Posted: May 1st, 2022

Robin Greenwood, Ravi Jagannathan, Sydney Ludvigson, Ian Martin, Jonathan Parker

Empirical Asset Pricing:
Eugene Fama, Lars Peter Hansen,
and Robert Shiller
John Y. Campbell1
Could 2014
1Department of Economics, Littauer Middle, Harvard College, Cambridge MA 02138, and NBER.
E mail john_campbell@harvard.edu. Cellphone 617-496-6448. This paper has been commissioned by the
Scandinavian Journal of Economics for its annual survey of the Sveriges Riksbank Prize in Financial
Sciences in Reminiscence of Alfred Nobel. I’m 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 useful feedback on an earlier draft. I additionally acknowledge the inspiration supplied by the Financial
Sciences Prize Committee of the Royal Swedish Academy of Sciences of their scientiÖc background paper ìUnderstanding Asset Pricesî, accessible on-line at http://www.nobelprize.org/nobel_prizes/economicsciences/laureates/2013/advanced-economicsciences2013.pdf.
Summary
The Nobel Memorial Prize in Financial Sciences for 2013 was awarded to Eugene Fama,
Lars Peter Hansen, and Robert Shiller for his or her contributions to the empirical examine of asset
pricing. Some observers have discovered it laborious to grasp the widespread parts of the
laureatesíresearch, preferring to focus on areas of disagreement amongst them. This paper
argues that empirical asset pricing is a coherent enterprise, which owes a lot to the laureatesí
seminal contributions, and that essential themes within the literature can greatest be understood
by contemplating the laureates in pairs. SpeciÖcally, after summarizing trendy asset pricing
principle utilizing the stochastic low cost issue as an organizing framework, the paper discusses
the joint speculation downside in exams of market e¢ ciency, which is as a lot a possibility
as an issue (Fama and Hansen); patterns of short- and long-term predictability in asset
returns (Fama and Shiller); and fashions of deviations from rational expectations (Hansen
and Shiller). The paper concludes by reviewing methods by which the laureates have already
ináuenced the observe of Önance, and should ináuence future improvements.
Key phrases: Behavioral Önance, Önancial innovation, market e¢ ciency, stochastic low cost
issue.
JEL classiÖcation: G10, G12.
1 Introduction
The 2013 Sveriges Riksbank Prize in Financial Sciences in Reminiscence of Alfred Nobel, awarded
for empirical Assessment of asset costs, was unforgettably thrilling for Önancial economists. The
2013 laureates, Eugene Fama, Lars Peter Hansen, and Robert Shiller, are giants of Önance
and designers of the mental construction inside which all up to date analysis in asset
pricing is performed.
The celebrity of the laureates extends far past Önancial economics. Eugene Fama is
one of many 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 founding father of behavioral economics, a creator of the CaseShiller home worth indexes, and the creator of essential and extensively learn books for a normal
viewers.
The 2013 prize attracted consideration within the media, and stimulated dialogue amongst economists, for 2 further causes. First, the habits of asset costs pursuits each investor,
together with each particular person saving for retirement, and is a core concern for the Önancial providers trade. Second, the laureates have interpreted asset worth actions in strikingly
di§erent methods. Robert Shiller is known for his writings on asset worth bubbles, and his
public statements that shares within the late 1990s and homes within the mid 2000s had grow to be
overvalued as the results of such bubbles. Eugene Fama is skeptical that the time period ìbubbleî
is a properly deÖned or helpful one. Extra broadly, Fama believes that asset worth actions can
be understood utilizing financial fashions with rational buyers, whereas Shiller doesn’t.
The aim of this text is to rejoice the 2013 Nobel Memorial Prize in Financial
Sciences, and to elucidate the achievements of the laureates in a means that brings out the
connections amongst them. I hope to have the ability to talk the mental coherence of
the award, however the di§ering views of the laureates on some unsettled questions.
I ought to say a number of phrases about my very own connections with the laureates. Robert Shiller
modified my life when he grew to become my PhD dissertation adviser at Yale within the early 1980s.
In the midst of my profession I’ve written 12 papers with him, the earliest in 1983 and the
most up-to-date (hopefully not the final) in 2009. Eugene Fama, the oldest of the 2013 laureates,
was already a legend over 30 years in the past, and his analysis on market e¢ ciency was intensively
