Lecture 10 - Topic 8 - Behavioral Explanations for Anomalies

[Behavioral Explanations for Anomalies]

Traditional Finance vs behavioural finance

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Behavioural finance

EMH: Empirical Challenges

Anomalies

  1. Excess volatility: Shiller (1981) and Le Roy (1981)
  1. Equity premium puzzle
  2. Time series stock market predictability puzzle
  3. Cross-sectional price-scaled anomalies: value premium
  4. Over- and under-reaction [Today’s focus]
  5. Seasonal effects
  6. “Twin shares” with different prices

Introduction: Behavioral Explanations or Anomalies

  1. the small-firm effect;
  2. lagged reactions to earnings announcements;
  3. value versus growth;
  4. momentum and reversal

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Review of Trading Rules that Have Shown to be Effective.

  1. Small cap portfolios vs. large cap portfolios?
  1. Portfolios formed based on P/Es:
  1. Earnings announcements momentum:
  1. Value vs. growth portfolios
  1. Predictable serial correlation:
  1. Long-term winners vs. losers:

What is Behind Value Advantage?

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  1. They are committing judgment errors in extrapolating past growth rates too far into the future and are thus surprised when value stocks shine and glamour stocks disappoint. This is so-called “expectational error hypothesis”
  2. Because of representativeness, investors may assume that good companies are good investments These first two reasons are mistakes of judgment. Likely individual investors are more subject to committing them than institutional investors.

What is Behind Value Advantage?

Next two reasons (Reason 3 and Reason 4) are due to agency considerations (rational reasons to shy away from value):

  1. Because sponsors view companies with steady earnings and buoyant growth as prudent investments, so as to appear to be following their fiduciary obligation to act prudently, institutional investors may shy away from hard-to-defend, out-of-favour value stocks.
  2. Also because of career concerns, institutional investors, who are evaluated over short horizons, may be nervous about tilting too far in any direction thus incurring tracking error. A value strategy would require such a tilt and may take some time to pay off, so it is in this sense risky.

Explaining Long-Run Value Outperformance

Such stocks have a period of anticipated higher-than-normal growth.

When it becomes clear that mean reversion is occurring, growth stocks deteriorate. Similar story (in reverse) can be told for value stocks.

Introduction: Behavioral Explanations or Anomalies

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Daniel-Hirshleifer-Subrahmanyam (DHS) Model: Explaining Reversal

DHS model is based on overconfident investors overestimating the precision of their own private signals.

== > This leads to a negative serial correlation in price movements (i.e., reversal).

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DHS model details

Formally, the private information at t=1 is: s1=θ+ϵs_1 = \theta + \epsilon

Black dot, equilibrium price

true value theta plus some error epsilon

s1=θ+ϵs_1 = \theta + \epsilon

Using σc2\sigma ^2_c instead of σϵ2\sigma ^2_\epsilon where, σc2\sigma ^2_c < σϵ2\sigma ^2_\epsilon

DHS Model: Price Response at t = 1

Consider the price at t = 1. The challenge is to separate the information from the noise.

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Example

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Price Path Graphs

The DHS model offers a number of testable implications.

Solid lines in the graph show price paths assuming that overconfident traders drive prices.

Broken lines show price paths assuming no overconfidence.

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Grinblatt-Han Model (to explain momentum)

Grinblatt-Han model (hereafter GH), is based on prospect theory, mental accounting, and the disposition effect.

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Grinblatt-Han Model – Intrinsic Value

ft+1=ft+ϵt+1f_{t+1} = f_t + \epsilon_{t+1}

D(R)t=1+b(ft−pt)D(R)_t = 1+b(f_t - p_t)

D(R)t=1+b(ft−pt)+λ(reft−pt)D(R)_t = 1+b(f_t - p_t) + \lambda (ref_t - p_t)

Investors are affected by their reference point refref and the stock market price ptp_t

Market Price

pt=ωft+(1−ω)reft;    ω=11+μλp_t = \omega f_t + (1- \omega ) ref_t; \;\; \omega = \frac{1}{1+ \mu \lambda}

To interpret, the market price is a weighted average of value and the reference point.

Grinblatt-Han Model – Intrinsic Value

reft+1=vpt+(1−v)reftref_{t+1} = vp_t + (1-v)ref_t

Grinblatt-Han Model – Simulation Based on GH Model

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Figure 13.3 shows the evolution of prices and reference points over the next 24 months (to t = 25).

Grinblatt-Han Model – Intrinsic Value

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Nevertheless, a stock’s unrealized capital gain is likely to be highly correlated with past returns, so standard momentum is easily implied by the model. Capital gain should be a better predictor of future returns than past returns.

For this reason, we turn to the final model, which explains both momentum and reversal. BSV model: Explaining momentum/reversal

Barberis-Shleifer-Vishy (BSV) Model: Explaining Momentum/Reversal

Recall sun and clouds example:

Markets overreact slowly!!!

BSV Model Formalises This Story

Suppose we assume that a random walk holds for earnings (nt):

nt+1=nt+ϵt+1n_{t+1} = n_t + \epsilon_{t+1}

Given a positive (negative) earnings change, there is a low probability of another positive (negative) earnings change in the next period. Underreaction.

Given a positive/negative earnings change, there is a high probability of another positive/negative earnings change in the next period. Overreaction

At all points in time, individuals must guess whether the world is in Regime 1 or 2. Estimated probabilities will rise and fall as events unfold:

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Simulation Based on BSV Model

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To see how the model works in terms of the revision over time of the probability that the world is in regime 1, refer to Figure 13.4.

Note that q t rises after a sign switch but falls after a sign continuation.

Explaining Momentum and Reversal

Investor beliefs about regime will dictate prices:

So, this model can explain both underreaction and overreaction.

And momentum and reversal empirical regularities can be simulated.

Simulated Returns from Earnings and Returns Sorts Based on BSV Model

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Rational Explanation - Inappropriate Risk Adjustment

Inappropriate Risk Adjustment.

Challenged the then-accepted CAPM model, suggesting it didn't work anymore. CAPM indicates only a security's beta should impact expected returns. Their data (from 1963-1990) contradicted this, showing no positive relation between stock returns and market betas.

Findings suggest that stock risks have multiple dimensions, including size and the book-to-market equity ratio. This led to the development of the Fama-French three-factor model.

Anomalies in stock returns either indicate investor errors or improper risk adjustment.

Fama-French Three Factor Model

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Conclusion

  1. Post-announcement earnings drift appears to be driven by anchoring on the part of investors and analysts.
  2. The value premium is likely due to both behavioral and agency-related institutional factors.
  3. A number of theoretical models have been formulated to account for momentum and reversal.
  4. The DHS model explains reversal using overconfidence; the GH model explains momentum using prospect theory, mental accounting, and the disposition effect; and the BSV model accounts for both momentum and reversal and is based on the anchoring and representativeness heuristics.
  5. Much of the empirical evidence is consistent with the implications of these models.
  6. Another view is that risk has been improperly accounted for in the research that has identified these anomalies, and a proper treatment of risk will render these anomalies as merely risk premiums.
  7. The Fama-French three-factor model has value and small cap as risk factors over and above market risk.
  1. Momentum is not credibly accounted for by any risk-adjustment technique.