Phc7006: covariance measures the strenght of the correlation between two sets of variable.
w = vector of weight of individual financial activa
r = return
i = universe of available activa
j= activa in portfolio
this formulas tells you that the risk of a portfolio ( measures as a variance) can be measured from the matrix of weighted relative correlation of returns,
that's part of the markowitz formula
lowyhong: Thanks, but my problem is figuring out why the equation looks like that. I apologize if my question wasn't clear. The summation signs are side by side - what do they mean? How would I expand out the right-hand side function if let's say n = 2?
Meanwhile I will try to look through my textbook again and see if I can make any sense of it. Thanks again phc.
you can vizualize the double summation as a table. let's take a simple case where there are 2 shares in the portfolio and 2 in the universe.
so you have say a first table "i" with i=1 , w(i=1)=0.20 and i=2, w(i=2)=0.8
and a second table j with the couples (1,0.4) and (2,0.6)
and a third with the covariances with the following items
coordinate (1,1) = 0,6; (1,2) = 0,9: (2,1) =0,8 and (2,2) = 1
the risk is then a sum of 4 numbers
0,20x0,4x0,6 + 0,20x0,6x0,9 + 0,8x0,4x0,8 + 0,8x0,6x1
that is if I remember well, because that kind of formula is as you may guess never used as such ( at best, a computer does the math for you, and uses much more complex matrixes like value at risk formula )
check here too www.mtsu.edu/~jee/pdf/richardson.pdf
