Which Beta Is Best? On the Information Content of Option‐implied Betas

DOIhttp://doi.org/10.1111/eufm.12065
Published date01 June 2016
Date01 June 2016
Which Beta Is Best? On the
Information Content of Option-implied
Betas
Rainer Baule
University of Hagen, Universit
atsstraße 41, D-58084 Hagen, Germany
E-mail: rainer.baule@fernuni-hagen.de
Olaf Korn
Georg-August-Universit
at G
ottingen and Centre for Financial Research Cologne (CFR), Platz der
G
ottinger Sieben 3, D-37073 G
ottingen, Germany
E-mail: okorn@uni-goettingen.de
Sven Saßning
Georg-August-Universit
at G
ottingen, Platz der G
ottinger Sieben 3, D-37073 G
ottingen, Germany
E-mail: ssassni@uni-goettingen.de
Abstract
Option-implied betas are a promising alternative to historical beta estimators,
because they are inherently forward-looking and can incorporate new information
immediately and fully. Recently, different implied beta estimators have been
developed, but very little is known about their properties and information content.
This paper presents a rst systematic comparison between six different implied
beta estimators, providing guidance for applications and identifying directions for
further improvement. The analysis identies explanatory factors for the predictive
performance of implied estimators both in the cross section of stocks and over time.
Furthermore, the analysis reveals patterns in the term structure of implied betas.
Keywords: beta, option-implied information
JEL classification: G11, G12, G13, G14, G17
We are grateful to John Doukas (the Editor), two anonymous referees, G
unther Gebhardt,
Fabian Hollstein, Marcel Prokopczuk and participants of the 2013 Meeting of the German
Finance Association, Wuppertal and the 2014 VHB Meeting, Leipzig, for helpful
comments and suggestions and to Alexander Jung, Rebecca von der Heide and Chris-
Henrik Werner for ca pable research ass istance. Financial support from Deutsc he
Forschungsgemeinschaft (DFG Grant KO 2285/2-1) is gratefully acknowledged. Some
of the results in this paper are contained in Sven Saßnings PhD dissertation Portfolio-
Optimierung und Beta-Bestimmung unter Verwendung impliziter Informationen, Cuvillier
Verlag, G
ottingen, 2012.
European Financial Management, Vol. 22, No. 3, 2016, 450483
doi: 10.1111/eufm.12065
©2015 John Wiley & Sons, Ltd.
1 Introduction
Beta coefcients play a prominent role in nance theory and practice. As measures of
systematic risk, they have a variety of applications in risk management, portfolio
management and investment evaluation. In risk management, for example, individual
stocks are frequently mapped on an index via beta coefcients to facilitate value-at-risk
calculations. Asset managers use beta to measure and control market risk over specied
rebalancing and evaluation periods and an investment projects cost of capital is often
based on beta as a crucial parameter.
A common, essential feature of most applications is the need for ex-ante beta
coefcients. Consequently, the need for predicting betas has received much attention in
the literature. Starting with the early literature, in the 1970s,
1
strong evidence revealed a
time variation of beta coefcients, which led to the development of different estimation
approaches.
2
Specic approaches apply multivariate GARCH models,
3
model beta as a
random coefcient within a state space model,
4
or use different economic conditioning
variables.
5
A major drawback of these techniques is, however, that they require the
stability of the assumed structures over time.
This paper investigates an alternative approach: the use of option-implied information
to obtain beta coefcients. Since option prices contain information on market
participantsviews of the underlying stocksreturn distributions, such an approach is
inherently forward looking. Moreover, no assumptions about structural stability are
necessary, since this approach relies only on current market prices. Therefore, option-
implied betas are a promising alternative to traditional beta estimators.
Surprisingly, until now very li ttle is known about the properti es and information
content of option-implie d betas. This paper lls the gap by providing a comparative
analysis of the different a pproaches to guide further theoret ical developments and
applications. The paper make s three contributions. Firs t, it compares ve different
fully implied beta estimator s that have been proposed in the lit erature and derives and
analyzes a new implied beta est imator based on implied kurt osis. The aim of this
analysis is to nd out how certain st ructural features of implie d betas, such as the
specic moment of the implie d return distribution used to calculate beta, in uence
their properties. Second, t his is the rst study to investigat e the potential determinant s
of an implied betas information content, both over time and in the cross section of
different stocks. Such kno wledge is essential for a better u nderstanding of implied
betas. For example, one hyp othesis, referring to the t ime dimension, is that impli ed
betas carry more informati on in periods of high informa tion ow, such as crisis
periods. Another hypothesis, re ferring to the cross-sectional d imension, is that stocks
with higher options trading ac tivity have more informative im plied betas than stocks
with lower options trading act ivity do. The third main contribu tion of this paper refers
1
See Blume (1971), Levy (1971) and Rosenberg and McKibben (1973).
