Working Papers
o "Markowitz in The Brain?" (with Kerstin Preuschoff and Steve Quartz)
Abstract: We review recent brain-scanning (fMRI) evidence that activity in certain sub-cortical structures of the human brain correlate with changes in expected reward, as well as with risk. Risk is measured by variance of payoff, as in MarkowitzÕ theory. The brain structures form part of the dopamine system (which consists of the neurons that emit a crucial chemical, namely, dopamine, and the areas to which the dopamine neurons project). The dopamine system had been known to regulate learning of expected rewards. New data show that it is also involved in perception, of expected reward, and of risk. The findings suggest that the brain may perform a higher-dimensional analysis of risky gambles, as in standard portfolio theory, whereby risk and expected reward are considered separately. That is, the human brain appears to literally record the very inputs that have become a defining part of modern finance theory.
o "Ambiguity and Asset Prices: An Experimental Perspective"
Abstract: The violations of expected utility axioms displayed in the Ellsberg paradox have recently been attributed to ambiguity aversion. In this paper, we study the impact of ambiguity aversion on equilibrium asset pricing and portfolio holdings in competitive financial markets. We pay particular attention to potential heterogeneity, because a significant minority usually does not violate expected utility axioms. Our analysis is carried out in the context of state securities, some of which pay in states for which probabilities are unknown (the ambiguous states) but others pay in states for which probabilities are known (the risky states). Heterogeneity in ambiguity aversion leads to a wider range of state price probability ratios (state prices divided by probabilities, also known as state price density). If the ambiguous securities are not all in low or high supply, heterogeneity in ambiguity aversion could merely be misinterpreted as higher risk aversion. Otherwise it potentially generates violations to the ranking of state price probability ratios typical under expected utility, as if the representative agent held state-dependent utility. Experiments confirm the predicted impact. Heterogeneity in ambiguity aversion is further evident in subjects' end-of-period holdings: cross-sectional variation of portfolio weights is higher under ambiguity than under risk, and more subjects hold ambiguous securities in approximately equal proportion. The holdings also reflect positive correlation between risk and ambiguity aversion. The latter suggests an explanation of the value effect, if value stock can be labeled `pure risk' securities and growth stock `ambiguous' securities.
o "Modelling Price Pressure In Financial Markets"
Abstract: We present experimental evidence that security
prices do not respond to pressure from their own excess demand, unlike traditionally
assumed in economic theory. Instead, prices respond to excess demand of all
securities, despite the absence of a direct link between markets. We propose a
model of price pressure that explains these findings. In our model, agents set
order prices that reflect the marginal valuation of desired future holdings,
called ``aspiration levels."
In the short run, as agents encounter difficulties
executing their orders, they scale back their aspiration levels. Marginal valuations,
order prices, and hence, transaction prices change correspondingly.
Our model makes a specific prediction about the nature of cross-security effects: the covariance between a security's transaction price and another security's excess demand will be proportional to the corresponding payoff covariance. This additional prediction is fully borne out by the data.
o "Equilibration under Competition in Smalls: Theory and Experimental Evidence"
Abstract: Many real-world markets are competitive only in smalls, taken to mean that price taking applies only to small orders. Starting from this observation, a theory of equilibration is derived where orders are optimal merely in a local sense. Prices are assumed to adjust in the direction of the order imbalance. In the context of financial markets populated with mean-variance optimizing agents, the theory predicts that a security's price will correlate with excess demands in other securities, and the sign of this correlation is the same as that of the covariance of the final payoffs. In the short run, prices tend to a local equilibrium where the risk-aversion weighted endowment portfolio (RAWE) is mean-variance optimal. Relative to the market portfolio, RAWE overweighs securities that are held disproportionally by more risk averse agents; RAWE puts less weight on securities that are held primarily by more risk tolerant agents. Throughout equilibration, portfolio separation is violated generically, and violations are more extreme when payoff covariances are positive. For a variety of patterns of initial allocations (including identical initial holdings), the equity premium is larger at the outset than at (CAPM) equilibrium. All these implications are confirmed in experiments.
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o "Equilibrium Asset Pricing Under Heterogeneous Information"(joint with Bruno Biais and Chester Spatt)
Abstract: We analyze theoretically and empirically the implications of
heterogeneous information for equilibrium asset pricing and portfolio choice.
