Information ratio

The information ratio asks whether your outperformance was consistent or lucky.

Beating a benchmark by 3% because you were steadily ahead all year is a different achievement from beating it by 3% because one holding exploded in March while everything else trailed. The information ratio separates the two by dividing your average active return by how much that active return jumped around.

How it is calculated

information ratio = mean active return / standard deviation of active returns × √252

Both halves come from the same daily series: your return minus the benchmark's return, day by day. The numerator is the average of those differences. The denominator is their standard deviation, which is exactly tracking error before annualisation.

So the information ratio is your active return per unit of tracking error, annualised with √252.

How to read it

Positive means you were ahead of the benchmark on average across the window. Negative means behind. The magnitude reflects how reliably, not how much.

A portfolio can have a large positive active return and a small information ratio, which is the signature of outperformance concentrated in a few days. That is worth knowing, because concentrated outperformance is much less likely to repeat than steady outperformance.

Unlike the Sharpe ratio, no risk-free rate enters this calculation. The benchmark plays that role: what you are being measured against is the alternative of simply holding the index.

Gylder does not define what a good information ratio is.

What it misses

It treats active volatility symmetrically. Days you beat the benchmark by a lot inflate the denominator exactly as much as days you trailed it by a lot, so sharp outperformance is penalised alongside sharp underperformance.

It is also unstable over short windows, for the same reason alpha is: a small number of days and an estimated relationship to a benchmark you chose. Over a few months this is close to noise.