Do Stock Prices Move Too Much to Be Justified by Subsequent Changes in Dividends?
Source: Shiller, R. J. (1981). American Economic Review 71(3), 421–436.
TL;DR
Shows that real stock prices are far more volatile than the present value of the dividends that actually followed — the excess-volatility puzzle. Under the efficient-markets present-value model, price should equal the optimal forecast of discounted future real dividends (the "ex-post rational price" p), which is necessarily smoother* than price itself because it is a long moving average of dividends. Empirically the implied variance bound is violated by a wide margin: the standard deviation of actual prices is roughly 5 to 13 times larger than the bound allows, suggesting prices move for reasons beyond rational dividend news.
The idea
A variance-bounds test of market efficiency. The "efficient markets model" sets the real price as the present value of rationally expected future real dividends discounted at a constant (or stable) real rate. Since price is the optimal forecast of p, the forecast error p − p must be uncorrelated with p, which implies Var(p) ≤ Var(p), i.e., σ(p) ≤ σ(p). The actual price should be less volatile than the ex-post rational price — the opposite of what is observed.
Evidence
Constructs the ex-post rational price p* as the actual discounted sum of subsequent detrended real dividends (with a terminal assumption about post-sample dividends), then compares variances.
Data set 1 (detrended real S&P Composite, 1871–1979): σ(p) = 47.17 vs. σ(p*) = 7.505 — actual prices about six times more volatile than the bound permits.
Data set 2 (modified real Dow Jones Industrial Average, 1928–1979): σ(p) = 595.6 vs. σ(p*) = 44.18.
Across the variance inequalities tested, the left-hand side is "always at least 5 times as great as the right hand side, and as much as 13 times as great" — all inequalities are dramatically violated for both data sets.
Regressing the price innovation Δp* onto the price level yields significant negative coefficients (−0.1576, t = −3.27 for data set 1; −0.2382, t = −2.62 for data set 2), inconsistent with the zero-covariance restriction.
Why it matters
A founding paper of behavioral finance and of the discount-rate-variation literature. It shifted the central question from "do prices reflect dividends?" to "why are prices so volatile?" To reconcile the data with efficiency one must assume the market expected real dividends to deviate from their long-run trend far more than they historically did. Shiller shared the 2013 Nobel partly for this line of work.
Caveats
The original variance-bounds tests are sensitive to non-stationarity, the assumed (constant) discount rate, the dividend-trend assumption, and small-sample/terminal-value issues (critiqued by Marsh–Merton and Kleidon).
Excess volatility can be partly reconciled with efficiency via time-varying discount rates / expected returns (the discount-rate-variation interpretation); the conclusion that markets are inefficient is debated.
Key references
Shiller, R. (1981) — Do Stock Prices Move Too Much to Be Justified by Subsequent Changes in Dividends? — American Economic Review (NBER WP 456, 1980)
LeRoy, S. & Porter, R. (1981) — The Present-Value Relation: Tests Based on Implied Variance Bounds — Econometrica
Marsh, T. & Merton, R. (1986) — Dividend Variability and Variance Bounds Tests for the Rationality of Stock Market Prices — American Economic Review
Cochrane, J. (2011) — Discount Rates — Journal of Finance
Provenance: verified/generated from the paper's full text.
