Investing in the stock market has the general assumption that, a priori, stocks are more likely to rise than to fall at any given point in time. Under that assumption, the all-at-once strategy has the better expected outcome. Of course, you can be unlucky and end up buying the all-time-high just before a crash. You can avoid that risk by splitting up the investment, at the cost of lowering the overall expected value. So it’s more about how you feel
about that risk, and whether you feel avoiding it is worth having a somewhat lower expected return.
Peter Lynch had a pretty interesting talk where he said that on average the stock market has a sizable dip every few 2-3 years, meaning it's lower at the end of that year than it was at the beginning. Generally though, it goes up over time.
Right, up to now the maximum interval where the market didn’t go up to a new all-time-high is about 15 years, but so far it always ended up reaching a new all-time-high in the end.
