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Two Pillars of Asset Pricing
Author(s): Eugene F. Fama
Source: The American Economic Review , JUNE 2014, Vol. 104, No. 6 (JUNE 2014), pp.
1467-1485
Published by: American Economic Association
Stable URL: https://www.jstor.org/stable/42920856
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American Economic Review 2014, 104(6): 1467-1485
http://dx.doi.org/10. 1257 /aer. 104.6. 1467
Two Pillars of Asset Pricing1
By Eugene F. Fama*
The Nobel Foundation asks that the Nobel lecture cover the work for
which the Prize is awarded. The announcement of this year's Prize
cites empirical work in asset pricing. I interpret this to include work
on efficient capital markets and work on developing and testing asset
pricing models - the two pillars, or perhaps more descriptive, the
Siamese twins of asset pricing. I start with efficient markets and then
move on to asset pricing models.
I. Efficient Capital Markets
A. Early Work
The year 1962 was a propitious time for PhD research at the University of Chicago.
Computers were coming into their own, liberating econometricians from their
mechanical calculators. It became possible to process large amounts of data quickly,
at least by previous standards. Stock prices are among the most accessible data,
and there was burgeoning interest in studying the behavior of stock returns, cen-
tered at the University of Chicago (Merton Miller, Harry Roberts, Lester Telser, and
Benoit Mandelbrot as a frequent visitor) and MIT (Sidney Alexander, Paul Cootner,
Franco Modigliani, and Paul Samuelson). Modigliani often visited Chicago to work
with his longtime coauthor Merton Miller, so there was frequent exchange of ideas
between the two schools.
It was clear from the beginning that the central question is whether asset prices
reflect all available information - what I labelled the efficient markets hypothesis
(Fama 1965b). The difficulty is making the hypothesis testable. We can't test whether
the market does what it is supposed to do unless we specify what it is supposed to do.
In other words, we need an asset pricing model, a model that specifies the character-
istics of rational expected asset returns in a market equilibrium. Tests of efficiency
basically test whether the properties of expected returns implied by the assumed
model of market equilibrium are observed in actual returns. If the tests reject, we
* Robert R. McCormick Distinguished Service Professor of Finance, Booth School, University of Chicago, 5807
S. Woodlawn Ave, Chicago, IL 60637 (e-mail: eugene.fama@chicagobooth.edu). In places, this lecture borrows
from Fama (2011). I am grateful for the comments of George Constantinides, Douglas Diamond, Anil Kashyap,
Richard Leftwich, Juhani Linnainmaa, Tobias Moskowitz, Lubos Pastor, G. William Schwert, Amir Sufi, and
Richard Thaler. Special thanks to John Cochrane and my longtime coauthor, Kenneth R. French. I am a consultant
to, board member of, and shareholder in Dimensional Fund Advisors.
Ť This article is a revised version of the lecture Eugene Fama delivered in Stockholm, Sweden, on December 8,
2013, when he received the Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel. This article
is copyright © The Nobel Foundation 2013 and is published here with the permission of the Nobel Foundation. Go
to http://dx.doi.Org/10.1257/aer.104.6.1467 to visit the article page.
1467
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1468 THE AMERICAN ECONOMIC REVIEW JUNE 2014
don't know whether the problem is an ineffi
equilibrium. This is the joint hypothesis pro
A bit of notation makes the point precise. Su
vector of payoffs at time t + 1 (prices plus d
assets available at t. Suppose f(Pl+í | 0(m) is th
t + 1 implied by the time t information set Qtm
of equilibrium prices for assets at time t. Fin
tion of payoffs implied by all information av
f{Pt+' 1 0,) is the distribution from which pr
efficiency hypothesis that prices at t reflect
(1) f{p,+ iiej =f(P,+i I©,).
The market efficiency condition is more typically state
returns. If E(Rt+ļ ' Qtm ) is the vector of expected returns im
the equilibrium prices P„ and E(Rt+l | ©,) is the expected
time t prices and f(Pt+[ 1 0ř), the market efficiency condition
(2) £(*,+i 1 0,J = E(R[+i'e,).
The prices observed at t + 1 are drawn from/(/?+1 1 ©,), so in th
and E(Rl+ļ ' ©,) are observable, but we do not observe f(P,+' | ©
As a result, the market efficiency conditions (1) and (2) are n
testable propositions, we must specify how equilibrium prices a
acteristics off{Pt+l I ©,m). In other words, we need a model of
an asset pricing model, no matter how primitive - that specifi
of rational equilibrium expected returns, E(Rt+ , | ©,m).
For example, in many early tests, market efficiency is assu
returns are unpredictable based on past information. The impl
equilibrium is that equilibrium expected returns are constant,
(3) E(Rt+l'Gtm) = E(R).
