A once-a-century stock decline: How common are stock returns like this year’s?

Recently I've been running some numbers on how individuals with personal accounts would have fared under current market conditions (although I may have to re-run them given that stocks are down since when I last posted a few days ago…). One question this exercise prompted is how uncommon are stock returns like today's, where the S&P 500 is down 32 percent year-to-date.

To give a quick answer I looked at inflation adjusted annual stock returns from 1871 through today (ok, meaning, literally yesterday). The arithmetic mean inflation-adjusted annual return from 1871 through today is 7.8 percent above inflation, which is equal to a compounded (geometric mean) return of 6.3 percent. The standard deviation of annual returns is 17.9 percent. From those numbers, and the assumption that returns are normally distributed, we can conclude that we should see stock returns like this year's about 0.8 percent of the time, meaning about once out of every 125 years. Here's an Excel file with the data and calculated for anyone interested.

But the year isn't over yet, so who knows where we'll end up…