A SURVEY OF BEHAVIORAL FINANCE
Redelmeier and Tversky (1992) provide a simple illustration, based on the gamble
1 ; 1 F ( 2 0 0 0 , 5 0 0 , 2 ) . 2
Subjects in their experiment were asked whether they were willing to take this bet; 57 percent said they would not. They were then asked whether they would prefer to play F five times or six times; 70 percent preferred the six-fold gamble. Finally they were asked:
Suppose that you have played F five times but you don’t yet know your wins and losses. Would you play the gamble a sixth time?
Sixty percent rejected the opportunity to play a sixth time, reversing their preference from the earlier question. This suggests that some subjects are framing the sixth gamble narrowly, segregating it from the other gambles. Indeed, the 60 percent rejection level is very similar to the 57 percent rejec- tion level for the one-off play of F.
3.2.2. ambiguity aversion
Our discussion so far has centered on understanding how people act when the outcomes of gambles have known objective probabilities. In reality, probabilities are rarely objectively known. To handle these situations, Sav- age (1964) develops a counterpart to expected utility known as subjective expected utility, SEU henceforth. Under certain axioms, preferences can be represented by the expectation of a utility function, this time weighted by the individual’s subjective probability assessment.
Experimental work in the last few decades has been as unkind to SEU as it was to EU. The violations this time are of a different nature, but they may be just as relevant for financial economists.
The classic experiment was described by Ellsberg (1961). Suppose that there are two urns, 1 and 2. Urn 2 contains a total of 100 balls, 50 red and 50 blue. Urn 1 also contains 100 balls, again a mix of red and blue, but the subject does not know the proportion of each.
Subjects are asked to choose one of the following two gambles, each of which involves a possible payment of $100, depending on the color of a
ball drawn at random from the relevant urn
a 1 : a b a l l i s d r a w n f r o m U r n 1 , a 2 : a b a l l i s d r a w n f r o m U r n 2 ,
$100 if red, $100 if red ,
$0 if blue, $0 if blue.
Subjects are then also asked to choose between the following two gambles:
b 1 : a b a l l i s d r a w n f r o m U r n 1 , b 2 : a b a l l i s d r a w n f r o m U r n 2 ,
$100 if blue, $100 if blue,
$0 if red, $0 if red.
a 2 i s t y p i c a l l y p r e f e r r e d t o a 1 , w h i l e b 2 i s c h o s e n o v e r b 1 . T h e s e c h o i c e s a r e i n c o n s i s t e n t w i t h S E U : t h e c h o i c e o f a 2 i m p l i e s a s u b j e c t i v e p r o b a b i l i t y t h a t