Momentum Path Quality: Why How a Stock Moved Matters
Two stocks are both up 60% over the past year. One climbed there through hundreds of small green days. The other sat flat for eleven months, then gapped 40% on two headlines.
Standard momentum cannot tell them apart — it only measures the endpoints. This view measures how the stock travelled, and the difference turns out to matter.
Where the name comes from
Drop a frog into boiling water and it jumps straight out. Put it in cool water and heat it slowly, the story goes, and it never notices.
Investors behave the same way with news. A dramatic one-day move grabs everyone's attention and gets priced immediately. A steady drip of small good news slips past — each day's move is too small to be worth reacting to — so the stock stays underpriced and keeps drifting upward.
This comes from Da, Gurun and Warachka's 2014 paper "Frog in the Pan: Continuous Information and Momentum". In their sample, momentum profits were concentrated almost entirely in the steady-path stocks, and those returns decayed far more slowly in the months that followed.
The Measure: Information Discreteness
The headline number in this view is ID, and it is deliberately simple:
ID = sign(Return) × (% negative days − % positive days)Take a stock that rose over the year. If 60% of its days were green, ID comes out around −0.2. If it gapped once and the rest of the year was a coin flip, ID sits near zero. Lower is smoother.
The sign(Return) term is what makes the number work in both directions. For a falling stock it flips the comparison, so a stock that bled out through many small red days also scores low. That way low always means continuous, whichever way the stock went.
Read it as: low or negative ID = continuous information (the path where drift continues). High ID = discrete information (already priced).
Understanding Each Column
ID is one angle on the question. The other columns come at it differently, so a stock that looks smooth on all of them is smooth in more than one sense.
Return
Cumulative return over the formation window. This is the plain momentum number every other column is trying to qualify.
(close at window end ÷ close at window start) − 1Up Days
How often the stock closed green. A steady grind shows a high share here; a stock that gapped once and drifted does not.
positive days ÷ total trading days in the windowID (Information Discreteness)
The core measure. Low or negative means the stock travelled through many small moves in the direction it ended up — continuous information. High means a few large jumps — discrete information.
sign(Return) × (% negative days − % positive days)Top 3 Days
How much of the whole move came from its three best days. Above 50% means the move was essentially three headlines. Blank for stocks with a negative return, where the share would read backwards.
sum of the 3 largest daily log returns ÷ total log returnTrend Fit (R²)
How closely the path tracks a straight line. Near 1.0 is a steady grind; a low value means the same return arrived through gaps and chop.
R² of log(price) regressed on timePath
The category badge, plus Q if the stock passes the momentum quality screen and J if its gains were jump-driven.
momentum decile × ID rankNote: a blank cell ("—") means the value could not be measured for that stock, which is not the same as zero. Blanks always sort to the bottom, whichever direction you sort in.
Reading the Path Badge
Every stock is ranked twice: once on momentum, once on ID. The badge names the corner it lands in.
Continuous Winner
Long candidateTop-decile momentum reached through many small up days. This is the corner the research says continuation lives in.
Discrete Winner
Momentum likely pricedThe same top-decile return, but delivered in a few jumps. The news was priced the day it landed, so the drift tends to fade.
Continuous Loser
Weakness may persistBottom-decile momentum bled out through many small down days. The mirror image, and the short candidate in the original study.
Discrete Loser
Drift less reliableA large fall concentrated in a few days. Often a single event already reflected in the price.
Neutral
No signalEverything between the momentum extremes. The effect is documented at the tails, so the middle is left unlabelled.
Two extra markers sit next to the badge. Q means the stock passed the momentum quality screen: top-decile momentum, and smoother than the median of its fellow winners. J means jump-driven — its three best days account for at least half the entire move.
Available Time Periods
Each window measures the same thing over a different reach:
| Period | Window | Best For |
|---|---|---|
| 13 Weeks | 63 trading days, ending ~1 month back | Quarterly momentum, faster rotation |
| 26 Weeks | 126 trading days, ending ~1 month back | Half-year trends, the classic 6-1 momentum window |
| 52 Weeks | 252 trading days, ending ~1 month back | The standard 12-2 momentum formation, and the horizon the research was built on |
Why the most recent month is skipped
Every window stops about a month before today. Over very short horizons stocks tend to reverse rather than continue, so including the last few weeks would work against the very effect being measured. Skipping a month is the standard convention in momentum research.
Why there is no 1w, 2w, 4w or 8w here
The New High screen offers those, but they would be meaningless on this page. Over a single week there are only five trading days, so ID can take only a handful of distinct values and nearly every stock ties with every other. The top-three-day share would be close to 100% for everyone. And at those horizons the documented effect is short-term reversal, not momentum — so a "continuous winner" label would point the wrong way.
How to Use This Tool Effectively
Start From the Winners
This is a filter on momentum, not a replacement for it. Momentum picks the candidates; path quality decides which of them to keep. A very smooth stock going nowhere is still going nowhere.
Filter to Continuous Winners
The category pill does the two-way sort for you. This is the corner where the research found the drift, and it is the natural starting list.
Turn On "Exclude Jump-Driven"
This drops stocks whose gains came from two or three sessions. Those overlap heavily with lottery-style names and post-earnings gaps that tend to give the move back.
Cross-Check Against New Highs
The 13w, 26w and 52w periods line up with the New High screen. A stock making a 52-week high that also reads as a continuous winner got there the slow way.
💡 Pro Tips
The tightest screen: Continuous Winners + "Quality momentum only" + "Exclude jump-driven". Expect a short list — that is the point.
Agreement across columns: high Up Days, low ID, low Top 3 Days and high Trend Fit together is a stronger read than any one of them alone.
Watch the disagreements: a high Up Days share with a poor Trend Fit means lots of small green days punctuated by sharp drops. Not the smooth grind it first appears to be.
Compare horizons: a stock that reads continuous at 13w, 26w and 52w has been grinding for a year, not just a quarter.
Behind the Scenes
- • We use adjusted closes, so splits and bonus issues are not mistaken for jumps
- • Windows are counted in trading days, not calendar days, and each ends 21 trading days before the as-of date
- • A stock needs enough history to fill most of the window, so recent listings are excluded rather than ranked on thin data
- • Ranks and deciles are computed within a single period and date. A 13w rank and a 52w rank are not comparable to each other
- • A day counts as a jump only if it clears both three times the stock's own daily volatility and 5% in absolute terms
- • Concentration shares are computed on log returns, which add up cleanly, so "this day was 40% of the move" is a well-defined statement
- • Everything refreshes once a day, after the market closes
Source research
- Da, Gurun & Warachka (2014), "Frog in the Pan: Continuous Information and Momentum", Review of Financial Studies 27(7) — the ID measure and the continuous/discrete split.
- Gray & Vogel, Quantitative Momentum — the momentum quality screen behind the Q marker.
Key Takeaways
- ✓ Standard momentum measures where a stock ended up; this measures how it got there
- ✓ Low ID means many small moves — the path where underreaction, and therefore continuation, lives
- ✓ Jump-driven winners already priced their news and tend to give the move back
- ✓ Use it as a filter on momentum, never as a standalone signal
⚠️ Disclaimer: This is a screening tool, not investment advice. Momentum in every form carries crash risk — it unwinds violently at market turning points — and high turnover. The underlying research was conducted on a specific sample, mostly US data, and how strongly the effect holds on this market is an open question rather than a given. Always consider trend, volume, fundamentals and your own risk tolerance alongside these metrics.