Empirical Asset Pricing:
\nEugene Fama, Lars Peter Hansen,
\nand Robert Shiller
\nJohn Y. Campbell1
\nMay 2014
\n1Department of Economics, Littauer Center, Harvard University, Cambridge MA 02138, and NBER.
\nEmail john_campbell@harvard.edu. Phone 617-496-6448. This paper has been commissioned by the
\nScandinavian Journal of Economics for its annual survey of the Sveriges Riksbank Prize in Economic
\nSciences in Memory of Alfred Nobel. I am grateful to Nick Barberis, Jonathan Berk, Xavier Gabaix,
\nRobin Greenwood, Ravi Jagannathan, Sydney Ludvigson, Ian Martin, Jonathan Parker, Todd Petzel, Neil
\nShephard, Andrei Shleifer, Peter Norman Sorensen (the editor), Luis Viceira, and the Nobel laureates
\nfor helpful comments on an earlier draft. I also acknowledge the inspiration provided by the Economic
\nSciences Prize Committee of the Royal Swedish Academy of Sciences in their scienti\u00d6c background paper \u00ecUnderstanding Asset Prices\u00ee, available online at http:\/\/www.nobelprize.org\/nobel_prizes\/economicsciences\/laureates\/2013\/advanced-economicsciences2013.pdf.
\nAbstract
\nThe Nobel Memorial Prize in Economic Sciences for 2013 was awarded to Eugene Fama,
\nLars Peter Hansen, and Robert Shiller for their contributions to the empirical study of asset
\npricing. Some observers have found it hard to understand the common elements of the
\nlaureates\u00edresearch, preferring to highlight areas of disagreement among them. This paper
\nargues that empirical asset pricing is a coherent enterprise, which owes much to the laureates\u00ed
\nseminal contributions, and that important themes in the literature can best be understood
\nby considering the laureates in pairs. Speci\u00d6cally, after summarizing modern asset pricing
\ntheory using the stochastic discount factor as an organizing framework, the paper discusses
\nthe joint hypothesis problem in tests of market e\u00a2 ciency, which is as much an opportunity
\nas a problem (Fama and Hansen); patterns of short- and long-term predictability in asset
\nreturns (Fama and Shiller); and models of deviations from rational expectations (Hansen
\nand Shiller). The paper concludes by reviewing ways in which the laureates have already
\nin\u00e1uenced the practice of \u00d6nance, and may in\u00e1uence future innovations.
\nKeywords: Behavioral \u00d6nance, \u00d6nancial innovation, market e\u00a2 ciency, stochastic discount
\nfactor.
\nJEL classi\u00d6cation: G10, G12.
\n1 Introduction
\nThe 2013 Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel, awarded
\nfor empirical analysis of asset prices, was unforgettably exciting for \u00d6nancial economists. The
\n2013 laureates, Eugene Fama, Lars Peter Hansen, and Robert Shiller, are giants of \u00d6nance
\nand architects of the intellectual structure within which all contemporary research in asset
\npricing is conducted.
\nThe fame of the laureates extends far beyond \u00d6nancial economics. Eugene Fama is
\none of the world\u00eds most cited economists in any \u00d6eld. Lars Peter Hansen is an immensely
\ndistinguished econometrician, so the \u00d6eld of econometrics naturally claims a share of his
\nNobel 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
\naudience.
\nThe 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,
\nincluding every individual saving for retirement, and is a core concern for the \u00d6nancial services industry. Second, the laureates have interpreted asset price movements in strikingly
\ndi\u00a7erent ways. Robert Shiller is famous for his writings on asset price bubbles, and his
\npublic statements that stocks in the late 1990s and houses in the mid 2000s had become
\novervalued as the result of such bubbles. Eugene Fama is skeptical that the term \u00ecbubble\u00ee
\nis a well de\u00d6ned or useful one. More broadly, Fama believes that asset price movements can
\nbe understood using economic models with rational investors, whereas Shiller does not.
