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The time has come to talk about U.S. stock valuations because we now have some unsettling metrics in our hands.

On Friday, the U.S. Commerce Department said that U.S. gross domestic product grew by just 1.2 per cent in the second quarter, far lower than the 2.5-per-cent growth that analysts expected. This is the third consecutive quarter of disappointing GDP growth – the U.S. economy grew by 0.8 per cent in the first quarter and by 0.9 per cent in the fourth quarter of 2015.

Just as troubling is the growing reluctance by companies to invest in capital and inventory (investments that lay the groundwork for future growth). Gross private domestic investment (which includes residential investment by landlords) declined by 9.7 per cent in the second quarter. This also follows declines in the first quarter and in the fourth quarter of last year of 3.3 per cent and 2.3 per cent, respectively.

Not surprisingly, corporate earnings are under pressure, too. Trailing 12-month operating earnings per share for the S&P 500 are down 5.4 per cent since peaking in the third quarter of 2014.

None of this means that the U.S. economy and corporate earnings will necessarily weaken further. But if they do, stock prices are likely to react badly.

So, how badly?

One way to think about the potential danger is to look at how much investors are currently paying for U.S. stocks. The simple logic is that the more expensive stocks are, the more room they have to fall.

The problem is that stock valuations don't just fall out of the sky. The price-to-earnings ratio for the S&P 500 is one of the most – if not the most – widely followed gauges of U.S. stock valuations. Still, ask 10 market observers to tell you the S&P 500's P/E ratio and you're likely to get 10 different answers.

Everyone agrees on price, of course, but the devil is in the earnings. For starters, different accounting conventions spit out different earnings numbers. "Operating" earnings, for example, exclude non-recurring income and expense, whereas "as reported" earnings do not. And on and on and on – accounting conventions take myriad shapes.

There's an even more fundamental stumbling block in the quest for those elusive earnings. A useful P/E ratio is one that reflects next year's earnings, but predicting earnings is a tricky business because earnings are nearly as volatile as stock prices. The S&P 500's operating EPS has had a standard deviation of 11.8 per cent since 1990 whereas the S&P 500 index has had a standard deviation of 14.5 per cent over the same period. (A higher standard deviation indicates more volatility.)

Since no one has a crystal ball, investors have had to find other ways of divining future earnings. Some look to analysts' estimates; others assume that the prior year's earnings are the best estimate of next year's earnings; still others use an average of the last several years' earnings.

Which raises the question: Which one comes closest to hitting the mark? I looked at the predictive powers of all three methods from the second quarter of 1996 to the second quarter of this year (the longest period for which data are available) by comparing each method's estimated operating earnings for the S&P 500 to the actual resulting operating earnings.

What I found was that prior year earnings were most predictive of the following year's earnings over the entire period. The 12-month trailing EPS understated actual EPS by an average of 4 per cent. By comparison, analysts overstated actual EPS by an average of 13 per cent, and a seven-year trailing average EPS understated actual EPS by an average of 17 per cent.

During the most turbulent periods, however, the trailing average earnings were most predictive. The seven-year trailing average EPS understated actual EPS by an average of 5 per cent from 2001 to 2002 and by an average of just 2 per cent in 2008. By contrast, the 12-month trailing EPS overstated actual EPS by an average of 11 per cent from 2001 to 2002 and by an average of 29 per cent in 2008. And analysts badly missed the mark on both occasions, overstating actual EPS by an average of 24 per cent from 2001 to 2002 and in 2008.

Investors concerned about overpaying for stocks will find value in thoughtfully estimated earnings. Just look at the effect of earnings estimates on P/E ratios. Based on Monday's closing price for the S&P 500, analysts' estimated EPS for next year of $125 (U.S.) results in a P/E ratio of 17.4. The 12-month trailing EPS of $107 (with two-thirds of companies reporting for the last quarter) results in a P/E ratio of 20.3, while a seven-year trailing average EPS of $96 results in a P/E ratio of 22.6. Those may not seem like big differences at first glance, but note that it would take a market decline of 23 per cent – a bear market and then some – to go from a P/E ratio of 22.6 to a P/E ratio of 17.4.

Investors may not care much about valuations while U.S. stocks are notching new all-time highs, but they may feel differently when fortune turns. And with the economy and corporate earnings flashing warning signs, now is probably a good time to ask what assumptions are baked into your P/E ratio.

Nir Kaissar is a columnist with Bloomberg News.

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