Agency‐Based Asset Pricing and the Beta Anomaly

Author:David Blitz
DOI:http://doi.org/10.1111/eufm.12039
Publication Date:01 Sep 2014
Agency-Based Asset Pricing and the
Beta Anomaly
David Blitz
Robeco Asset Management, The Netherlands
E-mail: d.c.blitz@robeco.nl
Abstract
I argue that delegated portfolio management can cause the equilibrium relation
between CAPM beta and expected stock returns to become at, instead of linearly
positive, and propose an alternative to the widely used Fama and French (1993)
3-factor asset pricing model which incorporates this agency effect. An empirical
comparison of the two models shows that the agency-based 3-factor model is much
better at explaining the performance of portfolios sorted on beta or volatility, and
at least as good at explaining the performance of various other test portfolios,
including those the original 3-factor model was designed to explain.
Keywords: asset pricing, beta anomaly, volatility anomaly, Fama-French 3-factor
model, agency problems, delegated portfolio management
JEL classification: C12, G11, G12, G14
1. Introduction
In this paper I argue that agency effects arising from delegated portfolio management can
cause the equilibrium relation between CAPM beta and expected stock returns to become
at, instead of linearly positive, and propose an agency-based alternative to the widely
used Fama and French (1993) 3-factor asset pricing model which incorporates this
insight. An empirical comparison of the two models shows that the agency-based
3-factor model is much better at explaining the performance of portfolios sorted on beta
or volatility, and at least as good at explaining the performance of various other test
portfolios, including those the original 3-factor model was designed to explain. These
results are consistent with empirical studies which have previously established that
market beta does not appear to be a priced risk factor in the cross-section of stock returns,
the so-called beta anomaly.
The author thanks four anonymous referees, the editor (John Doukas), Joop Huij, Simon
Lansdorp and Pim van Vliet for valuable feedback on earlier versions of this paper, and
Simon Lansdorp also for programming assistance.
European Financial Management, Vol. 20, No. 4, 2014, 770801
doi: 10.1111/eufm.12039
© 2014 John Wiley & Sons Ltd
Whereas some anomalies have weakened or even disappeared following their public
dissemination, the evidence for a beta anomaly has only grown stronger over time. The
history of the anomaly goes back to the initial empirical tests of the Capital Asset Pricing
Model (CAPM) in the early nineteen seventies, which already observed that low-beta
stocks have higher returns than predicted by the model; see, e.g., Black et al. (1972),
Fama and MacBeth (1973) and Haugen and Heins (1975). Two decades later, Fama and
French (1992) conclude in their seminal paper that, after adjusting for size effects, beta is
irrelevant for explaining the cross-section of expected stock returns. In addition, they
show that the CAPM fails to explain the small-rm effect of Banz (1981) and the value
effect of Stattman (1980) and Rosenberg et al. (1985). In order to address the latter
concerns, they propose a 3-factor model which augments the CAPM with size (SMB)
and value (HML) factors in Fama and French (1993). The empirical results in that study
show that, perhaps not surprisingly, this 3-factor model is signicantly better able to
explain the cross-section of stock returns than the CAPM, specically the variation in
return of portfolios sorted on size or book-to-market. Crucially, however, the 3-factor
model of Fama and French (1993) does not attempt to remedy the other failure of the
CAPM documented in Fama and French (1992), namely the at empirical relation
between market beta and the cross-section of stock returns. Similar to the CAPM, the
3-factor model still assumes a linearly positive relation between market beta and
expected stock returns. The same is true for the most popular extension of the 3-factor
model, the Carhart (1997) 4-factor model, which augments the 3-factor model with a
momentum (UMD) factor in order to explain the anomalous performance of portfolios
sorted on past return. Dimson and Mussavian (1998) do not even mention the beta
anomaly in their overview of the most important asset pricing anomalies that cannot be
explained by the CAPM.
Various studies over the past two decades, however, have conrmed the empirical
nding that market beta does not appear to be a positively priced risk factor within the
cross-section of stock returns; see, e.g., Black (1993), Haugen and Baker (1991, 1996,
2010), Falkenstein (1994), Clarke et al. (2010) and Baker et al. (2011). International
evidence is provided by Blitz and van Vliet (2007), who nd that the anomaly is also
present in the European and Japanese equity markets, and Blitz et al. (2013), who
document that the same anomaly exists in emerging equity markets. In addition, both
Blitz and van Vliet (2007) and Baker et al. (2011) nd that the anomaly is robust to the
choice of risk measure, and that, in fact, the anomaly appears to be even stronger for
portfolios sorted on volatility instead of beta. Baker and Haugen (2012) conrm the
existence of a strong volatility anomaly in over thirty different equity markets.
