Excess Volatility: Why Stock Prices Are Too Volatile to Be Rational
Summary by Robert Gorak | Published 2026-06-10 | Last reviewed 2026-06-10
Excess volatility describes the finding that real stock prices fluctuate far more than future dividends can justify. Shiller (1981) tested this using the real S&P Composite Stock Price Index (1871–1979) and a modified Dow Jones series (1928–1979). Actual price volatility was five to thirteen times higher than the efficient markets model allows. The standard deviation of actual S&P prices (50.12) exceeded the rational price benchmark (8.968) by more than a factor of five.
What the Study Found
σ(p) = 50.12 (S&P) exceeds σ(p*) = 8.968 by more than a factor of five, directly violating the efficient markets bound. For the Dow Jones (1928–1979), σ(p) = 355.9 versus σ(p*) = 26.80 — a factor-of-13 violation. The model's upper bound on price innovation volatility is 4.721 (S&P); actual price innovation volatility is 25.57. Regressing price innovations on current price yields a coefficient of −.1521 (t = −3.218, R² = .0890) for the S&P.
Methodology
Data Set 1 is the real S&P Composite Stock Price Index and associated dividend series from 1871 to 1979. Data Set 2 is a modified Dow Jones Industrial Average comprising 30 stocks from 1928 to 1979; no total observation count is reported. Both series are detrended by dividing by a long-run exponential growth factor estimated by regressing ln(P_t) on a constant and time. The constant real discount rate r̄ is estimated as the mean dividend-price ratio. The terminal value of p* is set to the average detrended real price over the sample.
Key Statistics
| Metric | Finding | Context |
|---|---|---|
| σ(p) — S&P | 50.12 | Actual detrended price, 1871–1979 |
| σ(p*) — S&P | 8.968 | Ex post rational price, 1871–1979 |
| σ(p) — Dow Jones | 355.9 | Actual detrended price, 1928–1979 |
| σ(p*) — Dow Jones | 26.80 | Ex post rational price, 1928–1979 |
| Volatility violation factor | 5 to 13× | Inequality σ(p) ≤ σ(p*) violated in both series |
| Upper bound σ(d)/√r̄₂ | 4.721 | Inequality (11), S&P; actual σ(Δp+d₋₁−r̄p₋₁) = 25.57 |
| Upper bound σ(d)/√(2r̄) | 4.777 | Inequality (13), S&P; actual σ(Δp) = 25.24 |
| cor(p, p*) — S&P | .3918 | Correlation of actual vs. rational price, 1871–1979 |
| Regression coefficient of p_t | −.1521 | δ_{t+1}p_{t+1} on p_t; t = −3.218, R² = .0890 (S&P) |
| Required σ(r̄_t) to save the model | ≥ 4.36 ppts | Implies r̄_t range of −3.91 to +13.52% (S&P) |
Why This Matters
The scale of the inequality violations makes data errors or index construction problems implausible as explanations. Rescuing the efficient markets model through time-varying discount rates would require interest rate behavior never observed in the historical record. The findings reframe stock market booms and crashes as possible systematic investor overreaction rather than rational responses to new information. The paper provided the foundational empirical evidence for the behavioral finance challenge to efficient markets theory.