October has been a scary month for U.S. stocks, with the market's two worst crashes occurring in October 1929 and 1987.

While the probability of an October 2024 crash is low, it is not zero. The best lesson for investors from the performance of the stock market in this past October and other major turbulent events is that large single-day declines in the stock market are an inevitable part of investing, and investors should be prepared accordingly.

That’s easier said than done because crashes are so rare. A modern person probably won’t experience a crash as severe as 1987, when the Dow fell 22.6% in a single trading day, or 1929, when the Dow fell 12.8% in a single day, in their lifetime. But sometimes a generation experiences multiple crashes.

This is where the so-called black swan strategy comes in. The term black swan became well-known on Wall Street thanks to the 2007 book The Black Swan by mathematician Nassim Taleb. Black swan events are sudden, scary, unpredictable and extremely rare, and stock market crashes definitely meet those criteria.

A brief history of market crashes

Before discussing black swan strategies, it is important to review the history of financial market crashes. 20 years ago, researchers derived a formula that tells people how many single-day crashes should be expected over a long period of time. The study was published in the May 2003 issue of the scientific journal (Nature), and readers interested in the specific formula can refer to the original study. The formula assumes that the probability of a crash is distributed according to a power law rather than the more common bell curve distribution.

The researchers’ formula works remarkably well in real time. For example, the model predicted in May 2003 that in the next 21.4 years — that is, until now — there would be a trading day with a market loss as large as during the October 1929 crash. In fact, there has been such a day in this period: On March 16, 2020, the Dow fell 12.9%.

The chart below summarizes the model's predictions over a 100-year period, as well as the Dow's actual performance over the past century. The model's record is impressive.

Why is a market crash inevitable? Xavier Gabaix, a finance professor at Harvard University and the lead author of the study, said in an interview that it is because large institutional investors sometimes want to collectively rush out of stocks, and regulators are powerless to stop them when they do so. These investors have many other ways to reduce their stock exposure, including derivatives and markets outside the United States. Therefore, suspensions are largely ineffective.

What's different about October?

The next question for many is whether there is anything about October that makes that month's markets particularly prone to market crash events. Unfortunately, the above model is inconclusive, in large part because crashes are so rare that there is not enough data to draw reliable statistical conclusions.

For example, three of the four trading days in the past century when the Dow fell more than 10% occurred in October, accounting for 75%, which seems significant, much higher than the 8.3% (100/12). However, no meaningful conclusions can be drawn from just four samples.

That being said, October does seem to be the most volatile month for stocks. Gabex said in an email that while he has not studied the relationship between crashes and volatility, he would guess that "crashes are more likely when volatility is high." So, in that sense, the risk of a market crash is higher in October.

Preparing for the Black Swan

However, according to Taleb, since crashes are so rare, even in October, traditional methods of reducing risk are of no use. If daily market changes followed a bell curve distribution, trying to protect your portfolio from "average" risk might be useful. But it is not the same when the left tail is fatter than expected in the bell curve distribution. And this is exactly the case with the stock market.

To protect yourself from left-side fat tails or black swans, Taleb recommends what he calls a “barbell” strategy: “Instead of being mildly aggressive or conservative, your strategy is to be as ultra-conservative and highly aggressive as possible. An example is an all-stock portfolio with a small portion allocated to long deep out-of-the-money index put options. Most of the time, these options expire worthless, but in the event of a black swan, they can generate huge returns.”

Take the performance of Universa Investments, the investment firm where Taleb serves as an advisor. According to media reports at the time of the stock market crash in March 2000, its investment strategy had a year-to-date return of more than 4,000%.

The views expressed in this article represent only the author’s personal views and do not constitute investment advice. The author does not make any guarantees about the accuracy, completeness, or timeliness of the information in the article, nor is he liable for any losses arising from the use or reliance on the information in the article.