This is good news for the many wine collectors out there. According to U.S. Trust’s Insights on Wealth & Worth study, 13 percent of all high-net-worth households collect fine wine. Of that group, 49 percent said they saw the wine as an investment. (The rest planned to drink it.)

But more than an affirmation that great wines appreciate as they age and become scarcer, the study found something unique. Great vintages rose quickly in value during the first couple of decades, which might be expected, but wines from mediocre, even bad, vintages started to catch up to the great ones after 50 years.

For the first 25 years, the good vintages were about 3 percent more expensive than the bad ones for each year of age. That price difference began to narrow around 50 years.

“There is a degree of convergence because 100-year-old bottles of wine rarely get drunk,” said Elroy Dimson, co-director for the Center of Endowment Asset Management at the University of Cambridge’s Judge Business School and one of the study’s authors. “But they look quite good on display.”

Another reason for this convergence of price was greater scarcity of the bad vintage than the good one, Mr. Dimson and his co-authors Peter L. Rousseau of Vanderbilt University and Christophe Spaenjers of HEC in Paris, found. “Suppose there was a poor-quality vintage — people had the good sense to drink it before it turned to vinegar,” Mr. Dimson said. “But if you want a vertical run of vintages, you might pay more than you ought to for one you need.”