In March 2000, the Nasdaq peaked at 5,048. Over the next two and a half years it fell 78%. In November 2021, Bitcoin hit $69,000. Twelve months later it was below $16,000. In both cases, the warning signs were visible in the data well before the crash. The problem was that most investors did not know what to look for.

Bubble Watch is our attempt to solve that problem. It combines decades of academic research on financial bubbles into a single daily index that scores bubble risk from 0 to 100 for individual stocks and entire sectors. This article explains the science behind it in plain terms.

What Makes a Bubble a Bubble

Not every rally is a bubble. Stocks go up for legitimate reasons: earnings growth, new products, expanding markets. A bubble is different. It is a self-reinforcing cycle where rising prices attract more buyers, which pushes prices higher, which attracts even more buyers. The fundamentals stop mattering. The price itself becomes the reason people buy.

Academics have studied this pattern for decades, and it turns out bubbles share measurable characteristics. Three research groups, working independently, identified overlapping signatures that appear before crashes. Our system combines all three.

The Academic Foundations

Sornette's Log-Periodic Power Law (LPPLS)

Didier Sornette is a physicist at ETH Zurich who spent his career studying how complex systems fail. Earthquakes, material fractures, stock market crashes — he found that they all share a common mathematical pattern.

His key insight: before a crash, prices do not just go up. They go up at an accelerating rate. The growth itself accelerates. If you plot the returns on a chart, you see the curve bending upward, getting steeper and steeper. Sornette called this "super-exponential growth." It is the mathematical fingerprint of a feedback loop — more buyers cause higher prices cause more buyers.

In a healthy market, a stock might return 15% per year consistently. In a bubble, it might return 15% one year, then 40% the next, then 80%. The rate of growth is itself growing. That acceleration is what eventually becomes unsustainable.

Sornette published this framework in 1997 in the journal Physica A, and later expanded it in his book Why Stock Markets Crash. The model has since been tested against dozens of historical bubbles, from the South Sea Bubble of 1720 to the Chinese stock market crash of 2015.

Our system captures this through what we call the momentum divergence signal: a comparison between how fast a stock has been rising over the past six months versus the past two and a half years. When short-term momentum dramatically exceeds long-term trend, the acceleration pattern is present.

Greenwood, Shleifer, and You: Extreme Returns Predict Crashes

In 2019, three Harvard economists published a landmark paper in the Journal of Financial Economics titled "Bubbles for Fama." The title was a nod to Eugene Fama, who famously argued that bubbles cannot exist because markets are efficient.

Greenwood, Shleifer, and You studied every industry in the US stock market from 1926 to 2014. Their finding was striking: when an industry's price doubles over two years (top decile of returns), it underperforms the market by an average of 15% over the following two years. The more extreme the run-up, the worse the subsequent performance.

But here is the nuance that makes their work so valuable. Not every extreme run-up crashes. The ones that do crash share a specific additional feature: low volatility during the ascent. When prices are surging but the day-to-day fluctuations are unusually calm, that combination is the strongest predictor of a future crash.

This makes intuitive sense. In the early stage of a bubble, everyone agrees on the direction. There is no tug of war between bulls and bears. Prices drift upward smoothly, almost eerily so. Volatility drops because there is no disagreement. This calm is not a sign of health — it is a sign that all the sellers have been exhausted, and when the narrative eventually breaks, there is no one left to buy.

Our system captures this through two signals: extreme returns (has the stock doubled?) and volatility suppression (is volatility unusually low while prices are rising?). When both fire simultaneously, the risk score jumps.

Zhou and Sornette: The Volatility-Return Sequence

More recently, in 2025, a paper by Zhou and Sornette in Applied Sciences formalized the temporal phases of a bubble. Every bubble, they argued, moves through distinct stages: growth, maturity, and pre-crash. Each stage has a different relationship between returns and volatility.

In the growth phase, returns are high and volatility is moderate. In the maturity phase, returns accelerate and volatility drops (the Greenwood pattern). In the pre-crash phase, volatility starts creeping back up while prices still rise — the first sign that disagreement is returning to the market.

Our system uses this research to score how far along the bubble trajectory a stock or sector has moved. A stock with high returns and dropping volatility is in the dangerous maturity phase. A stock with high returns and rising volatility may already be entering the unraveling.

The Five Price Signals

With the academic background in place, here is how the system translates theory into measurable signals. Each stock is scored on five independent dimensions, each producing a value between 0 (no risk) and 1 (maximum risk).

1. Absolute Returns

The simplest signal. How much has the stock gone up in the past year?

A stock that has returned 50% in a year scores 0.33. One that has returned 150% or more scores the maximum 1.0. This captures objectively extreme moves regardless of the stock's history. When NVIDIA returns 200% in a year, this signal notices.

