IDIOSYNCRATIC VOLATILITY

Transcription

1 STOCKHOLM SCHOOL OF ECONOMICS MASTER S THESIS IN FINANCE IDIOSYNCRATIC VOLATILITY - EVIDENCE FROM THE NORDIC EQUITY MARKETS Svante Jonasson Dmrs Karaksos ABSTRACT Usng the dsaggregated approach to study the volatly of common stocks at the market, ndustry, and frm levels, ntroduced by Campbell, Lettau, Malkel, and Xu (1), we present emprcal evdence on the volatly composon of stocks traded on the Nordc equy markets. Our results reject the common noton of rsng stock volatly wh respect to all three components of volatly, but unvel recent perods of ncreased hgh-frequency nose. However, we fnd that all volatly components have returned to ther longrun levels n the years followng the speculatve epsodes durng the late 10s and early 0s. Moreover, we fnd evdence that the components of volatly are sensve to changes n the composon of secures used n the estmaton Tutor: Andre Smonov, PhD Presentaton Date: 14 June 6 at 08:15 Venue: Room 750 Dscussants: Mara Dahlman and Madelene Wallmark 11@student.hhs.se 1@student.hhs.se We would lke to express our gratude to Andre Smonov for hs support and assstance n wrng ths thess.

2 Table of Contents 1 Introducton Background Purpose Delmatons Outlne... 4 Theoretcal Background Portfolo Theory Portfolo Mathematcs Why Idosyncratc Volatly Matters Prevous Research Emprcal Studes Possble Explanatons for Changes n Idosyncratc Volatly Research on the Implcatons of Changes n Idosyncratc Volatly Decomposon Methodology Data and Descrptve Statstcs Analyss Sweden Denmark Fnland Norway Common Observatons Lead-Lag Relatonshps and Cyclcal Behavour Results Concluson and Suggestons for Further Research References Appendx Quarterly GDP growth Frm Quanty and Sze Herfndahl-Hrschman Indces Classfcaton of Lsted Frms... 56

3 1 Introducton There s a wdespread percepton among the publc that equy markets have become more volatle over tme. Ths noton has been soldfed by the strong equy apprecatons n the 10s and durng the late 10s and early 0s, and the expresson n today s volatle markets s used regularly n the meda. However, ths percepton has generally had ltle support n academc lerature. In an nfluental paper, Schwert (10), documented a cyclcal pattern of volatly but dd not fnd any evdence of ncreased volatly n the aggregate market ndex of eques n a US sample. In a more recent paper publshed n The Journal of Fnance, Campbell, Lettau, Malkel, and Xu (1), reaffrmed Schwert s results usng US data for the perod 196 to 17. In addon, they employed a novel dsaggregated approach to measurng total stock volatly, whch allows a decomposon of the volatly of a typcal stock nto a market, ndustry, and frm specfc component. Ther results show that market and ndustry-level volatly has remaned on the same level over tme but that frm specfc,.e. dosyncratc, volatly exhbs a sgnfcant upward slopng trend over the sample. The paper of Campbell, Lettau, Malkel, and Xu (1) has nced sgnfcant nterest n dosyncratc volatly and the topc s one of the more actvely debated at the moment. Several hypotheses have been put forward to provde explanatons, and other authors have tred to expand the emprcal foundaton by applyng ther dsaggregated methodology to samples from other major equy markets. Ths thess uses the dsaggregated approach of Campbell, Lettau, Malkel, and Xu (1) to nvestgate the market, ndustry, and frm-level volatly on the Nordc equy markets 1. To our knowledge, ths has only been performed on less comprehensve Swedsh data prevously, and at that tme usng a sgnfcantly smaller sample. 1.1 Background Fnancal theory and standard asset prcng models stpulate that, n equlbrum, only systematc rsk s prced and accordngly, most emprcal studes have focused on the volatly of aggregate market ndces. In addon, sophstcated econometrc models such as GARCH have been developed to capture the tme varaton n volatly. The fact that stock market ndces exhb tme varyng volatly has been frmly establshed, and snce dosyncratc rsk can be dversfed away, ths s the volatly experenced by an nvestor holdng the market portfolo. However, defcent fnancal leracy or other exogenous factors may constran nvestors from holdng a fully dversfed portfolo. For these nvestors, ndustry-level and dosyncratc frm-level volatly are mportant factors affectng the rsk-reward relatonshp. 1 The Icelandc equy market has been excluded. For further dscusson of our sample, we refer to the Data and Descrptve Statstcs secton. 3

4 In an nfluental paper by Campbell, Lettau, Malkel, and Xu (1) the authors propose a dsaggregated approach to study the volatly of common stock returns at the market, ndustry, and frm levels. Ther results, that dosyncratc rsk exhbs a strong posve trend over the perod 1 to 17 n the US, has rekndled the nterest of fnancal economsts n the role of dosyncratc rsk as a component of total volatly and the mplcatons of these results carry over to asset prcng and portfolo management. As an example of ths, any rule of thumb concernng portfolo dversfcaton ultmately depends on the level of dosyncratc rsk and thus the adequacy of any approxmatons may change over tme. An ncrease n dosyncratc volatly may also affect the nformatveness and prcng effcency of stock markets because of the ncreased rsk faced by arbrageurs who trade to explo ndvdual stock prces that devate from ther ntrnsc value. Other mportant aspects of ncreased dosyncratc volatly nclude mplcatons for opton prcng and for measurng the statstcal sgnfcance of abnormal event-related returns n event studes. The fndngs of Campbell, Lettau, Malkel, and Xu (1) have also nced sgnfcant nterest n the ntertemporal lead-lag relatonshp between the dosyncratc volatly and stock market returns and also n how affects aggregate output n macroeconomc models. 1. Purpose The purpose of ths thess s to provde Nordc evdence of the hstorcal movements n market, ndustry, and frm-level volatly as a contrbuton to the overall understandng of volatly dynamcs n equy markets. Gven that the behavour and propertes of dosyncratc volatly on the Nordc stock markets have receved ltle attenton, our thess ams at provdng an ndependent assessment of the emprcal fndngs reported n the recent lerature on the topc (e.g. Campbell, Lettau, Malkel, and Xu (1), Guo and Savckas (5), Frazzn and Marsh (3), Chang and Dong (5), Angelds and Tessaromats (5), and Brandt, Brav, and Graham (5)). 1.3 Delmatons We lm the scale and scope of our thess to nclude data on stock prces, market values, nterest rates and real GDP growth for the Nordc countres Sweden, Denmark, Fnland and Norway. The length of the tme-seres of stock prces and market values s lmed by what s avalable through Datastream. Also, the methodologcal approach, developed by Campbell, Lettau, Malkel, and Xu (1), wll be dscussed but an exhaustve dscusson on the statstcal propertes of ther model does not le whn the scope of ths thess. 1.4 Outlne Ths paper s organzed as follows. In the next secton, we brefly descrbe the theoretcal background that underpns the methodology and the relevance of adoptng a dsaggregated approach to measurng dosyncratc volatly. In secton 3 we provde a bref survey of the lerature on the topc. 4

