Models that predict bubbles: Shiller CAPE, LPPLS and their limits

Why use a bubble detection model instead of an opinion?

A model states its inputs and its rule, so a second person can rerun it and obtain the same signal. An opinion cannot be rerun. This repeatability lets you test a model on past bubbles, count its hits and false alarms, and decide how much weight it earns. The test takes an afternoon and removes much guesswork. Keep the results in a log, so that the next quarter starts from evidence and not from memory.

Models also separate two questions that opinions mix. The first question is whether prices stand high against some measure of value. The second is whether growth has become unstable. The two models in this page answer one question each, which is why using both gives a fuller picture than using one.

How does the Shiller CAPE ratio measure a bubble?

The cyclically adjusted price-to-earnings ratio divides a price by the average of 10 years of earnings, adjusted for inflation. Economist Robert Shiller popularized it. The long average smooths booms and recessions, so the ratio shows whether today’s price is high against what a company earned across a full cycle.

A high reading says that buyers pay a lot for each unit of long-run earnings. Investors use it as a gauge of stretch for a whole market. It works as a thermometer: it shows heat and leaves the cause and the date to other tools. Many analysts compare the current value with its own history and with the level of other markets, which shows whether heat is local or global.

Where does the Shiller CAPE ratio mislead on AI stocks?

The ratio looks backward. Ten years of earnings describe a company whose business may have changed, and AI leaders have grown faster than their history suggests. A young AI firm may lack 10 years of profits, which makes the ratio unusable for it. Accounting changes and buybacks also shift earnings over a decade.

The ratio also fails on timing. A market can stay at a high reading for years, so a high value alone gives no date. Use it to size how much heat a market holds and to compare AI-heavy indexes with their own past, then pair it with a model that watches the pace of the climb. Add a note on which sectors weigh most in the index, since a few AI names can lift the whole ratio.

How does the LPPLS model detect a bubble?

LPPLS stands for log-periodic power law singularity. Physicist Didier Sornette pioneered it, and researchers later applied it to financial bubbles. The model treats a faster-than-exponential rise, with oscillations that come closer together, as the signature of a bubble. It fits a curve to the price history and estimates a critical time at which the pattern can no longer continue.

The idea is that herd behaviour feeds on itself: rising prices attract buyers, and buyers lift prices further. The growth rate itself keeps rising, which no real business can sustain for long. The model looks for that unsustainable acceleration and reports how closely the data follow it. A close fit raises the alarm level, and a loose fit lowers it.

What are the limits of the LPPLS bubble model?

The fit depends on choices: the window of data, the starting point, and the parameters. Small changes can move the estimated critical time by months, so serious users run many windows and look for agreement across them. A single fit proves little, and a published date from one fit deserves caution.

False alarms occur when a strong rise follows real news, because the curve looks like a bubble pattern while the cause is sound. The model flags a fragile state and cannot name the event that ends it. Treat its output as a range and a probability, and log every alarm with its outcome. After a year of logs you can state the hit rate of the model on your own watch list.

What can a bubble detection model not tell you about AI?

Price-based models see prices, so they miss the real economy behind them. They cannot see whether customers pay, whether projects reach production, or whether a rule will raise costs. The EQOS Asia AI study fills part of this gap with structural data: 95% of AI projects fail in production, and the market scores φ(S) = 0.337 (EQOS Asia AI study, April 2026).

Models also miss what is new. AI has features earlier bubbles lacked, such as very large capital spending on data centres funded by a few firms. The page on whether a model can spot a bubble covers how a decision engine adds these structural inputs to price signals.

How can you combine bubble detection models in practice?

Run three layers each quarter. Read the CAPE level against its own history for the heat. Run LPPLS on several windows for the acceleration. Add a structural score for the real economy. Write the three results in one table with the date. When all three point the same way, your confidence rises. When they split, you know where to dig.

Then judge the models themselves. The page on who predicted past bubbles correctly shows how to keep a record of hits and misses. For your own case, the Λ simulator returns a score in about 10 minutes, and the EQOS Asia method page explains the computation. This page is general information, not investment advice.

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About the author

Stéphane Jambu

President, EQOS Forecast Asia

Stéphane Jambu leads EQOS Forecast Asia and works as a consultant in e-commerce, search visibility, and AI. LinkedIn profile