1. Behavioral Finance EMH Definitions Jan 24, 2012 Behavioral Finance Economics 437

2. Behavioral Finance EMH Definitions Jan 24, 2012 Immediate Reading (today, Jan 24) Malkiel (online) Shiller (online) Shleifer (book, Ch 1)

3. Behavioral Finance EMH Definitions Jan 24, 2012 The Efficient Market Hypothesis (EMH) Price captures all relevant information Modern version based upon “No Arbitrage” assumption Why do we care? Implications Only new information effects prices Publicly known information has no value Investors should “index” Allocation efficiency

4. Behavioral Finance EMH Definitions Jan 24, 2012 Definition of EMH (Eugene Fama’s Definition) from Shleifer’s Chapter One Weak Hypothesis: past prices and returns are irrelevant Semi-Strong Hypothesis: all publicly known information is irrelevant Strong Hypothesis: public and private information is irrelevant

5. Behavioral Finance EMH Definitions Jan 24, 2012 The Malkiel View Burton Malkiel, author of “Random Walk Down Wall Street” His view is that the evidence shows that money managers cannot beat simple indexes like the S&P500 over time To Malkiel, that means the market is efficient

6. Behavioral Finance EMH Definitions Jan 24, 2012 Robert Shiller’s View Prices should be based upon fundamental Future cash flows (or dividends) and future interest rates Prices are way too volatile as compared to the modest changes over time in expectations of future cash flows and interest rates Thus, the market is not efficient – prices are too volatile to be consistent with efficiency

7. Behavioral Finance EMH Definitions Jan 24, 2012 A Martingale Process Imagine a process X(t) over time For any t, E[X(t)] is the “expected value of X at time” Either: ∑ X i *P(X i ) for i: 1 to n if only discrete values of X ∫ X * f(X) dX where f(X) is a probability density function “Expected value” is an average (weighted) A Martingale Process is defined as a process with the following property: E[X(t)] = X(s) for all t, s where s > t

8. Behavioral Finance EMH Definitions Jan 24, 2012 Example of a “Martingale Process” Coin flip X(t) where X(0) = 0 X(t+1) = X(t) plus F(t) Where F(t) = +1 if coin flip is heads Where F(t) = -1 if coin flip is tails If p(H) = P(T) = ½ Then E[X(t+1)] = X(t) And E[X(s)] = X(t) where s> t Hence X(t) is a Martingale Process

9. Behavioral Finance EMH Definitions Jan 24, 2012 Can stock returns be a “Martingale Process?” E[P(s)] = P(t) for all s > t ? But shouldn’t stocks earn a return? Suppose the mean return of a stock is r Create a new variable, Q and assume s > t Let Q (s) = P(s)*(1+r) -n where n = s – t Then Q(t) = P(t) E[Q(s)] = Q(t) for all s > t Means that, after subtracting out a mean return of r, P(t) is a Martingale Process

10. Behavioral Finance EMH Definitions Jan 24, 2012 Modern Finance Assumes Stock Prices (Adjusted) Follow a Martingale Process This is the definition of EMH in the modern finance literature Also known as “random walk”

11. Behavioral Finance EMH Definitions Jan 24, 2012 The End