mentioned in New Haven and each different heart of educational economics. I Örst met Lars
Peter Hansen after I visited Chicago whereas searching for my Örst tutorial job in 1984. I’ve
by no means forgotten the Örst dialog I had with him about Önancial econometrics, by which I
sensed his penetrating perception that might require e§ort to completely perceive however would amply
reward the endeavor.
Amongst Önancial economists, I’m not uncommon in these emotions of sturdy connection
with the 2013 Nobel laureates. The 2013 award ceremony in Stockholm was notable for
the celebratory environment among the many coauthors and college students of the laureates who have been
1
current, together with lecturers Karl Case, John Cochrane, Kenneth French, John Heaton,
Ravi Jagannathan, Jeremy Siegel, and Amir Yaron, central banker Narayana Kocherlakota,
and asset administration practitioners David Sales space, Andrea Frazzini, and Antti Ilmanen. Any
of them may write the same article to this one, though in fact the views expressed right here
are my very own and are in all probability not absolutely shared by another economists together with the Nobel
laureates themselves.
The group of this paper is as follows. Part 2 offers a primary rationalization of the
central idea of recent asset pricing principle, the stochastic low cost issue or SDF. Whereas
the essential principle isn’t as a result of laureates, their work has contributed to our understanding
of the idea and lots of of their empirical contributions can most simply be understood by
reference to it.
Part three discusses the idea of market e¢ ciency, formulated by Fama within the 1960s.
Fama Örst said the ìjoint speculation problemîin testing market e¢ ciency, which Hansen
later understood to be as a lot a possibility as an issue, main him to develop an
essential econometric technique for estimating and testing financial fashions: the Generalized
Technique of Moments.
Part four opinions empirical analysis on the predictability of asset returns within the quick and
long term. Famaís early work developed econometric strategies, nonetheless extensively used as we speak, for
testing short-run predictability of returns. Usually these strategies Önd very modest predictability, however each Fama and Shiller later found that such predictability can cumulate
over time to grow to be an essential and even the dominant ináuence on longer-run actions
in asset costs. Analysis on this space continues to be very energetic, and is distinctive in its
tight integration of Önancial principle with econometrics.
Part 5 discusses the work of the laureates on asset pricing when some or all market
contributors have beliefs concerning the future that don’t conform to goal actuality. Shiller
helped to launch the Öeld of behavioral economics, and its most essential subÖeld of behavioral Önance, when he challenged the orthodoxy of the early 1980s that financial fashions
should at all times assume rational expectations by all financial brokers. Later, Hansen approached
this subject from the very di§erent perspective of strong optimum management.
Part 6 explores the implications of the laureatesí work for the observe of Önance.
Modern strategies of portfolio development owe a fantastic deal to the work of Fama on
fashion portfolios, that’s, portfolios of shares or different property sorted by traits equivalent to
worth (measures of cheapness that evaluate accounting valuations to market valuations) or
momentum (current previous returns). The quantitative asset administration trade makes use of many
concepts from the work of the laureates, and Shillerís current work emphasizes the significance
of Önancial innovation for human welfare in trendy economies.
Every of those sections refers back to the work of greater than one of many 2013 Nobel laureates.
On this means I hope to foster an appreciation for the mental dialogue among the many laureates
and the numerous researchers following their lead.
2
2 The Stochastic Low cost Issue: The Framework of
Modern Finance
2.1 The SDF in full markets
The fashionable principle of the SDF originates within the seminal theoretical contributions of Ross
(1978) and Harrison and Kreps (1979). Right here I current a quick abstract in an elementary
discrete-state mannequin with two intervals, the current and the longer term, and full markets.
Think about a easy mannequin with S states of nature s = 1:::S, all of which have strictly
constructive likelihood (s). I assume that markets are full, that’s, for every state s a
contingent declare is offered that pays $1 in state s and nothing in another state. Write