5 In secton 4, the methodologcal framework of Campbell, Lettau, Malkel, and Xu (1) s presented n detal. In secton 5, we descrbe the data used n the thess. Secton 6 contans an analyss of the decomposed volatly tme seres and secton 7 examnes lead-lag relatonshps and cyclcal behavor. In secton 8, we present the results of the thess, followed by secton 9 whch presents concludng comments and suggestons for further research. The thess ends wh an ndex of references and an appendx. Theoretcal Background Ths secton provdes a bref background on the fnancal theory underpnnng the methodology employed by Campbell et al. (1). Moreover, a dscusson of the relevance of dosyncratc volatly s presented..1 Portfolo Theory Modern portfolo theory s largely attrbutable to the work of Harry M. Markowz and Wllam F. Sharpe. Markowz (1) studed the effects of asset rsk, correlaton and dversfcaton on expected nvestment portfolo returns, and descrbed how to combne assets nto effcently dversfed portfolos. Specfcally, a Markowz Effcent Portfolo s one where no added dversfcaton can lower the portfolo's rsk for a gven return expectaton or, alternately, no addonal expected return can be ganed whout ncreasng the rsk of the portfolo. Furthermore, the Markowz Effcent Fronter s the set of all portfolos that wll provde the hghest expected return for each gven level of rsk. Based on the work of Markowz, Sharpe (14) ntroduced the famous Capal Asset Prcng Model whch s used extensvely n academa and by practoners to determne the cost of capal of an asset. The formula takes nto account the asset s sensvy to non-dversfable rsk,.e. systematc rsk or market rsk, as well as the expected return of the market as a whole and the expected return of a theoretcal rsk-free asset. The model s based on the ratonal assumpton that nvestors should n equlbrum not be compensated for rsk that they can avod smply through dversfcaton,.e. at low or zero cost. The expected return, and equvalently the cost of capal, of any fnancal asset s accordng to the Capal Asset Prcng Model gven by equaton (1). E ( R ) ( R ) R + E( R ) = β (1) f m f Harry M. Markowz (born August 4, 197) and Wllam F. Sharpe (born June 16, 14) won the Bank of Sweden Prze n Economc Scences n Memory of Alfred Nobel n 10 jontly wh Merton Mller for ther contrbutons to the feld of fnancal economcs. 5

6 Although fercely dsputed snce s ncepton 3, the CAPM remans the most wdely used asset prcng model. It has a strong logcal appeal and s an underlyng assumpton on whch the methodology n ths paper s developed.. Portfolo Mathematcs The mathematcs governng the return and rsk of portfolos s rather straght-forward. The return of a portfolo s smply the weghted sum of ndvdual secury returns as gven by equaton () below. The varance of the return of a portfolo s gven by the covarance matrx as detaled n equaton (3). These portfolo formulas, n combnaton wh the Capal Asset Prcng Model, make up the foundaton on whch the methodology employed n ths paper s bult..3 Why Idosyncratc Volatly Matters R p = wr () σ p ww jσ σ j ρj (3) j j = ww jσ j = Fnancal theory and standard asset prcng models stpulate that, n equlbrum, only systematc rsk s prced. Therefore one may ask why s relevant to devote a study to dosyncratc rsk. There are, however, several mportant reasons as to why dosyncratc volatly matters: Investors may be restrcted from holdng well dversfed portfolos. The fact that many nvestors have large holdngs of ndvdual stocks can be explaned by transacton costs, ncomplete nformaton, the value of control, and nstutonal constrants such as taxes, lqudy needs, mperfect dvsbly of secures, or other exogenous factors. Investors facng varous restrctons to dversfcaton may be concerned wh not just market rsk, but wh the total rsk of secures. A useful rule of thumb n fnance s that most of the dosyncratc rsk of a portfolo can be elmnated by holdng 0 to 30 ndvdual stocks. However, Malkel and Xu (4) pont out that ths s only true f stocks are pcked randomly. Ths s seldom the case, and therefore, the adequacy of the current rules of thumb concernng portfolo dversfcaton ultmately depends on the level of dosyncratc volatly of the stocks makng up the portfolo. 3 As put forward n a paper by Rchard Roll n 17, and what s generally referred to as Roll's Crque, the CAPM my not be emprcally testable due to the nobservably of the true market portfolo. The market portfolo should n theory nclude every sngle asset that can be held as an nvestment, but n practce s common to use a stock ndex as a proxy for the true market portfolo. Ths smplfcaton can lead to false nferences as to the valdy of the CAPM. 6

