Economics 434 Theory of Financial Markets

1. Economics 434Theory of Financial Markets Professor Edwin T Burton Economics Department The University of Virginia

2. Efficient Market Hypothesis • Current Price is “best estimate” of value…..based upon • all relevant information • Stock Prices (adjusted) follow a “Martingale Process” • Three Versions: • Weak hypothesis (past prices) • Semi-strong (publicly known information) • Strong (all information, including inside info)

3. Martingale Process • Imagine you have $ Wealth • Now playing a game where you flip a coin: • Heads: you win $ 1 • Tails: you lose $ 1 • Assuming the coin is ”fair,” what is your expected wealth after one coin flip (or after the next n flips where n is any arbitrary integer) • Answer: E ($Wealth) = $ Wealth for any future time period

4. Martingale for a single stock Stock Price time

5. Martingale for a single stock (after one period) Stock Price time

6. No Arbitrage Assumption • It is not possible to make an infinite amount of money with a finite investment • Or • It is not possible to make a positive profit by investing zero or less • Means “no free lunch”

7. Modern Finance • If there are no arbitrage opportunities then markets are efficient • If markets are efficient then there are no arbitrage opportunities • It is possible that markets are not in equilibrium • If markets are in equilibrium, there are no arbitrage opportunities

8. Finite States of the World States: S1 S2 S3 Prob of States: π1π2π3 Securities: B1 B2 B3

9. Dividend Payoffs States 1 2 3 Securities 1 D11 D12 D13 2 D21 D22 D23 3 D31 D32 D33

10. Security Prices P1 P2 P3

11. A Portfolio (ϴ1, ϴ2, ϴ3) Value of a portfolio: ϴ1P1 +ϴ2P2+ ϴ3P3

12. The End