Equity-Bond Model
Selected range · January 1962 — May 2026
About this chart
The Equity-Bond Model compares the long-term valuation of the U.S. stock market with the yield available on 10-year U.S. Treasury securities.
The model is based on the idea that investors compare the potential return from equities with the return available from relatively low-risk government bonds. Changes in Treasury yields can therefore affect how attractive stocks appear relative to fixed-income investments.
To evaluate the stock market over a long period, historical S&P 500 prices are first adjusted for inflation. This removes the effect of changes in the purchasing power of money and makes prices from different decades more comparable.
An exponential long-term trend is then estimated from the inflation-adjusted S&P 500 series. The model measures how far the market is positioned above or below this trend and expresses the result as a standardized deviation from its historical range.
The 10-year Treasury yield is evaluated separately against its own historical average. The model measures whether the current yield is unusually high or low compared with previous observations.
The standardized stock-market measure and the standardized Treasury-yield measure are then combined into one indicator. This makes it possible to compare equities and bonds even though they are measured in different units.
Higher model values generally indicate that equities appear historically more attractive relative to 10-year Treasury bonds. Lower values generally indicate that Treasury bonds appear relatively more attractive.
The model should be used as a long-term historical comparison rather than as a short-term trading signal. Relationships between stocks and bonds can remain far from their historical averages for extended periods.
The model also does not account for every factor that influences equity and bond returns. Earnings growth, inflation expectations, monetary policy, economic conditions, credit risk, market sentiment, and investor preferences can all affect the relationship between the two asset classes.
Limitations
- The model combines standardized equity and bond measures, so its result is a relative comparison rather than a direct estimate of fair value for either asset class.
- The equity component is based on the inflation-adjusted S&P 500 index level and excludes reinvested dividends, while the bond component is based on Treasury yields rather than bond total returns.
- Bond yields and bond prices move in opposite directions, so the bond z-score must be interpreted according to the model’s exact sign convention.
- The two components have different economic drivers and statistical properties, and combining them into one score can conceal which market is responsible for the final reading.
- Historical averages and standard deviations depend on the selected sample period and may be affected by structural changes in inflation, monetary policy, interest rates, and the composition of the S&P 500.
- Standardized scores show how unusual each component is relative to its own history, but they do not imply that the underlying distributions are normal or directly comparable in economic magnitude.
- An extreme combined reading can persist for a long time and should not be interpreted as a precise allocation recommendation or 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 fitted to a linear time trend, and converting the result back into normal values creates an exponential long-term trend. The 10-year Treasury yield is compared separately with its historical average and expressed as a standardized deviation.
The model uses monthly observations beginning in January 1962. Standardizing both inputs allows the stock-market and Treasury-yield measures to be combined even though they use different units.
Data sources
Monthly S&P 500 index prices
Range: January 1962 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
10-Year Treasury Constant Maturity Rate
Range: January 1962 to the latest available observation
Source: Board of Governors of the Federal Reserve System (US), 10-Year Treasury Constant Maturity Rate [DGS10], retrieved from FRED, Federal Reserve Bank of St. Louis; https://fred.stlouisfed.org/series/DGS10
U.S. Consumer Price Index for All Urban Consumers, seasonally adjusted
Range: January 1962 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