# Tracking Error Question

#### cdbsmith

##### Member
Hi David,

I have been doing the GARP practice questions recently, and I encountered one, on tracking error calculation, that really has me perplexed (see attached).

According to the explanation, the correct answer is "c" 3.05%. But, when I performed the calculation (on my calculator and via excel spreadsheet) I get 3.44%. To clarify, I took the difference from between each return from the fund and the mean (arithmetic) return for the benchmark (i.e., 6%) and squared each difference, and took the average of the summed squared differences to get the average variance (i.e., 0.00001185). I then took the square root of the variance to get the standard deviation/tracking error and got 3.44%. I believe my calculation process is consistent with the explanation and actual reference text, but am not 100% sure.

Can you please take a look at this and let me know if you are able to get the same answer as the explanation? If so, can you tell me what I am doing wrong?

Thanks,

Charles

#### Attachments

• Tracking Error Question.pdf
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#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi cdbsmith I actually get 2.728% (I am going to send this link, with my comments, to GARP's attention) but I see how they got 3.05%: contrary to their text, they computed a sample standard deviation (which is arguably fine for a small sample, and could be called an ex-ante TE).
• I think we can all agree that the series of active returns is correct as: 8.0%, 4.0%, 2.0%, 1.0%, 0.5%.
• The mean active return = average (8.0%, 4.0%, 2.0%, 1.0%, 0.5%) = 3.10%
• The sum of squared differences (from the mean return) = 4.90%^2 + 0.90%^2 + (-1.10%)^2 + (-2.1%)^2 + (-2.6%)^2 = 0.3720%
• Then we have a choice to divide by 5 or 4
• "population" variance = 0.3720%/5 = 0.0744% with SQRT(0.0744%) = 2.7276% = STDEV.P(8.0%, 4.0%, 2.0%, 1.0%, 0.5%) = 2.7276%, or
• "sample" (aka, ex ante) variance 0.3720%/4 = 0.0930% with SQRT(0.0930%) = 3.0496% = STDEV.S(8.0%, 4.0%, 2.0%, 1.0%, 0.5%) = 3.0496%
I am not quite aware of anywhere in the FRM syllabus, current or past, that advocates the sample TE (3.05%), while the text seems to describe the "population" TE per its "take the average of those values," so I am going to submit this to GARP (I've never looked at the Sample Questions, I actually did not realize they exist in 2013!). I hope that helps,

#### cdbsmith

##### Member
Thanks David!

Your explanation cleared things up for me quite well. Thanks for forwarding the issue to GARP. Hopefully, they won't have this kind of question on the exam.

Regards,

Charles

#### cdbsmith

##### Member
Btw, would you like me to send the GARP 2013 sample questions? It's publicly available.