“If you look at the data, hedge funds have underperformed a simple 60/40 stock/bond mix every year for the past 10 years,” Mr. Lack told me this week. “They did well in the downturn of 2000-2. But that’s when assets under management were less than half what they are now. There’s no disputing that as assets have grown, performance has declined.”

Not surprisingly, Mr. Lack’s analysis has come under attack by a vast industry that depends on steering clients into alternative investments, among them the London-based Alternative Investment Management Association, a lobbying group that issued a detailed rebuttal. But Mr. Lack said he stood by his methodology, and pointed out that many of his critics had a financial stake in maintaining the status quo. Mr. Keating, who doesn’t advise endowments or pension funds, said he agreed with Mr. Lack. “He’s very controversial, but I found his analysis persuasive.”

Among those raising questions about the Ivy League model and its heavy dependence on alternative investments is Vanguard, the giant mutual fund company that has long promoted a radically simpler approach based on low-cost index and mutual funds. “I feel that there was endowment envy, or maybe emulation is a better word,” Francis M. Kinniry Jr., a principal in Vanguard’s Investment Strategy Group, told me this week. “Everybody wanted to look like the Yales and Harvards of the world. But they were early. They were doing these techniques in the mid-1990s and late 1990s when equities looked overvalued, and alternative strategies could capture market imperfections. That’s no longer true. Those universities were forward-looking and deserve a lot of credit. But emulating that process three, five or seven years later is very problematic.”

Even David Swensen, Yale’s chief investment officer, who is widely viewed as the godfather of what has become known as the Yale model, has cautioned that few could expect to replicate Yale’s results, because Yale had access to top managers whose doors were closed to all but a favored few. Mr. Kinniry agreed. “Because of their size and relationships, and the ability to commit to a continuing investment cycle, Harvard, Yale, M.I.T. and Notre Dame have unique access.”

It’s true that Harvard’s and Yale’s endowments, in contrast to most smaller endowments, have outperformed a simpler and more conventional mix of stocks and bonds, and a Harvard spokesman noted that over the last 10 years, Harvard’s endowment had generated over $12 billion more than a 60/40 model would have.

But that may be hard to replicate in the future, even for the Harvards and Yales of the world, since even access to top managers is no guarantee of future performance. “They’ll have to be very good at manager selection,” Mr. Lack said, “because there’s been very little return persistence. I looked at one-third of the hedge fund industry. Of those in top 40 percent of returns, only 7 percent stayed there throughout the period.” A recent example is the billionaire hedge fund manager John Paulson, who after a spectacular bet against mortgage-backed securities in 2007 attracted millions from investors, but then suffered crushing losses last year. “He deserves credit, but he had one great trade and that was it,” Mr. Lack said of Mr. Paulson. “He should have quit and done something else for a living.”