Portfolio tracking error

[sfad]

This is from CFAI 2012 q 20, question asks for portfolio tracking error:
- We have the following:
Investment Size Expected Alpha Expected tracking error
Manager A USD140 0% 0%
Manager B USD40 1.5% 2.5%
Manager C USD20 2.0% 4.0%
Answer= Portfolio tracking error = [(0.2 x 0.025)^2 + (0.1x0.04)^2]^0.5
The portfolio tracking error formula I have seen is:
[(active return - average active return)^2/n-1]^0.5
Why does their answer not have (n - 1) in the denominator?

 

[cpk123]

if you were using (3) the # of managers that would be true.
here you are using the portfolio % -> 40/200 = 0.2, 20/200 = 0.1 -> so you have already accounted for that aspect. The 3rd # would have been 0.7 * 0.

 

[sfad]

cpk i understand the use of portfolio %. But i’m referring to n-1 in the denominator being left out?

 

[jmsp]

I think the n-1 formula is only for calculating each manager’s tracking error, which is already calculated for you. If you are calculating a portfolio (consisting of multiple managers each with their own tracking error, you use the formula in the answer)

 

[cpk123]

When they give you the Portfolio Amount invested - and ask you to calculate the tracking error - it is akin to using the Probability percentage.
Go back to your level 1 days - when they gave you
a) a number of values and asked you to calculate std dev - use (n-1) since it is a sample or use if it is a population.
b) gave you some values with probability of occurrence - no division to calculate the std dev..
this is the same concept.

 

[Audacious]

jmsp wrote:
I think the n-1 formula is only for calculating each manager’s tracking error, which is already calculated for you. If you are calculating a portfolio (consisting of multiple managers each with their own tracking error, you use the formula in the answer)

This

 

[BaseballRedhawks]

Where is this question? CFAI real exam 2012? How is htere a question 20?