Journal of Banking & Finance

Journal of Bankng & Fnance 37 (203) 3733 3746 Contents lsts avalable at ScVerse ScenceDrect Journal of Bankng & Fnance journal homepage: www.elsever.com/locate/jbf Credt default swap spreads and varance rsk prema Hao Wang a,, Hao Zhou b,, Y Zhou c,2 a Tsnghua Unversty, School of Economcs and Management, 38 Welun Buldng, Bejng 00084, Chna b Tsnghua Unversty, PBC School of Fnance, 43 Chengfu Road, Hadan Dstrct, Bejng 00083, Chna c Florda State Unversty, Department of Fnance, College of Busness, Rovetta Busness Bldg, 353, 82 Academc Way, P.O. Box 3060, Tallahassee, FL 32306-0, USA artcle nfo abstract Artcle hstory: Receved 20 Aprl 202 Accepted 9 February 203 Avalable onlne 4 March 203 JEL classfcaton: G2 G3 G4 Keywords: Varance rsk prema Credt default swap spreads Opton-mpled varance Expected varance Realzed varance We fnd that the frm-level varance rsk premum has a promnent explanatory power for credt spreads n the presence of market- and frm-level control varables establshed n the exstng lterature. Such predctablty complements that of the leadng state varable the leverage rato and strengthens sgnfcantly wth a lower frm credt ratng, longer credt contract maturty, and model-free mpled varance. We provde further evdence that () the varance rsk premum has a cleaner systematc component than mpled varance or expected varance, (2) the cross-secton of frms varance rsk prema capture systematc varance rsk n a stronger way than frms equty returns n capturng market return rsk, and (3) a structural model wth stochastc volatlty can reproduce the predctablty pattern of varance rsk prema for credt spreads. Ó 203 Elsever B.V. All rghts reserved.. Introducton It has long been recognzed n the lterature that a crtcal component of systematc economc rsk may be mssng n credt rsk modelng (Jones et al., 984; Elton et al., 200; Colln-Dufresne et al., 200; Huang et al., 2003), whch s the man cause of the so-called credt spread puzzle. The relatvely larger spkes of hgh q We would lke to thank Turan Bal, Antje Berndt, Mchael Brennan, Darrell Duffe, Robert Geske, Bng Han, Jean Helwege, Robert Jarrow, George Jang, George Tauchen, Marlese Uhrg-Homburg, Jan Werner, Yelena Larkn, Luren Wu, Yuhang Xng, and Hong Yan; semnar partcpants at Tsnghua Unversty, the Unversty of Texas at Dallas, the Unversty of South Carolna, Baruch College, and Shangha Unversty of Fnance and Economcs; and conference partcpants at FDIC Dervatves and Rsk Management, the Fnancal Intermedaton Research Socety, the Chna Internatonal Conference n Fnance, the European Fnance Assocaton, the Fnancal Management Assocaton, and the Amercan Fnance Assocaton annual meetngs for helpful dscussons. We also thank Ellen Levy for edtng assstance. The authors acknowledge fundng support from the Global Assocaton of Rsk Professonals, the Centre for Hedge Fund Research at Imperal College London, the Specalzed Research Fund for the Doctoral Program of Hgher Educaton of Chna (Grant No. 2009000220025), and the Natonal Natural Scence Foundaton of Chna (Grant No. 7272023). Correspondng author. Tel.: +86 0 62797482. E-mal addresses: wanghao@sem.tsnghua.edu.cn (H. Wang), zhouh@pbcsf. tsnghua.edu.cn (H. Zhou), yzhou@cob.fsu.edu (Y. Zhou). Tel.: +86 0 62790655. 2 Tel.: + 850 644 7865. nvestment-grade credt spreads than speculatve-grade durng the recent fnancal crss hghlght a possble systematc shock that tends to explan the low-frequency cyclcal movements of credt spreads. In ths paper, we try to explan ndvdual frms credt spreads by the varance rsk premum (hereafter, VRP) and relate the VRP component of the credt spread to the exposure to systematc varance or economc uncertanty rsk (Bollerslev et al., 2009; Drechsler and Yaron, 20). VRP s defned as the dfference between expected varance under the rsk-neutral measure and expected varance under the objectve measure (see among others Brtten-Jones and Neuberger, 2000; Jang and Tan, 2005; Carr and Wu, 2008). Theoretcally, the varance rsk premum solates only frms exposure to systematc varance rsk that must be prced n all rsky assets snce, by constructon, the rsk-neutral and objectve