question on tracking error

[lkuo]

Sorry, if it is a stupid question. I thought tracking error is portfolio volatility *( portfolio Return - benchmark return). However, on your practice 1 a, the spreadsheet uses something else like this :TE={market variance + portfolio variance -(2*portfolio volatility*market volatility*correlation)}^0.5. I cannot make sense of it. Please help.

Lesley

 

[David Harper CFA FRM]

Lesley,

Tracking error, at least under the FRM definition, is volatility of [port vol - benchmark vol]. That's from Amenc, so it just *looks* like a product but it is the standard deviation of the series of differences.

Or, equivalently and importantly in Grinold's terms, where active return = portfolio - benchmark
TE = standard deviation of [active returns] = active risk

So, in the spreadsheet, I wanted to show a way (not the only way, I suppose) to calculate tracking error by using the Gujarati variance property (3.28): Var (x-y) = var(x) + var (y) - 2cov(x,y).

Such that:

variance (p - b) = TE^2 = var(p) + var(b) - 2cov(p,b)
TE = [var(p) + var(b) - 2cov(p,b)]^(1/2)

Hope that helps, David