two papers in behavioral economics -...
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Two Papers in Behavioral Economics Presentation by Olga Koslova, Kira Stearns, Yanzhi Xu, and Ye Zhang
NEUROECONOMICS: USING NEUROSCIENCE TO MAKE ECONOMIC
PREDICTIONS
Colin F. Camerer
1. Neuroscientific facts and tools
1.1. Facts
The important facts about the brain:
§ The brain is weakly modular (i.e. not every brain area contributes to every behavior).
§ The brain is plastic (i.e. responsive to environment as brain ‘software‘ is gradually
‘installed’)
§ Because attention and consciousness are scarce, the brain has evolved to off-load
decisions by automating activity through learning. For example, Americans going to
England are accustomed to looking to the left (automaticity) when crossing the street, but
in England cars are approaching from the left. To avoid this mistake (which can lead to
accident) the brain needs attention and consciousness, hence, people whose conscious
attention is absorbed elsewhere (e.g. talking on the phone), are more likely to be killed
when crossing the street.
§ The brain of the human is the primate
brain with an extra neocortex (see Figure
1), and the primate brain is simpler
mammalian brain with some neocortex.
Because of the similarities of the brain
structure, the experiments with animals
are so informative about human
behavior.
1.2. Tools
To identify the areas of the brain that are active in performing a particular task the following
technologies are used:
Figure 1: Location of neocortex.
____________________________________________________________________________________________________ § Functional magnetic resonance imaging (fMRI) uses magnetic resonance imaging to
measure the change in blood flow related to neural activity in the brain.
§ Positron Emission Tomograhpy (PET) is a scanning technology that injects radioactive
solution in the body to create 3D picture of the processes in the body (or brain in
particular).
To study whether the behavior of subjects studied changes when parts of the circuit are broken
or disrupted, scientists employ the following:
§ Studies of patients with brain lesions (abnormal tissues in the brain, caused by either
disease, congenital malformation, trauma, etc.)
§ Transcranial magnetic stimulations (TMS) performed on animals – ‘knocks out‘ or
activates certain brain areas to observe what targeted areas do.
Older tools:
§ Electroencephalogram (EEG) records electrical activity from outer brain areas by firing
the neurons within the brain; this can be used to interpolate activity in deep areas of the
brain.
§ Pshychophysiological recording of skin conductance, hear rate and pupil dilation. Its
benefit is that it is cheap and easy.
§ Eye tracking measure the motion of the eye relative to the head.
2. Evidence for Rational Choice Principles
Empirical evidence comes from the studies of animals:
§ Platt and Glimcher (1999) in their research ‘Neural correlates of decision variables in
parietal cortex’ find correlation between rate at which neurons in monkey lateral
intraparietal cortex (LIP) (area responsible for transforming visual signals into eye-
movement commands) fire and value of an upcoming juice reward. Hence, observing
larger gain (in a sense of higher value of juice reward) modulates higher activity of
neurons in the lateral intraparietal cortex.
§ Deaner et al. (2005) in their research ‘Monkeys pay per view: adaptive valuation of social
images by rhesus macaques’ find that monkeys can trade off juice rewards with exposure
to visual images. Hence, researchers conclude that monkeys can evaluate the information
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about other monkeys that is important for decision-making process (e.g. male monkeys
traded juice to view female monkeys from behind and the faces of high-status monkeys,
but required payment of juice to view the pictures of low-status monkeys).
§ Conover and Shizgal (2005) in ‘Employing labor-supply theory to measure
the reward value of electrical brain stimulation’ exploring the time-allocation decisions of
rats within work-leisure model where rats receive rewarding brain stimulation (‘neural
currency‘) for work (keeping down the lever) and can rest when choosing leisure find that
time-allocation decisions by rats explain well labor-supply theory of work and leisure
substitution, and thus, observing brains circuits at a real time provides an opportunity to
work out the principles underlying the decision process.
