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Eli had recently lost a tooth and also had come home with this mask of cut paper. We had been discussing the tooth fairy: Who is she? What form does he or she take? Does she fly? Walk? Is it a boy or a girl? Eli felt she was white, like a tooth in some way, and we made some photographs with the white shirt he had on, white mask, hovering around our backyard fence. We looked at the pictures, and he felt it wasn't really the tooth fairy but us trying to guess at the tooth fairy's shape in a photograph.
Eli had recently lost a tooth and also had come home with this mask of cut paper. We had been discussing the tooth fairy: Who is she? What form does he or she take? Does she fly? Walk? Is it a boy or a girl? Eli felt she was white, like a tooth in some way, and we made some photographs with the white shirt he had on, white mask, hovering around our backyard fence. We looked at the pictures, and he felt it wasn't really the tooth fairy but us trying to guess at the tooth fairy's shape in a photograph.
Timothy Archibald / Redux Pictures

It's widely accepted as fact that fundamentals like earnings and economic growth matter to stock prices.

So how do you explain that while Europe was mired in recession in 2012, equities there soared more than 20%? Or that U.S. corporate profits grew at a subpar 3% last year as stocks surged 16%?

It turns out, this seeming disconnect is more the rule than the exception, economists at the mutual fund company Vanguard found. They studied the stock market back to 1926 and determined that, when it comes to predicting market moves, variables such as GDP growth, earnings trends, and profit margins are about as useful -- and in some cases much less so -- as tracking rainfall is.

"We're not saying fundamental factors don't matter," says Roger Aliaga-Díaz, a study co-author and Vanguard senior economist. Rather, it's that using fundamentals to predict the future doesn't work because so many other factors can drive returns above or below historical averages for long stretches.

Related: Is it too late to get in on Pimco's bond ETF?

Market earnings forecasts aren't useful either. Not only are analysts overly optimistic, but they "tend to move in herds -- they don't want their forecasts to be that different from what others are saying," says Jason Hsu, chief investment officer at Research Affiliates. Thus earnings growth expectations tend to be close to one another and already priced into stocks.

So what fundamentals should you be looking at?

Consider valuations. If betting on your assessment of market fundamentals is folly, wager against others' opinions by using price/earnings ratios.

"With a really cheap market, investors are saying that things are going to be bad -- and will stay bad -- for a long time," says Ben Inker, co-head of asset allocation for the investment management firm GMO. "Conversely, a really expensive market assumes that things are going to be better than expected for some time."

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But over 10-year periods, excessively cheap or expensive markets tend to reverse course. Indeed, Vanguard's study found that among all fundamental factors, the price/earnings ratio that uses an average of 10 years' worth of earnings (known as the Shiller P/E, after the Yale economist who popularized it) comes closest to predicting market performance, and its record is mixed. Right now, that P/E predicts modest returns.

Focus on the small picture. Just because earnings trends can't help you divine broad market moves doesn't mean they're useless in analyzing individual stocks, says Simon Hallett, chief investment officer at Harding Loevner.

At the company level, a quarter or two's results can tell you something about the future. Sure, a profit or sales decline might be due to management missteps that can be fixed. If the business is losing ground to competitors, though, that could speak to its earnings growth -- and stock price -- for years to come.