7 The effcent market hypothess (EMH) s based on the noton that msprcngs n the market are corrected through the actons of arbrageurs who take large long and short posons n ndvdual stocks. They are thus exposed, not only to market rsk, but also to dosyncratc frm-specfc rsk. As an mplcaton of ths s, s possble that ncreasng dosyncratc rsk wll hamper market effcency as the rsk nvolved n holdng an undversfed portfolo becomes more costly for the arbrageur to bear. Idosyncratc volatly affects the statstcal sgnfcance of abnormal events n event studes, as the sgnfcance of abnormal events s determned by the volatly of ndvdual stock returns relatve to the market. Dsaggregated measures of volatly are mportant, not only n fnance, but also n economcs. Models of sectoral reallocaton mply that ncreases n ndustry volatly n productvy growth may reduce output as resources are dverted from producton to costly reallocaton across sectors. Optons are prced on total rsk of the underlyng nstrument, not just the market rsk. 3 Prevous Research Idosyncratc volatly s one of the most actvely researched topcs n fnancal economcs at the moment. The focus of dfferent authors has vared, but one can dstngush three major strands of lerature on the topc. One strand of lerature has focused on expandng the emprcal foundaton by employng the methodology of Campbell, Lettau, Malkel and Xu (1) on dfferent data samples. Another strand tres to explan the ncreasng dosyncratc rsk n the US market as dentfed by Campbell, Lettau, Malkel and Xu (1). Fnally, a thrd strand has focused on whether dosyncratc rsk matters and on studyng s role n the ntertemporal relaton between rsk and return. The followng subsectons provde a bref survey of the research n each respectve strand. 3.1 Emprcal Studes Campbell, Lettau, Malkel and Xu (1) examned the volatly of the US eques market over the perod 1 to 17 usng a novel dsaggregated approach and found strong evdence of a posve determnstc trend n dosyncratc frm-level volatly, whereas the market and ndustry level volatly were farly stable over the same perod. Consstent wh ths, they fnd that correlatons between ndvdual stocks have declned over tme and that the explanatory power of the market model has dmnshed. Furthermore, they fnd that frm-level volatly accounts for the largest share of total frm volatly and that market level volatly tends to lead ndustry level volatly and frm level volatly. All three volatly measures ncrease n economc downturns and tend to lead recessons. Also, the volatly measures help n forecastng economc actvy and reduce the sgnfcance of other explanatory varables commonly used n forecastng. They also fnd evdence 7

8 that the large number of small frms enterng the market over the sample perod may have caused the upward trend n frm level volatly. Savckas and Guo (5) analyze the aggregate dosyncratc volatly of eques markets n the G7 countres usng data up to 3. Consstent wh Campbell, Lettau, Malkel and Xu (1), they fnd a sgnfcant upward trend n some G7 countres when lookng at equally-weghted average dosyncratc volatly, ncludng the US. They fal, however, to observe such a trend when lookng at the value-weghted average dosyncratc volatly or equally-weghted dosyncratc volatly of the 5 largest companes n all seven countres, suggestng that there s a small-frm effect present n the data. In addon to the results n Campbell, Lettau, Malkel and Xu (1), they fnd a strong ncrease n dosyncratc volatly n the late 10s and early 0s, where after fell. These effects had no effect on the general upward trend however. Furthermore, they fnd that aggregate dosyncratc volatly s hghly correlated across the G7 countres. Frazzn and Marsh (3) nvestgated the relaton between dosyncratc volatles and a set of frm specfc observable varables to both US (-) and UK (15-3) stock return data and found that the clear upward trend n dosyncratc volatly n the US, concentratng on small stocks, s not shared by the UK market whch may have mplcatons for the sources of the US trend. They also present evdence of a relaton between dosyncratc volatly and the degree of nstutonalzaton of the US market. Brandt, Brav and Graham (5) present further evdence about the ncrease n dosyncratc volatly n the US through the 10s and early 0s. Accordng to ther study, n the three years endng n 4, dosyncratc volatly fell to pre-10s levels, thus reversng the tme trend observed through the 10s. Also, the perod between 196 and 13 exhbed a temporary ncrease n dosyncratc volatly closely resemblng the ncreasng trend dentfed n recent years. Fnally, the epsode of hgh and ncreasng dosyncratc volatly durng the 10s s concentrated prmarly n frms wh low stock prces and lmed nstutonal ownershp. Sternbrnk and Tengvall (1) performed a volatly decomposon on data from the Stockholm stock exchange on a sample rangng from 18 to 1 and found that market and ndustry level volatly have ncreased over tme, whereas frm level volatly was stable over tme. However, the posve trend n the market volatly component proved not to be stable to the excluson of large capalzaton frms. 3. Possble Explanatons for Changes n Idosyncratc Volatly Several hypotheses have been put forward as to why dosyncratc rsk may have ncreased. In theory, ncreased volatly can only result from three sources: an ncrease n the varance of the frm s expected cash flow, an ncrease n the varance of dscount rates, or from an ncrease n the covarance between the cash flow shocks and dscount rate shocks. (Campbell, Lettau, Malkel, and Xu (1)) 8

9 Denns and Strckland (5) argue that ncreased dosyncratc rsk can be explaned by two factors. Frst, they fnd that nstutonal ownershp has ncreased monotoncally over the past 0 years. Secondly, frm focus, measured by the number of busness segments, has ncreased over the last 0 years. Also, the tendency n corporate governance to break up conglomerates and replacng them wh more focused companes that specalze n a sngle ndustry has made possble to measure each company s dosyncratc rsk separately, whereas prevously was part of an already dversfed conglomerate. Hence, s credble that the whn conglomerate dversfcaton has kept frms dosyncratc volatly artfcally low. It s also possble that the ncreased volatly mght have ncreased due to ncreased relance on external funds rather than nternal. Another explanaton brought forward by Brandt, Brav and Graham (5), Gaspar and Massa (3) and Irvne and Pontff (5) s that product markets have become more competve. Lower search costs and better ables of consumers to compare products have resulted n consumers beng less loyal to a gven frm s product. The mplcaton s that competon nduces ncreased frm level prof volatly. Another possble explanaton could be the ncreased use of optons n management compensaton packages. As the relatve proporton of management s pay come from stock optons, management have stronger ncentves to maxmze the value of the optons by nducng more frm level volatly. It s not clear how management would nduce greater volatly but Cohen, Hall, and Vcera (0) detect a statstcally sgnfcant effect, albe small n magnude. Explanatons specfc to the Nordc settng seems to be the lberalzaton of the equy markets n the late 10s and 10s. Tradng on the Stockholm Stock Exchange ncreased very rapdly when the remanng laws constranng foregn ownershp and tradng n the Swedsh equy markets were lfted n 1. Selln (16) documented an ncrease n volatly after 1 and attrbuted ths ncrease to ncreased nose tradng that took place after the deregulaton and the ncreased partcpaton of foregn nvestors n the Swedsh equy markets. He does not, however, relate hs fndng of ths partcular tradng pattern to any measure of volatly. In a later study, Nlsson () reaffrmed these results and showed that hgher expected return, hgher volatly and stronger lnks wh nternatonal stock markets characterze the deregulated perod for all Nordc stock markets. However, the ncrease n volatly has been coupled wh an ncrease n expected returns and ncreased opportunes for Swedsh nvestors to cross-border dversfy. Hence, the rsk-return characterstcs have not changed adversely snce the lberalzaton of the Nordc equy markets. We and Zhang (3) nvestgate why ndvdual stocks n the US have become more volatle, focusng on the 16-0 perod. They report that corporate earnngs have deterorated on average, that ther volatly has ncreased over the sample perod and that ths s more evdent for newly lsted stocks than for exstng stocks. They also fnd that stock return volatly s negatvely related to the return-on-equy and posvely related to the volatly of the return-on-equy n cross-sectons. Accordng to ther study, the upward trend n average stock return volatly s fully accounted for by 9