expectatons of frms dosyncratc varance rsk cancel out wth each other. Emprcally, we estmate VRP as the dfference between the model-free opton-mpled varance and the expected varance based on the realzed measures estmated from hgh-frequency equty return data. We present robust evdence that frm-level VRP s the most promnent predctor for credt default swap (CDS) spread varatons relatve to the other macroeconomc and frm-specfc credt rsk determnants dentfed n the exstng lterature: VRP by tself predcts 29% of credt default spread varaton. Ths fndng echoes the recent studes that recognze the lnkage among 0378-4266/$ - see front matter Ó 203 Elsever B.V. All rghts reserved. http://dx.do.org/0.06/j.jbankfn.203.02.02

3734 H. Wang et al. / Journal of Bankng & Fnance 37 (203) 3733 3746 macroeconomc condtons, the equty rsk premum, and credt rsk prcng (see, e.g., Davd, 2008; Bhamra et al., 2009; Chen et al., 2009; Chen, 200), but our paper focuses on provdng cross-sectonal evdence of ndvdual frms. We also fnd that VRP complements the leverage rato, whch has been shown as a leadng explanatory varable for credt spreads (Colln-Dufresne and Goldsten, 200). Importantly, ths frm-level VRP measure crowds out the popular market VRP (or VIX) measure that has been shown as a strong predctor for aggregate credt spread ndces (Zhou, 2009; Burasch et al., 2009). Such predctve power turns out to be greater for speculatve-grade credt spreads, longer CDS contract maturtes, and VRPs constructed from model-free opton-mpled varances. The 2007 2008 sub-prme credt crss changed substantally the landscape of the CDS markets. We examne the consstency of the predctablty of VRP on CDS spreads before and after the crss. Durng both perods, VRP postvely and sgnfcantly predcts subsequent CDS spreads. Interestngly, the S&P 500 return, the aggregate credt prce ndex, and the fxed ncome market llqudty measure swtch to be sgnfcant n predctng frm CDS spreads after the crss, suggestng contagon n fnancal markets and that the ncrease n the perceved systemc rsk was manly drven by the heghtened rsk averson and lqudty squeeze (Longstaff, 200; Huang et al., 202). Prevous research suggests that mpled varance s nformatvely more effcent than realzed varance n predctng credt spreads (Cao et al., 200; Berndt et al., 2006; Carr and Wu, 200). However, by decomposng the mpled varance nto VRP and expected varance, we fnd that VRP can substtute for most of the explanng power of mpled varance, especally for lower frequences of monthly and quarterly horzons relatve to weekly. We also present evdence that the frst prncple component of VRP across all frms explans 79% of the total varaton, whle that of mpled varance only explans 58% and expected varance only 65%. Fnally, we show that, at the aggregate level, VRP Granger causes mpled and expected varances, but not vce versa. These addtonal fndngs mply that VRP may be an deal measure of frms exposures to a systematc varance rsk factor, and the economc nterpretaton of mpled varance n explanng credt spreads could largely rely on VRPs that are exposed to such a macroeconomc uncertanty rsk. To further corroborate the nterpretaton that frm VRPs are exposed to systematc uncertanty rsk, we provde two addtonal justfcatons. In the frst exercse, we run a two-pass regresson of ndvdual frms VRPs on the market VRP. The second-stage cross-sectonal regresson obtans an R 2 of 9%. In contrast, a smlar exercse wth frm equty returns obtans an R 2 of 4%. These results suggest that the cross-secton of frms varance rsk prema s able to capture systematc rsk factor(s) n a stronger way than frm equty returns n the CAPM framework. In another exercse, we smulate from a structural model wth stochastc volatlty and fnd that VRP can ndeed provde addtonal explanatory power for a representatve frm s credt spreads, even wth the control of a true leverage rato. On the contrary, the Merton model wthout stochastc volatlty cannot reproduce such a stylzed pattern found n our emprcal exercse. Our work s related to recent efforts to explan ndvdual frms credt spreads from several nnovatve angles. Campbell and Taksler (2003) fnd