1. Behavioral Finance Preferences Part II Feb18 Behavioral Finance Economics 437

2. Behavioral Finance Preferences Part II Feb18 Review of Utility Theory Under certainty Preference Orderings Utility function with dim marg rates of subst Certainty Orderings over “lotteries” Von Neumann – Morganstern “Expected Utility” Two parts Utility function for certain events New Utility function: Expected Utility

3. Behavioral Finance Preferences Part II Feb18 Under certainty Price Quantity

4. Behavioral Finance Preferences Part II Feb18 Under uncertainty In simplest terms: Imagine: 3 possible outcomes: X 1, X 2, X 3 A lottery consists of {p 1, p 2, p 3 } P 1 > 0, P 2 > 0, and P 3 > 0 P 1 + P 2 + P 3 = 1 First, assume a V(X i ) where the X i ’s are certain Then U = p 1* V(X 1 ) + p 2 *V(X 2 ) + p 3 *V(X 3 ) Which becomes, U = p 1 *U(X 1 ) + p 2 *U(X 2 ) + p 3 *U(X 3 )

5. Behavioral Finance Preferences Part II Feb18 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

6. Behavioral Finance Preferences Part II Feb18 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

7. Behavioral Finance Preferences Part II Feb18 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

8. Behavioral Finance Preferences Part II Feb18 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 >

9. Behavioral Finance Preferences Part II Feb18 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

10. Behavioral Finance Preferences Part II Feb18 Risk Aversion Utility Wealth X Y U(X) U(Y) αU(X) + (1 – α)U(Y)

11. Behavioral Finance Preferences Part II Feb18 Risk Preference Utility Wealth X Y U(X) U(Y) αU(X) + (1 – α)U(Y)

12. Behavioral Finance Preferences Part II Feb18 So, what is an anomalie Something we cannot explain by traditional economic theory Could be: Violation of assumptions That people have utility functions That they can maximize them That they do maximize them Violations of predictions Royal Dutch Shell Closed End Puzzle

13. Behavioral Finance Preferences Part II Feb18 Utility function issues Framing Endowment Effect Status Quo Effect Intransitivities Allais Effect Time Consistency

14. Behavioral Finance Preferences Part II Feb18 Even if people have well behaved utility functions: May not be able to perform the maximization (has lead to research on “bounded rationality”). May have other motives (sense of fairness, sense of retribution, etc.)

15. Behavioral Finance Preferences Part II Feb18 The End