1. Behavioral Finance
Economics 437

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

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

4. 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

5. 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

6. 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) U(0) > 0.11 U(1) U(0)
IF A is preferred to B:
U(1) > .1 U(5) U(1) U(0)
Combining:
0.1 U(5) + U(1) U(0) > .1 U(5) + U(1) U(0)
Cannot be >

7. 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

8. The End