Trend in aggregate idiosyncratic volatility

• Author: Shahriar Khaksari,Kiseok Nam,Moonsoo Kang
• Published date: 01 November 2017
• DOI: http://doi.org/10.1016/j.rfe.2016.11.001
• Date: 01 November 2017

Trend in aggregate idiosyncratic volatility

Kiseok Nam

a,

⁎, Shahriar Khaksari

a

, Moonsoo Kang

b

a

Departmentof Finance, SuffolkUniversity, Boston, MA02108, United States

b

Departmentof Marketing and Finance,Frostburg StateUniversity, Frostburg,MD 21532, United States

abstractarticle info

Articlehistory:

Received19 June 2016

Receivedin revised form 30 October 2016

Accepted1 November 2016

Availableonline 9 November 2016

JEL classification:

G10

G12

We suggestthat price interactionamong stocks is an important determinantof idiosyncraticvolatility. We dem-

onstratethat as more (less)stocks are listedin the markets, priceinteraction amongstocks increases(decreases),

and hence stocks,on average, become more(less) volatile. Our resultsshow that price interactionhas a signifi-

cant positiveeffect of idiosyncratic volatility.The results of various robustnesschecks indicate that the effectof

price interactionis still significant to the presence of liquidity, newly listedfirms, cash flow variables, business

cycle variables, and marketvolatility. Once the price interaction effect is taken into account, no trendremains

in idiosyncraticvolatility.We conclude that there is notrend, but a reflection of thepositive effect of priceinter-

action on idiosyncratic volatility.

© 2016 ElsevierInc. All rights reserved.

Keywords:

Idiosyncraticreturn volatility

Price interaction

Smallfirm effect

1. Introduction

In a seminal paper, Campbell, Lettau, Malkiel, and Xu (2001) find

that aggregate idiosyncratic vol atility exhibits a deterministi c time

trend throughthe late 1990s, whilemarket volatilityand industry vola-

tilitiesremain roughly constantduring this time. This findinghas led to

a series of researchregarding the importance of idiosyncratic volatility

for asset pricingand portfolio management.

1

A substantial body of literature hasattempted to explain the time-

series behaviorof aggregate idiosyncratic volatility. One line of studies

proposes that a cha nge in idiosyncratic cash flow variability contributes

to the time variation in aggregate idiosyncra tic volatility. Given that

stockprice is driven by both systematicdiscount factorand idiosyncrat-

ic cash flow, thesestudies argue that it is thetime-varying determinants

of firm-specificcashflowthat cause the timetrend of aggregate idiosyn-

cratic volatility. Comin and Mu lani (2006) address the role of R& D

in shaping idiosyncratic volatility while Guo and Savickas (2008) link

changes in aggregate idiosyncratic volatility to changes in the invest-

ment opportunityset related to the book-to-marketfactor. Cao, Simin,

and Zhao (2008) find that corporate growth options explainthe trend

in aggregate idiosyncraticvolatility. Moreover, Wei and Zhang (2006)

argue that the aggregate idiosyncraticvolatility trend is attributableto

deteriorating earnings qualit y. Both Irvine and Pontiff (20 09) and

Gaspar and Massa (2006) suggest that increased competition in the

product markets contributes to an increase in aggregate idiosyncratic

volatility.

In addition,a set of studies focuses on the roleof heterogeneous in-

vestors. Bennett, Sias, and Stark s (2003) and Xu and Malkiel (2003)

argue thatthe trend can be attributedto increased institutionalowner-

ship,especially the increasedpreference by institutionsfor smallstocks.

Foucault,Sraer, and Thesmar(2011) confirm that a change in indiv idual

investor participation affects a level of aggregate idiosyncratic volatility.

Severalstudies relate the timevariation in aggregateidiosyncratic vola-

tility to the time-varying composition of the market portfolio. Brown

and Kapadia (2007)attribute the time trend in aggregateidiosyncratic

volatility to the increase in new listi ngs of riskier firms. Fink, Fink,

Grullon, and Weston (2010) also find that this increasing trendis con-

sistent with an increase in new listingsand, as a result, with a decline

in the maturityof typical public firms in the market.

By providingevidence of a sharpdownturn in aggregateidiosyncrat-

ic volatility in the 2000s following a sign ificant positive trend in the

1990s, Brandt, Brav, Graham, and Kumar (2 010) argue that the ob-

served upward anddownward patterns of deterministictrends are at-

tributed to retail investors' tr ading patterns on low-priced stoc ks.

