What is the CAPE ratio (Shiller P/E)?
Definition
– CAPE stands for cyclically adjusted price-to-earnings. It is a valuation metric that divides a current share price (or index level) by the average real (inflation-adjusted) earnings per share over the previous 10 years. The 10-year averaging is intended to smooth the ups and downs of business cycles so the ratio reflects longer‑run valuation rather than short-term profit swings.
How the CAPE ratio is calculated — step by step
1. Gather nominal earnings per share (EPS) for each of the last 10 years.
2. Adjust each year’s EPS for inflation to convert it into “real” EPS (usually using the CPI or another price index).
3. Compute the arithmetic average of those 10 inflation‑adjusted EPS figures.
4. Divide the current price (or current index level) by that 10‑year real EPS average.
Formula (plain text)
CAPE = Current price / (10‑year average of inflation‑adjusted EPS)
Practical notes
– For broad indexes (e.g., S&P 500), researchers often use aggregate real earnings series made available by data providers rather than computing every constituent’s EPS and share counts.
– The 10‑year window was chosen to capture a full business cycle and reduce volatility in valuation caused by temporary profit spikes or troughs.
Why CAPE is useful
– Smoothing: By averaging earnings over a decade, CAPE reduces the influence of temporary booms or recessions on valuation.
– Long-horizon signal: It’s often used as a gauge of prospective long-term returns. Historically, higher CAPE values have been associated with lower subsequent long-term returns on average, and low CAPE values with higher returns — but this is a probabilistic, not deterministic, relationship.
– Comparisons: CAPE lets investors compare current market valuation to historical averages.
Limitations and what to watch for
– Backward‑looking: CAPE uses past earnings, so it may miss structural shifts in future profitability.
– Accounting changes: Changes in GAAP rules, buyback practices, or how firms report earnings can distort comparability across decades.
– Sector mix and payout changes: The index’s sector composition and corporate payout behavior (dividends vs. buybacks) affect earnings dynamics.
– Interest-rate and policy environment: CAPE does not explicitly adjust for prevailing interest rates or fiscal/monetary policy regimes that can justify higher or lower valuations.
– Not a timing tool: A high CAPE does not tell you exactly when a correction will occur; markets can remain expensive for extended periods.
Short checklist for using CAPE responsibly
– Use real (inflation‑adjusted) earnings, not nominal.
– Confirm you are averaging exactly 10 years of EPS.
– Check for accounting or corporate-structure changes that might skew historical EPS.
– Combine CAPE with other indicators (interest rates, profit margins, cash flows).
– Treat CAPE as one long‑term valuation input, not a short-term market-timer.
– Note the benchmark long‑term average you are comparing to and whether that average is still a valid reference given structural changes.
Worked numeric example
Suppose you are evaluating a broad index currently at a level of 4,500.
Step 1 — 10‑year real EPS average: after adjusting each of the past 10 annual EPS values for inflation and averaging them, you get real EPS_avg = 125.
Step 2 — Compute CAPE:
CAPE = 4,500 / 125 = 36.0
Interpretation: If the long-run historical CAPE for this index is 16.8, then the current CAPE of 36 is roughly 2.14 times (36 ÷ 16.8) the historical average — indicating the market is valued substantially above its long-term average. That is an observation about relative valuation; it is not a forecast of timing
— it is not a forecast of timing, speed, or certainty of any market move. Use it as a valuation signal, not a market-timing tool.
Limitations and common cautions
– Smoothing hides short-term information: averaging 10 years of earnings reduces volatility but can miss recent structural changes (tax law, buybacks, one-time shocks).
– Earnings measure choice matters: reported EPS can be distorted by accounting changes, share buybacks, or cyclical corporate margins.
– Interest-rate environment matters: lower real interest rates tend to support higher price multiples because discounted future cash flows are worth more.
– International and sector composition: a broad index’s CAPE can be affected if the index’s industry mix shifts toward high-multiple sectors (tech vs. utilities).
– Historic baseline may not be stable: comparing to a single long-run average assumes economic and financial structure are comparable over time.