10 the downward trend n the return-on-equy and the upward trend n the volatly of the return on equy. Other varables that have cross-sectonal explanatory power, such as frm equy sze and frm age, are not found to contrbute to the ncrease of stock return over tme. Chang and Dong (5), n a smlar study, use Japanese data from 15 to 3 to show that both nstutonal herdng and frm earnngs are posvely related to dosyncratc volatly. They reject the hypothess that nstutonal nvestors herd toward stocks wh hgh dosyncratc volatly and systematc rsk. The results suggest that there may be a behavoral explanaton to the negatve premum earned by hgh volatly stocks found by Ang, Dong, and Pazzes (4). They also fnd that the dsperson of change n nstutonal ownershp and return-on-asset move together wh the market aggregate dosyncratc volatly over tme. Ther results suggest that nvestor behavor and stock fundamentals may both help explan the tme-seres pattern of market aggregate dosyncratc volatly. Hamao, Me, and Xu () examne the market-and frm-specfc rsks n the Japanese market over dfferent market condons. The prce behavor of Japanese eques n the 10s s found to resemble that of US eques durng the Great Depresson. Both show ncreasng market volatly and a prolonged large co-movement n equy prces. What s unque about the Japanese case s the surprsng fall n frm-level volatly and turnover n Japanese stocks after s market crash n 10. Ths large decrease n frm-level volatly may have mpeded Japan s capal formaton process as has become more dffcult over the past decade for both nvestors and managers to separate hgh qualy from low qualy frms. Usng data on frm performance fundamentals and corporate bankruptces, they show that the fall n frm-level volatly and turnover could be attrbuted to the sharp ncrease n earnngs homogeney among Japanese frms and the lack of corporate restructurng. Bal, Cakc, Yan, and Zhang (4) show that the sgnfcantly posve relaton between the equal-weghted average stock volatly and the value-weghted portfolo returns found n Goyal and Santa-Clara (3) s drven by small stocks traded on the NASDAQ, and s n part due to a lqudy premum and that ther result does not hold for an extended sample up to 1 and for portfolos of stocks traded on the NYSE/AMEX and NYSE. More mportantly, they fnd no evdence of a sgnfcant lnk between the value-weghted portfolo returns and varous measures of the medan and value-weghted average stock volatly. Fnk, Fnk, Grullon and Weston (5) present emprcal evdence that the recent rse n dosyncratc rsk s drven by the ncreasng propensy of frms to ssue publc equy at an earler stage n ther lfe cycle. They fnd that the age of the typcal frm at s IPO date has fallen dramatcally from nearly 40 years old n the early 10s to less than 5 years old by the late 10s. They argue that snce younger frms tend to be rsker, ths systematc declne n the average age of IPOs, combned wh the ncreasng number of frms gong publc over the last 30 years, has caused a sgnfcant ncrease n dosyncratc rsk and that after controllng for the proporton of young frms n 10

11 the market, there s no trend n the tme seres of dosyncratc rsk. Moreover, they fnd a negatve trend n dosyncratc rsk after controllng for other measures of frm matury. Brown and Kapada (5) extend ther argument and clam that the ncrease n dosyncratc volatly s due solely to new lstngs by rsker companes. Ths s a result of fnancal development that allows rsker companes to access capal markets more easly or cheaply. They also show that the prevously documented declne n average R of a market model s due to the new lstng effect. Bennet and Sas (4) argue that the growth n frm-specfc rsk prmarly reflects changes n the composon of secures used to estmate frm-specfc rsk, rather than systematc changes n frm-specfc rsk. Specfcally, they propose that three key changes n the composon of the secures that are used to estmate frm-specfc rsk explan ths rsng trend: the growth of rsker ndustres, the ncreased role of small frms n the market, and the decrease n whn-ndustry concentraton. 3.3 Research on the Implcatons of Changes n Idosyncratc Volatly Goyal and Santa-Clara (3) examne US market data up to 19 and fnd a sgnfcant posve relaton between average stock varance, whch s largely dosyncratc, and the return on the market. In contrast, they fnd that the varance of the market has no forecastng power for the market return. Ang, Hodrckz, Xngx and Zhang (4) examne the prcng of aggregate volatly rsk n the cross-secton of stock returns and fnd that stocks wh hgh sensves to nnovatons n aggregate volatly have low average returns. In addon, they fnd that stocks wh hgh dosyncratc volatly relatve to the Fama and French (13) model have partcularly low average returns. Angelds and Tessaromats (5) use data from the UK eques market between 10 and 3 to examne the predctve ably of varous measures of dosyncratc rsk. They provde evdence whch suggests that s the dosyncratc volatly of small capalzaton stocks that matters for asset prcng and that small stocks dosyncratc volatly predcts the small capalzaton premum component of market returns and s unrelated to pure market rsk or the value premum. Brown and Ferrera (3) fnd that non-systematc volatles of small frms are posvely related wh future returns on all age and sze portfolos. They domnate systematc volatly, bg-frm volatly and other volatles. There s also strong evdence that dosyncratc rsk s prced n smallfrm returns. Small-frm volatly as a predctor of bg-frm returns s, n part, a proxy for systematc volatly and a consumpton-wealth rato. They rule out several hypotheses, ncludng a lqudy premum, as potental explanatons of the results, but not the dea that small-frm dosyncratc volatly s correlated wh the rsk of the total nvestor portfolo, whch ncludes non-equy assets. 4 Decomposon Methodology The theoretcal framework of Campbell, Lettau, Malkel, and Xu (1) for decomposng stock returns presented n ths subsecton ams at defnng volatly measures that sum to the total return 11