§ Chen et al. (2006) in ‘How basic are behavioral biases? Evidence from capuchin-monkey
trading behavior’ show that monkeys react rationally to price changes and display biases
when faced with gambles, e.g. loss aversion. Hence, they infer that loss aversion extends
beyond humans and may be inherited rather than learned.
3. Evidence for Behavioral Economics Principles
3.1. Time discounting
In the β - δ model, agents put a weight of one for current rewards and weight future rewards at
discrete time t > 0 by βδt. In their research ‘Doing it Now or Later’ O’Donoghue and Rabin
(1999) dub β to be ‘present bias’. The estimate of present bias is in the interval (0.6, 0.8). The
neoroscientific approach to estimation of the parameters implies presenting subjects with
choices between current reward and reward with a one-month delay and a reward with a one-
month delay and two-month delay, where in the first choice both β, δ systems are active,
while in the second only δ system is
active. They find that different areas are
active with respect to each system: for β
system areas associated with an
emotional limbic system are active, for δ
system lateral orbitofronal cortex
([10], [11], and [47] in Figure 2) and
dorsolateral prefrontral area ([9] and
[46] in Figure 2). Figure 2: Brodmann areas.
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3.2. Ambiguity-aversion
The Ellsberg paradox, which violates the expected utility hypothesis (explained in further
below), suggests that when two events are equally likely but poorly understood, revealed
decision weights seem to combine judgment of likelihood and additional factor, which leads
to an aversion to betting under ambiguity. Hsu et al. (2005) in ‘Nonlinear Probability
Weighting in the Brain’ found additional activity in the dorsolateral prefrontal area ([9] and
[46] in Figure 2), orbitofrontal cortex ([10], [11], and [47] in Figure 2), and the amygdala (a
‘vigilance area‘ which is shown to be responsible for processing and memory of emotional
reactions located deep in the medial temporal lobes of the brain). Subjects with higher right
orbitofrontal cortex (OFC) activity in response to ambiguity also had higher ambiguity-
aversion parameters.
3.3. Nonlinear probability weighting
The nonlinear probability weighting in particular overweighting low probabilities and
underweighting probabilities close to one is studied in the neuroeconomics by the way how
caudate (a temporal lobe area including the striatum which is associated with rewards of any
type) responds to anticipated reward. Hsu et al. (2006) in ‘Nonlinear Probability Weighting in
the Brain’ by observing activity in the left and right caudate areas controlling for the payoff
amount find modest nonlinearity of activity across levels or probability p.
3.4. Limited Strategic Thinking
Camerer et al. (2004) in ‘A cognitive hierarchy model of games‘ propose ‘cognitive hierarchy‘
theory which suggests there are three steps of strategic thinking: step-0 players randomize,
step-1 players anticipate randomization and best-respond it, step-2 players best-respond to a
mixture of step-0 and step-1 players, and so on. The highest step players anticiate correctly the
distribution of the actions of other players, hence, their beliefs are in equilibrium. The
empirical evidence of Bhatt and Camerer (2005) in ‘Self-referential thinking and equilibrium
as states of mind in games: fMRI evidence‘ looks at fMRI of players when they are making
choices and when they express beliefs about what other players will do. Because players who
are in equilibrium are imagining how others are choosing, then there is overlap between
making own choice and expressing beliefs about choice of other players, which is supported
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are out of equilibrium, there was higher activity when making a choice than when expressing
a belief (note that lower type players put higher weight in their own choice than to a choice of
other players).
