1. Behavioral Finance Biases Feb 23 Behavioral Finance Economics 437

2. Behavioral Finance Biases Feb 23 A. [0.001] B. [0.020] C. [0.65] D. [0.95] 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

3. Behavioral Finance Biases Feb 23 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) = p 1 U(X 1 ) + p 2 U(X 2 ) 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. Behavioral Finance Biases Feb 23 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. Behavioral Finance Biases Feb 23 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. Behavioral Finance Biases Feb 23 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. Behavioral Finance Biases Feb 23 Proof that Allais’s example involves violates “expected utility” hypothesis Violation occurs when people prefer both A and D 0.1 U(5) + 0.9 U(0) > 0.11 U(1) +.89 U(0) If D is preferred to C: 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. Behavioral Finance Biases Feb 23 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. Behavioral Finance Biases Feb 23 Risk Aversion Utility Wealth X Y U(X) U(Y) αU(X) + (1 – α)U(Y)

10. Behavioral Finance Biases Feb 23 Risk Preference Utility Wealth X Y U(X) U(Y) αU(X) + (1 – α)U(Y)

11. Behavioral Finance Biases Feb 23 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 A Dilemna

12. Behavioral Finance Biases Feb 23 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. Behavioral Finance Biases Feb 23 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. Behavioral Finance Biases Feb 23 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. Behavioral Finance Biases Feb 23 Make a choice You 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. Behavioral Finance Biases Feb 23 Make a choice You 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. Behavioral Finance Biases Feb 23 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 identicalB and D are identical

18. Behavioral Finance Biases Feb 23 Another Choice Which would you prefer? A: Certain gain of $ 30 B: 80% chance to win $ 45 and 20% chance to win $ 0

19. Behavioral Finance Biases Feb 23 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. Behavioral Finance Biases Feb 23 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. Behavioral Finance Biases Feb 23 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. Behavioral Finance Biases Feb 23 The End