…for the life of me I cannot remember the formulae for Vari(i) and Cov(i,j) for the Market Model i = asset m = market portfolio e = error Var(i) = B(i)^2*Var(m) + Var(e) Cov(i,j) = B(i)*B(j)*Var(m) Is there an intuitive way to remember this?
y1 = b1*x + e1 y2 = b2*x+e2 var(y1) = b1^2*var(x)+var(e1) because var(cx) = c^2*var(x) and var (x+z) = var(x) + var(z) if x and z are independent another way to remember is that Cov(y1,y2) = (y1,y2) = (b1*x+e1, b2*x+e2)= b1*b2*(x,x) + b1*(x,e2) + b2*(e1,x)+(e1,e2) and then realize that (x,e2)=(e1,x)=(e1,e2)=0 and (x,x) = Var(x) I hope that helps
! that’s the easy way to remember it !? thanks maratikus…the second one makes sense… what is c and C in the first equation… sorry you lost me there!!
sorry, mumukada. I had a dental appointment and had only two min to reply to your question. notation: cov(y,z) = (y,z) var(y) = cov(y,y)=(y,y) rules: cov(a+b,c+d) = (a+b,c+d)=(a,c)+(a,d)+(b,c)+(b,d) if e1, e2, e are error terms, then for each a not equal to the error term we have Cov(a,e) = (a,e)=0 and Cov(e1,e2)=(e1,e2)=0 and (e1,e1) = Var(e1) let’s practice with variance Var(y1)=(y1,y1)=(b1*x+e1,b1*x+e1)=(b1*x, b1*x) + (b1*x, e1) + (e1, b1*x)+(e1,e1)= b1^2*Var(x1)+0 + 0 + Var(e1) = b1^2*Var(x1)+Var(e1) Cov(y1,y2) = (y1, y2) = (b1*x+e1, b2*x+e2) = (b1*x, b2*x) + (b1*x, e2) + (e1, b2* x) + (e1, e2) = b1*b2*Var(x) + 0 + 0 + 0 = b1*b2*Var(x) I hope this explanation is more intuitive
Although it is easy enough to remember and calculate the Std Dev. for a 3 asset portfolio makes me want to puke. (of course that might be the coffee and Red Bull mixing).
^^ damn maratikus… just looking at that makes me crazy…but i’m going to save it…and read it a bit later… if it still won’t make sense…then maybe it’s just me thanks though…
I don’t think we need to know the calculation for 3 asset portfolio - the two asset portfolio is a must!
Hey deep2002…sorry to deliver the bad news, but: LOS 68.a: Discuss mean-variance…and calculate the expected return and the standard deviation of return for a portfolio of TWO OR THREE assets.
Quite frankly I hope we get a three asset standard deviation questions, as they are easy to run through if you know the formula.
Great, more BS formula’s to remember. I can dream can’t I lol
actually I find a general formula for portoflio variance. if B is covariance matrix and w is vector of weights, then Var(portfolio) = wT*B*w. If you learn how to apply this formula, you won’t have to memorize formulas for individual cases.
FastEd Wrote: ------------------------------------------------------- > Quite frankly I hope we get a three asset standard > deviation questions, as they are easy to run > through if you know the formula. Agree.