4. Evidence for New Psychological Variables
§ The largest payoff from neuroeconomics may come from pointing out biological
variables which have a large influence on behavior and are underweighted or ignored
in standard theory
§ Preferences are both are both the output of a neural choice process and an input which
can be used in economic theory to study responses to change in price and wealth
Summary of Hsu et all (2005)
§ Difference between “risky” (betting on roulette) and “ambiguous”(the possibility of a
terrorist attack) events
§ In subjective expected utility theory, the probabilities of outcomes should influence
choices, NOT one’s confidence in those probabilities
o However, people are more willing to bet on risky events than ambiguous ones,
when holding the perceived probability of the outcomes constant
§ The Ellsberg Paradox:
o Imagine one deck of 20 cards composed of 10 red and 10 blue cards (the risky
deck). Another deck has 20 red or blue cards, but the composition of red and
blue cards is completely unknown (the ambiguous deck). A bet on a color pays
a fixed sum (e.g. $10) if a card with the chosen color is drawn, and zero
otherwise. In experiments with these choices, many would rather bet on a red
draw from the risky deck than on a red draw from the ambiguous deck, and
similarly for blue draw. If betting preferences are determined only by
probabilities and associated payoffs, this pattern is a paradox: in theory,
disliking the bet on a red draw from the ambiguous deck implies that its
subjective probability is lower [Pamb(red)<Prisk(red)]. The same aversion for
blue bets implies [Pamb(blue)< Prisk(blue)]. But these inequalities, and the fact
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that the probabilities of red and blue must sum to 1 for each deck, imply 1 =
Pamb(red) + Pamb(blue) < Prisk(red) + Prisk(blue) = 1. This is a contradiction.
§ They explore the neural differences with various levels of uncertainty by using a
combination of data from fMRI and behavior data from lesion patients.
§ Look at the straitum (connected with reward anticipation), the OFC (patients with
lesions perform poorly in this area with tasks involving uncertainty), and the
amygdala (hypothesized as a general vigilance module in the brain).
§ The authors find that regions of the brain that were more active during the ambiguous
condition relative to the risk condition included the OFC, amygdala and the
dorsalmedial prefrontal cortex (DMPFC).
o Areas activated during the risk condition relative to ambiguity include the
dorsal striatum (reward prediction)
§ Suggests that ambiguity lowers the anticipated reward of decisions
§ The authors then conducted similar experiments using 12 subjects with brain lesions.
Six of the subjects had significant activation focus in the OFC and the other six had
temporal lobe damage such that the lesions did not overlap with the fMRI foci.
o Results: frontal patients are risk and ambiguity neutral while the other group
was risk and ambiguity averse.
Summary of Wang et all (2006)
§ Play a sender-receiver game where the sender has an incentive for biased transmission
(like a security analyst painting a rosy picture about earning prospects)
§ The sender observes state S (an integer from 1 to 5) and transmits message M (again,
an integer from 1 to 5). The receiver chooses an action A (another integer from 1 to
5).
§ The authors use eyetracking to show that senders look much less at receiver payoffs
compared to their own payoffs. Furthermore, sender’s pupils dilate when they send
deceptive messages. Hence, one can predict the propensity to misrepresent the state
and the degree of misrepresentation by looking at pupils.
Summary of Sanfey et all (2003)
§ The Ultimatum Game: Two players are given the opportunity to share a sum of
money. One player is deemed the proposer, the other, the responder. The proposer
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makes an offer to how this money should be split between the two. If the responder
agrees, they share the money as proposed. If the responder disagrees, no one gets
anything and the game is over. Standard Economic theory says that even as long as
the proposer suggests giving even a small amount of money to the responder, the
responder should agree because a little reward is better than no reward. However,
behavioral research as demonstrated that low offers (around 20% of the total) have a
50% chance of being rejected! Thus there must be some mechanism that causes people
to actively turn down monetary rewards.
§ Participant reports suggest that low offers are rejected after an angry reaction to offers
perceived as unfair. Do negative emotions lead people to sacrifice sometimes
considerable financial gain in order to punish their partner?
§ In this study, respondents were placed in an MRI and played the game with either a
human partner or a computer partner over a computer screen.
§ Results: Participants accepted al fair offers with decreasing acceptance rates as offers
became less fair. Unfair offers of 10%-20% made by human partners were rejected at
significantly higher rates than those offered by a computer.
