1. Behavioral Finance Law Of One Price Feb 2 2016 Behavioral Finance Economics 437

2. Behavioral Finance Law Of One Price Feb 2 2016 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

3. Behavioral Finance Law Of One Price Feb 2 2016 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

4. Behavioral Finance Law Of One Price Feb 2 2016 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

5. Behavioral Finance Law Of One Price Feb 2 2016 Coin flip (Net Heads = Heads – Tails) 0 1 2 -2

6. Behavioral Finance Law Of One Price Feb 2 2016 Can stock returns be a “Martingale Process?” (Accounting for Trend) 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

7. Behavioral Finance Law Of One Price Feb 2 2016 Random Walk Around a Rising Trend (This is a martingale with trend subtracted out) time 1 2

8. Behavioral Finance Law Of One Price Feb 2 2016 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” (not quite correctly, as Fama points out in his 1970 article)

9. Behavioral Finance Law Of One Price Feb 2 2016 Black on “Noise” Black strong believer in noise and noise traders in particular They lose money according to him (though they may make money for a short while) Prices are “efficient” if they are within a factor of 2 of “correct” value Actual prices should have higher volatility than values because of noise

10. Behavioral Finance Law Of One Price Feb 2 2016 What is a short sale? Sell 100 shares of GOOG at 1101 What happens? You enter an order to sell 100 shares at 1101 The order is “executed” – meaning that you have sold 100 shares to someone else somewhere Mechanically, how do provide the 100 shares to the buyer? You borrow the 100 shares from an institutional holder (like UVA’s Endowment) You provide collateral equal to the value of the stock ($ 110,100) and perhaps a little more collateral in case the stock price goes up. You mark to market If stock goes to 1096, you send $ 500 more in cash to lender If stock goes to 1106, lender sends you $ 500 in cash Where do you get the $ 110,100? The buyer gives you $ 110,100 and you pass that through to the stock lender On some future date, you buy 100 shares at say 900, paying $ 90,000 which you receive back from the stock lender when you return the 100 shares to the lender

11. Behavioral Finance Law Of One Price Feb 2 2016 Short Sale Mechanics 100 shares of GOOG at 1101 Short seller Stock buyer 100 shares $ 110,100 UVA Endowment Short seller 100 shares $ 110,100

12. Behavioral Finance Law Of One Price Feb 2 2016 The End