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Popular metrics of market valuation – such as price to forward earnings, price to book value, price to cash flow and cyclically adjusted price to earnings (CAPE) – indicate the U.S. stock market is overvalued by between 10 per cent and 60 per cent. With so many indicators flashing red, what is the likelihood that the stock market may crash?

Normally, it is difficult to determine whether a bubble exists until it is too late. But even if we know we are in a bubble, it is difficult to foresee when it will burst.

In light of this, a recent study on the topic of bubbles and crashes got my attention. Researchers in Taiwan's National Sun Yat-Sen University examined 40 world markets covering 30 years of data and found, not surprisingly, that stock market crashes come in different forms and their causes vary. But they also found that behavioural and certain other issues affecting the workings of the market are more significant than macroeconomic factors in explaining crashes.

They used an investors' sentiment measure from Google searches to get a sense of herding in the markets as a proxy of behavioural biases. They also used market liquidity and volatility as a proxy for market "microstructure" issues; and inflation, current account, growth rate in money supply, industrial production and the unemployment rate for macroeconomic factors.

They defined a "crash event" by examining three-month cumulative returns versus a benchmark based on a formula that includes the standard deviation of those three-month cumulative returns. When cumulative returns are below this benchmark, you have a crash event.

In the 40 markets examined, there were 681 crashes between 1985 and 2015. The average stock market decline was 25 per cent and average duration of the decline was 4.68 months. The impact of the crash was more severe in developing countries than developed countries.

As noted above, the study found that behavioural factors are the most important determinants of both cumulative decline and duration of decline. The higher the irrational behaviour, the greater the probability of a crash. Liquidity and volatility, on the other hand, affect the severity of the crash and the speed of the decline – the greater the liquidity and the smaller the volatility the less severe the subsequent crash. Moreover, the probability of the crash is negatively related to liquidity and positively related to volatility. Macroeconomic factors do not do as well as behavioural and liquidity/volatility factors in explaining a crash.

So what are the proxies for the aforementioned indicators currently saying about the U.S. market?

First, behavioural metrics: The put-to-call indicator stands at 0.76 currently, a multiyear low. This is a sign of bullishness in the markets and may signify that the herd is becoming exuberant. (Put prices are higher when market participants are more pessimistic about the direction of the market.)

In addition, the Google search volume index (SVI) for the question "when to invest" showed an average metric of about 70 over the past two years versus an average of 29 for the years between 2004 and 2014. The last two metrics taken together do indicate that the herd is becoming bullish regarding investing in the stock market, which, according to empirical evidence, increases the probability of a crash.

Second, a liquidity metric: The New York Stock Exchange annualized monthly volume to shares outstanding ratio, a proxy for liquidity, currently stands at 64 per cent, a level which is about the average for the past five years, and much lower than the preceding five years, over which it averaged about 95 per cent. Although liquidity has not changed very much in recent years, this indicator is low from a historical context and signifies an increased probability of a crash vis-à-vis earlier years.

Third, a volatility metric: The Chicago Board Options Exchange volatility index (VIX) currently stands at around 11, the lowest level in years. According to the research cited above, this indicator points against the possibility of a stock market crash.

So will there be a market crash? The proxy indicators based on this academic study give somewhat ambiguous signals about the possibility of a crash, despite the apparent overvaluation of the U.S. stock market.

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.