§ Brain areas that showed greater activation for unfair compared to fair offers from
human partners: bilateral anterior insula, dorsolateral prefrontal cortex (DLPFC),
and anterior cingulated cortex.
§ The magnitude of activation was also significantly greater for unfair offers from
human partners compared to those from computer partners. Implies sensitivity not just
to low offers, but to the context of the offer.
§ The anterior insula has been implicated in studies of negative emotional states,
especially anger and disgust (could incorporate emotional disgust as well)
§ The DLPFC is linked to processes such as goal maintenance and executive control. It
was activated during unfair offers but did not correlate to acceptance rates. Higher
cognitive demands may be placed on participants in order to overcome the tendency to
reject the offer (and hence focus on the goal of collecting as much money as possible).
§ ACC has been implicated in the detection of cognitive conflict. Its activation may
reflect the conflict between the cognitive and emotional part of the game.
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Summary Kosfeld et all (2005)
§ In non-human mammals, the neuropeptide oxytocin has a central role in general
behavioral regulation, particularly in positive social interactions.
§ They use a double-blind study to compare trusting behavior in subjects that receive an
intranasal dose of oxytocin and those who receive a placebo
§ The Experiment:
o Subjects anonymously interact with other subjects as either the “investor” or
the “trustee”
o The investor can choose to give the money to the trustee. If he gives him
money, the trustee can then choose to share the proceeds of the transfer with
the investor
§ The investor will have to trust the trustee to give him the costly
transfer; because the two only interact once, the trustee’s action will
have no effect on future interactions
§ The Results:
o 45% of the oxytocin group showed the maximal trust level, compared to 21%
in the placebo group
o The average transfer in the oxytocin group was 17% higher
§ These results could possibly be due to a property in oxytocin that makes people less
risk averse. To test this theory the authors conducted an experiment in which the
investors were giving transfers to a computer, hence the risk was not imbedded in a
social interaction
o The results were that there was no difference between the transfers in the
oxytocin group and the placebo group.
§ What is the mechanism behind oxytocin’s increase in trust?
o It helps subjects to overcome betrayal aversion
5. Conclusion
§ The goal of neuroeconomics is to group economic theory in details of how the brain
works in decision making, strategic thinking, and exchange.
§ Thinking about how the brain implements economic decisions compared to thinking
about choices as a result of preferences gives theorists many more variables to
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consider. Neuroeconomics gives theorists a mechanism that influences preferences—
biology
§ An approach to incorporating neuroeconomics is to take the revealed-preference model
seriously and see how far its language can be stretched to accommodate neural
evidence.
6. The Mindless Critique
The main points of Gul and Pesendorfer
§ Neuroeconomics is defined as research that implicitly or explicitly makes either of the
following two claims
o Pyschological and physiological evidence are directly relevant to economic
theories. In particular, they can be used to support or reject economic models
or even economic methodology.
o What makes individuals happy (‘true utility’) differs from what they choose.
Economic welfare analysis should use true utility rather than the utilities
governing choice (‘choice utility’)
§ In standard economics, utility maximization and choice are synonymous. The relevant
data are the revealed preference data. This can, at best, reveal what the agent wants
(or as chosen) in a particular situation. An individual’s coefficient of risk aversion can
only be revealed through choice behavior. Welfare is defined to be synonymous with
choice behavior. It has no therapeutic ambition, i.e., it does not try to evaluate or
improve the individual’s objectives. The purpose of economics is to analyze
institutions and ask how those institutions mediate the interests of different economic
agents.
§ Neuroeconomics is therapeutic in its ambitions: it tries to improve an individual’s
objectives. Its central questions are: How do invidiauls make their choices? How
effective are they at making the choices that increase their own wellbeing?
§ The neuroeconomic critique begins with the assumption that economics, psychology
and possibly other social sciences all address the same set of questions and differs only
with respect to the answers they provide. The authors insist that economics and
psychology do not offer competing, all-purpose models of human nature. Rather that
each discipline uses specialized abstractions that have proven useful for that discipline.