– Not a short-term signal: historically, high CAPE values have correlated with lower long-run (decade-plus) average real returns, but timing is very uncertain.
Worked continuation — converting CAPE to an earnings yield and a rough expected real return
Step A — Inverse (earnings yield)
– CAPE = 36 (from earlier example).
– Earnings yield ≈ 1 / CAPE = 1 / 36 ≈ 0.02778 = 2.78% (real).
This is the smoothed real earnings yield implied by the CAPE.
Step B — Compare to a real risk-free rate (illustrative)
– Suppose a long-term real government bond yields 1.00% (real). Then the smoothed equity “risk premium” ≈ earnings yield − real bond yield = 2.78% − 1.00% = 1.78%.
Step C — Add a plausible long-run real earnings growth assumption to estimate a rough long-run real total return
– Many practitioners assume long-run real earnings-per-share (EPS) growth roughly equals real GDP per share growth; pick an assumption (example: 1.5% real growth).
– Rough expected real total return ≈ earnings yield + real EPS growth ≈ 2.78% + 1.5% = 4.28% per year (very approximate).
Notes on the calculation:
– This is a simplified rule-of-thumb. It assumes dividend payout and valuation multiples remain stable; it does not account for buybacks, changing payout policies, or future shifts in CAPE.
– Small changes in the growth or bond-yield assumptions materially change the result.
Practical checklist for using CAPE responsibly
1. Confirm you’re using inflation-adjusted (real) EPS and consistent price level.
2. Check whether one-time events (financial crises, wars, tax changes) unduly skew the 10-year average.
3. Inspect profit margins: unusual margin levels (high or low) can distort averaged EPS; consider margin-normalized adjustments.
4. Compare CAPE to current real bond yields to estimate a smoothed equity premium (1/CAPE − real rate).
5. Use CAPE as a cross-check alongside other indicators: forward P/E, median P/E, price-to-sales, market-cap-to-GDP.
6. Avoid using CAPE alone to set exact buy/sell rules or timing; prefer longer-horizon portfolio tilts, risk budgeting, or position sizing changes.
7. Reassess periodically: structural changes (e.g., sustained low rates, regulatory shifts) may suggest recalibration of historical benchmarks.
Alternative or complementary metrics
– Forward P/E: uses analysts’ next-12-month earnings estimates; more sensitive and less smoothed.
– Median P/E: reduces outlier-company skew within an index.
– Tobin’s Q: market value of firms divided by replacement cost of assets — another market-level valuation measure.
– Market-cap-to-GDP (“Buffett indicator”): compares total market capitalization to national GDP; useful for country-level valuation.
– CAPE variants: some academics propose margin-adjusted CAPE or shorter/longer windows (5- or 20-year) to account for regime changes.
Example
Example — worked numeric example (step-by-step)
Goal: compute CAPE (cyclically adjusted price-to-earnings ratio) for an index and convert it into a simple, illustrative expected‑return starting point.
Data you need
– Current index level (price).
– Ten years of index earnings per share (EPS) or aggregate earnings for the index.
– A price index to deflate earnings to real terms (e.g., CPI — consumer price index).
Step 1 — inflate/deflate earnings to real terms
– Take each year’s nominal EPS and divide by the CPI for that year (or otherwise deflate to your base year). This produces 10 real EPS numbers (earnings adjusted for inflation).
Step 2 — compute the 10‑year average real EPS
– Example real EPS (per share) for the past 10 years: 120, 130, 140, 160, 170, 150, 140, 145, 160, 170.
– Sum = 1,485. 10‑year average real EPS = 1,485 / 10 = 148.5.
Step 3 — compute CAPE
– Formula: CAPE = Current index price / (10‑year average real EPS).
– Example: index level = 4,000. CAPE = 4,000 / 148.5 ≈ 26.94.
Step 4 — compute the 10‑year average earnings yield (the inverse)
– Earnings yield (10‑yr average) = 1 / CAPE.
– Example: 1 / 26.94 ≈ 0.0371 = 3.71% (real).
Step 5 — convert to a coarse expected real-return starting point (optional, heuristic)
– A common simple approximation: expected real return ≈ earnings yield + expected real growth in earnings per share (g).
