Arm's Length Range: IQR, Mid-Point and Testing the Price
The arm's length range defined: the band of acceptable profit levels derived from comparables, usually the interquartile range, and how a tested party is placed inside it.
Definition
The arm’s length range (ALR) is the band of profit levels — for a chosen profit level indicator — that the comparable evidence says is arm’s length for the tested party’s function. The tested party’s adjusted result is placed against it: inside the range, the price is supported; outside, the comparability analysis needs a second look.
Formula
For the standard OECD construction, the range is the interquartile range of the pool’s PLI values:
ALR = [Q1, Q3] Q1, Q3 = first and third quartiles of the pool's PLI values
mid-point = (Q1 + Q3) / 2Worked on nine OP/OC values (3.2, 3.6, 4.0, 4.5, 4.8, 5.1, 5.4, 5.9, 6.3%): Q1 = 3.8, Q3 = 5.65, mid-point 4.73. The mechanics, the even/odd cases and the full-range alternative are in IQR vs full range.
Example
A tested party’s adjusted OP/OC is 4.4% and the pool’s IQR is 3.8%–5.65%: inside the range, no adjustment is indicated. The same tested party at 5.9% is outside — the response is to examine the pool and the adjustments, not to conclude an adjustment exists.
See also
FAQ
Which range should a study use? The IQR is the OECD first choice and the default position in Indian practice; the full range (pool minimum to maximum) appears for small pools and as a secondary argument. The choice, and its reason, belongs in the file.
Is the mid-point the “correct” price? No. The mid-point is a single-number summary of the range — useful as a sensitivity reference, never as the target a study is built to hit.
Run the screens as a study, not a spreadsheet
Quartyl applies the method, PLI and screening steps above as a pipeline — and keeps a documented reason for every exclusion.
Related docs
Interquartile Range (IQR): The OECD Arm's Length Range
The interquartile range defined: the band between the first and third quartiles of the comparable pool — the OECD\'s preferred construction of the arm's length range.
Read docTested Party: Definition, Selection Logic and Documentation
The tested party defined: the entity whose result is benchmarked against the comparable pool — selected as the least complex party, and documented as a decision.
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