Empirical Asset Pricing:
Eugene Fama, Lars Peter Hansen,
and Robert Shiller
John Y. Campbell1
May 2014
1Department of Economics, Littauer Center, Harvard University, Cambridge MA 02138, and NBER.
Email john_campbell@harvard.edu. Phone 617-496-6448. This paper has been commissioned by the
Scandinavian Journal of Economics for its annual survey of the Sveriges Riksbank Prize in Economic
Sciences in Memory of Alfred Nobel. I am grateful to Nick Barberis, Jonathan Berk, Xavier Gabaix,
Robin Greenwood, Ravi Jagannathan, Sydney Ludvigson, Ian Martin, Jonathan Parker, Todd Petzel, Neil
Shephard, Andrei Shleifer, Peter Norman Sorensen (the editor), Luis Viceira, and the Nobel laureates
for helpful comments on an earlier draft. I also acknowledge the inspiration provided by the Economic
Sciences Prize Committee of the Royal Swedish Academy of Sciences in their scientiÖc background paper ìUnderstanding Asset Pricesî, available online at http://www.nobelprize.org/nobel_prizes/economicsciences/laureates/2013/advanced-economicsciences2013.pdf.
Abstract
The Nobel Memorial Prize in Economic Sciences for 2013 was awarded to Eugene Fama,
Lars Peter Hansen, and Robert Shiller for their contributions to the empirical study of asset
pricing. Some observers have found it hard to understand the common elements of the
laureatesíresearch, preferring to highlight areas of disagreement among them. This paper
argues that empirical asset pricing is a coherent enterprise, which owes much to the laureatesí
seminal contributions, and that important themes in the literature can best be understood
by considering the laureates in pairs. SpeciÖcally, after summarizing modern asset pricing
theory using the stochastic discount factor as an organizing framework, the paper discusses
the joint hypothesis problem in tests of market e¢ ciency, which is as much an opportunity
as a problem (Fama and Hansen); patterns of short- and long-term predictability in asset
returns (Fama and Shiller); and models of deviations from rational expectations (Hansen
and Shiller). The paper concludes by reviewing ways in which the laureates have already
ináuenced the practice of Önance, and may ináuence future innovations.
Keywords: Behavioral Önance, Önancial innovation, market e¢ ciency, stochastic discount
factor.
JEL classiÖcation: G10, G12.
1 Introduction
The 2013 Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel, awarded
for empirical analysis of asset prices, was unforgettably exciting for Önancial economists. The
2013 laureates, Eugene Fama, Lars Peter Hansen, and Robert Shiller, are giants of Önance
and architects of the intellectual structure within which all contemporary research in asset
pricing is conducted.
The fame of the laureates extends far beyond Önancial economics. Eugene Fama is
one of the worldís most cited economists in any Öeld. Lars Peter Hansen is an immensely
distinguished econometrician, so the Öeld of econometrics naturally claims a share of his
Nobel glory. Robert Shiller is a founder of behavioral economics, a creator of the CaseShiller house price indexes, and the author of important and widely read books for a general
audience.
The 2013 prize attracted attention in the media, and stimulated discussion among economists, for two additional reasons. First, the behavior of asset prices interests every investor,
including every individual saving for retirement, and is a core concern for the Önancial services industry. Second, the laureates have interpreted asset price movements in strikingly
di§erent ways. Robert Shiller is famous for his writings on asset price bubbles, and his
public statements that stocks in the late 1990s and houses in the mid 2000s had become
overvalued as the result of such bubbles. Eugene Fama is skeptical that the term ìbubbleî
is a well deÖned or useful one. More broadly, Fama believes that asset price movements can
be understood using economic models with rational investors, whereas Shiller does not.
The purpose of this article is to celebrate the 2013 Nobel Memorial Prize in Economic
Sciences, and to explain the achievements of the laureates in a way that brings out the
connections among them. I hope to be able to communicate the intellectual coherence of
the award, notwithstanding the di§ering views of the laureates on some unsettled questions.
I should say a few words about my own connections with the laureates. Robert Shiller
changed my life when he became my PhD dissertation adviser at Yale in the early 1980s.
