Tracking Risk - CFAI Volume 4 Page 18 (Fixed Income)

They say that in 2/3 of the time we can expect a manager’s active return to fall in the range of Benchmark Return +/- 30bps.

Shouldn’t it be Mean Active Return +/- 30 bps?

The mean active return in the above example is small (only .09%), so I guess to illustrate the point they are just assuming an average active return of zero in which case the portfolio return would be the benchmark return +/- 30bps … but technically speaking, it should be [benchmark return + 9 bps] +/- 30 bps right?


please remember what tracking risk and active return are …

active return = portfolio return - benchmark return.

tracking risk = std deviation of (portfolio return - benchmark return)

so since they are talking about tracking risk out here … the benchmark return should not apply.

We have a mean active return (the average return earned in excess of the benchmark) and we have the tracking risk (the standard deviation of that excess return). So to interpret a tracking risk of 30 bps:

2/3 of the time the excess return earned over the benchmark (portfolio return - benchmark return) should fall into the following range: Mean Active Return +/- 30bps

I agree benchmark return should not apply. The interpretation offered by the Fixed Income reading in the CFAI book (vol. 4) Page 18 reads:

“Statistically, the area that is one standard deviation either side of the mean captures approximately 2/3 of all the observations if portfolio returns approximately follow a normal distribution. Therefore, a tracking risk of 30 bps would indicate that, in approximately two- thirds of the time periods, the portfolio return will be within a band of the benchmark index’s return plus or minus 30 bps.”

I want to reconcile these two interpretations, as they have expressed tracking risk relative to a benchmark while I feel it should be relative to the mean active return.

The only way I can make sense of their interpretation is if we assume the mean active return is zero - on average he adds no value. The std. dev. of active returns is 0.30%, therefore, 2/3 of the time the manager’s active return would be within the range of 0 +/- 30 bps

The distribution of active returns within one standard deviation of the mean active return is in excess of the benchmark, so the total portfolio return would be the benchmark return +/- 30 bps.

I hope this is clearer for you.

Would appreciate an answer to this, maybe the magician can help?

S2000 where are you?

I think the text is incorrect - or just worded poorly. you would have to assume active = 0 for that statement to be correct. think about it this way. if the average active return was 5% and stdev was 1%, the managers active return is not expected to fall within -1 to 1%. or benchmark +/-1%… logically that doesn’t make sense, it can’t be - that’s not what the stdev is measuring…

Agree 100%. Fixed Income readings in general are a bit dodgy.

Agree with you Going_for_CFA . if Stdev is calculated on active return , it is wrong to say that the band around the active return is benchmark±30 bps. It should say that the active return would fall in a 1-stdev band around the mean active return not the mean benchmark return .