Library Class 09/12. Meets in Doe Library Room 105

Transcription

1 Library Class 09/12 Meets in Doe Library Room 105

2 Honor s Thesis Mantra 1. Why is this interesting? 2. Economic Theory (model) 3. Can one refute the model (theory?) testable implications 4. Test 5. Results 6. Conclusion

3 Efficient Markets September 2014

4 Can You Predict Stock Prices? Apple Price Apple Return Jan00 Jan02 Jan04 Jan06 Jan08 Jan10 Jan12 Jan Jan00 Jan02 Jan04 Jan06 Jan08 Jan10 Jan12 Jan Microsoft Price Microsoft Return Jan00 Jan02 Jan04 Jan06 Jan08 Jan10 Jan12 Jan Jan00 Jan02 Jan04 Jan06 Jan08 Jan10 Jan12 Jan14

5 Why is this interesting? Stock Prices look predictable Pundits offer (and sell) advice, eg, The Harvard-Educated Business Strategist and Best-Selling Author who anticipated every major boom and bust of the last 25 years now predicts... The Dow Will Plummet to 6,000! Turns out that returns are unpredictable Samuelson story

6 Intuitive Economic Story Expected Excess Return => buy (or sell) Buying (or selling) changes current price Equilibrium: No Expected Excess Return

7 Lot s of Applications for Efficient Markets Theory Valuing Professional Athletes Moneyball by Michael Lewis NFL Gambling Alex Kupper (2012 thesis)

8 Overview Intuitive Story: no expected excess returns Hard Part tractable testable model Simple model for stock market Compare random walk and mean reversion NFL Gambling odds should be probability of winning

9 Malkiel s Definition A capital market is said to be efficient if it fully and correctly reflects all relevant information in determining security prices. Formally, the market is said to be efficient with respect to some information set if security prices would be unaffected by revealing that information to all participants. Moreover, efficiency with respect to an information set.implies that it is impossible to make economic profits by trading on the basis of [that information set].

10 Information Sets (Fama) Weak-form Efficiency: The information set includes only the history of prices or returns. Semistrong-form Efficiency: The information set includes all publicly available information. Strong-form Efficiency: The information set includes all (public and private) information.

11 Statistical Tests require Mathematical model Formalization Capture essential characteristics Necessarily simplifies complex reality If you reject are you rejecting the economic hypothesis, or the simplified model? Fama s famous paper tests the constant expected returns model for stock mkt Your Group Assignment 1 tests the constant expected returns model

12 Constant Expected Returns Model S d rt 1 St Model r t 1 t 1 t 1 t 1 t 1 ln ; 2 ~ N( r, ) t which implies returns are "unpredictable", r r e 2 et 1 N(0, ) t

13 Is Equivalent to Random walk with Drift 1. r ln( S d ) ln S r e, where t 1 t 1 t 1 t t 1 2. E r r E ln( S d ) ln S t t 1 t t 1 t 1 t Rearrange 1 and this is a random walk with drift r, ln( S d ) r ln S e t 1 t 1 t t 1

14 Properties of Constant Expected Return and Random Walk Expected returns are unpredictable (constant) => no expected excess returns (Log) payoffs (prices + dividends) follow a random walk with drift r Model satisfies definition of an efficient market and is testable

15 An Alternative: Mean-Reversion ln( S d ) ln S r ((ln( S d ) ln S ) r ) u t 1 t 1 t t t t 1 t 1 2 0< 1, u ~ N(0, ) or in returns, r r ( r r ) u ; t 1 t t 1 r (ln( S d ) ln S ) t 1 t 1 t 1 t

16 Properties of Mean Reverting Walk Expected returns are predictable =>expected excess returns > r-r(bar) Realized Log payoffs (prices + dividends) return to trend r(bar) Model does not satisfy simple definition of an efficient market

17 Test Constant Expected Returns If one can predict future returns, then the model and (this form of the) efficient markets hypothesis are rejected r a b X u ' t 1 t t 1

18 Project: Test the Constant Returns Model See the assignment on the class webpage If it rejects (an a few will), then (not this problem set) an honors thesis should ask: Is this statistical (you reject 5% of the time when the null is true) Is the model wrong or is the theory wrong Is it economically significant? How much money can one make betting against the random walk model?

19 Surprisingly some resist testing (The Tea Party? or just Facts)

20 Theory Wrong: Shiller Rejects Constant Expected Returns Model Interprets the rejection as a rejection of The Efficient Markets Hypothesis

21 Shiller s picture

22 Theory Correct test wrong: Malkiel Mutual Fund Performance Model? Professional managers should beat amateurs

23 Malkiel s Results

24 NFL Betting: Efficient Markets Test Very Clean Test: Bettors set the odds (equilibrium price) Bettors have money on the line and the more they bet the more they affect the equilibrium price If the market is efficient, then the odds (translated to the probability) should be the best prediction of the probability of winning. Any (public) information should be in the market prediction. p = 1/(odds + 1); where p == probability of winning

25 What to take away from today Model for a thesis 1. Why is this interesting? 2. Economic Theory (model) 3. Can one refute the model (theory?) 4. Test hypothesis 5. Results Resisting testing can restrict your degrees of freedom