are more likely to sell stocks that have gone up in value relative to their
purchase price, rather than stocks that have gone down.
It is hard to explain this behavior on rational grounds. Tax considera-
tions point to the selling of losers, not winners.^35 Nor can one argue that in-
vestors rationally sell the winners because of information that their future
performance will be poor. Odean reports that the average performance of
stocks that people sell is better than that of stocks they hold on to.
Two behavioral explanations of these findings have been suggested. First,
investors may have an irrational belief in mean-reversion. A second possi-
bility relies on prospect theory and narrow framing. We have used these in-
gredients before, but this time it is not loss aversion that is central, but
rather the concavity (convexity) of the value function in the region of gains
(losses).
To see the argument, suppose that a stock that was originally bought at
$50 now sells for $55. Should the investor sell it at this point? Suppose that
the gains and losses of prospect theory refer to the sale price minus the pur-
chase price. In that case, the utility from selling the stock now is υ(5). Alter-
natively, the investor can wait another period, whereupon we suppose that
the stock could go to $50 or $60 with equal probability; in other words, we
abstract from belief-based trading motives by saying that the investor ex-
pects the stock price to stay flat. The expected value of waiting and selling
next period is then υ(0)+ υ(10). Since the value function υis concave in
the region of gains, the investor sells now. In a different scenario, the stock
may currently be trading at $45. This time, the comparison is between υ(−5)
and υ(−10)+ υ(0), assuming a second period distribution of $40 and $50
with equal probability. Convexity of υpushes the investor to wait. Intu-
itively, by not selling, he is gambling that the stock will eventually break
even, saving him from having to experience a painful loss.
The disposition effect is not confined to individual stocks. In an innova-
tive study, Genesove and Mayer (2001) find evidence of a reluctance to sell
at a loss in the housing market. They show that sellers whose expected sell-
ing price is below their original purchase price, set an asking price that ex-
ceeds the asking price of other sellers with comparable houses. Moreover,
this is not simply wishful thinking on the sellers’ part that is later corrected
by the market: sellers facing a possible loss do actually transact at consider-
ably higher prices than other sellers.
Coval and Shumway (2000) study the behavior of professional traders in
the Treasury Bond futures pit at the CBOT. If the gains and losses of
prospect theory are taken to be daily profits and losses, the curvature of the
value function implies that traders with profits (losses) by the middle of the
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(^35) Odean (1998) does find that in December, investors prefer to sell past losers rather than
past winners, but overall, this effect is swamped by a strong preference for selling past winners
in the remaining eleven months.