Can history offer a guide to understanding future stock-price bubbles? The answer is yes, but we have to learn how to bend time. Thankfully, a method called dynamic time warping offers a solution. Previous bubbles occur at different paces: some rise fast and others slowly; some crash after weeks while others persist for years.

By stretching and shrinking the timeline of thousands of bubble events, we systematically place them side by side and find more commonalities in their attributes‘ patterns than a calendar view suggests. We then use various attributes collectively to assess the likelihood of a developing bubble and identify its lifecycle stage, from inception to peak to conclusion. A simple trading rule seeking to invest in bubble run-ups and post-crash over reactions, while avoiding the peak, generates compelling performance in out-of-sample backtests.
 

Key highlights
Imagine that two people read aloud the same passage from a book. One speaks fast but takes long pauses between sentences. The other speaks slowly but races through exciting parts. We can all recognize that they are telling the same story.

Eventually computers learned this skill, often using a technique called dynamic time warping. Finding the similarities between fast and slow is not only useful for speaking or music – it helps with understanding bubbles in financial markets, too.

We identified more than 2,500 bubbles in stock prices since 1973, each of which crashed by at least 50 percent. Though the price paths all look like mountains, they have different speeds and contours up and down their sides. We use statistical time warping to compare every bubble to every other bubble, considering more than 6 million bubble pairs, and we mark new normalized time steps in each case. Then, using these synchronized views, we record the distribution of all 6+ million outcomes for 20 attributes at each standardized time interval of the life of a bubble. Stock attributes like investor flows and EPS growth have clear shapes in which they tend to rise and fall, on average, and none of this is apparent from comparisons in standard calendar time.

Thus, stock characteristics offer clues as to whether a bubble exists now in a particular stock, and whether it is near the beginning, peak or conclusion of its price path. We estimate the phase of a stock bubble, as it occurs, by comparing its set of observed attributes (fundamentals, analyst ratings, flows, sentiment and more) to the hallmark values of those same attributes at different stages of prior bubbles. A strategy that aims to hold stocks for the first 80 percent of their run-up and avoid getting caught in the crash beats the market in backtests, as shown in the Exhibit above. So does a strategy that holds stocks at the end of their bubble lifespan, which have overshot in losses. Bending time can be profitable.