CAPE explained: calculation methodology, 10-year real earnings average and Shiller inflation adjustment

Behind the acronym CAPE — Cyclically Adjusted Price-Earnings — sits a calculation of remarkable simplicity: real S&P 500 price as numerator, arithmetic mean of the previous ten years’ real earnings as denominator, double CPI deflation on both terms, series back-calculated to 1881.

Reconstructing the formula step by step and making explicit Shiller’s methodological choices — why ten years, why CPI, why the S&P 500 — is the prerequisite to any serious reading of the ratio and to any distinction with its cousins forward P/E and trailing P/E.

1. The Formula Step by Step

The CAPE is computed in four mechanical steps. Step 1: retrieve the monthly S&P 500 closing price at date t. Step 2: deflate that price by the U.S. consumer price index (CPI All Urban Consumers, FRED series CPIAUCSL) rebased to the current period, to obtain a real price. Step 3: retrieve the S&P 500 GAAP earnings over the ten years preceding date t — i.e. 120 quarterly values aggregated into 120 months of earnings — and deflate each value by the corresponding period CPI. Step 4: compute the arithmetic mean of these 120 monthly real earnings and divide the real price from step 2 by that mean.

This construction yields a compact formula: CAPE(t) = P_real(t) / [10-year mean of E_real]. An equivalent variant, more intuitive, uses annual earnings: CAPE(t) = P_real(t) / [arithmetic mean of annual real earnings over the ten years preceding t]. Both versions yield statistically indistinguishable results. Robert Shiller publishes the official monthly series on his Yale academic site — the reference Shiller Online Data — updated to the current month based on BLS data for CPI and S&P Dow Jones Indices for earnings.

The apparent simplicity masks a few technical subtleties. The earnings used are the GAAP reported earnings as they appear in the audited accounts of S&P 500 companies, aggregated by S&P Dow Jones Indices. This scope excludes pro forma adjustments or “adjusted” earnings published by certain companies to neutralize non-recurring charges — a distinction that becomes important after 2001 in the critical debate on the FASB 142 break. The general properties of the CAPE as the academic reference measure rest precisely on this GAAP discipline that ensures historical comparability before arbitration of the critiques.

The CAPE’s numerical result by mid-2026 — between 35 and 40 depending on the week — has no dimension: it is a unit-free multiple, directly comparable to historical multiples from 1881, 1929, 1999. This dimensionless property, obtained through double CPI deflation, is what makes the CAPE usable as a regime thermometer across 145 years.

2. Why Ten Years — the Cyclical Choice

The choice of a decadal average is not arbitrary. Shiller inherited the idea from Benjamin Graham and David Dodd, whose Security Analysis published in 1934 already advocated a seven-to-ten-year average to neutralize the cycle. The justification is empirical: U.S. business cycles since the mid-19th century have an average duration around five to seven years per NBER Business Cycle Dating Committee datings, and a ten-year average therefore systematically captures at least one complete cycle. A five-year average would remain sensitive to the cyclical phase of observation; a twenty-year average would dilute information across a sample whose sectoral composition would have meaningfully shifted.

The fundamental property sought is the stationarity of the denominator. Annual earnings of a broad index like the S&P 500 can fall 30 to 50% in deep recession then double in vigorous expansion — producing explosive annual P/Es at cycle troughs (trailing P/E > 100 on the S&P 500 in 2009 per FactSet data) and artificially low P/Es at peaks. Smoothing over ten years neutralizes these oscillations without introducing structural bias: the ratio between 10-year mean real earnings and long-run normalized real earnings stays approximately constant independently of the observation moment.

Shiller empirically tested several windows in his work and confirmed that the correlation between CAPE and forward 10-year real return is maximized around the decadal window. For the full breakdown, see what CAPE captures that forward P/E misses. A five-year window produces a slightly weaker and more volatile correlation across sub-periods; a fifteen-year window loses predictive power without gaining robustness. The ten-year window is an empirical optimum, not an imposed theoretical convention.

