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An electronic sign shows the Dow Jones Industrial Average at the New York Stock Exchange.

MIKE SEGAR/Reuters

One of the big reasons to be bullish on Canadian and U.S. stocks right now, we hear, is the low valuations. But are stocks really so cheap?

A Bloomberg News article on Monday pointed out that the S&P 500 was well below its average valuation, for numbers going back to 1950 – which is presumably a reference to the index's price-to-earnings ratio, or P/E.

The P/E ratio provides a nice snapshot of where share prices are in relation to earnings. And yes, the S&P 500's ratio is a tantalizing 13.6 right now, based on estimated earnings, which is below the long-term average of about 15.

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But Robert Shiller, an economics professor at Yale University, has created a different way of looking at P/E ratios, taking the business cycle into account. His approach – often referred to as cyclical adjusted P/E, or CAPE – takes the current price and divides by the inflation-adjusted earnings averaged over the previous 10 years.

Using this approach, the S&P 500's P/E ratio fell below 15 during the depths of the bear market meltdown in 2009, but has since rebounded to about 21 (at the end of June). In other words, the S&P 500 is no longer cheap after rebounding about 100 per cent from its bear market low.

Blogger Mebane Faber (via Abnormal Returns) used this approach for 32 indexes and then ranked them from lowest P/E to highest. The U.S. market is the most expensive in the developed world. Canada isn't far behind, with a P/E of 17.6.

This can be a big deal, since many observers believe that price-to-earnings ratios give a good indication of future returns. That is, a high P/E ratio can suggest that future returns will be slim or non-existent while a low P/E ratio can suggest relatively robust returns.

This is partly why global asset manager GMO believes the average annual returns for U.S. large-cap stocks will be a mere 0.8 per cent over the next seven years, after taking inflation into account. The average return is 6.5 per cent. For small-cap stocks, expectations are even lower, with an average expected loss of 0.5 per cent a year.

But what's interesting about U.S. stocks – and Canadian stocks, too – is that they stand in contrast to cheap valuations elsewhere, particularly in Europe. Again, using 10-year earnings, Mr. Faber calculated that the U.K. and Germany have P/Es below 13, France has a P/E below 11, Netherlands is close to 9 and Spain is below 9. And Greece? Its P/E is just 3.3.

Okay, cue the skepticism: If Greece's stock market is supposed to be a great value because of a low P/E, then just maybe there is something wrong with this indicator. Mr. Faber evidently felt a twinge of skepticism as well. In June, he looked at all cases where cyclically adjusted price-to-earnings ratios were below 5 at the end of the year. There were just nine examples, includng the U.S. in 1920, the U.K. in 1974, Thailand in 2000 and Greece today.

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"Can you imagine investing in any of these markets in those years? Me neither," he said. "In every instance the newsflow was horrendous and many of these countries were in total crisis."

Yet, on average, these markets rose 35 per cent in the next year, and 20 per cent annualized over the next five years.

For what it's worth, there is at least one exchange-traded fund that tracks the Greek stock market: the Global X Greece ETF (ticker: GREK). It's up 30 per cent since June 5!

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