EMPIRICAL ASSET PRICING: FAMA, HANSEN
Taras Shevchenko National University of Kyiv
Annotation. The article reveals the contribution
of Eugene Fama, Lars Hansen and Robert Schiller to the field of asset pricing model.
After summarizing modern asset pricing theory, the article discusses the joint hypothesis
problem in tests of market efficiency, 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
Asset Pricing Model (CAPM) developed by Sharpe (1964), Lintner (1965), and Mossin
(1966) is the best known asset pricing model. The CAPM has been very successful
as a pedagogical tool for presenting and quantifying the tradeoff between risk and
return, and it has also been widely used in practical applications. It captures
some important characteristics of the pricing in financial markets in a rather simple
way. 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.
laureates, Eugene Fama, Lars Peter Hansen, and Robert Shiller, are giants of finance
and architects of the intellectual structure within which all contemporary research
in asset pricing is conducted. The fame of the laureates extends far beyond financial
economics. Eugene Fama is one of the world most cited economists in any field. Lars
Peter Hansen is an immensely distinguished econometrician. Robert Shiller is a founder
of behavioral economics, a creator of the Case-Shiller house price indexes.
to the explanation of Royal Swedish Academy of Sciences three economists awarded
Nobel Memorial Prize due to the conducted innovative methods of asset pricing theory,
including stock and bond assets. University of Chicago
professor Eugene F. Fama is
regarded as a founder of a key "efficient market theory". His statistical
studies conducted in 1960 showed that past prices don’t allow to predict the future price changes. In 1969
Fama proved that the share prices immediately respond to the new market information,
but afterwards the share behavior becomes low-predictable again. Rearranging and
using the relation between the conditional mean of the SDF and the riskless interest
that the expected return on any asset is the riskless return times an adjustment
factor for the covariance of the return with the SDF. In the modern language of
the stochastic discount factor, Fama’s point can be stated as follows. Suppose we have
a model of equilibrium return that determines the right hand side of equation (1),
and write this as
(1) says that Zit is the conditional expectation of the return on asset i, so the
realized return on the asset satisfies
important contribution of the Fama survey is that it clearly states the so-called
joint hypothesis problem, that market efficiency implies a zero conditional mean
for asset returns measured relative to the riskless interest rate and the equilibrium
compensation for risk. The next important achievement was accomplished by Yale University professor
Robert Shiller. His works from the 1980s are dedicated to the stock prices volatility
and proved that in the short-term perspective stock quotes are extremely volatile
and expanding horizon to at least several years makes market movements much more
Lars Peter Hansen proposed a statistical method called "generalized method
of moments" (GMM) and proved the inability pricing CCAPM applying GMM model
to historical data of stock prices. The Generalized Method of Moments (GMM) of Hansen
is an econometric approach that is particularly well suited for testing models of
Several approaches exist in GMM model approach, the
first one being the most popular:
Two-step feasible GMM:
Step 1: Take W = I
(the identity matrix), and compute preliminary GMM estimate .
This estimator is consistent for и0, although not efficient.
Step 2: Take
where we have plugged in our first-step preliminary
estimate . This matrix converges in probability to Щ−1 and therefore if we compute with
this weighting matrix, the estimator will be asymptotically efficient.
Iterated GMM is essentially the same procedure as 2-step GMM,
except that the matrix is recalculated several times.
That is, the estimate obtained in step 2 is used to calculate the weighting matrix
for step 3, and so on. Such estimator, denoted , is equivalent
to solving the following system of equations:
Asymptotically no improvement can be achieved through
such iterations, although certain Monte-Carlo experiments suggest that finite-sample
properties of this estimator are slightly better.
Continuously Updating GMM estimates simultaneously
with estimating the weighting matrix W:
In Monte-Carlo experiments this method demonstrated
a better performance than the traditional two-step GMM: the estimator has smaller
median bias (although fatter tails), and the J-test for over identifying restrictions
in many cases was more reliable
1980s R. Shiller moved beyond a critique of rational expectations models with constant
discount rates to articulate an alternative vision of financial market equilibrium.
His Brookings paper “Stock Prices
and Social Dynamics” is an important
step in first direction. It is striking not only for its content but also for its
style, which is far more literary than is typical for an economics. The first part
of the 1984 paper argues that the true model of the economy is unknowable to economists
and investors alike. In this context, subjective views about future economic prospects
and asset payouts spread among investors in a manner analogous to the spread of
infections in epidemiological models. The second part of the paper writes down a
simple model of equilibrium in a stock market with both rational and irrational
investors. Irrational investors demand an exogenous value of shares; equivalently,
their equity demand function has unit price elasticity. In this model stock prices
can be written as a discounted present value of future dividends and exogenous irrational-investor
demands. Irrational investors have a larger effect on stock prices when they are
more persistent, and when the risk-bearing capacity of rational investors is smaller.
was an early contribution to what has become a vast literature on behavioral finance.
This literature addresses a number of important questions about equilibrium with
both rational and irrational investors. First, what determines the asset demands
of irrational investors? Shiller modeled these demands as an exogenous stochastic
process, but it is appealing to derive them from assumptions about irrational investors’ expectations and perhaps also their preferences.
Second, what prevents rational investors at a point in time from arbitraging away
the effects of irrational investors on asset prices? The most obvious answer, and
the one discussed by Shiller, is that rational investors are risk-averse. As rational
investors trade with irrational investors, they take on more or less stock market
exposure and the covariance of their marginal utility with stock returns varies
accordingly, justifying a time-varying expected stock return. Third, rational investors
don’t become richer than irrational investors over the
long run because they eventually die and leave their money to less rational descendants.
In parallel with the rational asset pricing literature, the behavioral finance literature
has explored asset pricing patterns within the cross-section of asset returns.
Memorial Prize in Economic Sciences for 2013 - Eugene Fama, Lars Hansen and Robert
Shiller - significantly changed the state of economic science and led to advances
in the financial industry and economic science overall. Fama proposed a simple tool
for pricing model evaluation that determines asset prices risks which are not limited
by a single market risk. Fama convinced that it’s impossible to gain on short-term changes in asset
prices. His first achievement allowed carrying out hundreds of empirical studies
in the asset pricing theory, the second achievement changed the approach to the
asset valuation and the third one modified the investment fund structure promoting
the "index" funds appearance. Hansen proposed a reliable methodology to
assess pricing models and created the generalized method of moments
which applies in the context of complex
or non-linear model and takes into account the large-scale data dynamics. Schiller
noted that serious excess of the average market price of their long-term average
leads to a rapid fall in prices in future, akin to a collapse of the bubble. So,
there is no way to predict the price of stocks and bonds over next few days or weeks,
but it is quite possible to foresees the broad course of these prices over longer
period. These findings, which might seem both surprising and contradictory, were
made and analyzed by Fama, Hansen and Shiller.
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