Calculation contract
IR_ann = mean(portfolio - benchmark) / sample_sd(portfolio - benchmark) * sqrt(K)| Input | Allowed values | Meaning |
|---|---|---|
| portfolio | 2-250 decimal returns | Equal-frequency portfolio series |
| benchmark | Same-length decimal returns | Aligned benchmark series |
| periods_per_year | Number, 1 to 366 | Explicit scaling factor |
Method and interpretation
The default mean active return is 0.00625 and the period tracking error is 0.0075. The period ratio is 0.8333333; multiplying by sqrt(12) gives approximately 2.8867513. A short invented example can produce a large ratio without supplying any evidence about future results.
An additive shift to every active observation changes the mean but not dispersion. That is useful as an arithmetic property test, not a way to manufacture a performance conclusion. The benchmark and full sample must be chosen on economic and research grounds, not selected to maximize this output.
Where the reference stops
A zero denominator returns null with an explanation. Annualizing a few observations does not create a year of evidence. The measure excludes estimation uncertainty, serial dependence adjustments, fees not already in the input and selection bias.
Published synthetic inputs
{
"portfolio": [
0.02,
-0.01,
0.03,
0.01
],
"benchmark": [
0.01,
-0.02,
0.02,
0.015
],
"periods_per_year": 12
}Frozen calculation output
{
"active_returns": [
0.01,
0.01,
0.009999999999999998,
-0.004999999999999999
],
"mean_active_return": 0.00625,
"sample_tracking_error": 0.0075,
"annualized_tracking_error": 0.025980762113533156,
"annualized_information_ratio": 2.8867513459481287
}Arithmetic period differences with sample n-1 dispersion. Square-root annualization assumes stationary, uncorrelated active returns; it is not a compounded wealth difference.
Verification coverage
- Known arithmetic ratio and zero-dispersion withholding tested.
- Negative means remain signed; no clipping to flattering values.
Unit and independent-reference checks test arithmetic and rejection rules, not future investment performance.
Method references
Read the assumptions in context
Validation examplesThe denominator defines the information ratio
Keep active-return means and tracking error on compatible scales, and separate a large historical ratio from evidence about repeatable performance.
Validation examplesOut-of-sample evidence and multiple testing
Separate chronological evaluation from repeated model selection, and quantify how a hypothetical search across many null tests changes the chance of a false discovery.