\nThe purpose of this article is to celebrate the 2013 Nobel Memorial Prize in Economic
\nSciences, and to explain the achievements of the laureates in a way that brings out the
\nconnections among them. I hope to be able to communicate the intellectual coherence of
\nthe award, notwithstanding the di\u00a7ering views of the laureates on some unsettled questions.
\nI should say a few words about my own connections with the laureates. Robert Shiller
\nchanged my life when he became my PhD dissertation adviser at Yale in the early 1980s.
\nIn the course of my career I have written 12 papers with him, the earliest in 1983 and the
\nmost recent (hopefully not the last) in 2009. Eugene Fama, the oldest of the 2013 laureates,
\nwas already a legend over 30 years ago, and his research on market e\u00a2 ciency was intensively
\ndiscussed in New Haven and every other center of academic economics. I \u00d6rst met Lars
\nPeter Hansen when I visited Chicago while seeking my \u00d6rst academic job in 1984. I have
\nnever forgotten the \u00d6rst conversation I had with him about \u00d6nancial econometrics, in which I
\nsensed his penetrating insight that would require e\u00a7ort to fully understand but would amply
\nreward the undertaking.
\nAmong \u00d6nancial economists, I am not unusual in these feelings of strong connection
\nwith the 2013 Nobel laureates. The 2013 award ceremony in Stockholm was notable for
\nthe celebratory atmosphere among the coauthors and students of the laureates who were
\n1
\npresent, including academics Karl Case, John Cochrane, Kenneth French, John Heaton,
\nRavi Jagannathan, Jeremy Siegel, and Amir Yaron, central banker Narayana Kocherlakota,
\nand asset management practitioners David Booth, Andrea Frazzini, and Antti Ilmanen. Any
\nof them could write a similar article to this one, although of course the views expressed here
\nare my own and are probably not fully shared by any other economists including the Nobel
\nlaureates themselves.
\nThe organization of this paper is as follows. Section 2 gives a basic explanation of the
\ncentral concept of modern asset pricing theory, the stochastic discount factor or SDF. While
\nthe basic theory is not due to the laureates, their work has contributed to our understanding
\nof the concept and many of their empirical contributions can most easily be understood by
\nreference to it.
\nSection 3 discusses the concept of market e\u00a2 ciency, formulated by Fama in the 1960s.
\nFama \u00d6rst stated the \u00ecjoint hypothesis problem\u00eein testing market e\u00a2 ciency, which Hansen
\nlater understood to be as much an opportunity as a problem, leading him to develop an
\nimportant econometric method for estimating and testing economic models: the Generalized
\nMethod of Moments.
\nSection 4 reviews empirical research on the predictability of asset returns in the short and
\nlong run. Fama\u00eds early work developed econometric methods, still widely used today, for
\ntesting short-run predictability of returns. Typically these methods \u00d6nd very modest predictability, but both Fama and Shiller later discovered that such predictability can cumulate
\nover time to become an important and even the dominant in\u00e1uence on longer-run movements
\nin asset prices. Research in this area continues to be very active, and is distinctive in its
\ntight integration of \u00d6nancial theory with econometrics.
\nSection 5 discusses the work of the laureates on asset pricing when some or all market
\nparticipants have beliefs about the future that do not conform to objective reality. Shiller
\nhelped to launch the \u00d6eld of behavioral economics, and its most important sub\u00d6eld of behavioral \u00d6nance, when he challenged the orthodoxy of the early 1980s that economic models
\nmust always assume rational expectations by all economic agents. Later, Hansen approached
\nthis topic (sample nursing essay examples by the best nursing assignment writing service) from the very di\u00a7erent perspective of robust optimal control.
\nSection 6 explores the implications of the laureates\u00ed work for the practice of \u00d6nance.
