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Robert A. Olstein finds the arguments for index funds personally insulting.

“What do you mean I can’t beat the market?” he says angrily. A forensic accountant-turned-mutual fund manager, he doesn’t aim to do as well as everybody else. “That’s mediocrity,” he says.

Olstein knows that very few investors manage to beat the market consistently, which is why so many people have poured so much money into index funds – more than $3 trillion, including traditional mutual funds and exchange-traded funds, according to the Investment Company Institute.

Such funds mirror the market, and that is enough – or so the thinking goes. Don’t even try to do better than average, because you probably won’t succeed. That’s the crux of the argument for using these funds to capture overall market returns, and it’s based on decades of academic research, including the work of Eugene F. Fama, one of the finance professors receiving the Nobel in economic science.

Nobel or not, Olstein is far from convinced. To the contrary, he says the rise of index funds is part of a trend toward sloppy investing – a willingness to follow the herd, to rely on momentum in a rising market.

“It’s like saying mediocrity is OK – that it’s more than OK; it’s the best that anyone should hope for,” Olstein says. “It’s saying a guy like me can’t beat the market – that he shouldn’t even bother trying. That’s wrong! It really ticks me off. I can beat the market. I have beaten the market.”

And, in fact, he has – not every year and certainly not every week or every quarter, but over the long run, which, in his case, started in September 1995. That’s when he founded the Olstein Financial Alert fund, now known as the Olstein All Cap Value fund. From its inception through November this year, including fees, his flagship fund returned 10.7 percent, annualized. That’s more than 2.4 percentage points better than the Standard & Poor’s 500-stock index and substantially better than comparable small-cap indexes.

It’s also slightly better than the comparable performance of shares of Berkshire Hathaway – a company headed by another value investor, Warren E. Buffett. Berkshire returned 10.3 percent, annualized, during that same period, according to Bloomberg data.

It hasn’t all been smooth sailing for Olstein. “I’ve made mistakes,” he readily acknowledges.

Olstein’s particular approach relies on skills that he says are “practically extinct.” They were honed as an auditor with the old Arthur Andersen & Co. and then, in the 1970s, as co-author of The Quality of Earnings, a financial newsletter that shed light on the murky areas of corporate accounting.

While he is aware of macroeconomic trends, he takes a bottom-up approach that isn’t very fashionable these days.

“On Wall Street, so many people are basically just momentum investors, looking for growth and following whatever is trending up,” he says. “The market is becoming a casino. I don’t play that game. I care about specific companies and whether they are good buys at their price, and if they are, we’ll hold on to them.”

Olstein looks for stocks that are underappreciated and that are strong in a metric he has always favored: “free cash flow yield.” (It is cash, after subtracting capital expenditures and working capital, divided by market capitalization.) “Cash is king,” he says. “That’s what you’re paying for when you buy a stock – the ability to generate cash. But few people even bother with it these days.”

He says he prefers “boring companies” - if their free cash flow excites him. One such company is John Deere, the agricultural equipment maker. He estimates that its free cash flow yield is about 7 percent, a very high level, and that it’s likely to grow to 10 percent over the next three years. Its recent prices have been depressed by temporary phenomena like poor weather and low corn prices, which have slowed worldwide equipment purchases. Over the long haul, though, with global population swelling and demand for food increasing, he says, the odds are good that Deere will rise in price.

He contrasts Deere with Cisco Systems, the Internet hardware company. Deere has been boring for decades, he says, while Cisco was one of the most exciting companies in the stock market in the late 1990s. Back then, he took a bearish view on Cisco – correctly, as it turned out.

“Too many people were excited about it,” he says. “It was a good fast-growing company, but there wasn’t enough free cash flow to justify the price of a share.”

While Deere shares have quadrupled in price since those days, Cisco is trading at a small fraction of its former price. Now, though, Cisco has become boring, too, he says, growing at only a modest pace but generating cash. Olstein now holds its shares.

He doesn’t buy initial public offerings, and he’s stayed clear of Twitter. “It might be a good company, but I don’t see the cash flow, not yet,” he says.

Most armchair investors aren’t able to do his kind of detailed financial analysis, he says, and he thinks that most professional investors don’t do it, either. But scores of money managers do, and he advises amateurs to find them. Turn to a pro for work like this, he says.

“I don’t try to fix my own teeth or cure myself when I’m sick. I go to a dentist, and I go to a doctor,” he said. “Find somebody good and go to them.”

Buffett, of course, is one of the good ones. And there are other veterans with long, proven track records, Olstein says. Active, value investing isn’t extinct yet.

But his success, and that of others like him, doesn’t disprove the academic theories that underlie index funds. In a recent conversation, Fama, the Nobel laureate, told me it’s not impossible for someone to beat the market consistently. It’s just not likely. There’s no way to know whether an investor like Olstein has been successful because he is skillful or just lucky.

“It could be an anomaly,” Fama said. “Life isn’t long enough to be able to tell for sure.”

Olstein doesn’t enjoy hearing that.

“The professors don’t advise their students to settle for mediocrity at school or in other aspects of their lives,” he says. “Why do it in investing?”