Paul Tudor Jones II leans back in his chair and grins. The stock market is going to crash, and he knows it. “There will be some type of a decline, without a question, in the next 10, 20 months,” he says in his rich Memphis drawl. “And it will be earth-shaking; it will be saber-rattling.”

Coming from a financial speculator as prominent as Mr. Jones, a man with about $19 billion of short-term trading capital at his disposal, the words might be enough to send ripples through a stock market that, apparently defying logic, has been hitting new highs each day.

Except that the crash to which Mr. Jones refers occurred Oct. 19, 1987. His prognostication — brazen, and as impudent as the man himself — was made in a documentary called “Trader,” which was filmed in the year preceding that day.

Now, 20 years after the 508-point decline, several strategists are anticipating that the earth will shake again. Valuations are stretched beyond historical comparisons. The market, ever more volatile, is reaching new highs, ignoring a buildup of bad news. Most crucially, the strategists say, the sentiment that the market’s rise is infinite seems to have taken permanent hold.