This contributes 25% of the composite score.

2. Price Extension Above the 200-Day Moving Average

The 200-day moving average is one of the most widely followed technical indicators. It represents the average closing price over roughly ten months of trading. When a stock trades far above its 200-day average, it means recent buyers have been paying significantly more than the prevailing trend.

A stock trading 20% above its 200-day average scores 0.5. At 50% or more above, it scores 1.0. The further prices stretch from this anchor, the more violent the snap-back tends to be.

This contributes 20% of the composite score.

3. Returns Relative to Own History

Here is where the system gets context-aware. A 50% annual return means something very different for a volatile biotech stock than for a utility company.

This signal compares a stock's current 2.5-year cumulative return to its own historical distribution. If the return is at the stock's 50th percentile, it scores 0. If it reaches the 95th percentile of its own history, it scores 1.0.

This means NVIDIA showing a 200% return might score lower on this signal than Google showing a 45% return, because 200% is within NVIDIA's historical range while 45% is unprecedented for Google. The signal catches behavior that is unusual for that specific stock.

This contributes 15% of the composite score.

4. Momentum Divergence (The LPPLS Proxy)

This is the most important signal in the system, capturing Sornette's super-exponential acceleration.

It works by comparing two speeds: how fast has the stock been rising over the last six months (short-term) versus the last two and a half years (long-term)? Both are annualized to make them directly comparable.

In a healthy trend, short-term and long-term momentum are similar — the stock is rising at a steady pace. In a bubble, short-term momentum dramatically exceeds long-term momentum — the stock is accelerating. That growing gap between the two is the mathematical signature of the feedback loop.

Like the returns signal, this is scored relative to the stock's own history. A divergence at the 95th percentile of historical divergence scores 1.0.

This contributes 25% of the composite score — the highest weight, because this is the signal most directly tied to the LPPLS research.

5. Volatility Suppression

This signal is scored in reverse: low volatility produces a high risk score. That may seem counterintuitive — should not calm markets be safe markets?

Not according to the research. The Greenwood paper showed that extreme returns combined with suppressed volatility is the strongest predictor of crashes. Low volatility during a rally means consensus. It means there are no dissenters selling, no healthy pushback against the trend. When the narrative eventually breaks, there will be no floor.

If current 30-day volatility is at the 30th percentile of the stock's historical volatility or below, this signal scores 1.0. If it is at the 70th percentile or above, it scores 0.

This contributes 15% of the composite score.

From Signals to Probability

The five signals produce a weighted average between 0 and 1. But a raw average does not behave the way we want — it is too linear. A stock scoring 0.4 on every signal is not really at 40% bubble risk, and a stock scoring 0.9 on every signal is not merely at 90% risk — it is at near-certainty.

To capture this, we pass the weighted average through a sigmoid function. A sigmoid is an S-shaped curve commonly used in statistics. It compresses extreme values and creates a clear threshold around the midpoint.

The sigmoid is centered at 0.4 with a steepness factor of 6. This means:

The sigmoid prevents the system from crying wolf at low risk levels while being appropriately aggressive at high levels. It is the same mathematical function used in logistic regression, one of the oldest and most trusted classification tools in statistics.

The Fundamental Shield

Here is where the system parts ways with purely technical models. A stock can have all five price signals screaming "bubble" and still be reasonably valued if earnings have kept pace with the price.

NVIDIA is the perfect example. Its stock price quadrupled in 2023, triggering high scores on every price signal. But its earnings also grew dramatically — AI chip demand was real, revenue was surging, margins were expanding. The price increase was at least partly justified by fundamentals.

The fundamental shield looks at two things:

Strong fundamental growth pulls the bubble probability down by up to 25 percentage points. Weak or negative growth pushes it up by the same amount.

The adjustment uses a hyperbolic tangent function (tanh) to keep it bounded. No matter how strong the fundamentals, they can reduce the score by at most 25 points — they cannot make a bubble mathematically impossible if all five price signals are at maximum.

This is a deliberate design choice. Fundamentals should temper the signal, not override it. Enron had fantastic earnings growth right up until it did not. The price dynamics have the final word.

Gamma Exposure: The Options Market Feedback Loop

The final layer comes from the options market. When traders buy call options, the dealers who sell those options need to hedge their risk by buying the underlying stock. This creates a feedback loop: rising prices cause more call buying, which causes dealers to buy more stock, which pushes prices higher.

This effect is measured through gamma exposure (GEX) — the net difference between call and put open interest across the nearest expiration dates.