If the market is efficient so that (2) holds, then
(4) E(RI+Ì I ©f) = E(R).
The testable implication of (4) is that a regression of
which are known at time t, should produce slopes that
zero. If the test fails, we don't know whether the pro
ket equilibrium (equation (3) is the culprit) or an ineffi
information in setting prices (equations (1) and (2) do n
hypothesis problem.
The joint hypothesis problem is perhaps obvious o
argue that it is implicit in Bachelier (1900), Muth (1
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VOL. 104 NO. 6 FAMA: TWO PILLARS OF ASSET PRICING 1469
Mandelbrot (1966). But its importance in work on market
nized before Fama (1970), which brought it to the forefron
For example, many early papers focus on autocorrelation
propose that market efficiency implies that the autocorrela
tinguishable from zero. The implicit model of market equ
edged in the tests, is (3), that is, the market is trying to
expected returns are constant through time.
A clean statement of the joint hypothesis problem, close
chapter 5 of Fama (1976b). Everybody in finance claims to
given its sales, they must be sharing the same copy.
Market efficiency is always tested jointly with a model
but the converse is also true. Common asset pricing mod
pricing model (CAPM) of Sharpe (1964) and Lintner (
intertemporal CAPM (the ICAPM), and the consumpti
and Breeden (1979), implicitly or explicitly assume that all
available to all market participants who use it correctly in
a strong form of market efficiency. Thus, tests of these a
test market efficiency.
B. Event Studies
In the initial empirical work on market efficiency, the tests centered on predict-
ing returns using past returns. Fama et al. (1969) extend the tests to the adjustment
of stock prices to announcements of corporate events. In Fama et al. the event is
stock splits, but the long-term impact of the paper traces to the empirical approach
it uses to aggregate the information about price adjustment in a large sample
of events.
Like other corporate events, the sample of splits is spread over a long period
(1926-1960). To abstract from general market effects that can obscure a stock's
response to a split, we use a simple "market model" time series regression,
(5) Rit = a¡ + b¡RMt + e,¡.
In this regression, Rit is the return on stock i for month t, RMt
and the residual eit is the part of the security's return that i
market return. The month t response of the return to a split is th
To aggregate the responses across the stocks that experience
time rather than calendar time. Specifically, t = 0 is the mont
about a split becomes available, t = - 1 is the previous month,
month, etc. Thus, period 0 is a different calendar month for
the average response of returns in the months preceding and
average the residuals for the stocks in the sample for each of
ing and following the split. To measure the cumulative respo
sum the average residuals.
The results of the split paper are striking. The cumulat
(Figure 1) rises in the months preceding a split. Thus, compan
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1470 THE AMERICAN ECONOMIC REVIEW JUNE 2014
Figure 1. Cumulative Average Residuals in the Months Surrounding a Split
Source: Fama et al. (1969).
stocks after good times that produce large increases in their stock prices. Once the
split becomes known, however, there is no further movement in the cumulative
average residual, despite the fact that about 75 percent of the companies that split
their stocks continue to experience good times (witnessed by subsequent dividend
growth rates larger than those of the market as a whole). In other words, on average,
all the implications of a split for the future performance of a company are incorpo-
rated in stock prices in the months leading up to the split, with no further reaction
thereafter - exactly the prediction of market efficiency.
The split paper spawned an event study industry. To this day, finance and account-
ing journals contain many studies of the response of stock prices to different corpo-
rate events, for example, earnings announcements, merger announcements, security
issues, etc. Almost all use the simple methodology of the split paper. Like the split
study, other early event studies generally confirm that the adjustment of stock prices
to events is quick and complete.
Early event studies concentrate on short periods, typically days, around an event.
Over short periods the assumed model for equilibrium expected returns is relatively
unimportant because the change in the price of the stock in response to the event is
typically much larger than short-horizon expected returns. In other words, the joint
hypothesis problem is relatively unimportant. More recently, researchers in behav-
ioral finance become interested in studying price responses for several years after an
event. Over such long periods, expected returns are larger relative to the price effect
of the event, and the joint hypothesis problem becomes important.
For example, the implicit model of market equilibrium in the split study is that
the regression intercept and slope, a, and b¡, in the market model regression (5) are
constant through time. It is now well known that a¡ and b¡ change through time. This
can produce drift in long-term cumulative average regression residuals that looks
like market inefficiency but is just a bad model for expected returns. These issues
are discussed in Fama (1998).