Our theoretical framework, directly inspired by Admati (1985), implies that
with partial information aggregation, portfolio separation fails, buy-and-hold
strategies are not optimal, and investors should structure their portfolios
using the information contained in prices in order to cope with winner's curse
problems. We implement empirically such a price-contingent portfolio allocation
strategy and show that it outperforms economically and statistically the
passive/indexing buy-and-hold strategy. We thus demonstrate that prices reveal
information, in contrast with the homogeneous information CAPM, but only
partially, consistent with Noisy Rational Expectations Equilibrium. The success
of our price-contingent strategy does not proxy for the success of trading
strategies based purely on historical performance, such as momentum investment.
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paper
o "Excess Demand And Equilibration In Multi-Security
Financial Markets: The Empirical Evidence"
(Joint with Elena Asparouhova and Charles Plott; published in The Journal of
Financial Markets)
(Get an old version including four-asset experiments)
o "Prices And Portfolio Choices In Financial Markets: Theory and
Experiment" (Joint with Charles Plott and
William Zame)
Abstract: Most tests of asset pricing models address only the pricing
predictions --- perhaps because the portfolio choice predictions are obviously
wrong. But how can pricing theory
be right if the portfolio choice theory on which it rests is wrong? This paper suggests an answer: the
assumptions about individual preferences that underly common asset-pricing
models are wrong, but the deviations between the demands predicted by these
models and the true demands have mean zero in the population, and hence wash out
in prices. This work is based on experimental markets in which risky and
riskless assets are traded. This
experimental setting offers an opportunity to study asset pricing in an
environment in which crucial variables can be controlled or observed --- in
contrast to field environments, in which these variables cannot be controlled
and frequently cannot be observed accurately. The experimental data exhibit the same puzzling
characteristics as the historical data: asset prices are consistent with the
price predictions of familiar theories (for instance, the market portfolio is
nearly mean-variance efficient) but portfolio choices are wildly divergent from
the portfolio choice predictions of the same theories (for instance, portfolio
separation does not obtain). To
explain the data, we build a structural model based on perturbations of
individual demand functions (in the familiar style of much applied work). The central feature of this model is
that the perturbations (i.e., the differences between individual demands and
the demands predicted by quadratic utility) have mean zero in the
population. We develop an
econometric test of the model which tests both prices and
portfolio choices, and find that the empirical distribution of the test
statistic is consistent with model predictions.
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paper
o " Discrepancies between Observed and Theoretical Choices In
Financial Markets Experiments: Subjects' Mistakes or the Theory's Mistakes?" (Joint with Charles Plott and William Zame)
Abstract: In financial markets experiments, the Capital Asset Pricing Model
(CAPM) has been demonstrated to predict prices well in spite of errors in
predicting choices, because CAPM's choice prediction errors average out across
subjects. Two calibration exercises, one involving a tenfold increase in
subject payments, another involving certainty-equivalent payments, suggest that
the choice prediction errors of CAPM are too big to only reflect mistakes that
subjects inevitably make. Therefore, even at modest levels of payment, choice
prediction errors represent genuine deviations in attitudes towards risk that
cannot be captured by CAPM's quadratic expected utility. The deviations average out, implying
substantial heterogeneity. But the deviations do not necessarily reflect
irrational behavior: violations of Afriat inequalities are smaller than typical optimization
mistakes for 90\% of the subjects. Consequently, choices reflect attempts to
optimize some utility function, but obviously not CAPM's.
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paper
o "The NYSE Opening Mechanism And Portfolio Trading"
Abstract: In principle, implementation of portfolio investment strategies
through market orders at the NYSE would be problematic because of execution
price uncertainty. This paper measures the impact, by comparing the actual
value at the end of the trading day against the value one would have obtained
if it were possible to observe opening prices when submitting orders. For
positively weighted portfolios of twnety-five securities, for instance, the
one-year cumulative risk of daily portfolio trading at the NYSE open is found
to be 7 cents per dollar invested. This is only one-third of the risk of
holding a typical security overnight during the year. In contrast of the
latter, however, execution price risk appears not to be compensated.
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paper
o " Learning-Induced Securities Price Volatility"
Abstract: This paper tests whether the high average returns on the S&P 500
index in recent history can be attributed to mistaken expectations (the ex-ante
risk premium -- taken to be constant -- is systematically less that the ex-post
measured risk premium), or, alternatively, whether can they be explained as the
result of selection bias (the U.S. experience is exceptional). The tests reject
these hypotheses over the periods 1/81 to 12/97 (p = 0.02), and 1/41-12/60 (p =
0.03). They do not reject over the periods 1/28-12/40 and 1/61-12/80. The tests
are based on a bound that the ex-post Sharpe ratios impose on the volatility of
the ratio of the market's prior and posterior beliefs about future outcomes.
