Compute the implied correlation of a Portfolio

If you suck at chess...don't play chess

 

I guess i should have looked at the prospectus first I read over a white to see the formula they were using (my original post), but did not notice the actual holdings.

Last question I have that will really get my head around this. Why is it that the formula
rho <-(iv**2 - crossprod(w**2,v**2)) / sum(outer(v,v) * outer(w,w) - diag(3) * diag(outer(v,v) * outer(w,w))) is equivalent to (basketVol/WeightedComponentVol)^2. This becomes almost exact as number of components increases to infinity. Since we are trading in vols and not vars doesn't it make sense to use sqrt(rho) or (basketVol/WeightedComponentVol) instead of rho?

Code:

#1000 asset portfolio
x<-runif(1000)
w = x/sum(x)
v = rnorm(1000, mean = .35, sd = .09)
vIndex = .21

rho = (vIndex**2 - crossprod(w**2,v**2)) /  sum(outer(v,v) * outer(w,w) - diag(length(v)) * diag(outer(v,v) * outer(w,w)))

.21/sum(v*w) - sqrt(rho)      
#[1,] 0.0007784934

 

Because when n is large sum(w^2 * v^2) is small and because (y - e) / (x - e) ~ y / x when e is small. The term -sum(w^2 * v^2) appears in both the numerator and denominator of the CBOE formula you posted (after some rearrangement). See the slightly reqritten formula in the function in the code section below.

And also because (basketVol/WeightedComponentVol)^2 is the actual correct approximation. In my original post I erred and left off the ^2. I was working from memory and didn't bother to check. Sorry about that.

Code:

impliedIdxCorFromVols <- function(w,v,iv)
{ w <- w / sum(w)
  rho <- (  iv**2  - sum(w^2 * v^2)) / 
  (sum((v*w) %*% t(v*w)) - sum(w^2 * v^2))
  return(rho)
}

Edit: Yes, also because we are working in var and covars to extract the implied correlation

 

thank you for the help kevin!

 

The man, the legend himself is back #TBS

 

don’t ever throw shots at my homie ever again, especially in his own thread.

this is a warning.

#ETGANGANGANG

 

you’re so smart is pisses me tf off.

time to get back in the books

 

Whaddya mean, "throw shots"? I was handing out a "pearl of trading wisdom".

Sometimes the pinnacle of sophistication is simplicity. Especially true in trading, though not many players catch on.

 

Nah...I highly doubt that players like Ren Tech or Citadel are finding alpha in simplicity. But whatever...keep paying their yachts