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VOL. 104 NO. 6 FAMA: TWO PILLARS OF ASSET PRICING 147 1
C. Predictive Regressions
The early work on market efficiency focuses on stock ret
I turn to bonds to study Irving Fisher's (market efficiency)
time t interest rate on a short-term bond that matures at t
equilibrium expected real return, E(rt+ļ), plus the best possib
tion rate, E(i r,+1),
(6) it+i = E(rl+ļ) + E(tt,+1).
The topic is not new, but my approach is novel. Earlier wor
the interest rate on lagged inflation rates,
(7) it+l = a + bļir, + b2n,_ , + • • • + e,+1.
The idea is that the expected inflation rate (along with the expected real return)
determines the interest rate, so the interest rate should be the dependent variable and
the expected inflation rate should be the independent variable. Past inflation is a noisy
measure of expected inflation, so equation (7) suffers from an errors-in- variables
problem. More important, in an efficient market the expected inflation rate built into
the interest rate surely uses more information than past inflation rates.
The insight in Fama (1975), applied by me and others in subsequent papers, is that
a regression estimates the conditional expected value of the left-hand-side variable
as a function of the right-hand-side variables. Thus, to extract the forecast of infla-
tion in the interest rate (the expected value of inflation priced into the interest rate),
one regresses the inflation rate for period t + 1 on the interest rate for t + 1 set at
the beginning of the period,
(8) 7 r,+1 = a + bil+i + eř+l.
The expected inflation rate estimated in this way captures all th
to set the interest rate. On hindsight, this is the obvious way to
regression, but it was not obvious at the time.
Reversing the regression eliminates one measurement error pr
introduce another, caused by variation through time in the exp
built into the interest rate. The model of market equilibrium in
the expected real return is constant, E(rt+l) = r. Near zero autoc
returns suggest that this proposition is a reasonable approximatio
1953-1971 period examined. Thus, at least for this period, the in
a direct proxy for the expected inflation rate - it is the expected
a constant.
The slopes in the estimates of (8) for the one-month, three-month, and six-mon
Treasury Bill rates and inflation rates of 1953-1971 are quite close to 1.0, and th
autocorrelations of the residuals are close to zero. Thus, the bottom line from Fa
(1975) is that interest rates on one-month, three-month, and six-month US Treasu
bills seem to contain rational forecasts of inflation one, three, and six months ah
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1 472 THE AMERICAN ECONOMIC REVIEW JUNE 2014
Fisher's hypothesis that expected asset returns
expected inflation applies to all assets. Fama and
term bonds, real estate, and stock returns. The
rium has two parts. First, as in Fama (1975), the
on bills are assumed to be constant through time
as the proxy for the expected inflation rate. Sec
expected real returns on other assets is assumed
inflation. With this model of market equilibrium
with regressions of the nominal return on an asse
beginning of period t + 1,
(9) /?(+1 = a + bit+l + Et+'.
The tests say that monthly, quarterly, and semiannual n
longer-term bonds and real estate compensate for monthly, qu
nual expected inflation: that is, for these assets the slopes in th
again near 1.0. Thus, we cannot reject the market efficiency p
and real estate prices incorporate the best possible forecasts o
model of market equilibrium in which expected real returns v
expected inflation.
The relation between common stock returns and expected in
perverse. The slopes in the estimates (9) for stocks are neg
returns are higher when expected inflation (proxied by the b
vice versa. Thus, for stocks we face the joint hypothesis probl
because of poor inflation forecasts (market inefficiency) or b
expected real stock returns are in fact negatively related to exp
chose a bad model of market equilibrium)?
The simple idea about forecasting regressions in Fama (1975)
sion of a return on predetermined variables produces estimat
the expected value of the return conditional on the forecasting
me well. I use it in a sequence of papers to address an old issue
literature, specifically, how well do the forward interest rates
from prices of longer-term discount bonds forecast future one
rates (Fama 1976a, c; 1984b, c; 1986; 1990a; 2006; and Fama
To see the common insight in these term structure papers,
maturity) premium in the one-period return on a discount bo
maturity at time t as the difference between the return, RTt+
"spot" interest rate observed at time t, S¡+1. Skipping the tedio
show that the time t forward rate for period t + T, Ft t+T, contain
premium, E(RTt+x) - S,+l, as well as a forecast of the spot rat
As a result, there is a pair of complementary regressions tha
between the forward rate and the current spot rate to forecast the
the future change in the spot rate,
(10) RTt+ 1 - Sř+1 =aj + bļ(Fti t+T - S,+1) + e1>i
(11) St+T - Si+1 = a2 + b2(Fu+T - St+i) + e2,t+T-
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VOL. 104 NO. 6 FAMA: TWO PILLARS OF ASSET PRICING 1473
The conclusion from this work is that the information in fo
about expected term premiums rather than future spot rates;
is near 1.0, and the slope in (11) is near 0.0. There is, how
predictability of spot rates due to mean reversion of the
1987), though not necessarily to a constant mean (Fama 2
In Fama (1984a), I apply the complementary regression a
ward foreign exchange rates as predictors of future spot
tion in forward exchange rates seems to be about risk pre
or no information about future spot exchange rates. The e
puzzled over this result for 30 years. Using the complemen
Fama and French (1987) find that futures prices for a wid
show power to forecast spot prices - the exception to the
D. Time-Varying Expected Stock Returns
As noted above, early work on market efficiency genera
rium expected stock returns are constant through time. T
The expected return on a stock contains compensation fo
return. Both the risk and the willingness of investors to
change through time, leading to a time- varying expected r
predetermined variables that can be used to track expect
regressions.
