April 2019 Q7

[newkid]

Bit late in the day but could someone show me the calcs for the information ratio and tracking error - just for one of the funds.

 

[Gresham Arnold]

For Fund A

The individual annual returns for the fund are: 5%, 10% and 0.6536% giving an annualised return of 5.15%, and the benchmark returns were -1%, 4%, 1% giving an annualised return for the benchmark of 1.31%.

So the relative returns were +6%, +6%, –0.346% which have a mean of 3.88%.

The tracking error is the annualised standard deviation of the relative performance of the fund against its benchmark.

So, we can calculate the tracking error as 3.66%.

The information ratio is defined in the course (Chapter 22) as relative return divided by tracking error

Therefore the information ratio is 1.06 (3.88%/3.66%)

[It was possible to use 5.15% - 1.31% = 3.84% on the top line, which gives a similar result.]
.

 

[newkid]

Thanks Gresham, can you just show me the calc for the 3.66% - it was the only part that i couldn't figure out - i may be doing something stupid.

 

[Nimisha]

You just need to add the following (relative return-mean of relative returns) and then square it and divide it by n-1 i:e 3-1 here.
Its just the formula for the standard deviationi:e summation(x -mean)^2/n-1.