§ Example of neuroeconomists critique of standard economics:
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“American visitors to the UK summer numerous injuries and fatalities because they
often look only to the left before stepping into streets, even though they know traffic
approaches from the right. One cannot reasonably attribute this to the pleasure of
looking left or to masochistic preferences. The pedestrian’s objectives—to cross the
street safely—are clear, and the decision is plainly a mistake.”
§ The standard economist’s retort: There are situations where outsiders can
improve an individual’s decisions. Such situations often arise due to
asymmetrical information. Hence, standard economics deals with ‘mistakes’
by employing the tools of information economics.
§ Conclusion: A combination of moral philosophy and activism has never been the goal
of economics. The neuroeconomic critique fails to refute any particular economic
model and offers no challenge to standard economic methodology.
Camerer’s Response to Gul and Pesendorfer
§ He believes that Gul and Pesendorfer only suggest one categorization of economics
and are too dogmatic in their assertion of what economics is and isn’t.
§ Theories that can explain neural facts and choices should have some advantage over
theories which explain only choices.
§ He thinks they ground their argument too much in the history of economic thought and
rely too much on definitions.
§ Edgeworth, Ramsey and Fisher all wrote about their hopes of measuring utility
directly.
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MYOPIC LOSS AVERSION AND THE EQUITY PREMIUM PUZZLE
Sholmo Benartzi and Richard H, Thaler
I Equity Premium Puzzle
This paper is a behavioral finance paper; its main purpose is to use the combination of
loss aversion and short period of evaluation, which is called myopic loss aversion, to explain
the equity premium puzzle in the finance market.
In this section, we will go through the concepts of equity premium puzzle, and
demonstrate the existence of it. Then we list the alternative explanations of equity premium
puzzle in previous studies. Finally we briefly introduce the behavioral finance explanation,
provided by Benartzi and Thaler.
§ Equity Premium Puzzle and Its Existence
The key difference of stocks and bonds is their different riskiness and return rates :
stocks have higher returns and higher variances while bonds are more stable but offer a lower
return. Siegel (1991,1992) shows that in 1926-1990, the real compound equity return was 6.4
percent, while the return of short-run government bond is 0.5 percent, implying that stocks
have outperformed bonds by a large margin. This phenomenon suggests that, even though
investment on stocks yields much higher return than bonds in a long run, the investors still
prefer bonds to stocks. MaCurdy and Shoven explain that “People must be confused about the
relative safety of different investments over long horizons”.
Mehra and Prescott (1985) demonstrate that in order to reconcile the much higher
returns of stocks compared to government bonds in the United States, individuals must have
an incredibly high risk aversion parameter, which should exceed 30 (we call it a explanatory
parameter) whereas the previous estimations and theoretical arguments suggest that the actual
parameter should be closer to 1. This huge gap between the explanatory risk aversion
parameter (30) and actual one (1) cannot be well explained by the risk-aversion theory alone.
[A vivid demonstration of this over 30 risk aversion parameter is as follows: when an
individual with such a risk aversion parameteris offered with a gamble, with a 50 percent
chance of winning $100,000, with a 50 percent chance of winning $50,000, the indifferent
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certainty equivalent should be $75,000 for a risk neutral individual.)
§ Previous Explanation of Equity Premium Puzzle
Explanation 1(Reitz, 1988):
Equity premium is a rational response to economic catastrophe.
Comments in this paper: Not a plausible explanation.
Reason: First, the great depression (1929) has been included in the data, but the high
premium still exists. Second, the catastrophe should affect stocks and not bonds, however, in
reality, a bout of hyperinflation affects bonds more than stocks.
Explanations 2:
Relax the link between the coefficient of relative risk aversion and the elasticity of
the intertemporal substitution to explain equity premium puzzle.
Model 2.1 Weil (1989) nonexpected utility preferences theory.
