Mean Reversion
Selected range · January 1947 — June 2026
About this chart
This chart compares the inflation-adjusted price of the S&P 500 with its estimated long-term growth trend.
Stock prices generally rise over long periods as companies grow, earnings increase and the purchasing power of money changes. However, market growth does not happen smoothly. Prices can move significantly above or below their longer-term path because of changing investor expectations, economic conditions, interest rates, earnings growth and market sentiment.
To make prices from different decades more comparable, historical S&P 500 values are adjusted for inflation. This expresses past index levels using approximately the same purchasing-power basis as the latest observation. Without this adjustment, older prices would appear artificially low simply because the general price level was lower.
The model then estimates a long-term exponential trend from the full available history of inflation-adjusted prices. An exponential trend is used because long-term growth is generally better represented by compounding than by a straight line. A straight-line trend assumes that the index increases by the same number of points over time, while an exponential trend represents growth at an approximately constant percentage rate.
The deviation line shows how far the inflation-adjusted S&P 500 is positioned above or below the estimated long-term trend.
A value of 0% means that the index is equal to the estimated trend.
A positive value means that the index is above the trend.
A negative value means that the index is below the trend.
The standard-deviation zones provide additional historical context. They show whether the current deviation is relatively common or unusually large compared with previous observations in the model’s history.
Values near the trend fall within the normal historical range. Values farther above the trend may be described as historically elevated, while values farther below the trend may be described as historically depressed.
The model is based on the concept of mean reversion. Over long periods, unusually large deviations from an established trend have often become smaller. This does not mean that prices must immediately return to the trend. The market can remain above or below its historical trend for many years, and the estimated trend changes as new observations are added.
The chart should be used as a long-term historical valuation tool rather than as a short-term market-timing indicator. It does not identify an exact fair value, predict the timing of future returns or provide a buy or sell signal.
Limitations
- The model uses the inflation-adjusted S&P 500 index level and excludes reinvested dividends, so it does not measure investors’ total returns.
- The historical average is calculated from the full available sample. This makes the benchmark retrospective because later observations influence how earlier periods are evaluated.
- A fixed long-term average assumes that the real S&P 500 has a stable central level. Persistent economic growth, changes in profitability, and shifts in market structure may weaken this assumption.
- The average and standard-deviation zones depend on the selected sample period and can be materially affected by extreme historical observations.
- Standard-deviation bands describe historical dispersion but do not imply that deviations are normally distributed or that observations outside the bands have fixed probabilities.
- Changes in the composition of the S&P 500, accounting standards, monetary regimes, interest rates, and investor participation can alter the relationship across different periods.
- An unusually high or low deviation can persist for a long time and does not guarantee a reversal or provide a market-timing signal.
Methodology
Monthly S&P 500 prices are adjusted for inflation using the U.S. Consumer Price Index. The natural logarithm of the inflation-adjusted price is then fitted to a linear time trend. Converting the result back into normal price values creates an exponential long-term trend.
The standard deviation of the full deviation series is used to create the ±1σ, ±2σ and ±3σ historical zones. The model uses monthly observations over the full available sample beginning in January 1947.
Data sources
Monthly S&P 500 index prices
Range: January 1947 to the latest available observation
Source: DataHub, S&P 500 Index Data, based on historical data prepared by Robert Shiller and more recent observations sourced through FRED; https://datahub.io/core/s-and-p-500
U.S. Consumer Price Index for All Urban Consumers, seasonally adjusted
Range: January 1947 to the latest available observation
Source: U.S. Bureau of Labor Statistics, Consumer Price Index for All Urban Consumers: All Items in U.S. City Average [CPIAUCSL], retrieved from FRED, Federal Reserve Bank of St. Louis; https://fred.stlouisfed.org/series/CPIAUCSL