Fama and Schwert (1977) document variation in monthly, quarterly, and
semiannual expected stock returns using predetermined monthly, quarterly, and
semiannual Treasury bill rates. In later work, the popular forecasting variable on the
right-hand side of the regression is the dividend yield, the ratio of trailing annual
dividends to the stock price at the beginning of the forecast period. The motiva-
tion, which I attribute to Ball (1978), is that a stock's price is the present value of
the stream of expected future dividends, where the discount rate is (approximately)
the expected stock return. Thus, a high stock price relative to dividends likely sig-
nals a lower expected return, and vice versa. The word "likely" is needed because
price also depends on expected future dividends, which means the dividend yield
is a noisy proxy for the expected stock return, a problem emphasized by Campbell
and Shiller (1988) and others. Cochrane (201 1) gives an elegant explanation of the
problem in terms of complementary regressions that use the dividend yield to fore-
cast long-term average stock returns and long-term dividend growth.
To my knowledge, the first papers that use dividend yields to track expected
stock returns are Rozeff (1984) and Shiller (1984). Fama and French (1987) add
an interesting wrinkle to the evidence. We find that the explanatory power of the
regression, measured by the regression R2, increases as the horizon for the return
is extended in steps from a month to four years. This result may seem surprising,
but it is just a consequence of the fact that dividend yields are persistent (highly
autocorrelated).
For example, with persistent dividend yields, the slope in the regression of the
quarterly stock return on the beginning of quarter yield will be about three times the
slope in the regression of the monthly return on the beginning of month yield. Thus,
the variance of the expected return estimate in the three-month regression is about
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1474 THE AMERICAN ECONOMIC REVIEW JUNE 2014
nine times the variance in the one-month reg
in the three-month regression (the unexpected p
times the variance of the residual in the one
higher in the three-month regression.
Higher R2 for longer return horizons due to
implies that the variance of the predictable part
ance of the unpredictable part, so in this sen
predictable. But unpredictable variation in ret
that is, the variance of forecast errors is larger
important sense, longer horizon returns are l
Efficient market types (like me) judge th
returns on stocks and bonds is rational, the r
to bear risk. In contrast, behaviorists argue th
irrational swings of prices away from fundam
Fama and French (1989) address this issue. T
ation in expected bond returns tracked by t
default spread (the difference between the y
low credit risk) and (ii) the term spread (the
short-term yields on high grade bonds), is s
dividend yields predict bond returns as well
spreads and dividend yields are related to lon
spreads are strongly related to short-term b
that expected returns are high when busines
they are strong.
The evidence that the variation in expected r
and related to business conditions leads Fama
the resulting predictability of stock and bon
disagree. Animal spirits can roam across mar
ness conditions. No available empirical eviden
convinces both sides.
Shiller (1981) finds that the volatility of stock prices is much higher than can
be explained by the uncertain evolution of expected future dividends. This result
implies that much of the volatility of stock prices comes from time- varying expected
returns. The market efficiency issue is whether the variation in expected returns
necessary to explain Shiller's results is beyond explanation by a model for rational
expected returns. It is certainly possible to develop models for expected returns that
produce this conclusion in empirical tests. But then we face the joint hypothesis
problem. Do the tests fail because the market is inefficient or because we have the
wrong model for rational expected returns? This and other market efficiency issues
are discussed in detail in Fama (1991).
E. "Bubbles"
There is one remaining result in the literature on return predictability that warrants
mention. The available evidence says that stock returns are somewhat predictable
from dividend yields and interest rates, but there is no statistically reliable evidence
that expected stock returns are sometimes negative. Fama and French (1987) find
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VOL. 104 NO. 6 FAMA: TWO PILLARS OF ASSET PRICING 1475
that predictions from dividend yields of negative returns
US stocks are never more than two standard errors below zero. Fama and Schwert
(1977) find no evidence of reliable predictions of negative market returns when the
forecast variable is the short-term bill rate.
