8.3. Challenges to Rational Pricing

Asset Pricing Anomalies

Traditional finance says prices should quickly reflect available information, leaving little predictable excess return. In practice, markets show persistent anomalies that are hard to reconcile with the simplest market efficiency benchmarks.

• Shiller’s Volatility Puzzle (1981) stated that stock prices fluctuate far more than subsequent dividends seem to justify under a standard present-value model.
  • With rational PV pricing, large price swings should track public information about dividends/discount rates; the excess volatility suggests prices move too much relative to fundamentals, violating EMH.
    • Possible answers mention time-varying rates of return: market periodicity (bubbles/recessions), long-term changes in growth and uncertainty, and changes in the perceived probability of catastrophic economic events.
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• The Predictability Puzzle states that returns are partially forecastable (e.g., using momentum, valuation ratios, post-earnings drift), contradicting the idea that price changes should be close to unpredictable given public information.
  • For example, when P/D or P/E ratios are low, future returns are high, and vice versa. These metrics have relatively weak power for forecasting future dividend/earnings growth, but have much stronger power for forecasting future excess returns.
    • Variation is interpreted mainly as variation in time-varying risk premia, or as mispricing/sentiment, rather than rational changes in expected cash-flow growth.
  • If prices already reflect public information, systematic predictors shouldn’t deliver predictable excess returns after risk adjustment.
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• The Equity Premium Puzzle (Mehra & Prescott, 1985) states that the historical return gap between equities and safe assets is too large to be explained by reasonable risk aversion in standard models. Let
  $\mathbb{E}[r_{\text{mkt}}]-r_f=\gamma \text{Cov}(\Delta c_{t+1},r_{\text{mkt}}),$
  for household consumption growth $\Delta c_{t+1}=\ln (C_{t+1}/C_t)$ and risk aversion constant $\gamma$.
  • In the consumption-based model, the equity premium is $\mathbb{E}[r_{mkt}]-r_f$, and empirically $\mathrm{Cov}(\Delta c_{t+1},r_{mkt})$ is small because aggregate consumption growth is smooth, so the model predicts a much smaller premium than the $\approx 6\%$ per year observed by U.S. stocks.
  • Matching a $\approx 6\%$ premium in this equation would require either an implausibly large $\gamma$ or a much larger covariance between market returns and consumption growth than the data show, which is why the observed magnitude looks too big for realistic risk aversion in the standard model.

See Also

• 8. Behavioral Finance — top-level course hub.
• 8.1. Principles of Behavioral Finance — the framework that responds to these anomalies.
• 8.7. Bubbles — the bubble literature that addresses the volatility and predictability puzzles.
• 8.6.7. Extrapolative Beliefs — the leading second-generation framework that jointly explains volatility, predictability, momentum, and reversal from a single mechanism.
• 8.8. Momentum — the cross-sectional manifestation of the predictability puzzle.
• 8.9. Reaction Models — the over- and under-reaction stories that account for predictability via behavioral biases.
• 8.10.1. Stock Market Non-Participation — the household-side mirror of the equity premium puzzle.