Moreover, the phenomenon does not appear to be limited to the equity market, as
Derwall et al. (2009) report the existence of a beta anomaly for US corporate bonds
(sorted on maturity) and Frazzini and Pedersen (2011) document beta anomalies for US
Treasuries, US corporate bonds (sorted on maturity or on rating) and futures markets
(considering equity index, bond index and commodity futures). Falkenstein (2009)
provides no less than twenty empirical examples of higher risk not being associated with
higher returns in all major asset classes, as well as some more exotic ones.
A popular explanation for the low-beta anomaly is benchmark-driven investing, or,
more specically, the agency effects that arise from delegated portfolio management;
see, e.g., Blitz and van Vliet (2007), Falkenstein (2009) and Baker et al. (2011). The
reasoning here is that because delegated portfolio managers are typically evaluated on
their performance vis-à-vis a benchmark portfolio, they have the incentive to overpay for
© 2014 John Wiley & Sons Ltd
Agency-Based Asset Pricing and the Beta Anomaly 771
high-beta stocks with high expected returns, and to ignore low-beta stocks with low
expected returns. As stressed by Black (1993), restrictions on the use of leverage also
play an important role in this regard, as otherwise a benchmark-driven investor might
simply exploit the beta anomaly by taking a leveraged position in low-beta stocks.
I model the agency effects that arise from delegated portfolio management by
considering a simple two-stage hierarchical investment process, in which investors rst
determine their desired allocation to risky assets based on absolute return and risk
considerations, and next delegate the management of these risky portfolios to managers
who are evaluated on their performance relative to a benchmark, which is assumed to be
the market portfolio. The incentive for delegated portfolio managers is then to bid up the
prices of high beta stocks and to ignore low-risk stocks, until an equilibrium is reached
where all stocks have the same expected return, and it is no longer attractive to deviate
from the benchmark. Note that although this resembles a risk-neutral outcome, this result
is not obtained by abandoning risk-aversion, but by assuming that the risk aversion of
delegated portfolio managers relates to benchmark-relative instead of absolute
performance. I argue that such a two-stage process with a shift from absolute to
relative performance objectives strongly resembles the practice of institutional investors,
who are nowadays the largest holder of equities, and that it is also a reasonable model for
the behaviour of private investors.
I incorporate these insights in an alternative asset pricing model, in which the market
portfolio takes on the role of risk-free alternative. Specically, I replace the risk-free
return on short-term Treasury Bills in the specication of the CAPM with the expected
return on the market portfolio. As a result of this change, market beta remains an
important factor for explaining the short-term cross-sectional variation in stock returns,
but, crucially, it is no longer a factor which carries an expected return premium in the
long run. Thus, although the replacement of one constant with another in the
specication of the model may at rst sight appear to be a minor, perhaps even trivial
change, it implies a fundamentally different relation between risk and return. I next
augment the agency-based 1-factor model with the SMB and HML factors of Fama and
French (1993), although not based on their argument that these reect additional risk
factors, but based on the argument that these reect premiums that arise from additional
agency effects involved with delegated portfolio management. As such, the full model
predicts that the expected return of a stock does not depend on its market beta, but equals
the market return plus a premium for small-size and value. Empirically I show that the
resulting 3-factor agency-based asset pricing model is much better able to explain the
returns of portfolios of stocks sorted on past beta or volatility. Moreover, I show that this
does not come at the expense of its explanatory power for other test portfolios, such as
portfolios sorted on book-to-market or industry portfolios, as my alternative 3-factor
model is able to explain the performance of these portfolios at least as well as the classic
3-factor model.
Ideally, a new model in economic theory yields new testable implications, but the
empirical performance of such theoretically founded models (e.g., the CAPM) has been
disappointing. Due to advances in data availability and computing power an increasing
amount of empirical insights have become available, which have inspired researchers to
basically reverse the process, i.e. to develop data-inspired theories. My agency-based
asset pricing model could be seen as an example of this, as one might say that it is merely
designed to explain a known anomaly in the data that prior pricing models do not.
However, this is arguably even more true for the widely accepted Fama and French
© 2014 John Wiley & Sons Ltd
772 David Blitz

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