12 volatly whout havng to calculate covarances and whout havng to estmate frm or ndustry betas. These can be dffcult to estmate correctly and may be unstable over tme. We follow Campbell, Lettau, Malkel, and Xu (1) and decompose the stock returns nto three components: the market level return, an ndustry level resdual, and a frm-specfc resdual, whch we then use to construct tme-seres of volatly measures of the three return components for a stock. Throughout the thess ndustres are denoted by, ndvdual frms are ndexed by j, and w j s the weght of frm j n ndustry. The logarhmc excess return of frm j n ndustry n perod t s denoted as R j. The excess log-return s measured as an excess return over the one month nterbank offered rate. The excess return of ndustry n perod t s gven by R = w R. Smlarly, the j weght of ndustry n the total market s denoted by w, and the excess return s R = w R. Usng CAPM we decompose frm and ndustry returns nto the three components. As mpled by CAPM we mpose a zero-ntercept restrcton for ndustry excess returns: and for ndvdual frm returns. In equaton (4) β m denotes the beta for ndustry wh respect to the market return, and ~ ε s the ndustry-specfc resdual. Correspondngly, n equaton (5) β j s the beta of frm j ndustry wh respect to s ndustry, and R j R j m mt j mt j = β R + ~ ε (4) = β j R + ~ η j = β β R + β ~ ε + ~ η m mt ~ η j s the frm-specfc resdual. The mplc assumpton s that β jm satsfes β jm = β j β m,.e. ~ η j s orthogonal to the ndustry return R, market return R mt, and the frm-specfc resdual. The weghted sums of the dfferent betas equal uny: w β m = 1, j The assumpton that the dfferent components of frm return are orthogonal perms a smple varance decomposon n whch all covarance terms are zero: Var Var Equaton (7) and (8), however, requre the estmaton of frm-specfc betas that are dffcult to estmate and may vary over tme. To avod ths, Campbell, Lettau, Malkel, and Xu (1) propose a smplfed model that does not requre any nformaton about betas. Omtng β m from equaton (4) we get the followng market-adjusted-return model : j w β = 1 ( R ) β Var( R ) + Var( ~ ε ) m mt j j j = (7) ( R ) β Var( R ) + β Var( ~ ε ) + Var( ~ η ) j jm mt j = (8) j (5) (6) 1

13 where ε s the dfference between the ndustry return R and the market return R mt. Comparng equatons (4) and (9), we have Thus, for the market-adjusted resdual ε to equal the CAPM resdual n equaton (7) must hold that β =1 or that the market return R mt =0. Ths decomposon, however, means that R mt and m R = + ε (9) R mt ε are not orthogonal, and thus the covarance between them cannot be gnored. The varance of the ndustry return s Var Takng nto account the covarance also means rentroducng the ndustry beta. However, when calculatng the weghted average of varances across ndustres, the covarance terms, and therefore also the betas, cancel out: ( m ) R mt ε = ~ ε + β 1 (10) ( R ) = Var( R mt ) + Var( ε ) + Cov( R mt, ε ) = Var( R ) + Var( ε ) + ( β 1) Var( R ) w Var mt ( R ) Var( R ) + w Var( ε ) = mt = σ mt + σ et m mt (11) (1) where σ Var( ) and Var( ) mt R mt σ ε t w ε. That betas cancel out was shown n equaton (6) w β = 1 and thus the resdual ε n equaton (9) can be used to construct a measure of m average ndustry-level volatly whout estmatng any betas. Correspondngly, for frm-level returns omtng β j from equaton (5) gves: where η j s defned as The varance of the frm return s Var j R The weghted average of frm varances n ndustry s therefore j R = + η (13) j j η = ~ η + β 1 (14) ( ) R ( R j ) = Var( R ) + Var( η ) + Cov( R, η j ) = Var( R ) + η ) + ( β 1) Var( R ) j j (15) 13

14 σ η w j j η j where Var( ) s the weghted average of frm-level volatly n ndustry. Usng equaton (1), the weghted average across ndustres cancel out any frm-specfc betas where σ ηt σ η = w w j Var( η j ) w s the weghted average of frm-level j volatly across all frms. As Campbell, Lettau, Malkel, and Xu (1) pont out, a volatly decomposon usng the market-adjusted-return model rather than a decomposon usng the CAPM has some mportant theoretcal mplcatons. Aggregatng equaton (7) and (8) across ndustres and frms we fnd that s the average varance of the CAPM ndustry shock ~ ε, and where ~ σ ε Var( ~ ) CSV t w ε ( β ) ( β ) t m w m 1 Correspondngly, on the frm-level s the cross-sectonal varance of ndustry betas across ndustres. where ~ σ t w w j ( ~ η Var η j ), CSV ( ) ( ) t β jm w w j β jm 1 j j s the crosssectonal varance of frm betas on the market across all frms n all ndustres, and CSV ( β ) w w ( β ) t j j j j 1 s the cross-sectonal varance of frm betas on ndustry shocks across all frms n all ndustres. What equaton (18) and (19) show that cross-sectonal varaton n betas can produce common movements n the three varance componentsσ, σ ηt even f the CAPM varance components ~ mt varanceσ w j w j j Var ( R ) β = Var( R ) w Var +, j j m ~ εt σ and ~ ηt σ η ( R j ) = w Var( R ) + w w j Var( η j ) σ = Var = σ mt ( R ) + w Var( ε ) mt + σ εt mt σ εt and σ do not move at all wh the market. However, Campbell, Lettau, Malkel, and Xu (1) show that realstc cross-sectonal varaton n betas has only small effects on the tme-seres movements of our volatly components. + σ ηt, ( β ) σ, ~ ε t εt + t m mt j + w σ η (16) (17) = σ CSV (18) ( β ) σ CSV ( β ) σ ~ ~ ηt σ ηt + CSVt jm mt t j εt σ = + (19) 14

