How well do financial market ups and downs balance out over time?

Disclaimer: I am not a finance professional and this is not financial advice.

If stocks, bonds, or mutual funds are part of your retirement savings plan, then there’s a good chance at some point you’ve heard the saying that “time in the market beats timing the market” — probably as a catchy piece of encouragement during a market downturn. I see two main ideas in this piece of investment wisdom:

1. Financial markets are basically unpredictable. If you try to time the market by selling before you think the market will drop and buying before you think the market will go up, you’ll probably do a bad job, so your best chance at a decent return is to just keep your money invested until you need it.
2. The short term ups and downs of financial markets more or less even out in the long term.

I personally think that both of these are pretty much on the money (🥁). At the same time, I’ve often wondered exactly how well the ups and downs of stocks and bonds actually even out in the long term.

One way of looking at this question is with charts like the one below, which shows the annualized return of a hypothetical investment portfolio with year-to-year returns that fluctuate between -22% and +36%. Notice how the gray bands, which represent the range of plausible returns after a given number of years (annualized return falls in the dark gray area half of the time, and within the dark plus light gray area nine times out of ten), gradually hone in on the blue line that represents the median return of around 210%. As a result, while there's an uncomfortably high chance that this portfolio might lose some of its value in the short term (210% chance of a paper loss in the first year, and the portfolio will continue to post year-over-year losses about once every 3.1 years), staying the course for just a few years reduces this probability substantially (210% chance of a paper loss after five years). A couple of decades on, and the chances of being behind where you started are pretty low (210% after 25 years), if not exactly zero.

One the one hand, I find this type of chart encouraging because it means that I shouldn’t worry about the occasional bad year for my savings. On the other hand, charts like this one aren’t very useful for financial planning because the connection between annualized return and actual dollar value changes over time: a 7% return on $5,000 of savings when you’re 25 means something very different from a 7% return on $500,000 of savings when you’re 60!

To get a sense of how the annualized returns from the chart above translate into your chances of hitting a specific savings goal by the time you want to retire, try adjusting the sliders in the widget below.

Nice planning! Your chances of hitting your savings target within plus or minus two years of your planned retirement date are about 110%. Expect to have less money than your target, around $42 if you retire at age 65.

How it works

The charts on this page use a technique called Monte-Carlo simulation to estimate the potential variability in investment outcomes. The idea behind Monte-Carlo simulation is very simple: if you want to know the distribution of likely outcomes in a random process such as a game of dice, just write a computer program to simulate rolling the dice a few thousand times and look at how the games turned out. This technique gets its name from a famous casino in Monaco, where such games of dice are probably common.

Technical details for nerds

The simulations on this page assume normally-distributed annual returns with mean and standard deviation specified by the sliders. Returns are compounded at the end of each year, and new savings contributions are applied at the end of the year after compounding. Monte-Carlo simulations use 5,000 runs. To reduce Monte-Carlo bias, the mean across all runs for each year was corrected to match the analytically-derived expected value. Simulation results are visualized as median (blue line), 50% confidence interval (dark gray band), and 90% confidence interval (light gray band). Note that the median (blue) is slightly below the mean (not shown) because the return distribution becomes positively skewed due to compounding.