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q
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1
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9
9
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(
1
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h
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(
1
9
9
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(
1
9
9
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)
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n
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ra
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ce
ch
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(1
9
8
8
),
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o
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n
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n
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a
l.
(
1
9
9
3
)
H
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t d
ay
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w
p
(l
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)
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al
an
ié
(
1
9
9
7
)
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et
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fe
ct
th
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en
d
o
f
th
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d
ay
ef
fe
ct
(1
9
5
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)
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su
ra
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B
u
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p
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o
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C
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uy
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h
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e
w
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e
in
su
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(l
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(
1
9
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is
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tf
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te
r
(1
9
9
3
)
150
C A M E R E R
1
. Finance: The Equity Premium
Two important anomalies in finance can be explained by elements of prospect
theory. One anomaly is called the
equity premium
. Stocks—or equities—tend to
have more variable annual price changes (or “ returns ”) than bonds do. As a re-
sult, the average return to stocks is higher as a way of compensating investors for
the additional risk they bear. In most of this century, for example, stock returns
were about 8% per year higher than bond returns. This was accepted as a reason-
able return premium for equities until Mehra and Prescott (1985) asked how large
a degree of risk-aversion is implied by this premium. The answer is surprising:
under the standard assumptions of economic theory, investors must be absurdly
risk averse to demand such a high premium. For example, a person with enough
risk-aversion to explain the equity premium would be indifferent between a coin
flip paying either $50,000 or $100,000 and a sure amount of $51,209.
Explaining why the equity premium is so high has preoccupied financial econ-
omists for the past 15 years (see Siegel and Thaler 1997). Benartzi and Thaler
(1997) suggested a plausible answer based on prospect theory. In their theory, in-
vestors are not averse to the variability of returns; they are averse to loss (the
chance that returns are negative). Because annual stock returns are negative much
more frequently than annual bond returns are, loss-averse investors will demand a
large equity premium to compensate them for the much higher chance of losing
money in a year. Keep in mind that the higher average return to stocks means that
the cumulative return to stocks over a longer horizon is increasingly likely to be
positive as the horizon lengthens. Therefore, to explain the equity premium
Benartzi and Thaler must assume that investors take a short horizon over which
stocks are more likely to lose money than bonds. They compute the expected
prospect values of stock and bond returns over various horizons, using estimates
of investor utility functions from Kahneman and Tversky (1992) and including a
loss-aversion coefficient of 2.25 (i.e., the disutility of a small loss is 2.25 times as
large as the utility of an equal gain). Benartzi and Thaler show that over a 1-year
horizon, the prospect values of stock and bond returns are about the same if
stocks return 8% more than bonds, which explains the equity premium.
Barberis, Huang, and Santos (1999) include loss-aversion in a standard general
equilibrium model of asset pricing. They show that loss-aversion and a strong
“house money effect” (an increase in risk-preference after stocks have risen) are
both necessary to explain the equity premium.
2
. Finance: The Disposition Effect
Shefrin and Statman (1985) predicted that because people dislike incurring losses
much more than they like incurring gains and are willing to gamble in the domain
of losses, investors will hold on to stocks that have lost value (relative to their pur-
chase price) too long and will be eager to sell stocks that have risen in value. They
called this the
disposition effect
. The disposition effect is anomalous because the
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