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There is a mystery afoot in the stock market, one that should concern anyone who invests in actively managed mutual funds.

The mystery boils down to this: Most of these funds appear to be deliberately ignoring much of the research about how to beat the stock market. Presumably the managers know all about this research. They just choose to go in a different direction.

This odd situation is the focus of a recent working paper from Martin Lettau and Paulo Manoel of the University of California, Berkeley, and Sydney Ludvigson of New York University. Their paper asks, “Where are the value funds?” and points out that there are virtually no funds on the U.S. market that actually hold only cheap stocks, even among the funds that label themselves as value investors.

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The same contrariness holds true with other factors that academics have found to be important in determining investment returns. For instance, researchers have demonstrated that investors can benefit from momentum strategies that buy stocks that have shot up in recent months. But most funds don’t appear to take advantage of this anomaly either.

The researchers conclude that their survey of actively managed U.S. mutual funds reveals “that these funds do not systematically tilt their portfolios towards profitable factors.” And, no, the researchers don’t understand why.

The mystery is deepest in the case of value funds. Many shelves of academic research have demonstrated that one of the more dependable ways to beat the market, at least on paper, is to buy cheap stocks and shun expensive ones.

Academics typically define value stocks by looking at book value, an accounting yardstick that measures the difference between a company’s assets and its liabilities. Businesses with a high amount of book value in comparison with their stock price are classic value plays because they are cheap in terms of the amount of book value you’re buying for your investment dollar.

The research tends to show that buying stocks with high book-to-market ratios results in superior returns. But funds – even the funds that swear they’re die-hard value investors – don’t actually seem to do this. Instead, Prof. Lettau and his colleagues discovered that most value funds hold more of their portfolios in expensive growth stocks than in cheap value investments.

At the very least, this demonstrates the importance of looking beyond labels and examining what a fund actually owns. But it still leaves open the mystery of why funds act this way.

One explanation comes from Dan Rasmussen, portfolio manager at Verdad Advisers in Dallas. He argues that value funds, in particular, face a structural problem: Many cheap stocks come from smaller “microcap” businesses, with limited amounts of shares and limited trading volumes.

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This poses a challenge for any fund manager seeking to invest lots of money. A manager like this can’t simply load up on the market’s cheapest stocks, because they would overwhelm the supply of these microcap investments and drive up prices, thereby destroying the value appeal of what they are trying to buy.

“To put it simply, the cheapest stocks are disproportionately small in terms of size and volume,” Mr. Rasmussen writes. “This means that an active manager looking to choose, say, the best 40 of these stocks would be unable to manage more than $200-million or so.”

Big fund companies don’t want to limit themselves in this way. They want to attract billions of dollars in assets, not just a couple of hundred million. The only way to find strategies with the capacity to handle such large amounts is to use different definitions of value.

Other forces may be in play as well, particularly in the Canadian market. The classic academic definition of value, the one that focuses on book value, doesn’t appear to work on this side of the border. Canadian stocks that look extremely cheap in comparison with their book value tend to have a hard time keeping up with the broad market, according to a 2014 report by Travis Fairchild of O’Shaughnessy Asset Management. Over several decades, Canadian investors have simply not been rewarded for buying these apparent bargains.

This raises the possibility that Canadian funds are actually being quite wise in avoiding these book-value wonders. But it’s still not clear how many cheap stocks are in a typical value-oriented fund. You should look carefully at the actual holdings of any fund that bills itself as a value proposition.

If you don’t like what you see, consider building your own value portfolio. My colleague Norman Rothery wrote a fascinating story last year that looked at simple value strategies that beat the Canadian market over the preceding 15 years.

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Mr. Rothery found that someone who made a practice of buying the 20 stocks with the lowest price-to-earnings (P/E) ratios on the S&P/TSX Composite Index every year, then selling them a year later, and reloading with a new group of low P/E stocks, would have beaten the broad market by five percentage points a year. There are, of course, no guarantees this stunning performance will continue. But if you want to ensure you have a true value portfolio, there is no surer way than to build your own.

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