Comments in this paper: Just transform the equity premium puzzle into a “risk free
rate puzzle”, and fail to truly solve the puzzle.
Model 2.2 Epstein and Zin (1990) use Yaari’s Dual theory of choice, which is also a
nonexpected utility preferences theory.
Comments in this paper: It can only explain ⅓ of observed equity premium.
Model 2.3 Mankiw and Zeldes (1991) investigate whether the homogeneity
assumtions necessary to aggregate across consumers could explain the puzzle. They found
only a minority of Americans hold stocks, whose consumption behaviors are different from
nonstockholders.
Comments in this paper: This can only partly explain the puzzle.
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Explanation 3 (Constantinides, 1990):
Habit-formation model, which means the utility of consumption is assumed to
depend on past levels of consumptions, especially averse to reduce their consumptions.
Comments in this paper: This model better explain the intertemporal dynamics of
returns, it fails to explain the differences in average returns across assets.
II Myopic Loss Aversion: Loss Aversion + Frequent Evaluation
Myopic loss aversion is a combination of loss aversion and frequent evaluation. In this
section, we will briefly introduce loss aversion and frequent evaluation. Then talk about the
Samuelson paradox, and the underlying connection of Samuelson paradox and equity
premium puzzle.
§ Loss aversion
According to prospect theory (Kahneman & Tversky,1979), loss aversion means
individuals are more sensitive to loss than to gain, e.g. the disutility of giving up 1
dollar is almost twice the utility of acquiring 1 dollar.
In this paper, the authors use cumulative prospect theory (Tversky & Kahneman, 1991)
and its corresponding parameter to measure loss aversion.
Equation 2 is the value function. X measures the loss or gains, rather level of wealth. λ is
the coefficient of loss aversion, which is set as 2.25 in this paper. α and β measure the
diminishing of sensitivity.
Equation 3 is the describe the weighted value of a gamble G, which pays off ix with
probability of ip .In the function, iπ is subjective decision weight, which is a simple nonlinear
____________________________________________________________________________________________________ transform of ip in prospect theory(1979), but in this paper, they use the cumulative prospect
theory, iπ depends on the cumulative distribution of the gamble, rather than on individual
ip .Denote w as the nonlinear transform of the cumulative distribution of the gamble G. The
parameter approximation of probability ip is
In equation 4, γ is 0.61 in the domain of gain, γ is 0.69 in the domain of loss. Here we
offer a graphic description of equation 4, which is cited from cumulative prospect theory
paper (Tversky & Kahneman, 1991).See figure I.
§ Frequent Evaluation
The evaluation period is a concept in mental accounting theory (Kahneman & Tversky
1984; Thaler 1985). Mental accounting refers to implicit methods individuals use to code
and evaluate financial outcomes, because the existence of loss aversion, mental accounting
causes the none-neutral dynamic aggregation rules. For example, assume an individual wins
$100 from a gamble, then loses $50 because of speeding ticket. If the gain and loss are
evaluated separately, his/her total utility is 0, because the loss of $50 is twice as painful as
gain and cancels the utility gaining from gaining $100. If the gain and loss are aggregated to
a net gain $50, then this individual will have a positive total utility. In this example, the
evaluation period matters, if they evaluate the outcome too often, they will always separate
the gains and loss, which makes them worse off.
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Figure I
§ Samuelson Paradox
Samuelson paradox is first posed by Samuelson in 1963. Samuelson asked a
colleague whether he would like to play a gamble with 50 percent of chance to win
$200 and 50 percent of chance to loss $100.
His colleague’s answer was if the gamble was played only 1 time, he rejected (the
rationale for the rejection is he that he would feel the $100 loss more than the $200,
which reflects the intuition of loss aversion). If the game were to be played 100 times,
he would it. Samuelson‘s colleague’s decision is regarded as irrational within the
framework of expected utility, so it is a paradox.
