https://www.ifa.com/12steps/step4/missing_the_best_and_worst_days/
This kind of analysis has always felt a bit silly to me, so I finally did some checking and confirmed my suspicions.
To actually miss the 20 biggest days in the way that results in a 9.22% return shrinking to a 3.02% return requires the following:
1) Selling the day before the big gain
2) Buying back in the very next day, after you just saw a giant gain
3) Being in the market every single other day that's not part of those 20.
Not even the world's dumbest market-timer would behave that way. First he has to have the magical ability to know when the next day is going to be one of the top-20 gaining days. Then, despite the fact that he's a magical genius, he has to be dumb enough to not *buy* on those days, but sell instead. And then this magical man has to be doubly-super-dumb and buy back in the very next day.
As I suspected, if he waits even one more day after that giant gain to buy back in, as even a slightly-less-stupid-than-stupidest-ever magical trader would do ("uh, maybe I'll hold off for a bit?"), his returns will be much better. Most of the top-20 days occur during periods of extreme volatility (
a full 10 of the top-20 gaining days in the S&P500 since 1970 occurred in a 6-month period in 2008-2009, in the midst of a giant market crash!!), so in most cases the very next day sees a drop, with nearly all cases seeing a significant drop within a week.
Any actual person who was out of the market for one of those top-gaining days in 2008-2009 was probably out of the market for most of those days, and if so, they probably far
outperformed the market because that means they avoided the broader crash.
I guess if it helps convince the naive investor to stay in the market, that's all well and good, but I think more rigorous arguments can be made to support the buy-and-hold strategy.