In the course of my career I have written 12 papers with him, the earliest in 1983 and the
most recent (hopefully not the last) in 2009. Eugene Fama, the oldest of the 2013 laureates,
was already a legend over 30 years ago, and his research on market e¢ ciency was intensively
discussed in New Haven and every other center of academic economics. I Örst met Lars
Peter Hansen when I visited Chicago while seeking my Örst academic job in 1984. I have
never forgotten the Örst conversation I had with him about Önancial econometrics, in which I
sensed his penetrating insight that would require e§ort to fully understand but would amply
reward the undertaking.
Among Önancial economists, I am not unusual in these feelings of strong connection
with the 2013 Nobel laureates. The 2013 award ceremony in Stockholm was notable for
the celebratory atmosphere among the coauthors and students of the laureates who were
1
present, including academics Karl Case, John Cochrane, Kenneth French, John Heaton,
Ravi Jagannathan, Jeremy Siegel, and Amir Yaron, central banker Narayana Kocherlakota,
and asset management practitioners David Booth, Andrea Frazzini, and Antti Ilmanen. Any
of them could write a similar article to this one, although of course the views expressed here
are my own and are probably not fully shared by any other economists including the Nobel
laureates themselves.
The organization of this paper is as follows. Section 2 gives a basic explanation of the
central concept of modern asset pricing theory, the stochastic discount factor or SDF. While
the basic theory is not due to the laureates, their work has contributed to our understanding
of the concept and many of their empirical contributions can most easily be understood by
reference to it.
Section 3 discusses the concept of market e¢ ciency, formulated by Fama in the 1960s.
Fama Örst stated the ìjoint hypothesis problemîin testing market e¢ ciency, which Hansen
later understood to be as much an opportunity as a problem, leading him to develop an
important econometric method for estimating and testing economic models: the Generalized
Method of Moments.
Section 4 reviews empirical research on the predictability of asset returns in the short and
long run. Famaís early work developed econometric methods, still widely used today, for
testing short-run predictability of returns. Typically these methods Önd very modest predictability, but both Fama and Shiller later discovered that such predictability can cumulate
over time to become an important and even the dominant ináuence on longer-run movements
in asset prices. Research in this area continues to be very active, and is distinctive in its
tight integration of Önancial theory with econometrics.
Section 5 discusses the work of the laureates on asset pricing when some or all market
participants have beliefs about the future that do not conform to objective reality. Shiller
helped to launch the Öeld of behavioral economics, and its most important subÖeld of behavioral Önance, when he challenged the orthodoxy of the early 1980s that economic models
must always assume rational expectations by all economic agents. Later, Hansen approached
this topic from the very di§erent perspective of robust optimal control.
Section 6 explores the implications of the laureatesí work for the practice of Önance.
Contemporary methods of portfolio construction owe a great deal to the work of Fama on
style portfolios, that is, portfolios of stocks or other assets sorted by characteristics such as
value (measures of cheapness that compare accounting valuations to market valuations) or
momentum (recent past returns). The quantitative asset management industry uses many
ideas from the work of the laureates, and Shillerís recent work emphasizes the importance
of Önancial innovation for human welfare in modern economies.
Each of these sections refers to the work of more than one of the 2013 Nobel laureates.
In this way I hope to foster an appreciation for the intellectual dialogue among the laureates
and the many researchers following their lead.
2
2 The Stochastic Discount Factor: The Framework of
Contemporary Finance
2.1 The SDF in complete markets
The modern theory of the SDF originates in the seminal theoretical contributions of Ross
(1978) and Harrison and Kreps (1979). Here I present a brief summary in an elementary
discrete-state model with two periods, the present and the future, and complete markets.
Consider a simple model with S states of nature s = 1:::S, all of which have strictly
positive probability (s). I assume that markets are complete, that is, for each state s a
contingent claim is available that pays $1 in state s and nothing in any other state. Write
the price of this contingent claim as q(s).
I assume that all contingent claim prices are strictly positive. If this were not true,
there would be an arbitrage opportunity in one of two senses. First, if the contingent
claim price for some state s were zero, then an investor could buy that contingent claim,
paying nothing today, while having some probability of receiving a positive payo§ if state s
occurs tomorrow, and having no possibility of a negative payo§ in any state of the world.
