Behavioral Finance
Economics 437
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


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Utility function for certain events
New Utility function: Expected Utility
Preferences Part II
Feb18
Under certainty
Price
Quantity
Behavioral Finance
Preferences Part II
Feb18
Under uncertainty
In simplest terms:
 Imagine: 3 possible outcomes: X1, X2, X3
 A lottery consists of {p1, p2, p3}


P1 > 0, P2 > 0, and P3 > 0
P1 + P2 + P 3 = 1
 First, assume a V(Xi) where the Xi’s are
certain
 Then U = p1*V(X1) + p2*V(X2) + p3*V(X3)
 Which becomes, U = p1*U(X1) + p2*U(X2) +
p3*U(X3)
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
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
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
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
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 >
Behavioral Finance
Preferences Part II
Feb18
But, Expected Utility Most Widely
Used
 Example


Capital Asset Pricing Model
But, for CAPM, you need


Behavioral Finance
Either a quadratic utility function, or
Normal distribution of returns
Preferences Part II
Feb18
Risk Aversion
U(Y)
Utility
αU(X) + (1 – α)U(Y)
U(X)
X
Behavioral Finance
Wealth
Y
Preferences Part II
Feb18
Risk Preference
U(Y)
Utility
αU(X) + (1 – α)U(Y)
U(X)
X
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Wealth
Y
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


Behavioral Finance
Royal Dutch Shell
Closed End Puzzle
Preferences Part II
Feb18
Utility function issues
 Framing
 Endowment Effect
 Status Quo Effect
 Intransitivities
 Allais Effect
 Time Consistency
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.)
Behavioral Finance
Preferences Part II
Feb18
The End
Behavioral Finance
Preferences Part II
Feb18