– This assumes no
no structural change in valuation multiples, no change in payout ratios, and that earnings revert toward a long-run mean. In practice those are strong assumptions — treat the resulting number as a coarse starting point, not a precise forecast.
Worked numeric example (continuing from prior numbers)
– CAPE = 26.94 (from prior step).
– 10‑year average real earnings yield = 1 / 26.94 = 0.0371 = 3.71% (real).
– Choose an assumed long‑run real EPS growth rate, g. Example: g = 1.5% (real).
– Simple heuristic expected real return ≈ earnings yield + g = 3.71% + 1.50% = 5.21% (real).
– To get a rough nominal expected return add expected inflation. Example: expected inflation = 2.0% → expected nominal return ≈ 5.21% + 2.00% = 7.21% nominal.
Formulas (recap)
– CAPE = Current price / (10‑year average real EPS).
– Earnings yield (CAPE inverse) = 1 / CAPE.
– Heuristic expected real return ≈ earnings yield + expected real EPS growth (g).
– Nominal ≈ expected real return + expected inflation.
Interpretation and practical use
– Relative signal, not a timing tool: CAPE is more useful as a long‑horizon valuation anchor (multi‑year expected returns) than for short‑term market timing.
– Higher CAPE → lower implied earnings yield → lower starting expected real returns (all else equal). Lower CAPE → higher implied starting returns.
– Use with other information: earnings quality, profit margins, interest rates, demographic trends, and macro outlook. Combine CAPE with forward earnings yields and balance‑sheet metrics rather than relying on it alone.
Common pitfalls and limitations
– Accounting and payout changes: buybacks, changes in tax law, and accounting standards can alter reported EPS and comparability over time.
– Structural shifts: lower real interest rates or persistent changes in profitability can change the “normal” CAPE level.
– Negative or volatile earnings years: the 10‑year smoothing helps but can still be distorted by extreme episodes.
– Nonstationarity: historical averages may not be reliable if the underlying economy or market structure has changed.
– Short‑term noise: CAPE has weak predictive power for returns over months and stronger, but still imperfect, power over decades.
Checklist for sensible use
1. Choose the index and retrieve consistent price and EPS series.
2. Inflate/deflate EPS to real terms using a consistent CPI or GDP deflator.
3. Compute the 10‑year trailing average of real EPS (arithmetic mean).
4. Compute CAPE and its inverse (earnings yield).
5. Decide an assumed long‑run real EPS growth (document your assumption).
6. Convert to nominal if needed by adding expected inflation.
7. Cross‑check with other valuation and macro indicators.
8. State uncertainty ranges (e.g., ± a few percent) rather than a single point estimate.
Alternatives and complements
– Trailing P/E (current price ÷ last 12 months EPS): more sensitive to the business cycle.
– Forward P/E (price ÷ expected next 12 months EPS): depends on analyst forecasts.
– Tobin’s Q, price‑to‑sales, dividend yield, and balance‑sheet metrics: provide different perspectives on valuation.
Quick example comparing nominal and real expectations
– Suppose CAPE = 26.94 → earnings yield (real) = 3.71%.
– If you assume g = 1.5% and inflation = 2.0%:
– Expected real return ≈ 5.21%.
– Expected nominal return ≈ 7.21%.
– If you instead assume g = 0.5% (slower growth), expected nominal return ≈ 6.21%. Small changes in g materially affect the estimate.
Short recommended reading and data sources
– Investopedia — CAPE Ratio overview and example: https://www.investopedia.com/terms/c/cape-ratio.asp
– Robert J. Shiller — historical data and CAPE series: http://www.econ.yale.edu/~shiller/data.htm
– FRED (Federal Reserve Economic Data) — CPI and price/earnings time series: https://fred.stlouisfed.org
– Aswath Damodaran (NYU Stern) — valuation resources and commentary: http://pages.stern.nyu.edu/~adamodar/
Educational disclaimer
This explanation is educational and not individualized investment advice. CAPE provides a rough starting point for thinking about long‑run expected returns; it is not a precise forecasting tool. Consider consulting a qualified financial professional before making investment decisions.