A behavioural explanation to the asymmetric volatility phenomenon: Evidence from market volatility index

• Published date: 01 November 2017
• DOI: http://doi.org/10.1016/j.rfe.2017.07.004
• Date: 01 November 2017

A behavioural explanation to the asymmetric volatility phenomenon:

Evidence from market volatility index

Pratap Chandra Pati ⁎, Prabina Rajib, Parama Barai

Vinod GuptaSchool of Management, IndianInstitute of Technology,Kharagpur 721302, India

abstractarticle info

Articlehistory:

Received25 May 2016

Receivedin revised form 30 May 2017

Accepted30 July 2017

Availableonline 5 August 2017

JEL classification:

C22

G12

G15

This study examines how the behaviouralexplanations, in particular loss aversion, can be used to explain the

asymmetricvolatility phenomenonby investigatingthe relationship betweenstock market returns andchanges

in investorperceptions of risk measuredby the volatilityindex. We study the behaviourof India volatility index

vis-à-visHong Kong, Australiaand UK volatilityindex, and provide a comprehensive comparativeanalysis. Using

Bai-Perron test, we identify structural breaks and volatility regimes in the time series of volatility index, and

investigate the volatility index-return relation during high, medium and low volatility periods. Regardless of

volatility regimes,we find that volatility index moves in opposite directionin response to stock index returns,

and contemporaneous re turn is the most dominatin g across the four markets. T he negative relation is

strongestfor UK followedby Australia, Hong Kong andIndia. Second, volatilityindex reacts significantlydifferent

to positiveand negative returns; negative returnhas higher impact on changes in volatility index than positive

return across the markets over full-sample and sub-sample periods. The asymmetric effect is stronger in low

volatility regime than in high and medium volatility periods for allt he marketsexcept UK. The strength of

asymmetriceffect is strongestfor Hong Kong and weakestfor India. Finally, negativereturns have exponentially

increasingeffect and positive returns haveexponentially decreasingeffect on the changes in volatilityindex.

© 2017 Elsevier Inc. All rights reserved.

Keywords:

Asymmetricvolatility

Loss aversion

GJR-GARCH

Bai-Perrontest

1. Introduction

Asymmetric volatility is one of the well-documented stylized facts in

the stock market. It refers to a phenomenon that neg ative returns

upsurge volatility more than positive returns of the same magnitude.

There are many studies that examinethe asymmetric volatility-return

relation on equity markets (Black, 1 976; Christie, 1982; French,

Schwert, & Stambaugh, 1987; Campbell & Hentschel,1992; Cheung &

Ng, 1992; Figlewski & Wang, 2000; Bek aert & Wu, 2000; Bollerslev,

Litvinova,& Tauchen, 2006). The leverageeffect and volatility feedback

effect are the two existing hypothes es that explain the negative and

asymmetric volatility-return relation. The leverage hypothesis(Black,

1976; Christie, 1982) states that a dec line in the value of the stock

causesfirms with a high debt-to-equityratio, and subsequently the vol-

atility increases. In contrast, the volatility feedback or time-varying risk

premium hypothesis (Campbell & Hentschel, 1992; Frenchet al., 1987)

postulates thatan anticipated increase in volatility raises theexpected

returnon equities. Assumingconstant dividend,an increase in expected

return leads toa decline in stock price. The leveragehypothesis claims

that negative returns cause hig her volatility. In contrast, vo latility

leads to negative returns in the volatility feedback hypothesis. However,

there is little consensus regarding th e explanations for the observed

asymmetricrelationship in the equitymarket.

Since the introduction of the volati lity index (VIX) based on S&P

100 index option by the Chicago Boa rd Options Exchange (CBOE) in

1993, it is widely used as a measure of expectedvolatility in the stock

market as well as a measure of investor sentiment. Furthermore, it is

often colloquially referred to as the ‘in vestor fear gauge’. Generally,

the upward spikes in the volatility index are associated with bouts of

market turmoil and uncertainty. High values of volatility index indicate

fear, anxiety and pessimistic expectations of investors about the stock

market. On the contrary, low valuesof volatility index reflect an opti-

misticattitude about the market.By tracking the movementof volatility

index, one can judgethe sentiment of the overall market.