15 5 Data and Descrptve Statstcs We have collected daly stock prces and market values, n local currences, for every stock ever lsted on the Nordc stock exchanges, as far back as there s data avalable through Datastream. In total, our sample ncludes,4 tckers and approxmately ten mllon dataponts. Iceland s stock exchange has been excluded from the study due to s lmed sze and low number of traded eques. A suffcent number of traded stocks s requred for a meanngful ndustry classfcaton and thus volatly decomposon; a creron whch Iceland does not meet. One month nterbank nterest rates are obtaned from IFS 4 for all countres, whch are used as a proxy for the rsk-free asset. Table I. Descrptve statstcs, Raw data The table presents descrptve statstcs for each of the four datasets used n the study. Sweden Denmark Fnland Norway Perod Jan 1 - Sep 5 Feb 10 - Sep 5 Jun 17 - Sep 5 Feb 10 - Sep 5 Dataponts (1) 3,9,8,541,34 1,,0,0,64 Total number of tckers 1, Number of ndustres used Total Mkt Cap, Sep ' MSEK 3,060,4 MDKK 1,5,477 MEUR 175,140 MNOK 1,346,33 (1) Half of whch are returns and half of whch are market caps Unfortunately, the ndustry classfcaton scheme suggested by Datastream proved to be erroneous and naccurate. The requred ndustry classfcaton has thus been based on the rather tme consumng process of manually researchng every sngle frm s operatons. A posve sde effect of ths approach s that has made possble an ndustry classfcaton talored specfcally to the spectrum of frms n each country. The choce of ndustry classfcaton s based on a trade-off between precson on one hand and the need for enough breadth to avod domnance by one or a few frms on the other hand. The number of ndustres per country are presented n table I, and detaled nformaton about frms and ndustry classfcaton can be found n the appendx. To get daly excess returns, we subtract the daly logarhmc returns by the daly logged return on the rsk-free asset. A handful of erroneous returns due to faulty data n Datastream have been manually removed from each of the four datasets. We follow the procedure presented n Campbell, Lettau, Malkel, and Xu (1) to estmate the three volatly components n equaton (17). Usng daly returns the sample volatly of the market return n perod t (MKT t ) s ( m ) MKT t = ˆ σ µ (0) mt = R ms s t 4 Internatonal Fnancal Statstcs, IMF 15

16 where µ m s defned as the mean of the market return R ms over the sample. The market returns are computed as the weghted average usng all frms n the sample, wh weghts based on market capalzaton. For weghts n perod t we use the market capalzaton of a frm n perod t-1 and hold them constant whn perod t. As expected, the calculated market ndex dffers slghtly from a comparable frm-wde value-weghted ndex. However, correlatons amount to % or above n each market. To estmate volatly n ndustry, we sum the squares of the ndustry-specfc resdual n equaton (9) whn a perod t: ˆ σ mt = ε (1) s t As mentoned, to ensure that the covarances of ndvdual ndustres cancel out we have to average over ndustres. The average ndustry volatly, denoted as IND t, s thus: IND t s = w ˆ σ ε () Smlarly, to estmate frm-specfc volatly we sum the squares of the frm-specfc resdual n equaton (13) for each frm: ˆ σ η j = η js (3) s t Then the weghted average of the frm-specfc volatles wh an ndustry s calculated as follows: ˆ σ = w j ˆ η σ ηj j To obtan a measure of average frm-level volatly, denoted as FIRM t, and also to ensure that frmspecfc covarances cancel out we average over ndustres: FIRM t (4) = w ˆ σ η (5) In addon, we wll elaborate on one of the possble explanatons for changes n dosyncratc volatly that has been presented n the lerature, namely that of changes n market and ndustry concentraton. It was evdent durng the process of performng the dsaggregated analyss on Nordc data, that the sensvy of the results to ndustry classfcaton s hgh. Hence, we fnd reasonable to beleve that results are sensve n a smlar way to concentraton whn ndustres and the market. To shed some lght on ths possbly, we wll match observed changes n the three volatly components wh changes n the total number of stocks lsted n a market, the average market capalzaton of stocks and the medan capalzaton of stocks. In addon, we wll calculate, 16

17 and analyze changes n, a measure of concentraton based on the Herfndahl-Hrschman Index 5. It s commonly used n economcs to measure of the degree of competon n a market and s calculated as the sum of squares of the market shares of all frms n accordance wh equaton 6. As s constructed, can range from 0 to 1 whch ndcates a move from a very large amount of very small frms to a sngle frm completely domnatng the market. Although the ndex s normally used n applcatons whch are of a dfferent nature than ours, we are of the opnon that the concept s applcable n ths context as well. We calculate three ndces per country usng ndvdual frms share of the whole market, ndvdual ndustres share of the whole market and fnally as a market capalzaton weghted average of whn-ndustry concentraton across all ndustres. 6 Analyss H n = ( ) s Unvarate statstcs for all twelve tme seres, three per country, are presented n table II below. It s evdent that the frm level volatly component s the largest on average n all countres except n the case of Fnland, where, somewhat unntuvely, the market component domnates by a small margn. In Denmark and Norway, the ndustry level volatly component s larger than the market level component, whereas the oppose s true for Sweden and Fnland. The sum of averages for the three components was 0.18 n Sweden, 0.0 n Denmark, n Norway and n Fnland. Ths corresponds to a weghted average total annual standard devaton of 35.8%, 31.5%, 41.% and 4.% respectvely for stocks n the four countres. Turnng to extreme values, Norway stands out wh a maxmum market level volatly component of and a maxmum volatly component of The tme seres wll be further nvestgated on a country-by-country bass n the followng subsectons. Table II. Descrptve statstcs, volatly tme seres Sweden Denmark Norway Fnland MKT IND FIRM MKT IND FIRM MKT IND FIRM MKT IND FIRM Mean Stdev Mn Max (6) 5 The Herfndahl-Hrschman Index (HHI) s attrbutable to the work of Orrs Herfndahl, an envronmental economst, and Albert O. Hrschman, a member of the Instute for Advanced Study at Prnceton Unversy. 17

