1. Behavioral Finance Alok Kumar Yale School of Management 8 December 1999

2. Agenda • Efficient Market Hypothesis (EMH) • Expected Utility; Rational Expectations • Few Examples • Prospect Theory (Kahneman and Tversky) • Behavioral Heuristics and Biases in Decision Making • Implications for Financial Markets

3. Market Efficiency • Fama: “The market price at any time instant reflects all available information in the market”. • Cannot “make money” using “stale information”. • Three forms • Weak form: past prices and returns. • Semi-strong form: all public information. • Strong form: all public AND private information. • Michael Jensen: “there is no other proposition in economics which has more empirical support than the EMH”.

4. Challenges to EMH • Investors are not “fully rational”. They exhibit “biases” and use simple “heuristics” (rules of thumb) in making decisions. • Empirical Evidence on investor behavior: • investors fail to diversify. • investors trade actively (Odean). • Investors may sell winning stocks and hold onto losing stocks (Odean). • extrapolative and contrarian forecasts.

5. Expected Utility Theory • A theory of choice under uncertainty for a single decision-maker. • Expected Utility = p1*u1 + p2*u2 + … + pn*un. p: probability of an event u: utility derived from the event • Based on several strong assumptions about preferences. Example: transitivity, cancellation.

6. Rational Expectations Paradigm • All investors are identical. • All investors are utility maximizers. • All investors use “Bayes rule” to form new beliefs as new information becomes available. • All investor predictions are accurate. Expected Utility + Rational Expectations => Market Efficiency

7. Are Financial Markets Efficient? • Weak form of market efficiency supported to a certain extent. • Challenges: • Excess market volatility • Stock price over-reaction: long time trends (1-3 years) reverse themselves. • Momentum in stock prices: short-term trends (6-12 months) continue. • Size and B/M ratio (stale information) may help predict returns.

8. Stock Price Reaction to Non-Information • Crash of 1987: 22.6% decline without any apparent news. • 50 largest one-day stock price movements: occurred on days of no major announcements. • Inclusion of a stock in the S&P500 index results in significant share price reactions. Example: AOL rose 18% on the news of its inclusion in the index.

9. Role of Investor Behavior • Bounded Rationality: “satisficing” behavior. Information processing limitations. Example: memory limitations. • Investor Sentiment: beliefs based on heuristics rather than Bayesian rationality. • Investors may react to “irrelevant information” and hence may trade on “noise” rather than information.

10. “Irrational” Behavior of Professional Money Managers • May choose a portfolio very close to the benchmark against which they are evaluated (for example: S&P500 index). • Herding: may select stocks that other managers select to avoid “falling behind” and “looking bad”. • Window-dressing:add to the portfolio stocks that have done well in the recent past and sell stocks that have recently done poorly.

11. An Example • Initial endowment: $300. Consider a choice between: • a sure gain of $100 • a 50% chance to gain $200, a 50% chance to gain $0. • Initial endowment: $500. Consider a choice between: • a sure loss of $100 • a 50% chance to lose $200, a 50% chance to lose $0.

12. Reversal in Choice • Case 1: 72% chose option 1, 28% chose option 2. • Case 2: 36% chose option 1, 64% chose option 2. => A reversal in Choice • Problem framed as a gain: decision maker is risk averse. • Problem framed as a loss: decision maker is risk seeking.

13. Allais Paradox • Case 1: consider a choice between: • $1 million with certainty. • $5 million with prob 0.1, $1m with prob 0.89 and $0 with prob 0.01 • Case 2: consider a choice between: • $1m with prob 0.11, $0 with prob 0.89. • $5m with prob 0.10 and $0 with prob 0.90.

14. Allais Paradox: Explanation u(1m) > 0.10*u(5m) + 0.89*u(1m) + 0.01*u(0m) Add 0.89*u(0m) - 0.89*u(1m) to both sides. 0.11*u(1m) + 0.89*u(0m) > 0.10*u(5m) + 0.90*u(0m) Violates Expected Utility Theorem!

15. Prospect Theory • Proposed by two psychologists: Daniel Kahneman and Amos Tversky. • Gambles are evaluated relative to a reference point. • Decision maker analyzes “gains” and “losses” differently. • Incremental value of a loss is larger than that of a loss. “the hurt of a $1000 loss is more painful than the benefit of a $1000 gain”.

16. Behavioral Heuristics and Decision-Making Biases • What strategies do decision makers use when faced with difficult decisions, especially ones that involve uncertainty? • Commonly Used Heuristics • Availability: “familiarity breeds investment”. • Representativeness: judgement based on similarity. “Patterns in random sequences”. • Reliance on the judgement of other people (Keynes beauty contest analogy).

17. Gambler’s Fallacy • Investors may apply law of large numbers to small sequences. Example: fair coin tossing. THTHTHHHHHH -> P(T) = ?, P(H) = ?. • Which of the 2 sequences is more likely to occur in a fair coin tossing experiment? • HHHHHHTTTTTTHHHHHH • HHTHTHHTHTTHTHHTTH

18. Some more Heuristics • Overconfidence:people overestimate the reliability of their knowledge. • Excessive trading • Framing Effect • Regret Aversion: anticipation of a future regret can influence current decision. • Disposition Effect: sell winners, hold on to the losers. • Anchoring and adjustment: can create under-reaction.

19. Fashions and Fads • People are influenced by each other. There is a social pressure to conform. • Herding behavior: “safety-in-numbers”. • Informational Cascades • Positive Feedback • Example: excessive demand for internet IPOs. Extremely high opening day returns.

20. Can arbitrage opportunities exist? • Yes! • Real-world arbitrage is always risky. No riskless hedge for the arbitrageur. • Arbitrageur faces“noise trader” risk: mispricing can become worse before it disappears. • Close substitutes (needed for arbitrage positions) may not be available. • Fundamentally identical assets may NOT sell at identical prices.

21. Behavioral Finance: Two Major Foundations • Investor Sentiment: creates disturbances to efficient prices. • Limited arbitrage: arbitrage is never riskfree, hence it does not counter irrational disturbances. • Prices may not react to information by the “right” amount. • Prices may react to non-information. • Markets may remain efficient.

22. Summary • Investor behavior does have an impact on the behavior of financial markets. How much? Not clear! • Both “social” and “psychological” must be taken into account in explaining the behavior of financial markets. • Market “anomalies” may be widespread. • Behavioral Finance: does not replace but complements traditional models in Finance.