S&P ROI Likelihood by Investment Duration

The graphs below show the likelihood of different effective annual ROIs for the S&P 500. The first two graphs show the same data, but the second one is zoomed in to show more detail in the central region.

Each line represents a different investment duration. For example, the dark red line represents five year invesments. Each point on the line gives the likelihood of earning the corresponding annual ROI or better. For example, we can see that across all five year invements in the S&P, there is a roughly 90% chance of breaking even (ROI=0.0) and nearly 70% chance of earning an effective annual ROI of at least 5%.

An effective annual ROI is the constant annual return-on-investment that explains the total ROI for the full investment period. So for a one year investment, the effective annual ROI is the actual ROI. For a 10 year investment that earns 96.7% overall, the effective annual ROI is 7% since 1.07^10=1.967. Using effective annual ROI instead of actual ROI allows us to directly compare the returns for different investment durations.

The graphs below show ROI without taking inflation into account. Move your mouse over the graphs to show the inflation-adjusted results.

One trend that immediately pops out of the graph is that longer investments have lower volatility. We can see this from the less steep decline exhibited by the shorter investments durations. For these durations, there is a higher chance of a big loss (e.g., only 90% of one year invesments earn more than -12% so 10% must lose more than 12%), but they also have a higher chance of a large gain (30% of 1 year invesments earn over 20% while almost no invesments longer than 10 years earn so much). Longer invesments are more tightly clustered around moderate gains. For example, almost all 40 year investments earn between 6% and 13% effective annual ROIs.

An important note concerning the graphs is that they assume tax-free growth and full dividend re-investment. The S&P data comes from Robert Shiller and was originally used for his book Irrational Exuberance. Inflation rates were computed using the consumer price index (CPI), which is also provided by Shiller. These graphs were generated using data starting in Januray 1871 and continuing through September, 2011.