18 6.1 Sweden Fgure 1 plots the market level volatly tme seres both as actual values and as a twelve month movng average. Vsual nspecton reveals no dscernable trend, but perods of ncreased volatly as well as ndvdual events causng spkes n the volatly seres are evdent. Large spkes can be observed durng the devaluaton n 1, n October 17 when the world experenced a major stock market crash, and n fall 18 durng the Russan debt crss. We also observe a spke n fall 1, when speculatve pressures on the Swedsh Krona forced the central bank to abandon the fxed currency regme. Durng the years 19 through 1 several spkes are present n the data. Possble explanatons could be the fall of the Sovet satelle regmes n Eastern Europe, the collapse of the Sovet Unon, the Iraq nvason of Kuwa and the subsequent nterventon by the alled forces n Iraq. A perod of ncreased volatly can also be observed durng the frst years of the new mllennum, n the aftermath of the speculatve bubble. Panel A. Market volatly Panel B. Market volatly, MA(1) Fgure 1. Market volatly, Sweden. Panel A shows the annualsed varance of each month from Jan 1 to Sep 5 calculated as MKT = ˆ = ( µ ) t σ mt R ms m. A twelve month movng average s shown n panel B. s t 18

19 The lnear trend estmaton presented n table III below shows that there s no statstcal evdence of a lnear trend n market volatly over the whole sample perod. The analyss has also been performed on the tme seres pre and post December 17, n whch cases statstcally sgnfcant negatve trends are revealed. However, these are lkely nfluenced by the market crashes of 17 and 18, and are not confrmed by the vsual nspecton. Table III. Lnear trend estmaton, MKT volatly tme seres Sweden Jan 8 - Sep Jan 8 - Dec Jan - Sep Lnear trend * ** -5.5*** t-value (1.9) (-.180) (-3.9) Panel A. Industry volatly Panel B. Industry volatly, MA(1) 8 9 Fgure. Industry volatly, Sweden. Panel A shows the annualsed varance of each month from Jan 1 to Sep 5 calculated as IND t = w ˆ σ. A backwards twelve month movng average s shown n panel B. ε Turnng to ndustry level volatly, shown n fgure, there s agan no strong vsual evdence of a trend n the tme seres. A spke n fall 18, concdng wh the Russan debt crss, s followed by 19

20 spkes n March 0 as the IT bubble burst and a few others endng wh October. It appears as f there s a perod of generally ncreased volatly from the late s to the end of year. Table IV reveals a statstcally sgnfcant posve trend n ndustry level volatly over the whole sample perod. However, the trend s posve over the pre December 17 tme seres and then strongly negatve over the remander of the sample when studed n solaton. Hence, we conclude that any posve trend has been reversed by the end of the sample. Table IV. Lnear trend estmaton, IND volatly tme seres Sweden Jan 8 - Sep Jan 8 - Dec Jan - Sep Lnear trend * *** 0.460*** -5.5*** t-value (7.147) (3.74) (-4.7) 0.30 Panel A. Frm volatly Panel B. Frm volatly, MA(1) Fgure 3. Frm volatly, Sweden. Panel A shows the annualsed varance of each month from Jan 1 to Sep 5 calculated as FIRM t = w ˆ σ. A backwards twelve month movng average s shown n panel B. η 0

21 By vsual nspecton of fgure 3, and dsregardng a handful of spkes, the frm level component of volatly seems to have moved n cycles. It s comparatvely low from 1 to 15, durng the md s and n the end of the sample perod, and comparably somewhat hgher nbetween. If one dsregards the return to low volatly n the frm level component n recent years, a vsual nspecton would have gven some support for an ncreasng trend over the perod n lne wh the fndngs of Sternbrnk and Tengvall (1). Accordng to the analyss n table V below, there s a statstcally sgnfcant posve trend when testng over the entre sample. However, as n the case of ndustry volatly, there s a strong reverson n the tme seres when studyng the post December 17 perod n solaton. Table V. Lnear trend estmaton, FIRM volatly tme seres Sweden Jan 8 - Sep Jan 8 - Dec Jan - Sep Lnear trend * *** *** t-value (3.) (1.3) (-4.366) Turnng to fgure 1 n the appendx, we see that the number of lsted stocks has shown a steady ncrease over the Swedsh sample. There s a partcularly steep ncrease of lsted frms durng the late 10 s, followed by a return to the long-term trend after the fnancal crss n the early 10 s, formng a major hump n the curve. One can also observe a slght declne n the number of lsted frms durng the early years of the new mllennum. The average and medan market capalzaton of stocks n the Swedsh market, shown n fgure 5 n the appendx, ncreases steadly from the years after the fnancal crss untl around the turn of the mllennum and the burst of the speculatve bubble. From year 3 on, the average and medan market capalzaton has contnued to ncrease. The Herfndahl-Hrschman ndces n fgure 31 are relatvely constant over the sample, except around the turn of the mllennum when all three ndces ncreased temporarly. An educated guess would be that ths s a manfestaton of the fact that Ercsson came to constute a large fracton of the market durng ths perod. Fgure 4. shows the development of all three volatly components over tme, added together. The top panel shows the absolute sum of the three measures whereas the bottom panel shows ther relatve contrbuton to the total weghted average volatly of Swedsh common stocks. Agan, there s no vsual evdence of a trend n the aggregated measure but perods of ncreased volatly can be observed. The relatve contrbuton of the three components appears to be relatvely constant. 1

22 Market Industry Frm Panel A. Volatlty decomposon, MA(1) Market Industry Frm Panel B. Volatlty decomposon, MA(1) Fgure 4. Volatly decomposon, Sweden. The absolute (A.) and relatve (B.) sum of twelve-month movng averages of the components of weghted average frm volatly w w j Var( R j ) = σ mt + σ ε t + σηt From table VII, we can determne that all three volatly seres exhb hgh autocorrelaton whch may be an ndcaton that they contan un roots. Hence, Augmented Dckey Fuller (ADF) tests are conducted on the tme seres and reported n table VIII. The tests are performed wh and whout a trend component and on the whole sample as well as a sample that ends n December 17 to make comparable wh Campbell et al. (1). The hypothess of a un root can be rejected at the fve percent sgnfcance level on all nstances, thus ndcatng statonary. j.