These results are important. The stock market run-up to 2007 and subsequent
decline is often called a "bubble." Indeed, the word "bubble," applied to many
markets, is now common among academics and practitioners. A common policy
prescription is that the Fed and other regulators should lean against asset market
bubbles to preempt the negative effects of bursting bubbles on economic activity.
Such policy statements seem to define a "bubble" as an irrational strong price
increase that implies a predictable strong decline. This also seems to be the defini-
tion implicit in most recent claims about "bubbles." But the available research pro-
vides no reliable evidence that price declines are ever predictable. Thus, at least as
the literature now stands, confident statements about "bubbles" and what should be
done about them are based on beliefs, not reliable evidence.
"Reliable" is important in this discussion. After an event, attention tends to focus
on people who predicted it. The ex post selection bias is obvious. To infer reliability
one needs to evaluate a forecaster's entire track record, and, more important, the
track records of all forecasters we might have chosen ex ante.
The absence of evidence that stock market price declines are predictable seems
sufficient to conclude that "bubble" is a treacherous term, but there is more. Figure 2
shows the December 1925 to September 2013 path of the natural log of US stock
market wealth, including reinvested dividends, constructed using the value-weight
market portfolio of NYSE, AMEX, and NASDAQ stocks from the Center for
Research in Security Prices (CRSP) of the University of Chicago. The recessions
identified by the NBER are shown as shaded areas on the graph.
In percent terms, the largest five price declines in Figure 2 are (i) August 1929
to June 1932, (ii) October 2007 to February 2009, (iii) February 1937 to March
1938, (iv) August 2000 to September 2002, and (v) August 1972 to December 1974.
All these price declines are preceded by strong price increases, so these are prime
"bubble" candidates.
These five periods are associated with recessions, and except for August 2000
to September 2002, the magnitude of the price decline seems to reflect the sever-
ity of the recession. The peak of the market in 1929 is the business cycle peak,
but for the other four episodes, the market peak precedes the business cycle peak.
Except for August 2000 to September 2002, the market low precedes the end of
the recession. This pattern in stock prices also tends to occur around less severe
recessions.
It thus seems that large swings in stock prices are responses to large swings in real
activity, with stock prices forecasting real activity - a phenomenon studied in detail
in Fama (1981, 1990b). All this is consistent with an efficient market in which the
term "bubble," at least as commonly used, has no content.
One might assert from Figure 2 that major stock market swings cause recessions
and market upturns bring them to an end. (One can also assert that the weather-
man causes the weather - a quip stolen from John Cochrane.) At a minimum, how-
ever, (i) the absence of evidence that price declines are ever predictable, and (ii) the
evidence that the prime "bubble" candidates seem to be associated with rather
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1476 THE AMERICAN ECONOMIC REVIEW JUNE 2014
Figure 2. Log of Cumulative Value of the CRSP Market Index, Including Dividends
Note: Shaded areas are US recessions identified by the National Bureau of Economic Research.
impressive market forecasts of real activity are sufficient to caution against use of
the "bubble" word without more careful definition and empirical validation.
Common "bubble" rhetoric says that the declines in prices that terminate "bub-
bles" are market corrections of irrational price increases. Figure 2 shows, however,
that major stock price declines are followed rather quickly by price increases that
wipe out, in whole or in large part, the preceding price decline. "Bubble" stories thus
face a legitimate question: which leg of a "bubble" is irrational, the up or the down?
Do we see "irrational optimism" in the price increase corrected in the subsequent
decline? Or do we see "irrational pessimism" in the price decline, quickly reversed?
Or both? Or perhaps neither?
Finally, it is difficult to evaluate expert forecasts of "bubbles" in asset prices since
we tend to hear only "success" stories identified after the fact, and for a particular
"bubble," we rarely know the all-important date of an expert's first forecast that
prices are irrationally high. For a bit of fun, however, we can examine two com-
monly cited "success" stories.
On the website for his book, Irrational Exuberance, Shiller says that at a
December 3, 1996, lunch, he warned Fed Chairman Allan Greenspan that the level
of stock prices was irrationally high. Greenspan's famous "Irrational Exuberance"
speech followed two days later. How good was Shiller's forecast? On December 3,
1996, the CRSP index of US stock market wealth stood at 1518. It more than dou-
bled to 3191 on September 1, 2000, and then fell. This is the basis for the inference
that the original bubble prediction was correct. At its low on March 11, 2003, how-
ever, the index, at 1739, was about 15 percent above 1518, its value on the initial
"bubble" forecast date. These index numbers include reinvested dividends, which
seem relevant for investor evaluations of "bubble" forecasts. If one ignores divi-
dends and focuses on prices alone, the CRSP price index on March 11, 2003, was
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VOL. 104 NO. 6 FAMA: TWO PILLARS OF ASSET PRICING 1477
also above its December 3, 1996, value (648 versus 618).
evidence that prices were irrationally high at the time
they have been irrationally high ever since.
