The New York Stock Exchange on Oct. 19, 1987 © Maria Bastone, AFP, Getty Images

A trader holds his head on the floor of the New York Stock Exchange on Oct. 19, 1987, after the Dow crashed 22.6%.

Prepare yourself for another stock market crash as big as the free-fall in October 1987.

That's a daunting prospect, indeed. At current levels, such a decline would mean a plunge in the Dow Jones Industrial Average ($NDU) of more than 3,000 points in a single trading session.

And we're kidding ourselves if we think that market regulatory reforms such as circuit breakers will be able to prevent it.

These sobering truths are what emerge from a fascinating line of recent academic research into the frequency of market crashes. Recognizing them is perhaps the best way for us to respect this week's 25th anniversary of the Oct. 19, 1987, "Black Monday" crash, when the Dow plunged 22.6%.

This research traces to "A Theory of Large Fluctuations in Stock Market Activity," a study you can find on the Social Science Research Network that was conducted a decade ago by Xavier Gabaix, a finance professor at New York University, and three scientists at Boston University's Center for Polymer Studies: H. Eugene Stanley; Parameswaran Gopikrishnan, and Vasiliki Plerou.

In numerous follow-up studies, Gabaix said in a telephone interview earlier this week, the original findings have only been strengthened.

No way to stop losses

The researchers crafted a complex mathematical formula for predicting the frequency of large daily stock market movements. Though they believe their formula rests on a solid theoretical foundation, the proof of the pudding is in the eating. And they found that not only does the U.S. stock market over the last century closely adhere to the formula, so do international markets.

A single-session drop of at least 20%, for example, is predicted -- over long periods -- to occur once every 104 years, on average, but it could happen at any time. That's why you always have to prepare for it, because you don't know when it will occur.

If the frequency of crashes of various magnitudes is predictable, shouldn't precipitous slides also be preventable?

Gabaix says no. Crashes are an inevitable feature of the investment arena because every market, to a more or less similar degree, is dominated by its largest investors. When those large investors collectively want to get out of stocks, which will happen on occasion, they will find ways to circumvent any downside protections, such as circuit breakers, that may be in place.

Gabaix therefore recommends that all of us -- whether individuals or large institutional investors, such as banks and mutual funds -- cushion our portfolios so that a crash as large as 1987's wouldn't be fatal.

Unfortunately, he added, for most investors that's easier said than done. Those cushions are a drag on portfolio performance as long as the market doesn't plunge. After big stretches in which no major crash occurs, the pressure becomes overwhelming to toss out those cushions in pursuit of short-term profits.

The bottom line? Regulators are tilting at windmills in trying to formulate reforms that would prevent large daily market drops. Even worse, these regulatory efforts lull gullible investors into a false sense of security.

Repeat after me: Another stock market crash as big as 1987's is going to happen. Period.

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