Their finding of a negative volatility tr end during the 2000s, though

used as evidence against the time tr end, pose a serious challenge to

Reviewof Financial Economics 35 (2017)11–28

⁎Correspondingauthor.

E-mailaddresses: knam@suffolk.edu(K. Nam), skhaksari@suffolk.edu(S. Khaksari),

mkang@frostburg.edu (M.Kang).

1

See, Bali, Cakici,and Whitelaw (2011),Ang, Hodrick, Xing, and Zhang(2006, 2009),

Bali and Cakici (2008),Aktas, De Bodt, and Cous in (2009),Comin and Mulani (2006),

Bali, Cakici, Yan, and Zhan g (2005),Kothari and Warner (2004),andXu and Malkiel

(2003).

http://dx.doi.org/10.1016/j.rfe.2016.11.001

1058-3300/©2016 Elsevier Inc. All rightsreserved.

Contents listsavailable at ScienceDirect

Review of Financial Economics

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

existing hypotheses that are p rimarily concerned with the pos itive

trend in idiosyncratic volatility.Credible theories concerningthis issue

should now be ableto explain the trends in both positiveand negative

directions.

In this paper, we suggest that price in teraction among stocks

plays an important role in generating the time variation in aggregate

idiosyncratic volatility . Stocks covary with each other su ch that

changes in stock prices cause price changes in other stocks. As more

stocks are listed in themarkets, investors have access to more choices

of stocks for trading. Consequently , when stock prices change, more

stocks are likely to follow suit in either directions, causing higher co-

movements in stock prices, which in turn incre ases idiosyncratic

volatility.

2

We suggest that asmore (less) stocks are listed in the mar-

kets, price interaction among stocks increases (decreases),and hence

increasing (decreasing) co-movements in stock prices. Thus, as more

(less) stocksare listed in the markets, stocksbecome more (less) vola-

tile, ceteris paribus. Theref ore, the trend in idiosyncratic vola tility

is the aggregate reflection of the price inte raction effect on return

volatility.

This paperis motivated by the observationthat the significantposi-

tive (negative) trend in the aggregate idiosy ncratic volatility from

1963.07 to 2000.04 (2000.05 to 2008.0 9) identified by Brandt et al.

(2010) coincides with the similarsignificant increase (decrease)in the

number of listed firms over the two periods. The plots (a) and (b) of

Fig. 1 show the level of monthlyequal- and value-weighted aggregate

idiosyncratic volatility in sq uare root, while the plots (c) shows the

numberof firms that is includedin computing theaggregate averageid-

iosyncratic volatilityin each month over the 1963.07–2008.09 sample

period. The plots indicate that the U.S. stock markets durin g 1990s

(2000s) ischaracterized by an upward(downward) trend in aggregate

idiosyncratic volatilitywith a persistent increase (a sharp drop) in the

number of firms listed in the markets for the sample period s. The

plots suggest thatthere is an important link between the trendsin ag-

gregateidiosyncratic volatilityand the price co-movementsfrom inter-

action amongstock prices.

3

To illustrate our arguments, let's consider a town where the level of

socialactivities per capitaexhibits a steady increasefor some time peri-

od and a sharp declinethereafter. Of course, there are many economic

and social factors that induce peoples' socialactivities over time. It is,

however,reasonable to considerpopulation size of thetown as a funda-

mentalfactor to induce the observedtrend patterns in the level of social

activities.As the town'spopulation increases(decreases),social interac-

tions among people increase (decrease). An increase(decrease) in so-

cial interactions per person induces more (less) soc ial activities per

person. Consequently, the tren d might be attributed to the effect of

the town'spopulation size on the social interactions among the inhabi-

tants over time.

We apply the same logicto explain the variation patterns inaggre-

gate idiosyncratic volatili ty. Stocks covary with each other , such

that changes in stock prices cause pric e changes in other stocks. As

more stocks arelisted in the markets, additionalstocks are included in

the category of the same or a related industry, a competing business,

or a related business. As such, investorshave access to more choices of

stocksfor trading. Thus, whenstock prices change,stocks are more like-

ly to follow suitin either direction, increasing the level of idiosyncratic

volatility.