High positive GEX means the options market is amplifying the rally through dealer hedging. It adds up to 25 percentage points to the bubble score. High negative GEX (more puts than calls) suggests the options market is providing natural resistance, and reduces the score by up to 25 points.

This adjustment is based on research by Gârleanu, Pedersen, and Poteshman, who showed in a 2009 paper in the Review of Financial Studies that demand-based option pricing creates measurable feedback effects on the underlying stock price.

Sector-Level Aggregation

Individual stock scores are interesting, but bubble risk is often a sector-wide phenomenon. The dot-com bubble was not about one stock — it was about the entire technology sector. The 2021 meme stock phenomenon swept across dozens of names simultaneously.

Bubble Watch tracks nine sectors: AI and semiconductors, crypto proxies, clean energy and EVs, critical resources (uranium, lithium), defense and aerospace, biotech, space, ETFs, and the Nasdaq top 30.

Each sector's index is calculated as the market-cap weighted average of its constituent stocks. This prevents a small-cap outlier from skewing the entire sector score. A $3 billion company scoring 95% does not move the needle the way a $3 trillion company scoring 75% does.

Reading the Score

The final output is a number from 0 to 100 for each stock and each sector:

0 to 44 — Moderate risk. Normal market conditions. No unusual patterns detected.

45 to 59 — Elevated. Some signals are firing. This is common during healthy bull markets and does not necessarily mean trouble. Monitor.

60 to 74 — High. Multiple signals are active. The price trajectory is starting to diverge from historical norms. Consider reducing exposure or tightening stop losses.

75 to 89 — Danger. Strong evidence of bubble dynamics. Historically, scores in this range have preceded corrections of 15% or more.

90 to 100 — Critical. All signals are at or near maximum. In historical testing, scores above 90 have never been sustained beyond two to four weeks before a significant crash:

What the System Does Not Do

Bubble Watch is a risk measurement tool, not a timing tool. It can tell you that bubble risk is at 85%, but it cannot tell you whether the crash will start tomorrow or in three months. Bubbles can persist longer than rational analysis would suggest.

It also cannot detect fundamental fraud. A company fabricating its earnings will have a strong fundamental shield right up until the fraud is discovered. The price signals would still fire, but the fundamental adjustment would mute them.

Finally, the system is trained on historical patterns. A genuinely novel type of bubble — one that does not follow the acceleration-then-complacency pattern — would not score correctly. The research suggests this pattern is deeply rooted in human psychology and unlikely to change, but no model can guarantee coverage of events it has never seen.

Daily Updates

The Bubble Watch index updates every weekday. At 3:30 AM UTC, a scheduled job pulls the latest price data, recalculates all five signals for every tracked stock, applies the fundamental shield and gamma adjustments, computes the market-cap weighted sector averages, and publishes the results. By the time markets open, the day's risk assessment is ready.

The data is available on the Bubble Watch page, which auto-refreshes every five minutes. Each sector page shows the aggregate index, the individual stock scores, and a breakdown of which signals are driving the reading.

Why This Matters

Markets have always had bubbles. Tulips in 1637, railroads in 1845, radio stocks in 1929, dot-coms in 2000, housing in 2007, crypto in 2017 and 2021. The pattern repeats because the underlying driver — human psychology reacting to rising prices — does not change.

What has changed is our ability to measure it. The academic research of Sornette, Greenwood, Zhou, and others has given us rigorous, testable models for identifying bubble dynamics as they develop. Bubble Watch translates that research into a practical tool that anyone can check every morning alongside the market open.

It will not tell you to sell. It will not predict the exact top. But when five independent signals — extreme returns, price extension, historical anomaly, momentum acceleration, and volatility suppression — all point in the same direction, that is information worth having.

References

  1. Sornette, D., & Johansen, A. (1997). Large financial crashes. Physica A, 245(3-4), 411-422.
  2. Sornette, D. (2003). Why Stock Markets Crash: Critical Events in Complex Financial Systems. Princeton University Press.
  3. Greenwood, R., Shleifer, A., & You, Y. (2019). Bubbles for Fama. Journal of Financial Economics, 131(1), 20-43.
  4. Zhou, W.-X., & Sornette, D. (2025). A Case Study of Bubble Risk Indicator. Applied Sciences, 15(10), 5613.
  5. Gârleanu, N., Pedersen, L. H., & Poteshman, A. M. (2009). Demand-based option pricing. The Review of Financial Studies, 22(10), 4259-4299.

Bubble Watch is an analytical tool for educational purposes. It measures statistical patterns associated with historical bubbles but cannot predict future market movements with certainty. Past patterns do not guarantee future outcomes. All investment decisions carry risk. Always consult with a qualified financial advisor before making investment decisions.