Shiller's 1981 Paper: Are Stock Prices Too Volatile? Variance Bounds Tests Reveal Market Irrationality

In his 1981 paper "Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends?", Robert Shiller challenged the Efficient Market Hypothesis. He constructed a valuation model arguing that actual stock prices should equal the rational expectation of the present value of future dividends. If this model holds, stock price volatility should be strictly bounded by changes in fundamentals.

To test this view, Shiller introduced the concept of "ex post rational prices" (p*), defined as theoretical values calculated based on dividends that actually occurred later. By comparing historical data of actual stock price indices (p) with p*, he found significant discrepancies between the two. These differences were not due to short-term information noise but represented structural deviations.

The core mechanism lies in the variance bounds test. According to efficient market theory, prediction errors should be uncorrelated with predictions, implying that the variance of actual prices must be less than or equal to the variance of ex post rational prices. However, data showed that the actual volatility of the S&P and Dow Jones indices far exceeded this theoretical upper limit. Shiller pointed out that such massive deviations indicate that markets do not always react rationally to information.

For example, the stock market crash from 1929 to 1932 could not be reasonably explained by dividend changes in subsequent years. Although corporate conditions were poor during the Great Depression, the decline in actual dividends was far insufficient to support such a drastic drop in stock prices. Shiller explicitly wrote in the text: "the stock market decline beginning in 1929 and ending in 1932 could not be rationalized in terms of subsequent dividends!"

Assuming current investors face similar severe market fluctuations, relying solely on the dividend discount model might lead them to underestimate risks or misjudge opportunities. Shiller's research suggests that when price volatility significantly deviates from fundamentals, there may be elements of overreaction or bubbles described by behavioral finance, rather than mere information updates. This provides an important theoretical framework for understanding market anomalies.