A recurring critique of the ten-year choice comes from the duration of secular cycles themselves. If a secular cycle lasts ten to twenty-five years (Great Moderation 1982-2008 for example), a decadal average can capture an atypical portion of the long cycle and produce a biased reading. This critique is valid for extreme phases but does not disqualify the ratio: it simply implies that the CAPE must be read against its historical distribution rather than against a fixed theoretical equilibrium — a point that structures the historical reading of the ratio over 145 years.

3. Why CPI — the Double Deflation

Inflation adjustment is the second founding statistical discipline of the CAPE. Without deflation, comparing a 1929 CAPE (32.56 in nominal terms) to a 2026 CAPE (35-40 in nominal terms) would be meaningless: 97 years of cumulative inflation mechanically modifies multiples without information about real valuation. The U.S. CPI multiplied prices by roughly a factor of 17 between 1929 and 2026 per BLS series, which would make any nominal comparison absurd.

Shiller applies deflation to the numerator (S&P 500 price) and denominator (earnings) simultaneously. This double deflation does not only make levels historically comparable — it also preserves the ratio’s dimensionality. A P/E is a unitless number (dollars over dollars), and deflation by a single index at numerator and denominator ensures this dimensionless property is preserved. If only the numerator were deflated, the ratio would mix real and nominal dollars, making it incomparable across periods.

The choice of CPI rather than PCE (Personal Consumption Expenditures, the price index officially retained by the Federal Reserve for its 2% inflation targeting) is conventional. CPI offers a longer and more methodologically stable series across the century. PCE is conceptually closer to consumer-perceived inflation and tends to print slightly below CPI (historical mean gap around 0.3-0.4 points per year). But over the CAPE’s decadal horizon, the cumulative gap remains marginal and does not modify the regime reading. Shiller stays with CPI by tradition and methodological continuity of his series since 1988.

A methodological variant occasionally invokes the use of operating earnings rather than GAAP. Operating earnings exclude non-recurring exceptional charges and provide a smoother but also more optimistic reading of underlying profitability. Shiller explicitly maintains GAAP as the convention because operating earnings carry a structural upward bias — “non-recurring” charges often proving recurring over the long run — and their definition varies from company to company, degrading historical comparability.

4. CAPE vs Trailing P/E vs Forward P/E — Differentiation

The CAPE must be distinguished from two other equity valuation measures that circulate continuously in financial commentary. Trailing P/E — often abbreviated to P/E without qualifier — is the current price divided by the GAAP earnings of the last twelve months (TTM, Trailing Twelve Months). It is volatile by construction: at cycle troughs, TTM earnings collapse and the P/E mechanically explodes (P/E > 100 on the S&P 500 in 2009 per FactSet); at cycle peaks, TTM earnings inflate and the P/E appears low. This cyclical property makes the trailing P/E poorly readable as a valuation-regime thermometer.

Forward P/E is the current price divided by sell-side consensus earnings projected over the next twelve months. It is less volatile than trailing P/E but carries a documented bias: sell-side consensus is systematically 5 to 10% optimistic against actually realized earnings, per FactSet and McKinsey studies published over 2000-2020. This analytical bias makes forward P/E structurally lower than the P/E that will actually be observed in retrospect.

The CAPE solves both problems through decadal smoothing of real earnings. It is not cyclical like trailing P/E and does not depend on sell-side projections like forward P/E. In return, it is less reactive to recent inflections: a structural shift in profitability — S&P 500 rotation toward high-margin services for example — takes ten years to fully incorporate into the decadal mean. This incorporation lag is the main critique addressed to the CAPE by Jeremy Siegel and others. The detailed comparison of the three measures quantifies historical gaps and examines when each ratio is analytically preferable.

For an investor readership, the typical usage of the three measures splits as follows: CAPE illuminates the long-term regime and the expected forward 10-year return, trailing P/E illuminates the raw cyclical reading, forward P/E illuminates sell-side anticipations. None of the three measures is universally superior; they answer distinct analytical questions. Conflating the three or privileging one as “the” valuation measure is precisely the methodological trap Shiller sought to avoid by formalizing the CAPE as an explicit construction. This positioning fits naturally within the reading framework of equity market valuation, real rates, multiples and earnings that structures the sub-pillar dedicated to equity multiples, with the raw historical data published openly through the canonical S&P 500 CAPE dataset.

Last updated — 23 May 2026