\nContemporary methods of portfolio construction owe a great deal to the work of Fama on
\nstyle portfolios, that is, portfolios of stocks or other assets sorted by characteristics such as
\nvalue (measures of cheapness that compare accounting valuations to market valuations) or
\nmomentum (recent past returns). The quantitative asset management industry uses many
\nideas from the work of the laureates, and Shiller\u00eds recent work emphasizes the importance
\nof \u00d6nancial innovation for human welfare in modern economies.
\nEach of these sections refers to the work of more than one of the 2013 Nobel laureates.
\nIn this way I hope to foster an appreciation for the intellectual dialogue among the laureates
\nand the many researchers following their lead.
\n2
\n2 The Stochastic Discount Factor: The Framework of
\nContemporary Finance
\n2.1 The SDF in complete markets
\nThe modern theory of the SDF originates in the seminal theoretical contributions of Ross
\n(1978) and Harrison and Kreps (1979). Here I present a brief summary in an elementary
\ndiscrete-state model with two periods, the present and the future, and complete markets.
\nConsider a simple model with S states of nature s = 1:::S, all of which have strictly
\npositive probability (s). I assume that markets are complete, that is, for each state s a
\ncontingent claim is available that pays $1 in state s and nothing in any other state. Write
\nthe price of this contingent claim as q(s).
\nI assume that all contingent claim prices are strictly positive. If this were not true,
\nthere would be an arbitrage opportunity in one of two senses. First, if the contingent
\nclaim price for some state s were zero, then an investor could buy that contingent claim,
\npaying nothing today, while having some probability of receiving a positive payo\u00a7 if state s
\noccurs tomorrow, and having no possibility of a negative payo\u00a7 in any state of the world.
\nSecond, if the contingent claim price for state s were negative, then an investor could buy
\nthat contingent claim, receiving a positive payo\u00a7 today, while again having some probability
\nof a positive payo\u00a7 and no possibility of a negative payo\u00a7 in the future.
\nAny asset, whether or not it is a contingent claim, is de\u00d6ned by its state-contingent
\npayo\u00a7s X (s) for states s = 1:::S. The Law of One Price (LOOP) says that two assets with
\nidentical payo\u00a7s in every state must have the same price. If this were not true, again there
\nwould be an arbitrage opportunity, this time in the sense that an investor could go long the
\ncheap asset and short the expensive one, receiving cash today while having guaranteed zero
\npayo\u00a7s in all states in the future. LOOP implies that we must have
\nP(X) = X
\nS
\ns=1
\nq(s)X(s): (1)
\nThe next step in the analysis is to multiply and divide equation (1) by the objective
\nprobability of each state, (s):
\nP(X) = X
\nS
\ns=1
\n (s)
\nq(s)
\n (s)
\nX(s) = X
\nS
\ns=1
\n (s)M(s)X(s) = E[MX]; (2)
\nwhere M(s) = q(s)= (s) is the ratio of state price to probability for state s, the stochastic
\ndiscount factor or SDF in state s. Since q(s) and (s) are strictly positive for all states s,
\n3
\nM(s) is also. The last equality in (2) uses the de\u00d6nition of an expectation as a probabilityweighted average of a random variable to write the asset price as the expected product of
\nthe asset\u00eds payo\u00a7 and the SDF. This equation is sometimes given the rather grand title of
\nthe Fundamental Equation of Asset Pricing.
\nConsider a riskless asset with payo\u00a7 X(s) = 1 in every state. The price
\nPf =
\nX
\nS
\ns=1
\nq(s) = E[M]; (3)
\nso the riskless interest rate
\n1 + Rf =
\n1
\nPf
\n=
\n1
\nE[M]
\n: (4)
\nThis tells us that the mean of the stochastic discount factor must be fairly close to one. A
\nriskless real interest rate of 2%, for example, implies a mean stochastic discount factor of
\n1=1:02 0:98.