In estimations,we employ the number of listed stocks as the proxy

for price interaction among stocks.Our estimation results indicatethat

price interaction among stocks has significant explanatory power for

the timevariation in aggregateidiosyncratic volatility. There areseveral

notable findings. First, there is a significa nt positive effect of price

interaction among stocks on aggregate idio syncratic volatility from

1926.07 to 2014.12 in U.S. stock markets, and a substantial portion of

time variation in aggregate idiosyncratic volatility is explained by this

positive effect. The results indicate that the price interaction effect is

still robust to the existing explanat ory variables, such as liquidity,

newly listed firms, cash flow variables, business cycle variables, and

market volatility.

The observedpattern of positive and negative time trends in aggre-

gate idiosyncratic volatility can be explained by the positive effect of

price interaction on return volatility. Th e estimation results indicate

that a steady increase in the number of stocks liste d in the markets

prior to the late 1990scaused stocks to be more volatile due to the in-

creased price interaction amon g stocks, thereby inducing a positive

trend in idiosyncratic volatility.Likewise, the steep negativetrend dur-

ing the 2000s is attributed to a sharp decline in the number of listed

firms during this period,which considerably reduced the levelof price

interaction among stocks inducing a negativetrend in aggregate idio-

syncratic vola tility.

Moreover, there is a significantfirm-size effect in the level of price

interaction amongthe size portfolios, which is observedin the level of

volatility reported by Bennett et al. ( 2003),Xu and Malkiel (2003),

and Brandt et al. (2010). Our estimationresults regarding the ten size

decile portfolios indicatethat the level of price co-movements from in-

teraction among stock prices increases monotonically as the size de-

creases. As such, the smalles t (largest) size decile port folio exhibits

the greatest (smallest) level of priceinteraction. More importantly,for

all ten sizedecile portfolios, the positive and negativepattern of trends

in idiosyncratic volatility completely disappearsunder the positive ef-

fectof price interactionon return volatility.These resultssupport our ar-

gument that priceinteraction among stock pricesis a key determinant

for the time variation of idiosyncratic volatility.

Our paper proceedsas follows. In Section 2, we present four empir-

ical implications of the priceinteraction hypothesis.In Section 3,were-

port the estimation results for aggregate idiosyncratic volatility with

various robustness checks.In Section 4, we provide the estimation re-

sults for the individual stocks'idiosyncratic volatility. In Section 5,we

present the estimation results for the size effect, while Section 6 pro-

vides our conclusion.

2. Price interactionhypothesis

Although the direct measure of price intera ction among stocks is

practically not available,it is well known that stocks covary with each

other. As more stocks are available in the market s, the number of

pairwise interactionsamong stocks, i.e.,

N

C

2

=N(N−1)/2, increases at

a faster growth rate than the growth rate of the number of stoc ks.

Thus, price interactionis a positive monotonicfunction of the number

of stocks. We thus employ the number of listed firms in the markets

as the proxy for priceinteraction among stocks.

We examinethe effect ofprice interactionon aggregate idiosyncratic

volatility bytaking a derivative of the numberof listed firms on aggre-

gate averageidiosyncraticvariance that is derivedfrom the relationship

betweenportfolio varianceand the individualstock's variance. Consider

the followingsimple market model for the i

th

stock:

ri;t¼αþβirM;tþεi;t;ð1Þ

2

The volatility feedback eff ect could be one of the channels t o induce price co-

movements among stocks. As more stocks are listed in the markets, volatility feedback

amongstocks increases, therebymaking stocks relatively morevolatile.

3

Theannual averagegrowth rate in the numberof firms listed in the marketswas 4.87%

until 1997, but it was −4.13% from 19 97 to 2008. Following Brandt et al. (2010),we

choose2000.04 as the singlebreakpoint in trend line.The two trend lines in the aggregate

averageidiosyncraticvolatility plotsare based on the estimated trendcoefficient from the

trend regressions of equa tions (16) for the 1963.07–2000.04 period and the

2000.05–2008.09 period, respectively. The two trend lines in the numbe r of firms are

based on the estimated trend coefficient from the trend regressions on the number of

firms. The estimated value of trend coefficient is 12.82 for the 1963.07–2000.04period

and −18.22for the 2000.05–2008.09 period.

12 K. Nam et al. / Reviewof Financial Economics35 (2017) 11–28