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Norman Rothery is the value investor for Globe Investor's Strategy Lab. Follow his contributions here and view his model portfolio here.

A band of swashbuckling accountants took a wrong turn and sailed right off the edge of the world in the Monty Python movie The Meaning of Life. If some value investors are right, a similar fate is in store for North American stocks.

Vito Maida, the president of Patient Capital Management, recently rang the alarm bell in a letter to investors. He painted a dire picture of the U.S. and Canadian stock markets and figures that both are extremely overvalued and pose significant risks to investors.

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It's not uncommon to hear such talk from value investors these days, but only a few do much about it. Mr. Maida is one of the few.

Back in the spring of 2000, near the peak of the Internet bubble, about 90 per cent of his portfolio was in cash. These days he's almost as pessimistic because his firm's new accounts have about 80 per cent of their assets in cash.

While timing the market is always a tricky thing to do well, conservative investors – who want to take on risks when the conditions are right – should think hard about paring back on stocks in the late stages of bull markets.

The problem is, it's easy to bail out too early. If you stick with relatively safe investments such as government bonds and treasury bills for too long, you might give up a lot of upside because stocks have a habit of outperforming over the long term.

According to the Credit Suisse Global Investment Returns Yearbook 2015, Canadian stocks generated average real (inflation-adjusted) returns of 5.8 per cent annually from 1900 to 2014. On the other hand, the real returns of Canadian bonds averaged 2.2 per cent annually and treasury bills clocked in at 1.5 per cent annually over the same period.

The global markets yielded similar returns overall. Global stocks provided average real returns of 5.2 per cent annually from 1900 to 2014, in U.S. dollar terms. Global bonds and U.S. bills saw annual real advances of 1.9 per cent and 0.9 per cent, respectively.

The large return difference between stocks and bonds means that it doesn't take long for fixed income investors to fall behind stock investors. Timers who jump into bonds early can miss out on the upside. Those who jump too late risk tumbling into bear markets.

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Professor Wade Pfau of the American College of Financial Services studied several simple valuation-based timing strategies in the United States that use Professor Robert Shiller's cyclically adjusted price/earnings ratio (CAPE). The results point to some of the benefits, and costs, of timing.

Prof. Pfau's timing strategies move into stocks when the S&P 500's CAPE ratio falls below its rolling median. Alternately, bonds are called for when the ratio moves above its median level.

He considered the results of tilting portfolios to varying degrees. In one case the timers moved to 80 per cent stocks (with the rest in bonds) when the ratio was low, and moved to 80 per cent bonds (with the rest in stocks) when the ratio was high. They outperformed investors who stuck with a half stock and half bond portfolio by about one percentage point per year based on back tests using data from 1871 to 2010. The timers also experienced smaller maximum drawdowns but slightly higher volatility over the same period.

While that sounds like great news, the timing method underperformed the S&P 500 by about 0.5 of a percentage point annually. Mind you, the S&P 500 was admittedly much more volatile and suffered from some huge drawdowns over the period. As a result, many conservative investors would be happy to make such a trade-off.

But the situation today is more extreme because the S&P 500's CAPE ratio hovers near 27, which is much more than its median of 16. It has been higher on only a few occasions.

Conservative investors should think about following Mr. Maida's lead and paring back on stocks because the markets might be sailing into trouble.

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