Guide · Indicator method · Updated 2026-09-20

Twenty five is a property of the smoothing period you chose, not a property of a trending market

What the reading computes, and the two averages stacked inside it

Three quantities come out of each session. True range is the largest of the high to low span, the distance from the high to the previous close, and the distance from the low to the previous close, so a gap counts as range rather than vanishing. Upward directional movement is how much the high rose, counted only when it rose by more than the low fell, and zero otherwise. Downward movement is the mirror. At most one of the two is non zero on any session: the inputs compete, they do not add.

Each series is then accumulated by the same recursion, which subtracts one fourteenth of the running total and adds the new session. Dividing each accumulated movement by accumulated range gives the two directional indicators. The directional index is the absolute gap between them over their sum, scaled to a hundred, and the published reading is that index put through the same recursion a second time.

Two properties follow and neither is optional. The first is that the reading is directionless: the gap is taken in absolute value, so the arithmetic cannot tell a clean advance from a clean decline. On this record the median was 22.7 where the upward indicator was on top and 22.6 where the downward one was, a difference of 0.12 of a point, and the record's highest reading, 62.8, came on the downward side against a highest upward reading of 52.9. Anyone treating a rising reading as bullish is reading a number that does not carry the information.

The second is that the reading is slow in a quantifiable way. The recursion with weight one over fourteen is algebraically an exponential average of span twenty seven, and it runs twice. The weight the finished reading places on each earlier session is the convolution of two such kernels, and that weighting has its centre of mass 26 sessions behind the present, half of it more than 22 sessions back and a tenth more than 51 sessions back. Nothing about the market produces that figure. It falls out of the period, before any data is seen.

A clean fall reads like a clean rise, and the turn reads highest of all

The directionless property has a consequence generic treatments omit. If the reading is high when a move has been one sided, it peaks just as a one sided move finishes, and a turning point is the end of a clean move.

That is measurable. Locating every turn with full hindsight, by a rule that ends a leg when the close retraces more than 3 average true ranges from its running extreme, gives 115 pivots. The median reading at the pivot itself was 24.5 against 22.6 across all sessions, and 48 per cent of pivots fell on a session already reading 25 or more, against 40 per cent generally. The strength measure is elevated at reversals, not depressed. Pairing it with the direction indicators is not a refinement; it is the minimum required to stop it pointing the wrong way at the wrong moment.

Where twenty five actually sits in the Indian record

The pair of numbers in circulation, twenty and twenty five, reached us through the indicator's 1978 exposition and decades of repetition. Wherever they came from, they were not derived from Indian index data, and the only way to learn what they say about it is to compute the distribution.

The fourteen period reading across 3,358 sessions has a median of 22.6 and a mean of 24.5, a tenth percentile of 14.4 and a ninetieth of 37.8, and never once exceeded 62.8 against a ceiling of a hundred. Against that distribution 20 sits at the 37th percentile and 25 at the 60th, so the two conventional lines separate the bottom 37.2 per cent of sessions, the middle 22.5 per cent and the top 40.2 per cent. A rule flagging two sessions in five as trending is not identifying an unusual state; it is splitting the record a little above the middle. Not a reason to abandon the indicator. A reason to stop quoting a percentile as though it were a property.

Change only the period and the same number means something else

The curves make the mechanism visible. A shorter average cannot smooth away as much of the peak in the directional index, so its distribution sits higher and a fixed line cuts it further down. Same sessions, same arithmetic, same index. Only the length of the averages changes.

Across those five settings the percentile of 25 travels 61 points, from the 25th to the 85th, and the share of sessions flagged falls from 75 per cent to 15 per cent. A page quoting a threshold without the period beside it has not stated a rule at all.

The argument runs one level down, to the recursion itself. Wilder's weight of one over the period is a convention; an exponential average with the customary weight of two over the period plus one is another, and both circulate under the same name. On identical sessions at period 14 the two differ by a median of 8.4 points, with a ninetieth percentile gap of 18.9, and they disagree about whether the reading is above 25 on 35.3 per cent of sessions. The exponential version has a median of 31.0 and puts 25 at its 27th percentile, because two over fifteen is a far shorter effective average than one over fourteen. Same finding: effective averaging length sets the level.

A broad index against a sector index

Whether a sector index needs its own threshold is the obvious next question. It does, and the correction is far smaller than the period effect, which is itself the useful result.

The spread across ten indices is 10 percentile points, from the 51st on the realty sector index to the 61st on the midcap index, against 61 points across five periods on one index. The direction is sensible: the more concentrated sector indices trend more cleanly by this measure, so their distributions sit higher. But a reader choosing between a per index threshold and a per period one should know which choice actually moves the answer.

One further cut contradicts an intuition the construction invites. The indicator divides by true range, so it ought to be indifferent to volatility. Sorting sessions into thirds by the previous session's published volatility index reading, the median was 21.3 in the calm third, 22.7 in the middle and 24.5 in the stressed third, with the share above 25 rising from 35 to 48 per cent. Normalising removes the size of the moves, not the tendency of disturbed markets to travel one way.

The lag, measured twice by two unrelated instruments

The centre of mass figure comes out of the arithmetic alone, so it needs a second opinion from the data. Take the directional efficiency of a fourteen session window, net distance travelled over distance actually walked: one for a straight line, near zero for a round trip. Then ask which window today's reading describes best, by shifting it through time and ranking the association at each offset.

