Don’t try to beat the stock market.

That, briefly, is the gospel according to Jack Bogle, the founder of Vanguard. He added that the best approach for the great majority of investors was to hold stocks and bonds in broadly diversified, low-cost index funds that mirror the market and to forget about picking individual stocks.

Many investors, including Warren Buffett, have accepted those principles. Basically, even in the middle of a pandemic and a tumultuous election season, I do too.

That belief has been reaffirmed by a new Yale study, which, as I’ll explain in a moment, suggests that it is even more difficult for successful fund managers to stay ahead of the market than is commonly understood.

Obviously, it is possible to outperform the stock market. Buffett beat it for years at Berkshire Hathaway, though he hasn’t managed to consistently outperform the S&P 500 lately, and he says most people shouldn’t even try.

Still, people try every day, and some generate fabulous returns.

For example, buying only Apple stock and nothing else would have put you leagues ahead of the S&P 500 over the 20 years through July 30, with an annualized return of 27.5% for Apple versus 6.3% for the index.

That would have been a dangerous bet, however. Imagine if the iPhone had faltered or the Apple Watch had bombed. Your shares would have plummeted in value. Wagering all of your money on one stock — or even 20 of them — is much riskier than an investment in the entire market.

Few people manage to beat the overall market steadily and reliably, without taking on greater risk, especially once the costs of investing are factored in. And while you can beat the market — and the index funds that track it — the data shows that most likely, you won’t manage to do it for very long.

That said, one factor worked well in the past for those attempting to defy the odds and beat the market fairly often. In a word, it is momentum.

That is, hold an actively managed mutual fund — one for which managers select stocks — that beat the market the previous year. That simple strategy was documented in a landmark study published in 1997 and taught widely in business schools.

That study, “On Persistence in Mutual Fund Performance,” by Mark Carhart, then a professor at the University of Southern California and now an asset manager, found that funds that rose in one year tended to rise in the next one, mainly because the stocks they held did the same thing.

Its findings seemed to defy the standard warning that “past performance doesn’t predict future returns” and prompted many people to scour past mutual fund returns in hope of scoring big future profits.

Well, don’t bother.

That’s the message of the new study by James Choi, a finance professor at Yale, and Kevin Zhao, a graduate student there. Their paper, “Did Mutual Fund Persistence Persist?” follows directly in the footsteps of Carhart, who studied mutual fund returns from 1962 to 1993. They examined what happened from 1994 until 2018 and found that the momentum effect in mutual fund performance that Carhart discerned is no longer apparent.

In an interview, Choi told me that, like finance teachers around the world, he has been instructing students about the “momentum effect” in fund performance for years. One day, though, he had something of an epiphany.

“I was teaching a class about ‘the momentum effect’ and realized that I was basing everything I was saying on a study that was done more than 20 years ago, based largely on findings from 30 or more years ago,” he said. “I thought it was time to check and see whether it still worked.”

He and Zhao found that the strategy does not work in picking mutual funds; in fact, Choi said, its effectiveness had diminished appreciably by about 1980, an apparent precursor of worse returns in subsequent years.

The research, available as a working paper, is to be published in the journal Critical Finance Review. Carhart, who reviewed it for the publication, called it “very solid. The efficacy of the momentum effect has declined over time. That’s in the data, and I buy that.” He added that the strategy is no longer effective for picking mutual funds.

Even when it did work, it was generally because fund managers held onto hot stocks from year to year, he said, not because managers were consciously and systematically attempting to harness the momentum of the stock market.

This isn’t the end of the story, however.

There is evidence that the momentum effect continues to operate in the stock market. Choi said that while stock-picking fund managers — those who run actively managed funds — haven’t been able to exploit the momentum factor lately, some index funds have.

This gets a little wonky. Bear with me for a moment.

While the first Vanguard index funds were set up to capture the returns of broad stock market indexes, these days index funds come in all manner of shapes and flavors. Some use algorithms to execute complex strategies.

There are now index funds that have been set up to use a momentum strategy — for example, one that winnows the highest performing stocks over the previous six and 12 months — on the assumption that they will outperform the broader market for the next six months.

One such fund is the iShares Edge MSCI USA Momentum Factor ETF. It’s got a solid track record: a 16.3% annualized return since its inception in April 2013, more than the S&P 500, which had an annualized return of 13% in that period. The fund has an expense ratio of just 0.15%.

Choi said he holds that fund in his own portfolio.

“Momentum isn’t dead,” he said. “It seems to work; it just hasn’t been working in actively managed mutual funds.”

Will this form of momentum investing continue to operate effectively for the foreseeable future? Maybe. I’m intrigued but skeptical. I think the standard warning is worth taking seriously: Don’t rely on past returns to predict future performance.

The safest bet is a simpler one: Invest in plain-vanilla, broad, low-cost index funds in a portfolio allocated appropriately between stocks and bonds for your own goals and risk tolerance.

This doesn’t guarantee that you will prosper. While stocks have risen over long periods, they sometimes have calamitous declines — most recently, in February and March of this year. When the stock market falls, you will lose money in stock index funds.

But that’s why it makes sense to allocate some of your money to bond funds, which, as I’ve pointed out in a recent column, have performed exceptionally well over the last 20 years. No one knows what the next month will bring — to say nothing of the next 20 years — so it is wise to hedge your bets.

One thing the new research certainly shows is that picking mutual funds based on recent performance doesn’t make sense, while long-term investing in the overall market through low-cost index funds still does.

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