\n2.1.1 Utility maximization and the SDF
\nConsider a price-taking investor who chooses initial consumption C0 and consumption in
\neach future state C(s) to maximize time-separable utility of consumption. Assume for now
\nthat the investor\u00eds subjective state probabilities coincide with the objective probabilities
\n (s), that is, the investor has rational expectations. The investor\u00eds maximization problem
\nis
\nMax u(C0) +X
\nS
\ns=1
\n (s)u(C(s)) (5)
\nsubject to
\nC0 +
\nX
\nS
\ns=1
\nq(s)C(s) = W0; (6)
\nwhere W0 is initial wealth (including the present value of future income, discounted using
\nthe appropriate contingent claims prices). The \u00d6rst-order conditions of the problem can be
\nwritten as
\nu
\n0
\n(C0)q(s) = (s)u
\n0
\n(C(s)) for s = 1:::S: (7)
\nThese \u00d6rst-order conditions imply that
\nM(s) = q(s)
\n (s)
\n=
\nu0
\n(C(s))
\nu
\n0
\n(C0)
\n: (8)
\nIn words, the SDF is the discounted ratio of marginal utility tomorrow to marginal utility
\ntoday. This representation of the SDF is the starting point for the large literature on
\nequilibrium asset pricing, which seeks to relate asset prices to the arguments of consumers\u00ed
\nutility and particularly to their measured consumption of goods and services.
\n4
\n2.1.2 Heterogeneous beliefs
\nThe discussion above assumes that all investors have rational expectations and thus assign
\nthe same probabilities to the di\u00a7erent states of the world. If this is not the case, we must
\nassign investor-speci\u00d6c subscripts to the probabilities, writing j (s) for investor j\u00eds subjective
\nprobability of state s. In general, we must also allow for di\u00a7erences in the utility function
\nacross investors, adding a j subscript to marginal utility as well. Then for any state s and
\ninvestor j,
\nq(s) =
\n j (s)u
\n0
\nj
\n(Cj (s))
\nu
\n0
\nj
\n(Cj0)
\n: (9)
\nThe state price is related to the product of the investor\u00eds subjective probability of the state
\nand the investor\u00eds marginal utility in that state. In other words it is a composite \u00ecutil-prob\u00ee
\nto use the terminology of Samuelson (1969).
\nA similar observation applies to the SDF, the ratio of state price to objective probability:
\nM(s) = q(s)
\n (s)
\n=<\/p>\n
j (s)
\n (s)
\n u0
\nj
\n(Cj (s))
\nu
\n0
\nj
\n(Cj0)<\/p>\n
: (10)
\nVolatility of the SDF across states may correspond either to volatile deviations of investor
\nj\u00eds subjective probabilities from objective probabilities, or to volatile marginal utility across
\nstates. The usual assumption that investors have homogeneous beliefs rules out the \u00d6rst of
\nthese possibilities, while the behavioral \u00d6nance literature embraces it.
\n2.1.3 The SDF and risk premia
\nI now return to the assumption of rational expectations and adapt the notation above to
\nmove in the direction of empirical research in \u00d6nance. I add the subscript t for the initial
\ndate at which the asset\u00eds price is determined, and the subscript t + 1 for the next period at
\nwhich the asset\u00eds payo\u00a7 is realized. This can easily be embedded in a multiperiod model, in
\nwhich case the payo\u00a7 is next period\u00eds price plus dividend. I add the subscript i to denote
\nan asset. Then we have
\nPit = Et
\n[Mt+1Xi;t+1] = Et
\n[Mt+1]Et
\n[Xi;t+1] + Covt(Mt+1; Xi;t+1); (11)
\nwhere 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
\nis included in the information set at time t, hence there is no need to take a conditional
\nexpectation of this variable. Since the conditional mean of the SDF is the reciprocal of
\nthe gross riskless interest rate from (4), equation (11) says that the price of any asset is its
\nexpected payo\u00a7, discounted at the riskless interest rate, plus a correction for the conditional
\ncovariance of the payo\u00a7 with the SDF.
