Researchers cracked the code on predicting market bubbles. Here’s what it’s saying about today’s stock prices.

Alan Greenspan will perhaps be remembered most for concluding that stock-market bubbles could only be identified after the fact — and not coincidentally, for not doing enough to prevent the internet-stock bubble from forming and then bursting.

Read more: Alan Greenspan’s legacy as Fed chair: the ‘Greenspan put’ and a shift to overprotecting markets

Most Read from MarketWatch

This is a complicated chapter in Greenspan’s almost 20-year leadership of the Federal Reserve, since he initially thought that bubbles could be forecast. His instincts eventually were confirmed by academic research. Also to his credit is inviting Yale University professor Robert Shiller in December 1996 to give a now-famous lecture to Fed staffers about stock market overvaluation, which led Greenspan in turn to give his infamous “irrational exuberance” speech about stock investors —more than three years before the top of the internet-stock bubble in early 2000.

Greenspan ultimately changed his tune, and Wall Street came to count on the Fed to provide a safety net under the market, no matter how overvalued it might be. The Fed came to the rescue during the 1997 Asian financial crisis and after the 1998 bankruptcy of Long-Term Capital Management. Traders began referring to the “Greenspan put,” and felt secure enough to continue investing in sectors even after they reached ridiculous overvaluations. Almost certainly, one consequence of the Greenspan put was that, when the internet-stock bubble burst, it was much more severe than it would have been otherwise.

The academic research confirming Greenspan’s initial instinct about market bubbles, “Bubbles For Fama,” was published in early 2017. The researchers studied the frequency of bubbles in the market’s different sectors, since the market as a whole has experienced so few bubbles that it’s almost impossible for any conclusions to have statistical significance. They focused on all instances since 1926 in which a sector outperformed the broad market by at least 100 percentage points over a two-year period.

The results: in 53% of these cases, the sector crashed within the subsequent two years, as defined by dropping by at least 40%. This crash probability rose to 76% when a sector’s trailing two-year alpha rose to 125 percentage points, and to 80% when its trailing two-year alpha got as high as 150 percentage points.