23 Table VI. Correlaton structure, Sweden The table shows the correlaton between the three monthly volatly tme seres over the Swedsh sample. MKT IND FIRM Table VII. Autocorrelaton structure, Sweden The table shows the autocorrelaton (ACF) and partal autocorrelaton (PACF) functon of the three monthly volatly tme seres; MKT, IND and FIRM n Sweden from Jan 1 to Sep 5. Autocorrelaton Partal Autocorrelaton MKT IND FIRM MKT IND FIRM ρ ρ ρ ρ ρ ρ Table VIII. Un Root Tests, Sweden Ths table reports the test statstcs of the Augmented Dckey Fuller (ADF) test appled to the three monthly volatly tme seres. The left panel shows the test statstcs for the whole sample whereas the rght panel s cut of at December 17 to enhance comparably wh Campbell et al. (1). The lag order s determned usng the Akake nformaton creron, and s reported for each test. The test s performed wh and whout the trend component (t), and the test specfcaton s Y t = β Jan 1 - Sep 5 m 1 + β t + δyt 1 + α Yt 1 + ε t = 1 Jan 1 - Dec 17 MKT IND FIRM MKT IND FIRM Constant t -test p -value Lag order Constant & trend t -test p -value Lag order

24 6. Denmark Panel A. Market volatly Panel B. Market volatly, MA(1) Fgure 5. Market volatly, Denmark. Panel A shows the annualsed varance of each month from Jan 10 to Sep 5 calculated as MKT = ˆ σ = ( µ ) t mt R ms s t m. Panel B shows the twelve month movng average. From a vsual nspecton of fgure 5 above, the market level volatly component n Denmark appears to lack any trend just as n the case of Sweden. Also, a spke at the tme of the global stock market crash n October 17 s evdent, as well as heghtened volatly n the late s and the frst few years of the new mllennum. Moreover, as n the case of Sweden, s also evdent that market volatly has returned to a low level n recent years. As a general observaton, market level volatly seems to have behaved very smlarly n Denmark and Sweden over the sample perod. Table IX. Lnear trend estmaton, MKT volatly tme seres Denmark Feb 80 - Sep Feb 80 - Dec Jan - Sep Lnear trend * *** ** t-value (0.58) (-3.8) (-.) 4

25 Table IX shows that, when tested n solaton, both the pre and post December 17 tme seres exhb statstcally sgnfcant negatve trends. However, there s no statstcally sgnfcant trend n market volatly when testng over the entre sample Industry level volatly n Denmark over the sample perod, shown n fgure 6, exhbs a steadly declnng pattern from the early 10 s to around 17, where after ncreases sharply and peaks n sprng 0. It then returns gradually to what appears to be a long term average level by the end of the sample perod Panel A. Industry volatly Panel B. Industry volatly, MA(1) Fgure 6. Industry volatly, Denmark. Panel A shows the annualsed varance of each month from Jan 10 to Sep 5 calculated as IND t = w ˆ σ. The twelve month movng average s shown n panel B. ε Statstcally, as shown n table X below, there s no lnear trend when testng over the entre ndustry volatly tme seres. The pre and post December 17 tme seres both exhb sgnfcant negatve trends, n lne wh the vsual evdence. However, n concluson, there does not seem to be any overall trend present n the data. 5

26 Table X. Lnear trend estmaton, IND volatly tme seres Denmark Feb 80 - Sep Feb 80 - Dec Jan - Sep Lnear trend * *** -.749*** t-value (0.7) (-10.4) (-.5) Turnng to the frm level component of volatly, a cyclcal pattern can be dscerned n fgure 7. From the begnnng of the sample perod untl the begnnng of the new mllennum, there appears to be a posve trend n the tme seres. However, as has been the case wh all the tme seres studed so far, the volatly returns to a relatvely lower level by the end of the sample perod, whch contradcts the noton of a posve trend n the frm level component of volatly. 0.5 Panel A. Frm volatly Panel B. Frm volatly, MA(1) Fgure 7. Frm volatly, Denmark. Panel A shows the annualsed varance of each month from Jan 10 to Sep 5 calculated as FIRM t = w ˆ σ. The backwards twelve month movng average s shown n panel B. η Table XI confrms the mpresson from the vsual nspecton, of a posve trend over the sample, whch however s reversed by the end of the tme seres. 6

27 Table XI. Lnear trend estmaton, FIRM volatly tme seres Denmark Feb 80 - Sep Feb 80 - Dec Jan - Sep Lnear trend * *** 1.5*** -6.5*** t-value (6.43) (3.56) (-3.811) Fgure n the appendx reveals that the number of lsted frms n Denmark has fallen snce the early 10 s and the Hrfendahl-Hrchman ndces n fgure 9 show that the concentraton of frms n the market s U-shaped over the sample, the concentraton of ndvdual ndustres as a share of the market has decreased steadly and that the concentraton of frms whn ndustres exhbs peaks that concde wh the shape of the ndustry volatly component. The volatly decomposon n fgure 8 reveals that the total weghted average volatly of Dansh stocks has been relatvely constant except durng the md 10 s, the fnancal crss n the early 10 s and, especally, around the turn of the mllennum. The bottom panel shows that the relatve sze of the market component has been farly stable over tme, whereas the frm component ncreased up untl the md 10 s after whch s pushed back by the ndustry component Market Industry Frm Panel A. Volatlty decomposon, MA(1) Market Industry Frm Panel B. Volatlty decomposon, MA(1)