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"Nowhere does history indulge in repetitions so often or so uniformly as in Wall Street. When you read contemporary accounts of booms or panics, the one thing that strikes you most forcibly is how little either stock speculation or stock speculators today differ from yesterday. The game does not change and neither does human nature."

Edwin Lefevre, a business journalist, wrote those words back in 1923. Just as he predicted, little has changed since then.

The Dow Jones industrial average recently celebrated the fourth birthday of its current bull market. Between March 9, 2009, and March 8, 2013, the index rose by 129 per cent, making this bull market one of the longest and strongest in history.

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Many wonder whether investors are getting carried away and another bubble is forming that will inevitably end in a crash, just like so many before.

It's a reasonable fear. But a bubble isn't just a period of strongly rising prices; it's when there is a significant deviation between an asset's fundamental value and its price.

Bubbles appear to be rooted in human nature. Nobel laureate Vernon Smith has demonstrated in laboratory experiments that investors are momentum traders. They chase whatever has been going up and avoid whatever has been losing ground, a process that eventually leads to bubbles and market crashes in Prof. Smith's market simulations.

As his experiments suggest, it can be infernally difficult to spot an overvalued market when you're in the middle of one. How can anyone know what the fundamental value of the stock market is, and when you're paying too much?

Actually, there is a reasonable answer to this question. Fundamental value depends both on corporate profits and on the return that investors expect to reap from investing in the stock market. Put another way, fundamental value is a function of how many dollars companies are generating in earnings, and how much investors are willing to pay for each dollar of those earnings.

Corporate profits are driven by several factors: how the economy is doing, the state of the labour market and the level of commodity prices. As profits go up, so do share prices.

At the same time, investors' expectations for the return they can reasonably expect to pocket is usually tied to the current level of interest rates. As interest rates fall, so does the expected return. This, in turn, pushes up the price that investors are willing to pay for a dollar in earnings – the so-called price-to-earnings multiple, or P/E. As the P/E multiple rises, so do share prices.

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The U.S. Federal Reserve's aggressive bond buying in recent years has resulted in record-low interest rates and therefore exceptionally low expected returns.

Meanwhile, corporate profits are booming because of declining commodity prices and a weak jobs market that has driven down the cost of labour – in fact, the share of U.S. GDP going to labour income is at its lowest level in 50 years.

Put strong corporate profits together with low expected returns and today's market levels appear somewhat rational. Because of low interest rates, the expected returns from the stock market are at record-low levels. A typical expected return nowadays is about 7 per cent. Assuming for simplicity that we expect no profit growth, this implies the market should be trading at a price-to-earnings multiple of 14.3.

During more normal times, when interest rates were substantially higher than they are now, a typical expected return would have been around 12 per cent. Under the no-growth assumption, this implies a market P/E of 8.3 – almost half of what it is today.

Essentially, low interest rates have boosted the P/E multiplier, inflating the value that investors put on a dollar of profits vis-à-vis earlier years. Meanwhile, weak labour and commodity markets have pushed up corporate profits. So what appears to be a bubble may not actually be.

The problem? When the economy starts to recover, all the forces that helped drive up share prices will go into reverse.

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When the Fed signals it's confident enough of the recovery to raise interest rates, investors are likely to drive down stock prices because higher rates will mean a lower P/E ratio. Moreover, the increasing wages and higher commodity prices that would result from a stronger economy may hurt corporate profits, pushing stock prices down further.

The surprising result is that a stronger economy may mean a much weaker stock market. And what is not a bubble today may quickly turn into one.

George Athanassakos is a professor of finance and holds the Ben Graham Chair in Value Investing at the Richard Ivey School of Business, University of Western Ontario.

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