that ncreases n bond spreads can be explaned by the upward trend n dosyncratc equty volatlty. Cremers et al. (2008) rely on an opton-mpled jump rsk measure to nterpret the cross-sectonal varatons n default rsk premums. Ercsson et al. (2004) and Ercsson et al. (2006) explot credt dervatves n explanng credt spreads and evaluatng structural models. In partcular, Cao et al. (200) document that volatlty rsk prema (volatlty-based VRPs) strongly covary wth the CDS spreads. Our study shares the same sprt as thers n terms of rsk-based explanatons and fnds consstent results. We, however, emphasze usng VRP as a novel tool to solate the frm s exposure to systematc varance rsk from ts dosyncratc counterpart. We further demonstrate the consstency of VRP s predctve power before and after the sub-prme credt crss. Importantly, we document that the cross secton of frms varance rsk prema capture systematc varance rsk n a stronger way than frms equty returns n capturng market return rsk n the CAPM framework. Thus, our fndng provdes an economc nterpretaton for the superor predctve power of mpled varance on credt spread and ponts to a clear drecton for mprovng the structural credt rsk modelng by ncorporatng a systematc varance rsk factor. The rest of the paper wll be organzed as follows: Secton 2 ntroduces the varance rsk premum measure and our emprcal methodology, and t s followed by a descrpton of data sources and summary statstcs n Secton 3, Secton 4 then presents emprcal fndngs of varance rsk premums wth respect to predctng credt spreads and dscusses some economc nterpretatons, and Secton 5 concludes. 2. Varance rsk prema and emprcal methodology In ths secton, we ntroduce the concept of VRP for ndvdual frms, followng the recent lterature n defnng the market VRP as a dfference between the model-free mpled varance and the forecasted realzed varance. Then we outlne our emprcal strategy for explanng the CDS spreads of ndvdual frms, usng such a frm-specfc VRP varable, together wth other establshed market and frm control varables notceably the frm leverage rato and the rsk-free rate. 2.. Constructng the VRP measure for ndvdual frms To construct the benchmark measure of frm VRP, we compute the model-free mpled varances from the OptonMetrcs data of the ndvdual frms equty opton prces and the forecasted realzed varances from hgh-frequency stock returns of ndvdual companes. Followng Brtten-Jones and Neuberger (2000), we apply the Cox et al. (979), or CRR, bnomal lattce model to translate the Opton- Metrcs prces of Amercan call optons of dfferent maturtes and moneyness nto mpled volatltes. By fttng a smooth cubc splnes functon to the mpled volatltes, we compute the term structure of mpled volatltes at varous strkes for call optons of T-maturty. Then, the term structure of mpled volatltes are translated back nto the term structure of call prces at varous strkes usng the CRR model. Note that such a procedure s not model-dependent, as the CRR model serves merely as a mappng devce between opton prces and mpled volatltes (Jang and Tan, 2005). Wth the term structure of call opton prces, we compute rskneutral or model-free mpled varance by summng the followng functonal form over a spectrum of densely populated strke prces: IV ;t E Q t ½Varance ðt; t þ TÞŠ 2 Z 0 C ðt þ T; KÞ=Bðt; t þ TÞ max½0; S ;t =Bðt; t þ TÞ KŠ dk; K 2 ðþ where S,t denotes the stock prce of frm at tme t. C (t + T, K) denotes the opton prce of a call opton maturng at tme T at a strke prce K. B(t, t + T) denotes the present value of a zero-coupon bond that pays off one dollar at tme t + T. Ths way of calculatng