The second "success" story is the forecast in the mid-2
were irrationally high. Many academics and practitione
but an easy one to date is Case and Shiller (2003), which
late 2002 or early 2003. To give their prediction a good
the date of the first forecast of a real estate "bubble." T
Home Price Index is 142.99 in July 2003, its peak is 206
subsequent low is 134.07 in March 2012. Thus, the price
be the first forecast date is only 6.7 percent. The value t
services during the almost nine years from July 2003 t
6.7 percent of July 2003 home values. Moreover, on th
2013, the real estate index, at 165.91, is 16 percent abo
"bubble" forecast date. Again, there is not much eviden
nally high at the time of the initial forecast.
I single out Shiller and Case and Shiller (2003) only bec
of these two "bubbles" are relatively easy to date. Man
some of my colleagues, made the same "bubble" claims a
F. Behavioral Finance
I conclude this section on market efficiency with a complaint voiced in my
review of behavioral finance 15 years ago (Fama 1998). The behavioral finance
literature is largely an attack on market efficiency. The best of the behaviorists (like
my colleague Richard Thaler) base their attacks and their readings of the empirical
record on findings about human behavior in psychology. Many others don't bother.
They scour databases of asset returns for "anomalies" (a statistically treacherous
procedure), and declare victory for behavioral finance when they find a candidate.
Most important, the behavioral literature has not put forth a full blown model for
prices and returns that can be tested and potentially rejected - the acid test for any
model proposed as a replacement for another model.
II. Asset Pricing Models
This year's Nobel award cites empirical research in asset pricing. Tests of market
efficiency are one branch of this research. The other is tests of asset pricing mod-
els, that is, models that specify the nature of asset risks and the relation between
expected return and risk. Much of my work is concerned with developing and test-
ing asset pricing models, the flip side of the joint hypothesis problem.
A. Fama and MacBeth (1973)
The first formal model of market equilibrium is the CAPM of Sharpe (1964) and
Lintner (1965). In this model market ß, the slope in the regression of an asset's
return on the market return is the only relevant measure of an asset's risk, and the
cross section of expected asset returns depends only on the cross section of asset /3s.
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1478 THE AMERICAN ECONOMIC REVIEW JUNE 2014
In the early literature, the common approach t
regressions of average security or portfolio ret
variables. Black et al. (1972) criticize this ap
of the slope for ß (the premium in expected
precise, given the high volatility of market
problem is cross-correlation of the residuals
estimated standard errors. They propose a c
this problem.
Fama and MacBeth (1973) provide a simple solution to the cross-correlation prob-
lem. Instead of regressing average asset returns on ßs and other variables, one does
the regression period by period, where the period is usually a month. The slopes in
the regression are monthly portfolio returns whose average values can be used to test
the CAPM predictions that the expected ß premium is positive and other variables
add nothing to the explanation of the cross section of expected returns. (This is best
explained in chapter 9 of Fama 1976b.)
An example is helpful. Fama and French ( 1992) estimate month-by-month regres-
sions of the cross section of individual stock returns for month t, Rit, on estimates
b¡ of their ßs, their (logged) market capitalizations at the beginning of month t,
MC i and their book-to-market equity ratios, BM¡ ,
(12) Rit = a, + aubt + a2l MQ(_, + a3,ßM,- + eit.
In the CAPM the cross section of expected returns is completely described by the
cross section of ßs, so MC¡ ,_¡ and BM¡ ,_x should add nothing to the explanation
of expected returns. The average values of the slopes a2„ and ait for MC, and
BMi t-' test this prediction, and the average value of the slope au for b¡ tests the
CAPM prediction that the premium for ß is positive.
The key to the test is the simple insight that the month-by-month variation in the
regression slopes (which is, in effect, repeated sampling of the slopes) captures
all the effects of the cross-correlation of the regression residuals (and of multicol-
linearity of the explanatory variables). The time series standard errors used to calcu-
late r-statistics for the average slopes thus capture the effects of residual covariance
without requiring an estimate of the residual covariance matrix. And inferences lean
on the relatively robust statistical properties of t tests for sample means.
The Fama-MacBeth approach is standard in tests of asset pricing models that
use cross-section regressions, but its benefits carry over to panels (time series of
cross sections) of all sorts. For example, Kenneth French and I use the approach
to examine issues in corporate finance (Fama and French 1998, 2002). In applica-
tions in which the dependent variable in the regression is asset returns, autocorrela-
tion of the period-by-period regression slopes (which are portfolio returns) is not a
problem. When autocorrelation of the slopes is a problem, as is more likely in other
applications, correcting the standard errors of the average slopes is straightforward.
