Today is the 28th anniversary of 1987’s Black Monday, a reminder that large declines are a feature of equity markets (MarketWatch) — There’s a 1-in-26,238 chance the U.S. stock market over the next 24 hours will plummet as much as it did on Black Monday, the day of the 1987 crash, whose 28th anniversary we “celebrate” today. You may take comfort from those low odds of stocks falling more than 20% in a single session, which was the magnitude of the 1987 decline. (The Dow Jones Industrial Average tumbled 23%, the most ever.) But, from a risk-management view, what’s noteworthy is that the odds aren’t zero. Stock market crashes are inevitable, and we’re kidding ourselves if we think otherwise. That, at least, is the stark conclusion to emerge from research conducted several years ago into the frequency of crashes: “Institutional Investors and Stock Market Volatility,” 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. The researchers derived a complex mathematical formula that does a remarkably good job of predicting the frequency of large daily stock market movements, not just in the U.S. but on foreign bourses as well. The success of their model led them to conclude that crashes are an inherent feature of securities markets. A single-session drop as big as the one in 1987, for example, is predicted — over long periods of time — to occur once every 104 years, on average. I hasten to add that this doesn’t mean a crash of this magnitude will occur like clockwork every 104 years. Instead, the researchers believe that this will be their average frequency over long periods. So it’s possible we’ll get two 20% crashes in our lifetimes — or none. Haven’t securities regulators figured out how to prevent crashes as big as 1987’s? After all, they’ve had decades to study why it occurred, as well as similar events like the infamous “Flash Crash” of 2010. Haven’t they instituted any number of structural changes designed to prevent future crashes, such as circuit breakers, trading halts and the like? Gabaix believes such structural changes cannot prevent another crash. Every market, to a more or less similar degree, is dominated by its largest investors, he told me. And when something spooks those large investors into simultaneously selling, they will inevitably find ways of doing so, regardless of the regulators’ reforms. The investment implication is clear: We should construct our portfolios so that declines like 1987’s won’t be fatal. If big drops are intolerable, then that probably means you are too exposed to the stock market in the first place. Learning that lesson would be a fitting way of commemorating the 28th anniversary of 1987’s Black Monday.