H. Wang et al. / Journal of Bankng & Fnance 37 (203) 3733 3746 3735 model-free mpled varance s vald as long as the underlyng stock prce follows a jump-dffuson process (Carr and Wu, 2008). In practce, the numercal ntegraton scheme can be set accordngly to a lmted number of strke prces to ensure that the dscretzaton errors have a mnmal effect on the estmaton accuracy of model-free mpled varance. 3 The model-free mpled varance could be more nformatve than the mpled varances usng only at-the-money (out-of-the-money or n-the-money) optons, as the model-free approach ncorporates the opton nformaton across dfferent moneyness (Jang and Tan, 2005). In order to defne the realzed varance that we use n estmatng the expected varance, let s,t denote the logarthmc stock prce of frm. The realzed varance over the [t, t] tme nterval may be measured as RV ;t Xn h 2 s ;t þ j s n ;t þ j! Varance ðt ; tþ; ð2þ n j¼ where the convergence reles on n? ;.e., an ncreasng number of wthn-perod prce observatons. 4 As demonstrated n the lterature (see, e.g., Andersen et al., 200a; Barndorff-Nelsen and Shephard, 2002), ths model-free realzed varance measure based on hgh-frequency ntraday data can provde much more accurate ex-post observatons of the ex-ante return varaton than those based on daly data. For a monthly horzon and monthly data frequency, where IV,t s the end-of-month rsk-neutral expected varance for frm of the next month, and RV,t s the realzed varance of the current month, we adopt a lnear forecast of the objectve or statstcal expectaton of the return varance as RV,t+ = a + biv,t + crv,t +,t+, and the expected varance s smply the tme t forecast of realzed varance from t to t + based on estmated coeffcents ^a and ^b n the lnear regresson, EV ;t E P t ½Varance ðt; t þ TÞŠ c RV ;tþ ¼ ^a þ ^biv ;t þ ^crv ;t ; where c RV ;tþ s the forecasted realzed varance of frm of the next month. We use ths partcular projecton because the model-free mpled varance from the optons market s an nformatonally more effcent forecast for the future realzed varance than the past realzed varance (see, e.g., Jang and Tan, 2005); whle the realzed varance based on hgh-frequency data also provdes addtonal power n forecastng the future realzed varance (Andersen et al., 200b). Therefore, a jont forecast model wth one lag of mpled varance and one lag of realzed varance seems to capture the most forecastng power from the tme-t avalable nformaton (Drechsler and Yaron, 20). The varance rsk premum of an ndvdual frm, or VRP,t, underlyng our key emprcal fndngs s defned as the dfference between the ex-ante rsk-neutral expectaton and the objectve expectaton of future return varaton over the [t, t + ] tme nterval, VRP ;t IV ;t EV ;t : Such a construct at the market level has been shown to possess remarkable capablty n forecastng the aggregate credt spread ndces (Zhou, 2009). Here we nvestgate n detal how the VRP of ndvdual frms can help us understand the cross secton of ndvdual frms CDS spreads. 3 We set the grd number n the numercal ntegraton at 00, although wth a reasonable parameter settng a grd number of 20 s accurate enough (Jang and Tan, 2005). 4 In practce, we use 5-mn returns, although for a smlar sample of 307 US frms usng 5-mn returns produces a smlar qualty estmaton of realzed varances (Zhang et al., 2009). ð3þ ð4þ 2.2. Emprcal mplementaton strategy We examne the relatonshp between the panels of CDS spreads and VRPs n the presence of market- and frm-level credt rsk determnants suggested by theory and emprcal evdence. We focus on monthly data to avod pckng up the market mcrostructure nose nduced by hgh-frequency comovements between opton and credt markets. For spreads and mpled varance, we use only the matched last-avalable end-of-month (daly) observatons. Because mssng dates and stale quotes sgnfy that daly or even weekly data qualty s not relable, and f we just gnore the daly mssng values, we wll ntroduce a seral-dependent error structure n the ndependent varable CDS spread, whch may artfcally ncrease the predcton R 2 or sgnfcance. Monthly data wll gve us a more conservatve but relable estmate and s typcally the shortest horzon compared wth quarterly or annual data for pckng up the low-frequency rsk premum movement. CDS spreads should also be nfluenced by the leverage rato of the underlyng frm and the rsk-free spot rate. As suggested by the structural form credt rsk models (e.g., Merton, 974), leverage s the most mportant credt rsk determnant all else beng equal, a frm wth hgher leverage has a hgher lkelhood of default (Colln-Dufresne and Goldsten, 200). The leverage rato, denoted by LEV,t, s computed as the book value of debt