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What’s the likelihood the stock market this year will experience a 1987- or 1929-style crash?

Evidently quite high, according to billionaire investor Carl Icahn. His net equity position as of the end of March was 150% short—a very aggressive bet that the stock market will plunge.

Nor is Icahn alone. A new study from the National Bureau of Economic Research finds that the average investor believes there to be a greater than one-in-five chance of a huge crash at some point in the next six months. The study, “Crash Beliefs From Investor Surveys,” was conducted by Yale University finance professors William Goetzmann and Robert Shiller (the Nobel laureate) and Dasol Kim, a finance professor at Case Western Reserve University.

Their study is based on surveys conducted periodically since 1989 that asked respondents to assess the risk over the subsequent six months of a 1987- or 1929-magnitude crash. In 1987, of course, the Dow Jones Industrial Average dropped 22.6% in a single session; the 1929 crash involved a 12.8% single-session plunge.

On average over the last three decades, respondents believed there to be a 19% risk of such a daily plunge in the subsequent six months. Though the average probability varied over time, in no single survey did it drop into the single digits. In the most recent survey it was 22.2%, above the historical average.

To put these survey responses into context, consider that the 1987 and 1929 crashes were the two worst one-day plunges since the DJIA was created in 1896. Given that there have been more than 32,000 trading sessions since then, the judgment of at least this swath of history is that in any given six-month period there is a 0.79% chance of a daily crash that severe.

And there’s no reason to believe that the frequency of future crashes will be significantly higher. Xavier Gabaix, a finance professor at New York University, has derived a crash-frequency formula that he believes captures a universal trait of all markets, not just equity markets or those in the U.S. According to that formula, the odds of a 12.8% crash in any given six-month period are 0.92%, almost as low as the actual frequency in the U.S. stock market over the last century.

This means that the average investor over the last three decades has believed a severe crash to be more than 24 times more likely than U.S. history would suggest, and that investors currently believe the risks to be 28 times more likely.

It’s furthermore worth noting that the survey’s respondents weren’t just a bunch of Chicken-Little “sky is falling” investors. When the professors focused on responses from just institutional investors such as Carl Icahn, they found that subjective crash possibilities averaged almost as high—never dropping below 11.2%, for example.

A number of factors contribute to these wildly exaggerated estimates, according to the professors. One is the stock market’s performance over the few months prior to each survey: During bear markets, investors tend to believe crash probabilities are greater. During the dark days of the 2008-2009 Great Recession, for example, the average investor believed there to be a 25% probability of a big crash over the subsequent six months—six percentage points higher than the long-term average.

The news media are another contributing factor, according to researchers. Subjective crash probabilities tended to rise following an increase in the number of recent news-media uses of the word “crash” or other words indicating severe market losses.

These factors are unable to account for all of investors’ exaggeration of crash probabilities, however, since at no point did the average individual investor believe those probabilities to be lower than 13.5%—17 times higher than the probability based on historical frequencies alone.

The bottom line? You almost certainly are more worried about a crash than is justified. While the risks of a crash are certainly not zero, they still are quite low. And very few, if any, of us are able to assess these risks objectively or rationally.

What, then, should you do? You can get lots of answers to this question from the sub-industry that Wall Street created in the wake of the 2008 housing crisis—when talk of “tail risk” and “black swans” became all the rage. A number of firms are eager to sell you investment products designed to protect you against such risk.

Notwithstanding the merits of those specific products, here are a few good rules of thumb:

• No one can confidently predict when a crash may occur, regardless of what they might claim. So the best you can hope to do is insure against tail risks by purchasing one of the myriad products Wall Street has created in recent years. But bear in mind that the insurance carries a cost: You will forfeit longer-term returns.

• It’s therefore OK to “self insure”—provided your investment horizon is at least 10 years. You save the premiums of disaster insurance, and 10 years is most likely more than enough time for the stock market to recover. It may even take a lot less than 10 years, in fact: It took just nine months for the dividend-adjusted average stock to make it to its pre-1987 crash level. In 1929’s case, it took just six months.

• As your investment horizon shrinks as you approach or are in retirement, you should be diversifying your equity portfolio into other asset classes that have low correlations with the stock market. That way you will become less and less vulnerable to a stock market crash.

Scary as another 1987- or 1929-magnitude crash would be, there are plenty of other things that are more deserving of your attention and concern. Investors can own the companies in key U.S. stock indexes by buying the SPDR Dow Jones Industrial Average (ticker: DIA ) exchange-traded fund and SPDR S&P 500 ( SPY ) ETF.

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