Second, if the contingent claim price for state s were negative, then an investor could buy
that contingent claim, receiving a positive payo§ today, while again having some probability
of a positive payo§ and no possibility of a negative payo§ in the future.
Any asset, whether or not it is a contingent claim, is deÖned by its state-contingent
payo§s X (s) for states s = 1:::S. The Law of One Price (LOOP) says that two assets with
identical payo§s in every state must have the same price. If this were not true, again there
would be an arbitrage opportunity, this time in the sense that an investor could go long the
cheap asset and short the expensive one, receiving cash today while having guaranteed zero
payo§s in all states in the future. LOOP implies that we must have
P(X) = X
S
s=1
q(s)X(s): (1)
The next step in the analysis is to multiply and divide equation (1) by the objective
probability of each state, (s):
P(X) = X
S
s=1
(s)
q(s)
(s)
X(s) = X
S
s=1
(s)M(s)X(s) = E[MX]; (2)
where M(s) = q(s)= (s) is the ratio of state price to probability for state s, the stochastic
discount factor or SDF in state s. Since q(s) and (s) are strictly positive for all states s,
3
M(s) is also. The last equality in (2) uses the deÖnition of an expectation as a probabilityweighted average of a random variable to write the asset price as the expected product of
the assetís payo§ and the SDF. This equation is sometimes given the rather grand title of
the Fundamental Equation of Asset Pricing.
Consider a riskless asset with payo§ X(s) = 1 in every state. The price
Pf =
X
S
s=1
q(s) = E[M]; (3)
so the riskless interest rate
1 + Rf =
1
Pf
=
1
E[M]
: (4)
This tells us that the mean of the stochastic discount factor must be fairly close to one. A
riskless real interest rate of 2%, for example, implies a mean stochastic discount factor of
1=1:02 0:98.
2.1.1 Utility maximization and the SDF
Consider a price-taking investor who chooses initial consumption C0 and consumption in
each future state C(s) to maximize time-separable utility of consumption. Assume for now
that the investorís subjective state probabilities coincide with the objective probabilities
(s), that is, the investor has rational expectations. The investorís maximization problem
is
Max u(C0) +X
S
s=1
(s)u(C(s)) (5)
subject to
C0 +
X
S
s=1
q(s)C(s) = W0; (6)
where W0 is initial wealth (including the present value of future income, discounted using
the appropriate contingent claims prices). The Örst-order conditions of the problem can be
written as
u
0
(C0)q(s) = (s)u
0
(C(s)) for s = 1:::S: (7)
These Örst-order conditions imply that
M(s) = q(s)
(s)
=
u0
(C(s))
u
0
(C0)
: (8)
In words, the SDF is the discounted ratio of marginal utility tomorrow to marginal utility
today. This representation of the SDF is the starting point for the large literature on
equilibrium asset pricing, which seeks to relate asset prices to the arguments of consumersí
utility and particularly to their measured consumption of goods and services.
4
2.1.2 Heterogeneous beliefs
The discussion above assumes that all investors have rational expectations and thus assign
the same probabilities to the di§erent states of the world. If this is not the case, we must
assign investor-speciÖc subscripts to the probabilities, writing j (s) for investor jís subjective
probability of state s. In general, we must also allow for di§erences in the utility function
across investors, adding a j subscript to marginal utility as well. Then for any state s and
investor j,
q(s) =
j (s)u
0
j
(Cj (s))
u
0
j
(Cj0)
: (9)
The state price is related to the product of the investorís subjective probability of the state
and the investorís marginal utility in that state. In other words it is a composite ìutil-probî
to use the terminology of Samuelson (1969).
A similar observation applies to the SDF, the ratio of state price to objective probability:
M(s) = q(s)
(s)
=
j (s)
(s)
u0
j
(Cj (s))
u
0
j
(Cj0)
: (10)
Volatility of the SDF across states may correspond either to volatile deviations of investor
jís subjective probabilities from objective probabilities, or to volatile marginal utility across
states. The usual assumption that investors have homogeneous beliefs rules out the Örst of
these possibilities, while the behavioral Önance literature embraces it.
