to allocate their portfolio between the two funds over the next month. They
are then shown the realized returns over that month, and asked to allocate
once again.
A second group of investors—Group II—is shown exactly the same series
of returns, except that it is aggregated at the annual level; in other words,
these subjects do not see the monthly fund fluctuations, but only cumula-
tive annual returns. After each annual observation, they are asked to allo-
cate their portfolio between the two funds over the next year.
A final group of investors—Group III—is shown exactly the same data,
this time aggregated at the five-year level, and they too are asked to allocate
their portfolio after each observation.
After going through a total of 200 months worth of observations, each
group is asked to make one final portfolio allocation, which is to apply
over the next 400 months. Thaler et al. (1997) find that the average final al-
location chosen by subjects in Group I is much lower than that chosen by
people in Groups II and III. This result is consistent with the idea that peo-
ple code gains and losses based on how information is presented to them.
Subjects in Group I see monthly observations and hence more frequent
losses. If they adopt the monthly distribution as a frame, they will be more
wary of stocks and will allocate less to them.
4.1.2.ambiguity aversionIn section 3, we presented the Ellsberg paradox as evidence that people dis-
like ambiguity, or situations where they are not sure what the probability
distribution of a gamble is. This is potentially very relevant for finance, as
investors are often uncertain about the distribution of a stock’s return.
Following the work of Ellsberg, many models of how people react to am-
biguity have been proposed; Camerer and Weber (1992) provide a compre-
hensive review. One of the more popular approaches is to suppose that
when faced with ambiguity, people entertain a range of possible probability
distributions and act to maximize the minimum expected utility under any
candidate distribution. In effect, people behave as if playing a game against
a malevolent opponent who picks the actual distribution of the gamble so
as to leave them as worse off as possible. Such a decision rule was first ax-
iomatized by Gilboa and Schmeidler (1989). Epstein and Wang (1994)
showed how such an approach could be incorporated into a dynamic asset-
pricing model, although they did not try to assess the quantitative implica-
tions of ambiguity aversion for asset prices.
Quantitative implications havebeen derived using a closely related frame-
work known as robust control. In this approach, the agent has a reference
probability distribution in mind, but wants to ensure that his decisions
aregood ones even if the reference model is misspecified to some extent.
Here too, the agent essentially tries to guard against a “worst-case” mis-
specification. Anderson, Hansen, and Sargent (1998) show how such a
30 BARBERIS AND THALER