but covriance would be the same
thanks
 
X to X and Y to Y is Varance (Std. Dev squared) and X to Y is covariance.
 
cov (x,x) = var (x)
remember that and you will be fine.
cov (x,y) = rxy * sigma x * sigma y
cov (x,x) = 1 * sigmax^2 = var(x)
since correlation of a variable with itself = 1.
 
how is it that cpk123 rating is ccc and mine is A? No way.
 
@Dreary
back after a long time ? I remember seeing you when I took L1 in 2010 , or was it FRM forum
 
Factor, I’m only doing CFA, and this will be the 4th time (no typo, it’s the 4th)… I don’t think my starting around this time everytime is contributing in any positive way to my chance of passing!
 
this time you will …2 months is quite a decent time given the exam experience ,you might just have to cover the materials and do practice exams
 
I like to think of it like this:
Variance vs Covariance
‘Co’ like ‘Co’operation, you’re working with someone other than yourself so
Covariance is cov(x,y) or cov(y,x)
Variance has no ‘Co’ so you’re working by yourself:
Variance is cov(x,x) or cov(y,y)
 
Now that you guys raised this, I wonder why Cov(x,y) = 0, if x or y has zero variance? The equation for covariance is the sum of (x-x_bar) * (y-y_bar).
The difficullty for me here is visualizing what the covariance is. Variance is clear: roughly, it’s how the data varies around the mean. If all the x’s are equal, x_bar = x, and the variance is zero. If you add another series, y, with a non-zero variance, how does that make the covariance zero?
 
if you multiply x * y and x is zero what is the answer?
if there is no varriance then x is not differant from x_bar so x-x_bar is zero.
this is the base principle on why the CAL works in portfolio. if the risk free asset did not have zero varriance you would not have a linear relationship with the tangency portfolio
 
Because you’re multiplying by 0 everywhere…
If one of the two variables doesn’t ever change, how can the two variables change simultaneously?
As to the original post, variance matrices are *extremely* common. So are correlation matrices.
 
Thecodont and aaronhotchner, can you define covariance in teh same simple way I defined variance above (i.e., roughly, it’s how the data varies around the mean)? Try doing that for covariance and see if the picture is clear.
 
It measures how frequently the large values of X correspond to the large values of Y.
A much easier way to describe covariance than summing all of the components is E(X - E(X)) * E(Y - E(Y)) = E(X * Y) - E(X) * E(Y). Whenever X and Y are independent, covariance is 0, always. Whenever either variable has a mean of 0, covariance is also 0.
 
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