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Stocks are considerably cheaper than they were a few months ago, but not as cheap as many optimists would like to think.

Investors should keep this in mind as they contemplate how much to bet on the market rebound continuing.

The bullish case focuses on how inexpensive stocks appear in comparison with their expected earnings per share over the next year. For instance, Canadian stocks are near their cheapest levels in five years if you look at what analysts are expecting over the next few months.

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This is indubitably comforting. So is precedent on Wall Street.

Lori Calvasina, head of U.S. equity strategy at RBC Capital Markets, says it is highly unusual for the S&P 500 to fall two years in a row. “Since the 1930s, down years in the S&P 500 have been followed by up years 74 per cent of the time, with a median gain of 15 per cent,” she noted in a report on Wednesday.

So why worry? For all the comforting readings on what to expect over the next few months, share prices still look lofty on some sophisticated measures of value.

A few of these valuation gauges were recently highlighted by O’Shaughnessy Asset Management in Stamford, Conn. In its January letter, the money manager and market researcher compared four ways to assess whether U.S. stocks are cheap or expensive.

The most conventional method is to look at how share prices stack up against operating earnings over the preceding 12 months. By that yardstick, U.S. stocks are trading at 16.17 times their trailing earnings, which is a mere 10.7 per cent more expensive than they have been on average between 1952 and 2018. Not much to fret about there.

However, a more worrisome picture emerges if you examine how much the average investor has allocated to stocks. This measure, which compares the total supply of stocks in the economy to the total supply of all financial assets, including cash and bonds, has historically been a good predictor of future returns, according to O’Shaughnessy. When allocations are unusually high, future returns tend to be low, and vice versa.

Right now, the average investor equity allocation suggests caution. It is about 24.2 per cent above its historical average.

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More red lights flash if you examine how share prices compare with their average inflation-adjusted earnings per share over the past decade. This measure, known as the cyclically adjusted price-to-earnings ratio, or CAPE, says stocks are more than 43 per cent above normal levels.

A similar story is told by a yardstick known as price to retained earnings, which compares the market’s price with the sum total of its retained earnings over its history, adjusting all numbers for inflation. This, too, suggests that share prices are about 43 per cent above where history suggests they should be.

These are intimidating comparisons and show why many observers are downbeat about the long-term results that investors can expect from here. But some caveats are important.

One is that the most glaring signals apply to U.S. stocks, but not necessarily Canadian or other international shares. Most analysts don’t see the same level of overvaluation in markets outside the United States.

The lower valuations on international stocks may not provide immunity against downturns – in a crisis, stocks around the world tend to move in unison – but they do suggest that eventual losses are likely to be lower outside of the United States if valuations ever do revert to historical norms.

An equally important caveat is that valuation gauges like this are “useless over the short term,” according to O’Shaughnessy. Expensive markets can go on getting more expensive and vice versa. It’s only over periods of a decade or more that valuation bites.

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One way to bridge the gap between short term and long term is to assume that we are late in the business cycle but not at its end. Volatility is normal at a time like this, but it’s still possible to make money if you stick to bigger, more solid companies in the largest, most heavily traded markets.

This is the view of PIMCO LLC, the giant bond manager. It sees opportunities in U.S. stocks over the next 12 months but argues investors should focus on high-quality, defensive, large-cap names. It’s also fond of the outlook for oil and metals, including gold.

“Typical of late cycles, one has to be more selective and prudent in one’s investments,” PIMCO asserts in its outlook for 2019. That sounds about right.

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