Outside of finance, research in economics that uses panel regressions has slowly
come to acknowledge that residual covariance and autocorrelation are pervasive
problems. Robust regression "clustering" techniques are now available (for exam-
ple, Thompson 201 1). The Fama-MacBeth approach is a simple alternative.
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VOL. 104 NO. 6 FAMA: TWO PILLARS OF ASSET PRICING 1479
B. The Problems of the CAPM
The evidence in Black et al. (1972) and Fama and Mac
favorable to the CAPM, or at least to Black's (1972) versio
there is no risk-free security. The golden age of the mod
the 1980s, violations, labeled anomalies, begin to surfa
market ß does not fully explain the higher average retur
capitalization) stocks. Basu (1983) finds that the positive re
ing-price ratio (E/P) and average return is left unexplain
(1985) find a positive relation between average stock retur
equity ratio ( B/M ) that is missed by the CAPM. Bhandar
lar result for market leverage (the ratio of debt to the mar
As noted earlier, Ball (1978) argues that variables like size
natural candidates to expose the failures of asset pricing
expected returns since all these variables use the stock pri
dividends, is inversely related to the expected stock return
Viewed one at a time in the papers that discovered them
seemed like curiosity items that show that the CAPM is
expected to explain the entire cross section of expected s
tests, Fama and French (1992) examine all the common an
ing all the negative evidence in one place leads readers
that the CAPM just doesn't work. The model is an elegan
appealing tour deforce that lays the foundations of asset prici
prediction that market ß suffices to explain the cross se
seems to be violated in many ways.
In terms of citations, Fama and French (1992) is high on
all-time hit list. Its impact is somewhat surprising since
paper, aside from a clear statement of the implications of
problems of the CAPM.
C. The Three-Factor Model
An asset pricing model can only be replaced by a model that provides a better
description of average returns. The three-factor model of Fama and French (1993)
addresses this challenge. The model's expected return equation is
(13) E(Rit) - Rf, = b,[E(RMl) - RFi] + s i E (SMB,) + h,E(HMLt).
The time-series regression used to test the model is
(14) R¡t - Rpi = a¡ + b,(RMt - RFl) + s¡SMB , + h¡ H ML, + e¡,.
In these equations /?„ is the return on security or portfolio i for period t, RFl is the
risk-free return, RMl is the return on the value-weight (VW) market portfolio, SMB,
is the return on a diversified portfolio of small stocks minus the return on a diversi-
fied portfolio of big stocks, HML, is the difference between the returns on diversi-
fied portfolios of high and low B/M stocks, and eit is a zero-mean residual. The
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1480 THE AMERICAN ECONOMIC REVIEW JUNE 2014
three-factor model (13) says that the sensitivitie
in (14) capture all variation in expected return
in (14) is zero for all securities and portfolios
The three-factor model is an empirical asset
models work forward from assumptions abou
tunities to predictions about how risk should
risk and expected return. Empirical asset pric
as given the patterns in average returns, and
three-factor model is designed to capture th
size (market capitalization) and the relation be
like the book-to-market ratio, which were th
returns at the time of our 1993 paper.
To place the three-factor model in the ration
French (1993) propose (13) as the expected ret
(1973a) ICAPM in which up to two unspecifie
premiums that are not captured by the marke
not themselves state variables, and SMB and H
variables. Instead, in the spirit of Fama (1996),
lios that provide different combinations of co
ables. And the zero intercepts hypothesis for ( 1
risk-free asset, SMB and HML span (can be use
efficient set. In this scenario, ( 13) is an empiric
capture the expected return effects of state vari
There is another more agnostic interpretati
for (14). With risk-free borrowing and lendin
risky assets that is the risky component of al
of Markowitz ( 1 952) . If the tangency portfolio
risk-free asset, the market portfolio, SMB an
Kandel (1987) implies that the intercept in (1
the three-factor model covers the ICAPM int
and the behavioral stories discussed later.
Kenneth French and I have many papers that address the empirical robustness of
the three-factor model and the size and B/M patterns in average returns the model
is designed to explain. For example, to examine whether the size and B/M patterns
in average returns observed for the post- 1962 period in Fama and French (1992)
are the chance result of data dredging, Davis et al. (2000) extend the tests back to
1927, and Fama and French (1998, 2012) examine international data. The results are
similar to those in Fama and French (1992, 1993). Fama and French (1996, 2008)
examine whether the three-factor model can explain the anomalies that cause prob-
lems for the CAPM. The three-factor model does well on the anomalies associated
with size, sales growth, and various price ratios, but it is just a model and it fails
to absorb other anomalies. Most prominent is the momentum in short-term returns
documented by Jegadeesh and Titman (1993), which is a problem for all asset pric-
ing models that do not add exposure to momentum as an explanatory factor, and
which in my view is the biggest challenge to market efficiency.
