Tracking error.

[NNath]

Suppose the daily returns of a portfolio and a benchmark portfolio it is replicating are as
follows: Portfolio Return (bps) Benchmark Portfolio Return (bps) Day 1 34 30 Day 2 -89 -87 Day 3
108 102 Day 4 70 70 What is the tracking error over the four day period?

A. 2 bps
B. 10 bps
C. 2.39 bps
D. 3.16 bps

Please solve, I am not getting any of the answers. I am getting s.d. of Portfolio as 73.92 bps and that of the benchmark as 71.53.

calculating tracking error by variance formula tracking error I am getting is 102.86. There is no co-variance term right ?

 

[ShaktiRathore]

Tracking error is std. Deviation of (return of portfolio-return of benchmark).it measures the standard devition of portfolio returns wrt the benchmark.difference of returns are day1:34-30=4,day2: -89-(-87)=-2,day3:108-102=6,day4:70-70=0
Mean of these returns=(4-2+6+0)/4=8/4=2
Std deviatoin of these retur differences=sqrt(((4-2)^2+(-2-2)^2+(6-2)^2+(0-2)^2)/4)=sqrt(4+16+16+4/4)=sqrt(40/4)=3.16 bps
Thanks

 

[CK2015]

Tracking error is std. Deviation of (return of portfolio-return of benchmark).it measures the standard devition of portfolio returns wrt the benchmark.difference of returns are day1:34-30=4,day2: -89-(-87)=-2,day3:108-102=6,day4:70-70=0
Mean of these returns=(4-2+6+0)/4=8/4=2
Std deviatoin of these retur differences=sqrt(((4-2)^2+(-2-2)^2+(6-2)^2+(0-2)^2)/4)=sqrt(4+16+16+4/4)=sqrt(40/4)=3.16 bps
Thanks

What's the significance of the tracking error? How do we interpret it and use it in real life? Thanks

 

[CK2015]

Let me try to answer my own question! I hope others benefit as well. Please jump in, if I state any of this incorrectly.

If we are comparing two or more portfolios against benchmark portfolio to figure out which portfolio did better, information ration helps. The higher the ratio, the better it is. IR = Active Return / Active Risk. Higher numerator and lower denomitor favors higher information ratio.

Terminology is killing here. Here are my questions, some of them sound stupid. I'm sure every term has its own reason for its existence.

Why " Information" word for this ratio? Is it because the portfolio manager is using information wisely compared to that of market as a whole?

Why "Active" word in "Active Risk/ Return"? - is it because portfolio manager is managing portfolio actively bs passively?

 

[ShaktiRathore]

Hi
Information is used to denote information quotient of manager,a higher information indicates more reason for manager to deviate from the benchmark and earn returns which is nothing but returnd relative to the benchmark. In a sense information ratio implies how much better the manger is informed so that resulting deviation from benchmark creates higher returns,a well informed manager would earn higher returns relative to benchmark as compared to less informed manager as also therefore reflected in the resulting information ratio.
Yes its Active return because manager is activrly taking positions in securities and deviating from benchmark rather than just put the money in the benchmark w/o actively taking positions and deviating from the benchmark in way active means over/underweghing a security/sector of the benchmark.
Thanks

 

[CK2015]

Thanks. But what if if IR is negative? Does that imply that manager didn't actively seek/leverage information (passively managed) or completely misinterpreted/misjudged/information overloaded?

Also this implies that unless the portfolios are actively managed, it won't beat the benchmark indexes ....not sure in real life, are the managers rewarded based on these ratios? Will investors rely on these ratios to invest in funds manger by these managers with high IRs?

 

[ShaktiRathore]

Yes a negative IR does imply poor information on managers part,having information means having high quality and accurate information the better the information the well informed the mangerand a positive IR and a negative IR means less worthy /accurate information implying less informed manager because if he had been better informed in the first place active returns would not have got awry into negative zone. In a way IR signifies how much manager knows and whats the quality of his information in a way how well informed he is.
Yes in real life Managers are awarded based on a set of perfornance appraisal ratios,information ratio is one of these ratios which helps compare managers performances and reward them based on how they perform relative to their peers. Infirmation comes in handy when conparing same style managers relative to a benchmark, e.g. How two value managers performed relarive to a value benchmark and thus compare their performances similarly compare growth managers following a certain growth index. Yes investors rely on IR ti make investments for e.g. If i need to choose b/w two growth fubds i would find IR for both fubds relative o a growth index/benchmark and identify a higher IR fund as a better fund to invest.
Thanks

 

[CK2015]

That makes sense. The only concern that I have with this ratio is around false positives and negatives. Just because IR is more, it doesn't necessarily mean that the manager have actively/effectively leveraged the information. But I get the concept. Thanks!!

 

[Meredius]

That's true. But if you're analyzing a ratio, you wouldn't do it as a standalone number pulled out of a hat. Saying I'm a 1.8 doesn't really mean anything in itself (a danger of blindly looking at a VaR number without understanding the mechanics and assumptions behind is another example).

You'd need a time-series to see an evolution of the returns and other similar port-folio managers [investment methodology and sector] to benchmark against to really put context on the number and what it means relatively to other managers and the market itself.

Cheers!