by itself cannot explain the results, since the distribution of final payoffs is
virtually the same for the three gambles. It is actually the combination of
loss aversion and myopia that describes the observed behavior.
The subjects were also presented with the explicit distribution of final out-
comes that the three gambles entail. Once the subjects viewed the distribution
of final outcomes, virtually all of them (95%) preferred the gamble to the cer-
tain amount. Hence, the subjects found the gambles much more attractive
when the data was aggregated on their behalf. This result suggests that, left
alone, the subjects overestimated the likelihood of losing money. We tested
this hypothesis directly, by asking subjects to estimate the probability of los-
ing money after all the one hundred and fifty trials of the first gamble were
completed. The average (median) answer was 0.237 (0.150), whereas the cor-
rect answer is 0.003. The gross overstatement of the chances to lose money is
consistent with myopic loss aversion. However, it is in complete contrast to
what Samuelson called “the fallacy of large numbers.” We elaborate on this
issue and discuss new experimental data below.
As you might recall, Samuelson offered his colleague the following bet:
heads you win $200, tails you lose $100. Samuelson’s colleague rejected a
single play of the bet, but expressed a desire to play it 100 times. Samuelson
proved that this combination of responses is inconsistent, and accused his
colleague of the fallacy of large numbers. Specifically, Samuelson argued
that his colleague did not understand that the variance of final outcomes
grows proportionally to the number of plays. If Samuelson’s colleague was
typical, then most people would prefer the series of plays to the single play.
In addition, once the explicit distribution is presented, people are expected
to change their mind and reject the series of bets. We found just the oppo-
site. People tend to accept the single bet, but then reject the series of bets.
Furthermore, once the explicit distribution of the series is presented, virtu-
ally everybody accepts it. We conclude that Samuelson’s colleague is atypi-
cal. Most people, we believe, tend to follow the “fallacy of small numbers.”
Not only do they not understand that the variance of final outcomes in-
creases proportionally to the number of plays, they often think it grows
much faster than the number of plays.
We end our tests by turning to an important implication of myopic loss
aversion, which relates to the worldwide trend toward investor autonomy.
In the United States, for instance, people are responsible for managing their
retirement funds through 401(k), among other, defined contribution saving
plans. One interesting question is whether the frequency at which perfor-
mance is evaluated influences investment choices. In particular, myopic loss
aversion predicts that frequent reporting will accentuate the perceived risk
of stocks, because the likelihood of stocks experiencing a loss in the short-
term is relatively high.
To test the role of myopic loss aversion in retirement saving plans, we
presented USC staff employees with the distribution of either the historical
220 BENARTZI AND THALER