\n5
\nFor assets with positive prices, one can divide through by Pit and use (1 + Ri;t+1) =
\nXi;t+1=Pit to get
\n1 = Et
\n[Mt+1(1 + Ri;t+1)]
\n= Et
\n[Mt+1]Et
\n[1 + Ri;t+1] + Covt(Mt+1; Ri;t+1): (12)
\nRearranging and using the relation between the conditional mean of the SDF and the riskless
\ninterest rate,
\nEt
\n[1 + Ri;t+1] = (1 + Rf;t+1)(1 Covt(Mt+1; Ri;t+1)): (13)
\nThis says that the expected return on any asset is the riskless return times an adjustment
\nfactor for the covariance of the return with the SDF.
\nSubtracting the gross riskless interest rate from both sides, the risk premium on any asset
\nis the gross riskless interest rate times the covariance of the asset\u00eds excess return with the
\nSDF:
\nEt(Ri;t+1 Rf;t+1) = (1 + Rf;t+1)Covt(Mt+1;Ri;t+1 Rf;t+1): (14)
\n2.2 Generalizing and applying the SDF framework
\nThe above discussion assumes complete markets, but the SDF framework is just as useful
\nwhen markets are incomplete. The work of Hansen and Richard (1987) and Hansen and
\nJagannathan (1991) is particularly important in characterizing the SDF for incomplete markets. Shiller (1982) is an insightful early contribution. Cochrane (2005) o\u00a7ers a textbook
\ntreatment.
\nIn incomplete markets, the existence of a strictly positive SDF is guaranteed by the
\nabsence of arbitrage\u00f3 a result sometimes called the Fundamental Theorem of Asset Pricing\u00f3
\nbut the SDF is no longer unique as it is in complete markets. Intuitively, an SDF can be
\ncalculated from the marginal utility of any investor who can trade assets freely, but with
\nincomplete markets each investor can have idiosyncratic variation in his or her marginal
\nutility and hence there are many possible SDFs.
\nThere is however a unique SDF that can be written as a linear combination of asset payo\u00a7s
\nand that satis\u00d6es the fundamental equation of asset pricing (2). This unique random variable
\nis the project ( help with nursing paper writing from experts with MSN & DNP degrees)ion of any SDF onto the space of asset payo\u00a7s, and thus any other SDF must
\nhave a higher variance.
\n2.2.1 Volatility bounds on the SDF
\nShiller (1982), a comment by Hansen (1982a), and Hansen and Jagannathan (1991) used
\nthis insight to place lower bounds on the volatility of the SDF, based only on the properties
\nof asset returns<\/p>\n
—-<\/p>\n
Eugene Fama, Lars Peter Hansen, Eugene Fama, Lars Peter Hansen, Lars Peter Hansen, Lars Peter Hansen, Lars Peter Hansen, Lars Peter Hansen<\/p>\n
as well as Robert Shiller<\/p>\n
Campbell, John Y.1<\/p>\n
In May of 2014,<\/p>\n
1Department of Economics, Littauer Center, Harvard University, Cambridge MA 02138, and NBER.<\/p>\n
Email john_campbell@harvard.edu. Phone 617-496-6448. This paper has been commissioned by the<\/p>\n
Scandinavian Journal of Economics for its annual survey of the Sveriges Riksbank Prize in Economic<\/p>\n
Sciences in Memory of Alfred Nobel. I am grateful to Nick Barberis, Jonathan Berk, Xavier Gabaix,<\/p>\n
Robin Greenwood, Ravi Jagannathan, Sydney Ludvigson, Ian Martin, Jonathan Parker, Todd Petzel, Neil<\/p>\n
Shephard, Andrei Shleifer, Peter Norman Sorensen (the editor), Luis Viceira, and the Nobel laureates<\/p>\n
for helpful comments on an earlier draft. I also acknowledge the inspiration provided by the Economic<\/p>\n
Sciences Prize Committee of the Royal Swedish Academy of Sciences in their<\/p>\n","protected":false},"excerpt":{"rendered":"
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