The idea that prior outcomes may affect willingness to take risk is also
supported by recent studies in psychology. Thaler and Johnson (1990)
study risk-taking behavior in an experimental setting using a large sample
of Cornell undergraduate and MBA students. They offer subjects a sequence
of gambles and find that outcomes in earlier gambles affect subsequent be-
havior: following a gain, people appear to be more risk seeking than usual,
taking on bets they would not normally accept. This result has become
known as the “house money” effect, because it is reminiscent of the expres-
sion“playing with the house money” used to describe gamblers’ increased
willingness to bet when ahead. Thaler and Johnson argue that these results
suggest that losses are less painful after prior gains, perhaps because those
gains cushion the subsequent setback.
Thaler and Johnson also find that after a loss, subjects display consider-
able reluctance to accept risky bets. They interpret this as showing that
losses are more painful than usual following prior losses.^15
The stakes used in Thaler and Johnson (1990) are small—the dollar
amounts are typically in double digits. Interestingly, Gertner (1993) obtains
similar results in a study involving much larger stakes. He studies the risk-
taking behavior of participants in the television game show Card Sharks,
where contestants place bets on whether a card to be drawn at random
from a deck will be higher or lower than a card currently showing. He finds
that the amount bet is a strongly increasing function of the contestant’s
winnings up to that point in the show. Once again, this is evidence of more
aggressive risk-taking behavior following substantial gains.
The evidence we have presented suggests that in the context of a sequence
of gains and losses, people are less risk averse following prior gains and more
risk averse after prior losses. This may initially appear puzzling to readers fa-
miliar with Kahneman and Tversky’s original value function, which is con-
cave in the region of gains and convex in the region of losses. In particular,
the convexity over losses is occasionally interpreted to mean that “after a
loss, people are risk seeking,” contrary to Thaler and Johnson’s evidence.
Hidden in this interpretation, though, is a critical assumption, namely that
people integrateor “merge” the outcomes of successive gambles. Suppose
that you have just suffered a loss of $1,000, and are contemplating a gamble
equally likely to win you $200 as to lose you $200. Integration of outcomes
238 BARBERIS, HUANG, SANTOS
this evidence into account, although we do not attempt it here. Second, we assume that in-
vestors rationally forecast future changes in the reference level StRf,t. It is sometimes claimed
that such rationality is inconsistent with loss aversion: if people know they are eventually
going to reset their reference level after a stock market drop, why are they so averse to the loss
in the first place? Levy and Wiener (1997) provide one answer, noting that changing the refer-
ence level forces the investor to confront and accept the loss, and this is the part that is painful.
(^15) It is tempting to explain these results using a utility function where risk aversion de-
creases with wealth. However, any utility function with sufficient curvature to produce lower
risk aversion after a $20 gain, regardless of initial wealth level, inevitably makes counterfac-
tual predictions about attitudes to large-scale gambles.