# Excess Volatility: Why Stock Prices Are Too Volatile to Be Rational

Cite as: Gorak, R. (2026). Excess Volatility: Why Stock Prices Are Too Volatile to Be Rational. Tradicted. https://www.tradicted.com/research/shiller-excess-1981/
Paper: Robert J. Shiller — *Do Stock Prices Move Too Much to Be Justified by Subsequent Changes in Dividends?*
Published in: American Economic Review (1981)
Original: https://www.jstor.org/stable/1802789

Key finding: Actual S&P stock price volatility (σ(p) = 50.12, 1871–1979) exceeds the ex post rational price volatility (σ(p*) = 8.968) by a factor of more than five, violating the efficient markets inequality σ(p) ≤ σ(p*).

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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.

## FAQ

### What is the excess volatility puzzle?

50.12 versus 8.968: those are the standard deviations of actual S&P prices and the ex post rational price in Shiller (1981). The efficient markets model requires actual prices to be no more volatile than the rational benchmark. The observed ratio of more than 5.5 constitutes the excess volatility puzzle.

### How did Shiller test whether stock prices were too volatile?

5 to 13 times: that is the factor by which Shiller's (1981) bound σ(p) ≤ σ(p*) is violated. He computed p* as the present value of dividends actually paid afterward and compared it to actual prices. The S&P (1871–1979) violates by a factor of over 5; the Dow Jones (1928–1979) by over 13.

### Could time-varying real discount rates explain the excess volatility?

4.36 percentage points is the minimum standard deviation of real discount rates needed to explain the S&P discrepancy in Shiller (1981). This would require real rates to oscillate between −3.91 and +13.52 percent — far larger than observed nominal interest rate swings over the sample period.

### What does the regression evidence show about price predictability?

−.1521 is the coefficient when price innovations (δ_{t+1}p_{t+1}) are regressed on current S&P price p_t (t = −3.218, R² = .0890). A significant negative coefficient means current prices predict future price innovations. The efficient markets model requires these innovations to be unforecastable.

## Source

Shiller, R. J. (1981). Do Stock Prices Move Too Much to Be Justified by Subsequent Changes in Dividends? *American Economic Review*, 71(3), 421–436.

[Read the full paper →](https://www.jstor.org/stable/1802789)