Despite equity valuation ratios that suggest stocks are in nosebleed territory, it's actually a good bet the market will produce decent returns over the next decade. That's the implication of a recently completed study that argues investors have been incorrectly interpreting stock market valuation formulas -- such as the price/earnings ratio; the cyclically adjusted P/E, or CAPE, ratio; the dividend yield; and the Buffett Indicator, to name a few. Entitled " The Hidden Trend in Stock-Market Cash Flows," the study was conducted by Sebastian Hillenbrand of Harvard's Business School and Odhrain McCarthy of NYU's Stern School of Business.

Consider the P/E ratio, which for the S&P 500 index currently stands at 25.2 -- suggesting significant overvaluation. After all, it is far higher than the average of 16.2 since 1871, according to data from Yale University's Robert Shiller, and higher than 92% of all prior monthly readings back to 1871.

That analysis is misguided, according to the professors. Their core argument is that valuation ratios' fluctuations are caused by two separate developments, and Wall Street largely focuses on just one of these two: the well-known market cycle that oscillates between bull and bear markets. From this perspective, a higher ratio -- such as the P/E -- indicates that the market has become more richly valued and its expected future returns have become correspondingly lower.

The second development -- the one that's largely ignored -- is the long-term trend of increasing earnings growth rates. According to the study's authors, a higher valuation ratio does not necessarily mean that the market's expected future return has deteriorated -- but could instead mean that corporate earnings are expected to grow at even faster pace in coming years.

Consider that recent decades' average P/E ratio is nearly double what prevailed 150 years ago. The S&P 500's average P/E over the past 30 years is 25.7, for example, versus 14.7 over the last 30 years of the 19th century. Some of the increase since then undoubtedly reflects a faster earnings growth rate.

In recent decades, as you can see from the chart below, the S&P 500's earnings per share have grown at a 7.0% annualized pace; the comparable pace over the last decades of the 19th century was an annualized 0.6%. The P/E ratio therefore deserves to be markedly higher -- to compare its current level with what prevailed more than a century ago is comparing apples and oranges.

It's not easy to separate out what portion of today's higher P/E ratio is due to increasing valuation and how much is due to a faster earnings-growth rate. The professors employed sophisticated statistical methods to do that, and interested readers are directed to their study for details. But the bottom line, Hillenbrand told Barron's in an interview, is that the forecasting power of the valuation ratios jumps markedly once you adjust for the effects of faster earnings growth. Absent that, Hillenbrand pointed out, most of the most popular valuation ratios have out-of-sample track records that are statistically indistinguishable from a coin flip.

There's another consequence of adjusting valuation ratios for the long-term trend toward faster earnings-growth rates: It increases their forecasted returns. To illustrate, Hillenbrand calculated the five- and 10-year return forecasts of the unadjusted P/E ratio. Absent that adjustment, the stock market is projected to be largely flat in coming years. After adjusting, according to Hillenbrand, the stock market's forecasted five-year return grows to 7.0% annualized, and the forecast 10-year return grows to 7.7% annualized.

Though these returns are modestly below the stock market's long-term average of around 10% annualized, they are far better than the negative returns that many of the valuation indicators are otherwise forecasting.