the worth of this contingent declare as q(s).
I assume that each one contingent declare costs are strictly constructive. If this weren’t true,
there can be an arbitrage alternative in one among two senses. First, if the contingent
declare worth for some state s have been zero, then an investor may purchase that contingent declare,
paying nothing as we speak, whereas having some likelihood of receiving a constructive payo§ if state s
happens tomorrow, and having no chance of a unfavourable payo§ in any state of the world.
Second, if the contingent declare worth for state s have been unfavourable, then an investor may purchase
that contingent declare, receiving a constructive payo§ as we speak, whereas once more having some likelihood
of a constructive payo§ and no chance of a unfavourable payo§ sooner or later.
Any asset, whether or not or not it’s a contingent declare, is deÖned by its state-contingent
payo§s X (s) for states s = 1:::S. The Legislation of One Value (LOOP) says that two property with
equivalent payo§s in each state will need to have the identical worth. If this weren’t true, once more there
can be an arbitrage alternative, this time within the sense that an investor may go lengthy the
low-cost asset and quick the costly one, receiving money as we speak whereas having assured zero
payo§s in all states sooner or later. LOOP implies that we will need to have
P(X) = X
S
s=1
q(s)X(s): (1)
The following step within the Assessment is to multiply and divide equation (1) by the target
likelihood of every 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)
the place M(s) = q(s)= (s) is the ratio of state worth to likelihood for state s, the stochastic
low cost issue or SDF in state s. Since q(s) and (s) are strictly constructive for all states s,
three
M(s) can also be. The final equality in (2) makes use of the deÖnition of an expectation as a probabilityweighted common of a random variable to write down the asset worth because the anticipated product of
the assetís payo§ and the SDF. This equation is usually given the slightly grand title of
the Elementary Equation of Asset Pricing.
Think about a riskless asset with payo§ X(s) = 1 in each state. The worth
Pf =
X
S
s=1
q(s) = E[M]; (three)
so the riskless rate of interest
1 + Rf =
1
Pf
=
1
E[M]
: (four)
This tells us that the imply of the stochastic low cost issue have to be pretty shut to 1. A
riskless actual rate of interest of two%, for instance, implies a imply stochastic low cost issue of
1=1:02 zero:98.
2.1.1 Utility maximization and the SDF
Think about a price-taking investor who chooses preliminary consumption C0 and consumption in
every future state C(s) to maximise time-separable utility of consumption. Assume for now
that the investorís subjective state chances coincide with the target chances
(s), that’s, the investor has rational expectations. The investorís maximization downside
is
Max u(C0) +X
S
s=1
(s)u(C(s)) (5)
topic to
C0 +
X
S
s=1
q(s)C(s) = W0; (6)
the place W0 is preliminary wealth (together with the current worth of future earnings, discounted utilizing
the suitable contingent claims costs). The Örst-order situations of the issue could be
written as
u
zero
(C0)q(s) = (s)u
zero
(C(s)) for s = 1:::S: (7)
These Örst-order situations indicate that
M(s) = q(s)
(s)
=
u0
(C(s))
u
zero
(C0)
: (eight)
In phrases, the SDF is the discounted ratio of marginal utility tomorrow to marginal utility
as we speak. This illustration of the SDF is the start line for the massive literature on
equilibrium asset pricing, which seeks to narrate asset costs to the arguments of consumersí
utility and significantly to their measured consumption of products and providers.
four
2.1.2 Heterogeneous beliefs
The dialogue above assumes that each one buyers have rational expectations and thus assign
the identical chances to the di§erent states of the world. If this isn’t the case, we should
assign investor-speciÖc subscripts to the chances, writing j (s) for investor jís subjective
likelihood of state s. Usually, we should additionally enable for di§erences within the utility operate
throughout buyers, including a j subscript to marginal utility as properly. Then for any state s and
investor j,
q(s) =
j (s)u
zero
j
(Cj (s))
u
zero
j
(Cj0)
: (9)
The state worth is expounded to the product of the investorís subjective likelihood of the state
and the investorís marginal utility in that state. In different phrases it’s a composite ìutil-probî
to make use of the terminology of Samuelson (1969).
An identical remark applies to the SDF, the ratio of state worth to goal likelihood:
M(s) = q(s)
(s)
=