After 1993, empirical research that uses an asset pricing model routinely includes
the three-factor model among the alternatives. When the issue is the performance of
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VOL. 104 NO. 6 FAMA : TWO PILLARS OF ASSET PRICING 1 48 1
a proposed new asset pricing model, victory is declared if th
what close to explaining as much of the cross section of a
three-factor model. Research on the performance of managed
ple, mutual funds) routinely uses the intercepts ("alphas") pr
augmented with a momentum factor (for example, Carhart 19
Kosowski et al. 2006 or Fama and French 2010).
A long time passed before the implications of the work on m
portfolio choice had an impact on investment practice. Even t
(who propose to invest in undervalued securities) attract far
sive managers (who buy market portfolios or whole segments
is puzzling, given the high fees of active managers and four
(from Jensen 1968 to Fama and French 2010) that active man
for investors.
In contrast, the work on the empirical problems in the CAP
returns, culminating in Fama and French (1992, 1993), had an
investment practice. It quickly became common to characteriz
aged portfolios in terms of size and value (high B/M) or gro
And it quickly became common to use the regression slopes
model to characterize the tilts and to use the intercept to me
returns (alpha).
There is long-standing controversy about the source of the
the value premium, in average returns. As noted above, Fam
1996) propose the three-factor model as a multifactor versio
ICAPM. The high volatility of the SMB and HML returns is c
view. The open question is: what are the underlying state varia
tion in expected returns missed by the CAPM market /?? The
proposes answers to this question, but the evidence so far is u
The chief competitor to our ICAPM risk story for the value prem
action hypothesis of DeBondt and Thaler (1987) and Lakonish
postulate that market prices overreact to the recent good tim
and the bad times of value stocks. Subsequent price correctio
premium (high average returns of value stocks relative to grow
ness of this view is the presumption that investors never le
ioral biases, which is necessary to explain the persistence of
Moreover, Fama and French (1995) find that the high average
and the low average returns of growth stocks persist for at
stocks are allocated to value and growth portfolios, which se
attributed to correction of irrational prices.
Asset pricing models typically assume that portfolio decisio
properties of the return distributions of assets and portfolios
suggested by Fama and French (2007) and related to the s
Titman (1997) and Barberis and Shleifer (2003), is that tastes f
tics of assets play a role. ("Socially responsible investing" is a
many investors get utility from holding growth (low B/M)
be profitable fast-growing firms, and they are averse to val
to be relatively unprofitable with few growth opportunities.
they can have persistent effects on asset prices and expected r
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1482 THE AMERICAN ECONOMIC REVIEW JUNE 2014
don't lead to arbitrage opportunities. This is a b
irrational behavior. In economics, we take taste
about them.
To what extent is the value premium in expec
state variable risks, investor overreaction, or tas
We don't know. An agnostic view of the three-
a choice among stories is that the model uses
many markets to find portfolios that together span
Markowitz (1952). The analysis in Huberman and
the model can be used to describe expected retur
III. Conclusions
In my view, finance is the most successful branch of economics in terms of rich
theory, extensive empirical tests, and penetration of the theory and evidence int
other areas of economics and real-world applications. Markowitz's (1952, 1959
portfolio model is widely used by professional portfolio managers. The portfolio
model is the foundation of the CAPM of Sharpe (1964) and Lintner (1965), and
it gets a multifactor extension in Merton (1973a). The CAPM is one of the most
extensively tested models in economics, it is well known to students in areas of
economics other than finance, and it is widely used by practitioners. The options
pricing model of Black and Scholes (1973) and Merton (1973b) is a must for stu-
dents in all areas of economics, and it is the foundation for a huge derivative
industry. However one judges market efficiency, it has motivated a massive body
of empirical work that has enhanced our understanding of markets, and, like it
or not, professional money managers have to address its challenges. Its sibling
rational expectations, first exposited by Muth (1961), has had a similar run in mac-
roeconomics. The three-factor model of Fama and French (1993) is arguably th
most successful asset pricing model in empirical tests to date, it can't be avoided
in tests of competing asset pricing models, and it is a handy tool that has shaped
the thinking of practitioners. Can any other branch of economics claim similar
academic and applied impact?
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VOL. 104 NO. 6 FAMA: TWO PILLARS OF ASSET PRICING 1483
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