Calculation of Tracking Risk

[mp2438]

cfaboston,
I’ve done this example using a different benchmark weight, and your theory holds (roughly).
For benchmark weight = 50%, tracking risk = 8.5% * 50% = 4.25% (vs. 4.24% actual).
For benchmark weight = 60% (I’ve changed portfolio 1 weight to 10% and portfolio 2 weight stays the same), tracking risk = 3.35% with TheChad’s formula, and 6.5% (our formula) * 60% weight = 3.37%…so roughly the same.
Good little trick to know IMO.

 

[mp2438]

Nope…logic doesn’t really work once you move outside the 50% range. (i.e - 40% yields 4.2% and 5.4%)

 

[AMC]

Please note that the assumption here is that correlations are 0 because Portfolio A is investing in large-cap growth stocks and Portfolio B is investing in small-cap value stocks.

 

[dpcfa]

TheChad Wrote:
——————————————————-
> sqrt((.2^2)((.2-.05)^2)+(.3^2)((.15-.05)^2)+(.5^2)
> ((.05-.05)^2)) = 4.24%?
i understand everything happening here except the assumption that the risk of the broad market index is 5%.
is this a standard assumption? the problem in the original post did not mention a risk number for the broad market index.
can someone please explain?
thanks

 

[AMC]

I mentioned that the Broad Market Index is the benchmark and its expected Risk is 5%.

 

[cfaboston28]

AMC, I don’t see the expected risk of benchmark - 5% in the problem.

 

[dpcfa]

ok i didnt catch ALL the “please notes”
one more question -
this:
“Please note that the assumption here is that correlations are 0 because Portfolio A is investing in large-cap growth stocks and Portfolio B is investing in small-cap value stocks.”
that was also written explicitly in the question?
if so, then yeah the answer is pretty simple, no need for shortcuts. it’s just the standard portfolio risk formula, only with excess risk instead since it’s tracking risk, and the big terms all zero out due to the zero correlations

 

[AMC]

cfaboston28 Wrote:
——————————————————-
> AMC, I don’t see the expected risk of benchmark -
> 5% in the problem.
Please see the 4th post !

 

[AMC]

dpcfa Wrote:
——————————————————-
> one more question -
>
> this:
>
> “Please note that the assumption here is that
> correlations are 0 because Portfolio A is
> investing in large-cap growth stocks and Portfolio
> B is investing in small-cap value stocks.”
>
> that was also written explicitly in the question?
No, this assumption is not explicit. But I think the reason that the correlations are assumed to be 0 is because large-cap growth stocks & small-cap value are completely different asset class. I don’t understand why the correlations of large-cap growth stocks & small-cap value with the Broad Market Index can be assumed to be 0 too. No explanation in its solution.

 

[rosengri]

tracking risk=excess risk versus market risk, so
excess risk for portfolio A is 0.15 (0.2 - 0.05) for portfolio B=0.1
formula is = sqrt of weight A^2*excess risk A^2 + weight B^2*excess risk B^2=0,0424
page 158 Schweser, study notes book 3

 

[AMC]

rosengri,
Please advise which reading ? As I am using 2009 study notes. TKVM !