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Behavioral Finance

Behavioral Finance. Economics 437. Imagine that one in every thousand athletes use steroids. Imagine also that the test for steroids has a 5 % false positive rate. If a particular athlete tested positive for steroids what is the probability that that athlete was a steroid user. [0.001]

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Behavioral Finance

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  1. Behavioral Finance Economics 437

  2. Imagine that one in every thousand athletes use steroids. Imagine also that the test for steroids has a 5 % false positive rate. If a particular athlete tested positive for steroids what is the probability that that athlete was a steroid user • [0.001] • [0.020] • [0.65] • [0.95]

  3. Expected Utility Theory • Begin with a utility function defined only for certain dollar amounts: • Increasing in wealth (positive marginal utility) • Risk averse (diminishing marginal utility) • Then, using U(W), define expected utility as: • U(lottery) = p1 U(X1) + p2 U(X2) • Expected Utility is the “expected value of utility gained from different outcomes (X’s)” • If U(W) = W, then expected utility equals expected value

  4. Maurice Allais Example Choose between A and B A: $ 1 million gain with certainty B: Either $ 5 million with probability .10 $ 1 million with probability .89 $ 0 with probability 0.01

  5. Maurice Allais Example Choose between C and D C: Either $ 1 million with probability 0.11 or, nothing with probability 0.89 D: Either $ 5 million with probability 0.1 nothing with probabiolity 0.9

  6. Maurice Allais Example Choose between A and B A: $ 1 million gain with certainty B: Either $ 5 million with probability .10 $ 1 million with probability .89 $ 0 with probability 0.01 Choose between C and D C: Either $ 1 million with probability 0.11 or, nothing with probability 0.89 D: Either $ 5 million with probability 0.1 nothing with probabiolity 0.9

  7. Proof that Allais’s example involves violates “expected utility” hypothesis Violation occurs when people prefer both A and D If D is preferred to C: 0.1 U(5) + 0.9 U(0) > 0.11 U(1) + .89 U(0) IF A is preferred to B: U(1) > .1 U(5) + .89 U(1) + .11 U(0) Combining: 0.1 U(5) + U(1) + 0.9 U(0) > .1 U(5) + U(1) + 0.9 U(0) Cannot be >

  8. But, Expected Utility Most Widely Used • Example • Capital Asset Pricing Model • But, for CAPM, you need • Either a quadratic utility function, or • Normal distribution of returns

  9. Risk Aversion U(Y) Utility αU(X) + (1 – α)U(Y) U(X) Wealth X Y

  10. Risk Preference U(Y) Utility αU(X) + (1 – α)U(Y) U(X) Wealth X Y

  11. A Dilemna • US is preparing for the outbreak of an unusual foreign disease which is expected to kill 600 people • Program A: 200 people will be saved • Program B: 1/3 probability that 600 will be saved; 2/3 probability that no one will be saved

  12. Another Dilemna • Program C: If adopted 400 people will die • Program D: 1/3 probability that no one will die and 2/3 probability that 600 people will die

  13. Concurrent Decisions: • Choose Between: • A: A sure gain of $ 240 • B: 25 % gain of $ 1,000 and 75 % chance to gain nothing • Choose Between: • C: A sure loss of $ 750 • D: 75 % chance to lose $ 1,000 and 25 % chance to lose nothing

  14. Oops • Choose Between: • A: A sure gain of $ 240 • B: 25 % gain of $ 1,000 and 75 % chance to gain nothing • Choose Between: • C: A sure loss of $ 750 • D: 75 % chance to lose $ 1,000 and 25 % chance to lose nothing • If you chose A & D: • 25 % gain of $ 240 and 75 % chance to lose $ 760 • {B & C} dominates {A & D} • 25 % gain of $ 250 and 75 % chance to lose $ 750

  15. Make a choiceYou have been given $ 2,000 • Choose between A and B • A: 50 % chance of losing $ 1,000 or receiving nothing • B: A sure loss of $ 500

  16. Make a choiceYou have been given $ 1,000 • Choose between C and D • C: 50 % chance of winning $ 1,000 or receiving nothing • D: A sure $ 500

  17. Make a choice • Choose between A and B (assuming you have been given $ 1,000) • A: 50 % chance of winning $ 1,000 • B: A sure gain of $ 500 • Choose between C and D (assuming you have been given $ 2,000) • C: 50 % chance of losing $ 1,000 or receiving nothing • D: A sure loss of $ 500 A and C are identical B and D are identical

  18. Another Choice • Which would you prefer? • A: Certain gain of $ 30 • B: 80% chance to win $ 45 and 20% chance to win $ 0

  19. Another • C: 25 % chance to win $ 30 and 75 % chance to win nothing, or • D: 20 % chance to win $ 45 and 80 % chance to win nothing

  20. And again • A Two Stage Game • 75 % chance of ending the game winning nothing and 25 % chance of going to second stage of the game • At second stage • R:Certain win of $ 30, or • S:80% chance to win $ 45 and 20% chance to win nothing

  21. Two kinds of schools • School A has 65 % boys; 35 % girls • School B has 45 % boys; 55 % girls • A class has 55 % boys: Which school is it most likely to be taken from?

  22. The End

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