j (s)
(s)
u0
j
(Cj (s))
u
zero
j
(Cj0)

: (10)
Volatility of the SDF throughout states might correspond both to risky deviations of investor
jís subjective chances from goal chances, or to risky marginal utility throughout
states. The standard assumption that buyers have homogeneous beliefs guidelines out the Örst of
these prospects, whereas the behavioral Önance literature embraces it.
2.1.three The SDF and danger premia
I now return to the idea of rational expectations and adapt the notation above to
transfer within the path of empirical analysis in Önance. I add the subscript t for the preliminary
date at which the assetís worth is set, and the subscript t + 1 for the following interval at
which the assetís payo§ is realized. This could simply be embedded in a multiperiod mannequin, in
which case the payo§ is subsequent periodís worth plus dividend. I add the subscript i to indicate
an asset. Then we now have
Pit = Et
[Mt+1Xi;t+1] = Et
[Mt+1]Et
[Xi;t+1] + Covt(Mt+1; Xi;t+1); (11)
the place the t subscripts on the imply and covariance point out that these are conditional moments calculated utilizing chances perceived at time t. The worth of the asset at time t
is included within the info set at time t, therefore there isn’t a must take a conditional
expectation of this variable. Because the conditional imply of the SDF is the reciprocal of
the gross riskless rate of interest from (four), equation (11) says that the worth of any asset is its
anticipated payo§, discounted on the riskless rate of interest, plus a correction for the conditional
covariance of the payo§ with the SDF.
5
For property with constructive costs, one can divide by means of 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 utilizing the relation between the conditional imply of the SDF and the riskless
rate of interest,
Et
[1 + Ri;t+1] = (1 + Rf;t+1)(1 Covt(Mt+1; Ri;t+1)): (13)
This says that the anticipated return on any asset is the riskless return instances an adjustment
issue for the covariance of the return with the SDF.
Subtracting the gross riskless rate of interest from each side, the chance premium on any asset
is the gross riskless rate of interest instances the covariance of the assetís extra 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 making use of the SDF framework
The above dialogue assumes full markets, however the SDF framework is simply as helpful
when markets are incomplete. The work of Hansen and Richard (1987) and Hansen and
Jagannathan (1991) is especially essential in characterizing the SDF for incomplete markets. Shiller (1982) is an insightful early contribution. Cochrane (2005) o§ers a textbook
remedy.
In incomplete markets, the existence of a strictly constructive SDF is assured by the
absence of arbitrageó a consequence generally referred to as the Elementary Theorem of Asset Pricingó
however the SDF is now not distinctive as it’s in full markets. Intuitively, an SDF could be
calculated from the marginal utility of any investor who can commerce property freely, however with
incomplete markets every investor can have idiosyncratic variation in his or her marginal
utility and therefore there are lots of attainable SDFs.
There’s nevertheless a singular SDF that may be written as a linear mixture of asset payo§s
and that satisÖes the basic equation of asset pricing (2). This distinctive random variable
is the projection of any SDF onto the area of asset payo§s, and thus another SDF should
have a better variance.
2.2.1 Volatility bounds on the SDF
Shiller (1982), a remark by Hansen (1982a), and Hansen and Jagannathan (1991) used
this perception to put decrease bounds on the volatility of the SDF, primarily based solely 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

in addition to Robert Shiller

Campbell, John Y.1

In Could of 2014,

1Department of Economics, Littauer Middle, Harvard College, Cambridge MA 02138, and NBER.

E mail john_campbell@harvard.edu. Cellphone 617-496-6448. This paper has been commissioned by the

Scandinavian Journal of Economics for its annual survey of the Sveriges Riksbank Prize in Financial

Sciences in Reminiscence of Alfred Nobel. I’m 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 useful feedback on an earlier draft. I additionally acknowledge the inspiration supplied by the Financial

Sciences Prize Committee of the Royal Swedish Academy of Sciences of their

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