2
Faff et al. (2000) provide an overview and comparison of different modeling techniques.
3
See, for example, Braun et al. (1995) and Koutmos and Knif (2002).
4
See, for example, Jostova and Philipov (2005).
5
Conditional betas play an important role in the asset pricing literature. See, for example,
Jagannathan and Wang (1996), Lettau and Ludvigson (2001) and Ammann and Verhofen
(2008).
©2015 John Wiley & Sons, Ltd.
Which Beta Is Best? 451
to a specic feature of implied betas. In cont rast to historical betas, implied betas have
a clear notion of time horizo n, derived from the maturity date of the options used to
calculate them. Since opt ions with different times t o maturity are available
simultaneously, a term st ructure of implied betas e xists. Our work is the rst to
investigate such term str uctures. Specically, we a sk to what extent betas for dif ferent
time horizons are related an d how term structures evolve over time.
Our study is naturally related to other work on implied betas. French et al. (1983) were
the rst to use option-implied information for beta estimation by combining implied
volatilities
6
with historical correlations. Buss and Vilkov (2012) incorporate option-
implied information into correlation modeling. However, their estimators still require
historical correlations. Fully implied beta estimators (i.e., estimators that do not require
any time series data) have been suggested by Siegel (1995) and Husmann and Stephan
(2007). A drawback of these betas, however, is the need for cross-correlation derivatives
between single stocks and the index, or the reliance on the validity of a very specic
option pricing model.
Several fully implied beta estim ators have recently been develop ed in the literature.
Skintzi and Refenes (2005) in troduce a markets average impli ed correlation based on
the assumption of a homogeneo us correlation between all ass ets. This fully implied
correlation can be combined with im plied variances of individual sto cks and the
market index to obtain implied betas . Chang et al. (2012) derive a fully impl ied beta
by starting from a market model and assumi ng that an individual stocksimplied
skewness has no idiosyncrat ic component.
7
They show that option-implie d betas
perform well compared to traditional historical betas. K empf et al. (2015) develop a
family of implied betas based on th e implied variance, implied sk ewness and implied
kurtosis, respectively. Be tas are identied via cross-sect ional restrictions on the
systematic and idiosyncrati c components of individual stocksimp lied moments.
Kempf et al. (2015) use implied betas to con struct minimum variance port folios to
show that these portfolio s lead to a lower out-of-samp le variance than historica l and
passive benchmarks do.
The main ndings of our paper are as fo llows: (i) beta estimators ba sed on implied
variances provide more accu rate predictions of realized betas than estimators based on
implied skewness; (ii) the cr oss-sectional restriction that the market beta must equal
one is important for the accurac y of implied betas. In this sense , implied information
on all stocks in the cross sec tion should be used to estima te an individual stocksbeta;
(iii) implied betas perform r elatively better when the time horizon is shorter, comp ared
to historical betas; (iv) imp lied betas are positively related to historical betas est imated
over a short window of recent data. Howe ver, implied betas also differ sig nicantly
from historical betas, si nce the correlation of pred iction errors is far below on e; (v)
while crisis periods have litt le impact on the predictive perf ormance, the
outperformance of implied be tas over historical betas is posi tively related to the
6
Implied volatilities are well-established tools for volatility estimation and forecasting. See
Poon and Granger (2003) and Poon and Granger (2005) for survey articles. The survey by
Christoffersen et al. (2012) also reviews recent developments concerning higher-order
implied moments and correlations.
7
Fouque and Kollman (2011) derive a similar estimator that can be seen as a simplied
version of the option-implied beta of Chang et al. (2012).
©2015 John Wiley & Sons, Ltd.
452 Rainer Baule, Olaf Korn and Sven Saßning

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