§ How the Samuelson Paradox Connects to the Equity Premium Puzzle
When Samuelson’s bet is repeated, the probability of monetary loss deceases. When
the game is not repeated, the chance of monetary loss is 0.5; when played twice, the
chance is 0.25; when played 3 times, the chance is 0.125, when played an infinite
number of times, the probability of monetary loss will non-monotonously decrease to
zero. The simple repetitions of the single bet are unattractive if they are evaluated one
at a time, but if the outcomes of repetitions are aggregate together and evaluated
together (evaluated less frequently), the decision makers will be more willing to accept
the bet.
Samuelson’s bet is an analogy of the stock and bond market.
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Playing Samuelson bet ⇒ Buying Stocks
Rejecting Samuelson bet ⇒ Buying Bonds
The underlying similarity of Samuelson‘s bet and the stock market is that both of
them yield a much higher return, but are risky. Even though the risk can be
systematically reduced by repetitions and portfolio diversification, the decision makers
are reluctant to play Samuelson‘s bet or to buy stocks, implying they would reject
Samuelson‘s bet or buy stable but less profitable bonds.
In Samuelson paradox, the colleague is willing to accept the bet, if repeated 100
times and he does not have to watch the bet being played out. By the same logic, the
attractiveness of the risky asset (stocks) will depend on the time horizon of the investor,
and the frequency of evaluation. The longer one intends to hold the stocks, the less
frequent of evaluation, the more attractive stocks will be.
Then in this article, the authors conclude that an investor’s unwillingness to bear the
risks associated with holding equities is because of two factors: loss aversion and the
necessity of frequent evaluation, the combination of which are called myopic loss
aversion.
III. Evidence of Myopic Loss Aversion from History Data Simulation
When scholars try to explain the equity premium puzzle with risk aversion theory, they
asked questions about how risk averse the representative investor would have to be to explain
the historical data (Mehra & Prescott). In this paper, the authors try to use the myopic loss
aversion theory to explain this, and they wonder how often the representative investor would
have to evaluate their portfolios to explain the same historical data of equity premium. They
plug empirical evidence into the cumulative prospect theory to answer their own question.
They want to answer this question in two ways: firstly, they want to know what evaluation
period would make investors indifferent between holding all-stock asset or all-bond assent. If
the estimated period is consistent with reality in finance market, the theory of myopic loss
aversion would be inexplicitly confirmed. Secondly, they want to set the estimated evaluation
period as given and ask what combinations of stocks and bonds would maximize prospective
utility. If this estimated combination is consistent with the real financial market asset
combination then their myopic loss aversion theory is implicitly confirmed again.
§ How Often Are Portfolios Evaluated?
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Method: The authors draw samples from the historical (1926-1990) monthly returns on
stocks, bonds, and treasury bills provided by CRSP. They then compute the
prospective utility of holding these different assents correspondingly for evaluation
periods starting at one month and then increasing one month at a time.
Simulation Procedure:
(1) Generate distributions of returns for various time horizons by drawing 100,000 n-
month returns with replacement from the CRSP time series.
(2) Rank the returns from best to worst, and compute the return at 20 intervals along the
cumulative distributions. (This procedure aims at plugging the historical data into the
cumulative prospect theory function.)
(3)Compute out the prospective utility of the given asset for the specified holding
period, e.g. all-bond asset in 5 month evaluation period.
(4) Draw graphs to show their simulation results, prospective utility as function of
evaluation period.
They run four simulations to make robust estimations (with nominal or real returns,
with bonds or treasure bills). People prefer bonds to treasury bills, prefer nominal to
real returns and state the reason that for long-term investors, bonds are the closest
substitutes; returns are reported annually in nominal dollars and simulations reveal that
when they use real dollars, the treasury bill always yields negative prospective utility. If
this were true, nobody would buy treasury bills, which is inconsistent with reality. In
Panel A and Panel B bellow, they show their simulation results.
