utility. In other words, they choose ω, the fraction of financial wealth in
stocks, to maximize
Eπυ[(1−ω)Rf,t+ 1 +ωRt+ 1 −1], (10)where πand υare defined in Eq. (2). In particular, υcaptures loss aversion,
the experimental finding that people are more sensitive to losses than to
gains. Rf,t+ 1 and Rt+ 1 are the gross returns on T-Bills and the stock market
between tand t+1, respectively, making the argument of υthe return on
financial wealth.
In order to implement this model, BT need to stipulate how often in-
vestors evaluate their portfolios. In other words, how long is the time inter-
val between tand t+1? To see why this matters, compare two investors:
energetic Nick who calculates the gains and losses in his portfolio every
day, and laid-back Dick who looks at his portfolio only once per decade.
Since, on a daily basis, stocks go down in value almost as often as they go
up, the loss aversion built into υmakes stocks appear unattractive to Nick.
In contrast, loss aversion does not have much effect on Dick’s perception of
stocks since, at ten-year horizons, stocks offer only a small risk of losing
money.
Rather than simply pick an evaluation interval, BT calculate how often
investors would have to evaluate their portfolios to make them indifferent
between stocks and T-Bills: in other words, given historical U.S. data on
stocks and T-Bills, for what evaluation interval would substituting ω= 0
and ω=1 into Eq. (10) give the same prospective utility? Roughly speak-
ing, this calculation can be thought of as asking what kind of equity pre-
mium might be sustainable in equilibrium: how often would investors need
to evaluate their gains and losses so that even in the face of the large histor-
ical equity premium, they would still be happy to hold the market supply of
T-Bills.
BT find that for the parametric forms for πand υestimated in experi-
mental settings, the answer is one year, and they argue that this is indeed a
natural evaluation period for investors to use. The way people frame gains
and losses is plausibly influenced by the way information is presented to
them. Since we receive our most comprehensive mutual fund reports once a
year, and do our taxes once a year, it is not unreasonable that gains and
losses might be expressed as annual changes in value.
The BT calculation therefore suggests a simple way of understanding the
high historical equity premium. If investors get utility from annual changes
in financial wealth and are loss averse over these changes, their fear of a
major drop in financial wealth will lead them to demand a high premium as
compensation. BT call the combination of loss aversion and frequent evalu-
ations myopic loss aversion.
BT’s result is only suggestiveof a solution to Mehra and Prescott’s equity
premium puzzle. As emphasized at the start of this section, that puzzle is in
A SURVEY OF BEHAVIORAL FINANCE 27