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Economics 434 Theory of Financial Markets

Economics 434 Theory of Financial Markets. Professor Edwin T Burton Economics Department The University of Virginia. Efficient Market Hypothesis. Current Price is “best estimate” of value…..based upon all relevant information Stock Prices (adjusted) follow a “ M artingale P rocess”

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Economics 434 Theory of Financial Markets

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  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

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