Breadth · 52-week extremes
High-Low Index, The Bounded Extremes
New highs as a share of all issues at a yearly extreme. Bounding the counts is what lets a reading from this decade be compared with one from the 1970s, and it is also what the index throws away.
The calculation
high-low index = new highs ÷ (new highs + new lows) × 100, usually with a ten-day moving average on top.
Fifty means the two counts were equal. A hundred means every issue that reached a 52-week extreme reached it on the high side; zero means the reverse. Everything that did not reach an extreme — which on any ordinary session is the overwhelming majority of the list — never enters the arithmetic at all.
What bounding buys, and what it costs
The trade is exact and worth seeing in a table rather than described.
| New highs | New lows | Raw net | High-low index |
|---|---|---|---|
| 400 | 100 | +300 | 80.0 |
| 4 | 1 | +3 | 80.0 |
| 300 | 280 | +20 | 51.7 |
| 6 | 5 | +1 | 54.5 |
Rows one and two are the whole argument in both directions. As a comparison across decades the index is right and the raw net is not: 80 per cent of extremes on the high side means the same thing on any list, in any era. As a description of the day in front of you the raw net is right and the index is not: five hundred issues at yearly extremes is a market doing something, and five is a market doing nothing.
Rows three and four add the case that ruins a smoothed reading. With denominators that small, one issue changing sides moves the index by ten points, so an extreme reading on a quiet day is an artefact of arithmetic. The counts are the check, and they take one glance.
The rolling window, again
Both inputs are 52-week counts, so the index inherits the artefact described on the new highs and lows page: the bar for a "new high" moves every day as old data drops out of the back of the window. A year after a severe decline the comparison period contains that decline, and new highs become mechanically easier to reach.
The effect on this index is a step rather than a drift, because both counts change at once and in opposite directions. A reading that shifts substantially on a date with no market significance (an anniversary of a crash, say) is describing the calendar, and it is worth checking the date before interpreting the level.
Reading it over a period rather than a day
The daily value is rarely the thing worth looking at. What the index is good for is a stretch: six weeks in which it has held above 70 describes a market where the issues reaching yearly extremes have been overwhelmingly on the high side, and that is a statement about participation with a fixed meaning in any era.
Two habits make that usable. Read the smoothed line for the condition and the raw counts for whether it mattered, a stretch above 70 on ten issues a day is a different market from the same stretch on three hundred. And date the change: writing down the session on which a long run above 70 ended converts an impression into something that can be checked later, including on the occasions when nothing followed it.
Where it misleads
| Situation | What goes wrong |
|---|---|
| Small denominators | With a handful of issues at extremes, one changing sides moves the index ten points. Smoothing hides this rather than fixing it. |
| Scale discarded | 500 issues at extremes and 5 produce the same reading. Keep the raw counts on the same screen. |
| Rolling-window step | A year after a crash the comparison period contains it, and both counts shift for calendar reasons. |
| Read as independent of the counts | It is a transformation of them. Agreement between the two is one observation seen twice. |
| Newly listed issues | An issue with less than a year of history cannot set an extreme, so heavy listing periods shrink both counts. |
| Non-operating issues | Funds and preferreds set yearly extremes on rate moves, not on business performance. |
The pattern this page shares with two others
Three measures in this section deliberately throw information away, and it is worth seeing them together because the discipline is the same each time. This index discards the scale to gain comparability. The absolute breadth index discards the direction to isolate unanimity. The advance/decline line discards the size of each company to count participation.
In every case the thing discarded is what somebody else’s measure is for, and the reading is only safe when you know which. That is the argument for reading two of them rather than one, and for never treating two views of the same input as two pieces of evidence.
Frequently asked questions
How is the high-low index calculated?
New 52-week highs divided by the sum of new highs and new lows, expressed as a percentage, and usually smoothed with a ten-day moving average. Fifty means the two counts were equal; 100 means every issue at a yearly extreme was at a high; 0 means every one was at a low. Unchanged issues and everything that did not reach an extreme are simply not in the calculation.
Why bound it at all: what is wrong with the raw counts?
The raw counts carry the size of the exchange list. Two hundred new highs is a broad market on a list of 1,500 issues and an ordinary session on a list of 3,500, and the American exchanges have changed size substantially through waves of listings, delistings and the growth of funds and preferred issues. Dividing the counts by each other removes the dependence, which is what makes a reading from one decade comparable with one from another.
What does the index lose by being bounded?
Whether anything was happening at the extremes at all. A session with 400 highs and 100 lows and one with 4 highs and 1 low both read 80. The first describes a market with 500 issues at yearly extremes; the second describes a quiet day with five. The ratio is comparable across time precisely because it has thrown away the scale, and the scale is sometimes the more interesting half, which is why the raw counts belong on the same screen.
Why is it usually smoothed?
Because the daily reading is extremely noisy when both counts are small: with 6 highs and 4 lows the index reads 60, and one issue changing sides moves it ten points. A ten-day average makes the series legible and is the form almost every published version plots. The smoothing does not fix the small-denominator problem, it only hides it, which is a reason to look at the counts before trusting a smoothed extreme.
What levels are read?
Fifty is the only level with a definition rather than a convention behind it. Readings that hold above about 70 or below about 30 describe stretches in which one side of the extremes has dominated for weeks. The smoothed series spends most of its life between those markers, so reaching either is uncommon without being rare enough to act on by itself.
How does it relate to the raw new-high and new-low counts?
It is the same data with the scale divided out, so the two are not independent evidence. The counts answer "how many issues are at yearly extremes"; the index answers "of those, which side". Reading both is the sensible practice and treating their agreement as confirmation is not, since one is a transformation of the other.
Does the rolling 52-week window distort it?
It distorts both counts and therefore the index, in a way worth knowing. The threshold for a new high moves every day as old data leaves the back of the window, so a year after a severe decline the comparison period contains that decline and new highs become mechanically easier to reach. A step in the index on a date with no market significance is usually the calendar rather than the market.
Is it useful for timing?
No more than any breadth measure, which is to say rarely and mostly at extremes. Its strength is descriptive: it says whether the issues reaching yearly extremes have been predominantly on one side, over a period, in a form that can be compared with any other period. Reading a crossing of 50 as a signal produces the same long series of premature calls that every other breadth crossing does.