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

• DOI: http://doi.org/10.1111/eufm.12065
• Author: Olaf Korn,Rainer Baule,Sven Saßning
• Published date: 01 June 2016
• Date: 01 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 first systematic comparison between six different implied

beta estimators, providing guidance for applications and identifying directions for

further improvement. The analysis identifies 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 Saßning’s PhD dissertation ‘Portfolio-

Optimierung und Beta-Bestimmung unter Verwendung impliziter Informationen’, Cuvillier

Verlag, G€

ottingen, 2012.

European Financial Management, Vol. 22, No. 3, 2016, 450–483

doi: 10.1111/eufm.12065

©2015 John Wiley & Sons, Ltd.

1 Introduction

Beta coefficients play a prominent role in finance 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 coefficients to facilitate value-at-risk

calculations. Asset managers use beta to measure and control market risk over specified

rebalancing and evaluation periods and an investment project’s 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

coefficients. 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 coefficients, which led to the development of different estimation

approaches.

2

Specific approaches apply multivariate GARCH models,

3

model beta as a

random coefficient 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 coefficients. Since option prices contain information on market

participants’views of the underlying stocks’return 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 fills 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 five 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 find out how certain st ructural features of implie d betas, such as the

specific moment of the implie d return distribution used to calculate beta, in fluence

their properties. Second, t his is the first study to investigat e the potential determinant s

of an implied beta’s 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 flow, 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 specific 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 first to

investigate such term str uctures. Specifically, 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 first 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 specific

option pricing model.

Several fully implied beta estim ators have recently been develop ed in the literature.

Skintzi and Refenes (2005) in troduce a market’s 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 stock’simplied

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 identified via cross-sect ional restrictions on the

systematic and idiosyncrati c components of individual stocks’imp 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 findings 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 stock’sbeta;

(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 nificantly

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 simplified

version of the option-implied beta of Chang et al. (2012).

©2015 John Wiley & Sons, Ltd.

452 Rainer Baule, Olaf Korn and Sven Saßning