Does Option‐Implied Cross‐Sectional Return Dispersion Forecast Realized Cross‐Sectional Return Dispersion? Evidence From the G10 Currencies

• DOI: http://doi.org/10.1002/fut.21798
• Published date: 01 January 2017
• Author: Jari‐Pekka Heinonen,Klaus Grobys
• Date: 01 January 2017

Does Option-Implied Cross-Sectional

Return Dispersion Forecast Realized

Cross-Sectional Return Dispersion?

Evidence From the G10 Currencies

Klaus Grobys* and Jari-Pekka Heinonen

This study employs option-price data to back out the implied cross-sectional return variance in

the G10 currencies. It investigates the relation of implied cross-sectional return dispersion in

the currency market and subsequent realized cross-sectional return dispersion. We find that

implied cross-sectional return variance, based on option-price data with 1- and 3-month

maturity, outperforms past cross-sectional return variance in forecasting future cross-sectional

return variance. © 2016 Wiley Periodicals, Inc. Jrl Fut Mark 37:3–22, 2017

1. INTRODUCTION

A broad strand of literature explores the extent to which the implied information in the option

market can predict future volatility. Christensen and Prabhala (1998) argue that the volatility

implied in an option’s price is widely regarded as the option market’s forecast of future return

volatility over the remaining life of the relevant option. Many studies have demonstrated that

option-implied volatility is an accurate predictor of subsequently realized volatility.

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In recent

research Nikolaou and Sarno (2006) focus on the options markets and substitute the

standard forward contract with an option equivalent contract to test option-based

unbiasedness. This approach allows the above mentioned research to compare the two

derivatives markets—the forward and the options market—in terms of the statistical

Klaus Grobys and Jari-Pekka Heinonen are at the Department of Accounting and Finance, University of

Vaasa, Wolffintie 34, 65200 Vaasa, Finland. We received valuable comments from seminar participants at a

research seminar in accounting and finance at the University of Vaasa and 2015. In particular, we want to

thank Jukka Sihvonen for useful comments. We also received valuable comments from participants at the

2015 winter workshop organized by the Graduate School of Finance in Helsinki. In particular, we are grateful

to Joonas Hamalainen for providing a very helpful discussion on our paper. We are also very grateful for the

valuable and helpful comments received from an anonymous reviewer.

JEL Classification: G12, G14

*Correspondence author, Department of Accounting and Finance, University of Vaasa, Wolffintie 34, 65200 Vaasa,

Finland. Tel: þ358466110151, e-mail: klaus.grobys@uwasa.fi; grobys.finance@gmail.com

Received February 2016; Accepted June 2016

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Classic contributions include Day and Lewis (1992), Canina and Figlewski (1993), Lamoureux and Lastrapes

(1993), Christensen and Prabhala (1998), Fleming (1998), and Blair, Poon, and Taylor (2001), Szakmarya, Orsb,

Kimc, and Davidson (2003), Busch, Christensen, and Nielsen (2011), and Chang, Christoffersen, Jacobs, and

Vainberg (2011).

The Journal of Futures Markets, Vol. 37, No. 1, 3–22 (2017)

© 2016 Wiley Periodicals, Inc.

Published online 7 July 2016 in Wiley Online Library (wileyonlinelibrary.com).

DOI: 10.1002/fut.21798

properties of the resulting contracts. That comparison in turn makes it possible to evaluate

whether or not the bias puzzle recorded in the literature is forward specific or a problem of a

more general nature. Della Corte, Sarno, and Tsiakas (2011) explore the relation between

spot and forward implied volatility in foreign exchange by formulating and testing the forward

volatility unbiasedness hypothesis that postulates that forward implied volatility conditional

on today’s information is an unbiased predictor of future spot implied volatility. The study

makes use of implied volatilities for nine US dollar exchange rates quoted on over-the-

counter (OTC) currency options. In a recent paper, Della Corte, Ramadorai, and Sarno

(2016) use the currency volatility risk premium to implement a trading strategy long on

currencies with relatively cheap volatility insurance and short on currencies with relatively

expensive volatility insurance. Making use of the volatility risk premium requires estimating

the expected future realized currency volatility derived from the currency options.

Interestingly, those papers focus on option-implied volatility because there are apparently

no articles exploring the predictive power of option-implied cross-sectional currency return

dispersion. It is important to note that the concept of implied volatility and implied cross-

sectional return dispersion are very different (Maio, 2016).

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The purpose of this article is to investigate the information content of option-implied

cross-sectional return dispersion in the foreign exchange (FX) market for forecasting realized

cross-sectional returndispersion. If option marketsare efficient, impliedcross-sectional return

dispersion should be an unbiasedpredictor of future cross-sectional returndispersion, that is,

impliedcross-sectionalreturn dispersionshould integratethe informationcontained in all other

variables in the market information set in explaining future cross-sectional return dispersion.

This study expresses the cross-sectional currency return dispersion in the G-10

currenciesas a sum of the weighted differences of the variancesof individual currencies and an

equally weighted basketof USD/G-10-crosses. This form of expression allows the exploitation

of information drawn from the option market to construct the forward-looking dispersion

measurewith implied variances and the currencies’fullimplied G-10 correlation structure. We

collect the at-the-money (ATM) volatility data on four different maturities (1-,3-, 6-, and 12-

month) of European OTC foreignexchange options, covering the full cross section of 45 G-10

cross-pairs and spanning the period October 2007–August 2015. Exploiting the full cross

section of monthly implied variance observations and the holding triangular parity condition,

we back out four (1-, 3-, 6-, and 12-month) monthly time series of full (9 9) implied

correlation matrices. Owingto some inefficiencies in Bloomberg’s volatility data on the most

exotic of the 45 crosses, we adjusted the eigenvalues of the backed out matrices in a process

detailed in Higham (2002) in order to obtaintrue correlation matrices. With the full expected

(option-implied) correlation matrices in four tenors and their respective variances, we

calculated the forward-looking measure of dispersion by constructing four time series of

equally weightedG-10 basket variances in the spirit of Markowitz (1952)and distracting them

from the weighted basket of individual variances. These 1-, 3-, 6-, and 12-month forward-

looking measures were labeled implied dispersions. They represent the option markets

(tradable) view on the expected cross-sectional variance (hence the term dispersion) at four

different future points in time. Asa result, based on the option’s maturity, we employed four

implied cross-sectional currency return dispersion measures.

Although the works of Nikolaou and Sarno (2006), Della Corte et al. (2011), and Della

Corte et al. (2016) are important precursors to this paper, our empirical setting is different

and more general, and thus resembles that used in an earlier study by Christensen and

Prabhala (1998). We employed four different series of implied cross-sectional return

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The volatility surfaces of the options not only provide information about implied volatility, but also on implied cross-

sectional return dispersion.

4 Grobys and Heinonen