The association peaks at +0.38 when the window ends 6 sessions in the past, placing the described stretch centred about 13 sessions behind the reader. For the window ending today it is +0.26. It crosses zero about 6 sessions into the future and stays mildly negative: at fourteen sessions forward, -0.08. Against absolute net travel in average true ranges rather than efficiency, the same asymmetry appears, +0.30 looking back against -0.03 forward.

Two instruments sharing no arithmetic, both placing the reading's content behind the reader. That is not a criticism; it is what a double smoothed average is for. The error is in the language around it, where a crossing is called a signal that a trend is beginning when the arithmetic can only report that one has been running for a while.

How much of the move was already over

Correlation is abstract. The same lag goes into the currency a reader cares about. Keeping the 112 hindsight legs of at least five sessions, find for each the first session on which the reading exceeded a threshold with the matching direction indicator on top, and measure how much of the leg's travel had been delivered by then.

At the 25 line, 62 of 112 legs confirmed and 50 never did. Of those confirmed, the median had delivered 59 per cent of its travel by then, 65 per cent were more than half done, and median remaining travel was 3.0 average true ranges against 4.3 already spent. Raising the line to 30 cuts confirmations to 45 and the median lag rises from 10 sessions to 18. Lowering it to 20 confirms 92 legs at a median 7 sessions with 51 per cent of travel gone. The trade is monotonic and no setting escapes it, which is why no threshold is recommended here.

Those legs were identified after the fact with the whole record visible, and nobody watching in real time knows where a leg started until well after it did. The measured lag is a floor.

How long a crossing lasts, and whether that makes it actionable

A slow reading can still earn its place if a crossing means something durable. One that clears a line and falls back within two sessions is noise dressed as a state change, so measure the spells.

This part of the picture favours the indicator. At the 25 line the record holds only 55 spells in 3,358 sessions, median length 13 sessions, mean 25 pulled up by a longest spell of 112, with 9 per cent ending within three sessions and 64 per cent lasting ten or more. The reading does not flicker. Whatever it describes, it describes for weeks at a time.

Note what happens as the line rises. At 30 the share of spells dying within three sessions jumps to 19 per cent, more than double the figure at 25, because a higher line is crossed near the top of the distribution where the series spends least time. At 35 it falls back to 4 per cent, but on only 23 spells in the whole record, which is a small sample announcing itself rather than stability returning. A stricter threshold can land in the flicker band without the chooser noticing, and a percentile table shows none of it. The spell count is also the honest measure of the evidence: 55 spells is not 3,358 independent observations, and any claim conditioned on the reading being above 25 rests on something nearer the former.

A calibrated threshold is still fitted to a sample

Everything above argues for deriving a threshold from the index's own distribution rather than importing one. That is the right direction and not an escape: a percentile has to be estimated, and an estimate carries its sample.

The seventy fifth percentile, the statistic such a rule would use, ranged from 23.7 in 2026 to 36.0 in 2020, and the percentile at which 25 falls ran from the 33rd in 2014 to the 80th in 2022. In 2014 the conventional line caught 67 per cent of that year's sessions, which is no filter at all; in 2022 it caught 20 per cent. Same line, same index, opposite behaviour.

The out of sample test settles it. Estimate the seventy fifth percentile on the first half of the record and it comes out at 30.9. Carry that into the second half and it lands at the 80th percentile, because the second half's own figure is 28.6. Run it the other way and the second half's threshold lands at the 67th percentile of the first. A rule meant to flag the top quarter of sessions flagged 20 per cent instead. Smaller than the error from importing across markets and eras, and not zero.

Window choice makes it worse. A window covering 2020 to 2024 gives a seventy fifth percentile of 29.94 here, almost exactly the full record's 30.00. Applied to sessions from 2025 onward it lands at the 86th percentile, flagging 14 per cent of sessions where it was built to flag twenty five. The year table says why: 2020 carries the record's highest seventy fifth percentile at 36.0 and 2026 its lowest at 23.7, so a threshold estimated over a span carries that span's average rather than the present.

This governs every fitted parameter and is not a quirk of this indicator. Searching a grid of thresholds and keeping the best inflates whatever survives, and a threshold still has to beat the right null, which for a percentile rule means beating one drawn at random from the plausible range. A calibrated number is a better stated rule than an imported one. It is not a discovered constant.

The method, stated so a reader can run it

No setting is recommended here, because the measurements above make any recommendation a claim about a sample. The procedure is what can be handed over.

Fix the implementation first. Write down which recursion you use, since the two conventions disagree on the 25 line on 35.3 per cent of sessions, and confirm your arithmetic reproduces a worked session by hand as in the first table. Fix the period next, on grounds unrelated to the result: how long a move has to run before you want to hear about it. That choice, not the threshold, sets both the level of the series and the lag of every crossing.

Then compute the distribution on the index you actually intend to use, over a window long enough to hold several volatility regimes, and express the threshold as a percentile rather than a number, re-estimated on a rolling or expanding basis so it cannot encode a period you already saw. Measure the spells as well as the percentiles, because a line producing single session bursts is not describing a state. Measure the lag against legs identified independently, and accept the figure rather than tuning the threshold until it looks acceptable, since that is how a calibration becomes a fit. Then write it down, because a result that cannot be re-derived from its stated inputs is an opinion with decimals.

Used that way the indicator does something real. What it will not do is tell you what happens next, and no threshold reaches the lag, because the lag is in the arithmetic. Classifying a market state and reading a result conditioned on it are where this measurement earns its place, and both need the lag quantified first.