Since the launch of CBOE VIX, volatilityindices have mushroomed

across the globe. Many empirical studies were undertaken to investigate

the volatility-return relation using volatility index as a measure of

volatility, and provided strong evidence of a negative and asymmetric re-

lation (Badshah, 2013; Fleming, Ostdiek, & Whaley, 1995; Frijns, Tallau, &

Tourani-Rad, 2010; Giot, 2005; Hibbert, Daigler, & Dupoyet, 2008; Low,

2004; Simon, 2003; Whaley, 2000). Low (2004), for the first time, sug-

gested a behavioural explanation to the asymmetric volatility phenome-

non following the principle of loss aversion(Kahneman & Tversky, 1979).

He found an asymmetric and nonlinear relation between CBOE VIX and

contemporaneous returns on S&P 100 index. He contended that this

asymmetric relation is similar to the phenomenon of loss aversion.

Reviewof Financial Economics 35 (2017)66–81

⁎Correspondingauthor.

E-mailaddresses: pratap.pati@vgsom.iitkgp.ernet.in (P.C. Pati),

prabina@vgsom.iitkgp.ernet.in(P. Rajib), parama@vgsom.iitkgp.ernet.in (P. Barai).

http://dx.doi.org/10.1016/j.rfe.2017.07.004

1058-3300/©2017 Elsevier Inc. All rightsreserved.

Contents listsavailable at ScienceDirect

Review of Financial Economics

journal homepage: www.elsevier.com/locate/rfe

Loss aversion is the cornerstone of prospect theory (Kahneman &

Tversky, 1979). In prospect theory, the value function, which represents

the psychological value or the perception of gains and losses, has three

key features that influence the decision-making process. This value func-

tion is drawn based on individual's decision in an experimental setting.

First, value function is definedover the perception of gains and losses

relative to a reference point. Second, losses loom larger than gains

i.e. reaction of people to losses is greater to gain of the same magnitude.

This asymmetry is called loss aversion which is represented by a kink in

the value function. The valuefunction is steeper forlosses than it is for

gains. Third, the value function is concave for the domain of gain above

the reference point, and convex for the domain of loss below the reference

point. People have a tendency to be risk seeker when they experience loss

but to be risk averse at the time of gain. Low (2004) used the CBOE VIX

instead of the value function and analyzed the effect of gain (rise in the

stock market) or loss (fall in the stock market) in the behaviour of VIX.

He interpreted the loss aversion as a greater responsivenessof downside

pressure on raising risk relative to the responsiveness of upside pressure

on lowering risk. The VIX reflects the sentiment of the market i.e. whether

the market is complacent or anxious. According to him, convexity in the

downside returns partitions indicates an accelerating increase in the VIX

and concavityin the upside returns partitionsindicates as accelerating

decrease in the VIX. He found that VIX tends to increasewhen downside

volatility increases more than upside volatility. Hence the volatility index-

return relation is asymmetric and non-linear.

Most of the studieson volatility index are confined to the US stock

markets, but very few or no research on the volatility indices of the

European and Asia-Pacific market has been carried out. The empirical re-

sults obtained from developed marketsmay not be generalized to emerg-

ing marketslike India. Followingthe loss aversion principle, we extend

the work of Low (2004)and examine the asymmetric volatility index-

returns relation in the context of India vis-à-vis Hong Kong, Australia

and UK, and provide a comprehensive comparative analysis in an interna-

tional perspective. We statistically identify structural breaks and volatility

regimes in the behaviour of volatilityindex time series and investigate

the nature of volatility index-return relation during crisis periods of

high volatility and post-crisis periods of medium or low volatility regimes.

Our study contributesand extends the existing literaturein several

dimensions.First, the study differs from earlier studies in the natureof

dataset, theoretical constructs, and methodologicalapproach. Second,

we select the sample volatility indices which are not studied previously;

hence the results provide new insigh ts on market behaviour. Third,

most of the studies are undertaken using single-country dataset. But

in our cross-country study, weanalyze the behaviour of Indiavolatility

index from emerging markets in a c omparative setting against th e

developedmarkets such as HongKong, Australia, and UK.So it provides

several useful insights for p otential traders and investors in volatile

markets. Finally, this study inve stigates the asymmetric volati lity

index-return relation under va rious structural breaks and vo latility

regimes identified by Bai-Perrontest.

The rest ofthe paper is structured as follows.Section 2 discusses the

related literature on volatility-return relation and developsthe testable

hypotheses. Section 3 describes data sample and reports preliminary

analysis. In Section 4, model specifications are outlin ed. Section 5

reports the empirical results. The final section summarizes the major

findings andconcludes the study.