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Interpretation of the results:
From the Panel A, the indifferent evaluation period of stocks and bonds are about 12
months. This estimation is very well consistent with the real behaviors of financial
market participants, because individual investors file taxes annually and receive their
most comprehensive reports from their brokers, mutual funds and retirement accounts
once a year. This result inexplicitly confirms the myopic loss aversion theory.
§ Optimal Asset Portfolio for Representative Investor (Myopic loss averse)
The previous result can be criticized on the grounds that investors make their own
portfolios rather than choose between all-bond or all-stock assets. To reply to this
criticism, the authors run another simulation to estimate the optimal asset portfolio of a
representative myopic loss averse investor, whose estimation period is 1 year.
Then they compute the prospective utility of each portfolio mix between 100 percent
bonds and 100 percent stocks, in 10 percent increments, using nominal returns. The
results are shown in Figure II.
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Figure II
The figure shows that the optimal prospect utility comes at the interval of 30 percent and 55
percent. This result is well consistent with real market observations. Institutions invest, on
average, 47 percent on bonds, 53 percent on stocks. Individual investors allocate their
investments about 50-50 between stocks and bonds. Again this result supports the theory of
myopic loss aversion.
§ Myopia and the magnitude of the Equity Premium
Panel A&B show that stocks become more attractive as evaluation period increases. The
observation naturally leads to the question that, by how much would be equality premium
fall if have longer evaluation period?
The answer shows in figure III below, the results imply that for an investment with 20-year
horizon, the equity premium should be 1.4 percent, while in reality it is 6.5 percent, there
are a 5.1 percent loss (psychic cost), just because people evaluate their asset performance
too often!
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IV Organizational Myopic Loss Aversion and Explanation
The previous sections of this paper are all based on the individual decision making. While
in reality, lots of assets are held be organizations, particularly, pension funds and
endowments. In this section, the authors discuss the organizational level of myopic loss
aversion, especially on pension funds and foundation and university endowment.
§ Pension Funds
A common allocation of pension funds is about 60 percent stocks and 40 percent bonds
and treasury bills. Given the historical equity premium and the fact that pension funds
have an infinite time horizon, it seems that they do not invest enough in stocks.
The authors argue that myopic loss aversion is a possible explanation. Though the
pension funds (principle) themselves have infinite investment horizon, the manager
(agency) does not expect to be in that position forever. The managers have to make
regular reports on the funding performance. The authors conclude that for investors
who must account for near term loss, these long-run results may have little significance,
hence the agency costs produce myopic loss aversion.
§ Foundation and University Endowments
There are similar even split between stocks and bonds in institutional investors in
endowment fund held by university and foundations. The authors offer to explanations.
First, the similar agency problems as pension funds. Second, the spending rules used by
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most universities and foundations restrict the investment horizon to short periods to
maintain a steady operating budget.
V Conclusions and Relevant Research
The myopic loss aversion is a possible explanation for the equity premium puzzle. If you
are interested in this topic, you can visit Professor Shlomo Benartzi’ website.
We recommend you to read those most relevant papers which are all Benartzi’s and
Thaler’s work.
Thaler, Richard, and Shlomo Benartzi, "Save More Tomorrow: Using Behavioral Economics
to Increase Employee Savings," Journal of Political Economy, February 2004, Vol. 112.1,
Part 2, pp. S164-S187.
Benartzi, Shlomo, "Excessive Extrapolation and the Allocation of 401(k) Accounts to
Company Stock?" Journal of Finance, October 2001, Vol. 56.5, pp. 1747-1764.
Benartzi, Shlomo, and Richard Thaler, “Naive Diversification Strategies in Retirement Saving
Plans,” American Economic Review, March 2001, Vol. 91.1, pp. 79-98.
Benartzi, Shlomo, and Richard Thaler, “Risk Aversion or Myopia? Choices in Repeated
Gambles and Retirement Investments,” Management Science, March 1999, Vol. 45.3, pp.
364-381.