00Thaler_FM i-xxvi.qxd

local curvature to reject Eover a wide range of wealth levels, it must be an
extraordinarily concave function, making the investor extremely risk averse
over large stakes gambles.
The final piece of prospect theory is the nonlinear probability transfor-
mation. Small probabilities are overweighted, so that π(p)>p. This is de-
duced from KT’s finding that

(5000, 0.001) (5, 1),

and

(−5, 1) (−5000, 0.001),

together with the earlier assumption that υis concave (convex) in the do-
main of gains (losses). Moreover, people are more sensitive to differences in
probabilities at higher probability levels. For example, the following pair of
choices,

(3000, 1) (4000, 0.8; 0, 0.2),

and

(4000, 0.2; 0, 0.8) (3000, 0.25),

which violate EU theory, imply

The intuition is that the 20 percent jump in probability from 0.8 to 1 is
more striking to people than the 20 percent jump from 0.2 to 0.25. In par-
ticular, people place much more weight on outcomes that are certain rela-
tive to outcomes that are merely probable, a feature sometimes known as the
“certainty effect.”
Along with capturing experimental evidence, prospect theory also simulta-
neously explains preferences for insurance and for buying lottery tickets.
Although the concavity of υin the region of gains generally produces risk
aversion, for lotteries which offer a small chance of a large gain, the over-
weighting of small probabilities in figure 1.2 dominates, leading to risk-
seeking. Along the same lines, while the convexity of υin the region of losses
typically leads to risk-seeking, the same overweighting of small probabilities
induces risk aversion over gambles which have a small chance of a large loss.
Based on additional evidence, Tversky and Kahneman (1992) propose a
generalization of prospect theory which can be applied to gambles with
more than two outcomes. Specifically, if a gamble promises outcome xi
with probability pi, Tversky and Kahneman (1992) propose that people as-
sign the gamble the value

πυii (2)

i

∑ (),x

π

π

π

π

(. )

(.)

()

(.)

.

025

02

1

08

<

f

f

f

f

A SURVEY OF BEHAVIORAL FINANCE 19