How Time Horizon Affects Investment Returns

In this post we’ll look at the uncertainty of stock returns over time periods longer than one year and how the length of time invested affects the uncertainty of returns.

Cumulative Return

The graph above shows the distribution of how much an investment in the S&P 500 grew over different timeframes¹. For example, 5 ‘Years Invested’ visualizes all five-year periods on a rolling monthly basis (January 1871-January 1876, February 1871-February 1876, March 1871-March 1876, …, January 2021-January 2026) using a five-number summary:

• All returns were within the grey shaded area, such that the top and bottom edges of the area represent the highest and lowest returns over that time period, respectively.
• The blue line represents the 50th percentile, or the median, of the returns. Half of the returns were below this line, and half of the returns were above this line.
• The green and red lines split the top 50% and bottom 50% of returns in half again. The green, blue, and red lines therefore split the grey area of all returns into four sections, each with 25% of the returns within that section.

These data give an idea of how spread out the historical cumulative returns were for different numbers of years invested.

• Half of the returns were between the green and red lines, showing that returns closer to the median were more likely.
• As Years Invested increases, the green, blue, and red lines get farther away from each other. This shows that the amount of money you end up with gets increasingly uncertain as the amount of time invested increases. The lines are also all higher though, so you are rewarded for this increased uncertainty in the final value with a better chance at a higher final value.

Annualized Return

Years Invested	Worst	25th percentile	Median	75th percentile	Best
1	-58%	-3%	9%	20%	151%
2	-44%	0%	8%	16%	54%
3	-35%	2%	8%	13%	39%
4	-21%	1%	8%	13%	39%
5	-13%	2%	7%	12%	33%
6	-10%	2%	7%	11%	31%
7	-8%	3%	7%	11%	25%
10	-6%	4%	7%	11%	20%
15	-2%	4%	7%	10%	16%
20	0%	5%	7%	9%	14%
30	2%	5%	7%	8%	11%

Another way to look at the uncertainty of returns over different time horizons is to look at the uncertainty of the annualized return.

If a $1000 investment grew to $1200 over 3 years, that means it returned 20% over 3 years. We can then ask: how much is that return per year? In other words, if each of the three years had the same annual return, what would that annual return be so that after three years it would result in a 20% increase? The answer is called the annualized return or CAGR (Cumulative Annual Growth Rate).

As you can see, the distribution of annualized returns gets tighter as the number of years invested increases. This is one reason for the “stocks for the long-term” adage: historically, the longer a stock fund was held, the lower the variance of its historical annual returns².

Historical Loss Rate

This graph shows the percentage of historical returns for a given time horizon that resulted in losing money after that time period. It shows that, historically at least, the longer the stock investment was held the less likely it was to end in a loss. This is another argument in favor of “stocks for the long-term.”

Conclusion

Past performance is no guarantee of future performance, but we can at least use historical performance under similar conditions to get a better estimate of what to expect than nothing. The historical data suggest that the longer a stock fund is held, the less likely it is to end in a loss and the more predictable its annualized return becomes. This suggests that the longer the investing time horizon, the more attractive stock funds become.

Sources

S&P 500 data

Code used to generate this post

Footnotes

1. Returns shown are real (inflation-adjusted), using Shiller’s Real Total Return Price series. ↩

2. Note that this is not the same as saying that because you’ve held a stock fund for 29 years you can be very confident the 30th year’s return will be within a tight margin — that would be a 1-year return, which the graph correctly shows has high variance. The takeaway is future-looking: if you plan on investing over 30 years, you can look at the 30 year values to get a sense of the distribution of historical annual returns over that time. After 15 years, you have 15 years of future investing, so you should look at the 15 years invested values which show the distribution of historical returns over 15 years to help you get a sense of what you might expect over the next 15 years, etc. ↩