2.1.3 The SDF and risk premia
I now return to the assumption of rational expectations and adapt the notation above to
move in the direction of empirical research in Önance. I add the subscript t for the initial
date at which the assetís price is determined, and the subscript t + 1 for the next period at
which the assetís payo§ is realized. This can easily be embedded in a multiperiod model, in
which case the payo§ is next periodís price plus dividend. I add the subscript i to denote
an asset. Then we have
Pit = Et
[Mt+1Xi;t+1] = Et
[Mt+1]Et
[Xi;t+1] + Covt(Mt+1; Xi;t+1); (11)
where the t subscripts on the mean and covariance indicate that these are conditional moments calculated using probabilities perceived at time t. The price of the asset at time t
is included in the information set at time t, hence there is no need to take a conditional
expectation of this variable. Since the conditional mean of the SDF is the reciprocal of
the gross riskless interest rate from (4), equation (11) says that the price of any asset is its
expected payo§, discounted at the riskless interest rate, plus a correction for the conditional
covariance of the payo§ with the SDF.
5
For assets with positive prices, one can divide through by Pit and use (1 + Ri;t+1) =
Xi;t+1=Pit to get
1 = Et
[Mt+1(1 + Ri;t+1)]
= Et
[Mt+1]Et
[1 + Ri;t+1] + Covt(Mt+1; Ri;t+1): (12)
Rearranging and using the relation between the conditional mean of the SDF and the riskless
interest rate,
Et
[1 + Ri;t+1] = (1 + Rf;t+1)(1 Covt(Mt+1; Ri;t+1)): (13)
This says that the expected return on any asset is the riskless return times an adjustment
factor for the covariance of the return with the SDF.
Subtracting the gross riskless interest rate from both sides, the risk premium on any asset
is the gross riskless interest rate times the covariance of the assetís excess return with the
SDF:
Et(Ri;t+1 Rf;t+1) = (1 + Rf;t+1)Covt(Mt+1;Ri;t+1 Rf;t+1): (14)
2.2 Generalizing and applying the SDF framework
The above discussion assumes complete markets, but the SDF framework is just as useful
when markets are incomplete. The work of Hansen and Richard (1987) and Hansen and
Jagannathan (1991) is particularly important in characterizing the SDF for incomplete markets. Shiller (1982) is an insightful early contribution. Cochrane (2005) o§ers a textbook
treatment.
In incomplete markets, the existence of a strictly positive SDF is guaranteed by the
absence of arbitrageó a result sometimes called the Fundamental Theorem of Asset Pricingó
but the SDF is no longer unique as it is in complete markets. Intuitively, an SDF can be
calculated from the marginal utility of any investor who can trade assets freely, but with
incomplete markets each investor can have idiosyncratic variation in his or her marginal
utility and hence there are many possible SDFs.
There is however a unique SDF that can be written as a linear combination of asset payo§s
and that satisÖes the fundamental equation of asset pricing (2). This unique random variable
is the projection of any SDF onto the space of asset payo§s, and thus any other SDF must
have a higher variance.
2.2.1 Volatility bounds on the SDF
Shiller (1982), a comment by Hansen (1982a), and Hansen and Jagannathan (1991) used
this insight to place lower bounds on the volatility of the SDF, based only on the properties
of asset returns
—-
Eugene Fama, Lars Peter Hansen, Eugene Fama, Lars Peter Hansen, Lars Peter Hansen, Lars Peter Hansen, Lars Peter Hansen, Lars Peter Hansen
as well as Robert Shiller
Campbell, John Y.1
In May of 2014,
1Department of Economics, Littauer Center, Harvard University, Cambridge MA 02138, and NBER.
Email john_campbell@harvard.edu. Phone 617-496-6448. This paper has been commissioned by the
Scandinavian Journal of Economics for its annual survey of the Sveriges Riksbank Prize in Economic
Sciences in Memory of Alfred Nobel. I am grateful to Nick Barberis, Jonathan Berk, Xavier Gabaix,
Robin Greenwood, Ravi Jagannathan, Sydney Ludvigson, Ian Martin, Jonathan Parker, Todd Petzel, Neil
Shephard, Andrei Shleifer, Peter Norman Sorensen (the editor), Luis Viceira, and the Nobel laureates
for helpful comments on an earlier draft. I also acknowledge the inspiration provided by the Economic
Sciences Prize Committee of the Royal Swedish Academy of Sciences in their