2. Related literature and hypotheses

The literatureprovides mixed andconflicting evidence withrespect

to the explanations for the observed volatility-returns relation. Black

(1976), the pioneer of leverage effect, found a strong inverse relation

between volatility changes and returns for the Dow Jones Industrials

constituents 30 stocks i.e. 1% decline in the summed-return resultsin

N1% increase in volatility. Black claimed that a decline in the value of

the firm's equity increases levera ges which, in turn, leads to higher

volatility. Christie (1982) doc umented that equity volatility is an

increasingfunction of financial leverage, but the strengthof this associ-

ation declines with increasing le verage. Using EGARCH-M model,

Cheung and Ng (1992) found a negative relation between stock price

and future stock volatility, and the leverage effect is greater for small

firms than large firms. Figlewski and Wang (2001) provided a strong

evidence of leverage effect in stock index relative to individual stock.

They found leverage effect is a down marketeffect that may have little

direct connectionto the firm's leverage. Bekaert andWu (2000), using

conditional CAPM model with a GARCH-i n-mean parameterization,

found that the volatility feedback effect dominates the le verage hypoth-

esis for the Japanese stock market. B ollerslev et al. (2006),using

5-minute data on S&P 500 futures, documented that there are significant

negative correlations between absolutereturns, and current as well as

with past returns. They supported the leverage effect explanation.

There are many empirical studies that employ market volatility index

as a measure of volatility and investigate the volatility index-return

relation. Fleming et al. (1995) were among the first to investigate the sta-

tistical properties of the CBOE VIX as a measure of expected stock market

volatility and studied the relationship betweenchanges in the VIX index

(now VXO) and S&P 100 indexreturns. They found contemporaneous

market returns is the most dominant relative to lagged and leads returns.

Moreover,they document a negative andasymmetric relation. Whaley

(2000) investigated weekly changes in the VIX against weekly S&P 100

index returns for the period January 1986–December 1999.He found

that a 100 basispoints fall in VIX leads to 0.469% rise in S&P 100index

returns, but a 100 basis points rise in VIX leads to 0.707% decline in S &P

100 index returns. Therefore, CBOE VIX is popularly known as ‘investor

fear gauge’.Simon (2003) found a negative and asymmetric relation be-

tween Nasdaq volatility Index (VXN) and Nasdaq 100 returns over

1995–2002. Furthermore, he observed stableresults across the bubble

and post bubble periods. Low (2004) examined the relation between

CBOE VIX and returns on S & P 100 index over the year 1986–98 and con-

cluded that the return-volatility relation is both asymmetric and nonline-

ar. Further, he has shown that downside and upside returnpartitions

have convexand concave profile respectively. Convexity and concavity

imply accelerating increases and decreases in the VIX respectively. Giot

(2005) found a strong negative and asymmetric relationbetween chang-

es in the VIX (VXN) and stock market return on S&P 100 (Nasdaq 100)

over the period August 1, 1994–January31, 2003. Further, the asymmetric

relation is weak in the case of Nasdaq 100 and its implied volatility index.

The asymmetric effect is stronger in low-volatility periods than in high-

volatility periods. Hibbert et al. (2008), using various regression models

and quintile regressions, have shown a significant negative and an asym-

metric relation between changes in volatility index (CBOE VIX and VXN)

and their corresponding stock market returns. Their results are more con-

sistent with behavioural explanations involving representative,affect,

and extrapolation bias. Frijns et al. (2010), regressingthe daily changes

in volatility index on leads, lags, and contemporaneous and absolute

market returns, documented a negative and asymmetric relation between

S&P/ASX 200 VIX andits market index returns. Badshah (2013),using

quantile regression models, has provided evidence of negative and

asymmetric relations for the S&P 500, NASDAQ,DAX 30, STOXX index,

and their corresponding volatility index. He found that asymmetry

effect is more pronounced in uppermost quantile relative to median

quantile. Further, the behavioural affect and representativeness heuristics

can explain the asymmetric relation much better than the leverage and

volatility feedback hypothesis. Padungsaksawasdi and Daigler (2014)

studied the stock index ETFs and their corresponding stock indexes

(S&P 500, Dow Jones, and NASDAQ) over the 2008 financialcrisis com-

pared to normal time periods. They have shown that volatility-returns

relation is asymmetric and it is most pronounced for the largest positive

volatility changes.

Extending the work of Low (2004) and Hib bert et al. (2008),we

attempt to examine the implications of the loss aversion principle in

explaining the asymmetric relationship between volatility index and

67P.C. Patiet al. / Review of Financial Economics35 (2017) 66–81