The bound derives from a property of Bayesian learning recently established
elsewhere. Qualitatively, for the bound not to be violated, higher absolute
mean excess returns may need to be accompanied with higher volatility. This
should be interpreted as predicting that large price movements (positive as
well as negative) may have to be erratic. We confirm this prediction for the
S&P 500 data.
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Paper
o " Martingale Restrictions On Equilibrium Prices of Arrow-Debreu
Securities Under Rational Expectations And Consistent Beliefs"
Abstract: Consider the Rational Expectations price history of an Arrow-Debreu
security that matures in the money: p(1), p(2), ..., p(T). Past information can
be used to predict the return (p(t+1)-p(t)/p(t). Now consider a simple
alternative performance measure: (p(t+1)-p(t)/p(t+1). It differs from the
return only in that the future price is used as basis. This variable cannot be
forecasted from past information. The result obtains even if investors' beliefs
are biased, i.e., prices are not set in a Rational Expectations Equilibrium
(REE). It depends only on investors' using the rules of conditional probability
to process information. More precisely, the result continues to hold in the
Bayesian Equilibrium with Consistent Beliefs (CBE) introduced by Harsanyi
[1967]. Many related results are proved in this paper and extensions to the pricing
of equity subject to bankruptcy risk are discussed.
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o " A Theorem On (Certain Kinds Of) Out-Of-Sample Prediction Tests in
Finance"
Abstract: A theorem is proven that provides a justification for certain
out-of-sample prediction tests in finance, as well as an explanation of the
results they have generated.
(Under revision; pdf version will be released soon)
o " Rational Expectations Equilibrium When Priors Are Inconsistent"
Abstract: In a Rational Expectation Equilibrium (REE), agents are given the
function that maps states into prices. If agents realize that this function
obtains as a result of market equilibrium, they can check it against their own
beliefs (about equilibrium). If beliefs differ across agents, they will find
inconsistencies unless their higher-order beliefs are correct. Since
correctness of beliefs is at odds with the assumption of differences in
beliefs, REE is debatable as an equilibrium concept when agents disagree.
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paper
o " Arbitrage-Based Pricing When Volatility Is Stochastic" (Joint with Eric Ghysels and Christian Gourieroux)
Abstract: In one of the early attempts to model stochastic volatility, Clark
[1973] conjectured that the size of asset price movements is tied to the rate
at which transactions occur. To formally analyze the econometric implications,
he distinguished between transaction time and calendar time. The present paper
exploits Clark's strategy for a different purpose, namely, asset pricing. It
studies arbitrage-based pricing in economies where: (i) trade takes place in
transaction time, (ii) there is a single state variable whose transaction-time
price path is binomial, (iii) there are riskfree bonds with calendar-time
maturities, and (iv) the relation between transaction time and calendar time is
stochastic. The state variable could be interpreted in various ways. E.g., it
could be the price of a share of stock, as in Black and Scholes [1973], or a
factor that summarizes changes in the investment opportunity set, as in Cox,
Ingersoll and Ross [1985] or one that drives changes in the term structure of
interest rates (Ho and Lee [1986], Heath, Jarrow and Morton [1992]). Property
(iv) generally introduces stochastic volatility in the process of the state
variable when recorded in calendar time. The paper investigates the pricing of
derivative securities with calendar-time maturities. The restrictions obtained in
Merton [1973] using simple buy-and-hold arbitrage portfolio arguments do not
necessarily obtain. Conditions are derived for all derivatives to be priced by
dynamic arbitrage, i.e., for market completeness in the sense of Harrison and
Pliska [1981]. A particular class of stationary economies where markets are
indeed complete is characterized.
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paper
o " Has the Cross-Section of Average Returns Always Been The Same?
Evidence from Germany, 1881-1913" (Joint
with Caroline Fohlin)
Abstract: The cross section of average annual returns on German common stock in
the period of 1881-1913 exhibits several of the patterns that have been
observed in more recent U.S. data. Market beta is hardly important, and its
explanatory power is swamped by size and the ratio of book value to market
value. A book-to-market risk measure (covariance with a portfolio long in high
book-to-market firms and short on low book-to-market firms) has no effect on
the explanatory power of the book-to-market characteristic. But the size effect
appears to be caused by selection bias in the sample. And the book-to-market
effect is opposite that of the recent U.S. experience (and, hence, can
certainly not be attributed to selection bias). Finally, a momentum portfolio
constructed on the basis of the error of the basic 3-characteristic model
(market beta, size and book-to-market) does not generate significant returns.
These findings highlight the variability in the power of certain
characteristics in explaining the cross section of average returns.
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paper