Behavioral Finance Economics 437

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

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

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

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

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 >

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

The End