over the sum of the book value of debt and market value of equty. Moreover, structural models predct that rsk-free nterest rates negatvely nfluence the credt spread (Longstaff and Schwartz, 995) when the rsk-free rate s ncreasng, t typcally sgnfes an mprovng economc envronment wth better earnng growth opportunty for the frms, therefore a lower default rsk premum. Alternatvely, when the short rate s rsng, nflaton rsk s also ncreasng, and nomnal asset debt becomes less valuable compared to real asset equty (Zhang et al., 2009). We defne the rsk-free rate varable to be the -year swap yeld, denoted by r t. Emprcal research also shows that n practce, CDS spreads contan compensaton for non-default rsks as well as rsk premums, whch may be dffcult to dentfy wthout the aggregate macro varables. Henceforth, we wll not lmt our analyss to the tradtonal theoretcally motvated regressors but augment our set of varables by the followng market varables: () the market varance rsk premum based on the S&P 500 denoted by MVRP t to measure systemc varance or macroeconomc uncertanty rsk all else equal, hgh market VRP leads to hgh credt spreads (Zhou, 2009); 5 (2) the S&P 500 return, denoted by S&P t to proxy for the overall state of the economy when the economy s mprovng, the credt spread should be lower as proft s rsng (Zhang et al., 2009); (3) Moody s default premum slope, denoted by DPS t, s computed as Baa yeld spread mnus Aaa yeld spread to capture the default rsk premum n the corporate bond market the coeffcent of the default premum slope should be postve, consstent to the noton that CDS and corporate bond markets are contegrated (Blanco et al., 2005; Ercsson et al., 2004; Zhu, 2006); and (4) the dfference of the 5-year swap rate and the 5-year Treasury rate, denoted by STS t, as a proxy for fxed-ncome market llqudty, whch s expected to move postvely wth CDS spreads (Tang and Yan, 2008). For frm characterstc varables, besdes leverage rato, we nclude the followng controls: () asset turnover, denoted by ATO,t, s computed as sales dvded by total assets; (2) prce-earnngs 5 The market varance rsk premum s defned as the dfference between the rskneutral and objectve expectatons of the S&P 500 ndex varance (Zhou, 2009), where the rsk-neutral expectaton of varance s measured as the end-of-month observaton of VIX-squared and the expected varance under the objectve measure s a forecasted realzed varance wth an AR(2) process. Realzed varance s the sum of squared fve-mnute log returns of the S & P 500 ndex over the month. Both varance measures are n percentage-squared format on a monthly bass.

3736 H. Wang et al. / Journal of Bankng & Fnance 37 (203) 3733 3746 rato denoted by PE,t ; (3) market-to-book rato, denoted by MB,t ; (4) return on assets, denoted by ROA,t, computed as earnngs dvded by total assets; (5) the natural logarthm of sales, denoted by SALE,t. As a proxy for frm sze, SALE,t should nfluence CDS spread negatvely as larger and more mature frms tend to be nvestment grade n our sample, all else beng equal. Frm asset turnover, market-book rato, and return on assets are all expected to be negatvely related to CDS spreads, because frms of hgh proftablty and future growth tend to have lower credt rsk. The prce-earnngs rato may have two opposte effects on CDS spreads: on the one hand, a hgh prce-earnngs rato mples hgh future asset growth that reduce the lkelhood of fnancal dstress and credt rsk; on the other hand, hgh growth frms tend to have hgh return volatltes that ncrease credt rsk. These hypotheszed sgns of regresson coeffcents are consstent wth the basc Merton (974) model s mplcatons and are largely confrmed by the emprcal lterature (see, e.g., Colln-Dufresne et al., 200). Gven the nature of our cross-sectonal and tme-seres data, we adopt the robust standard error approach of Petersen (2009) to account for both frm and tme effects n large panel data sets. Therefore, the above dscussons suggest the followng one-month ahead forecastng regresson CDS ;tþ ; ¼ a þ b VRP ;t þ b 2 MVRP t þ b 3 LEV ;t þ b 4 S&P t þ b 5 r t þ b 6 DPS t þ b 7 STS t þ b 8 ATO ;t þ b 9 PE ;t þ b 0 MB ;t þ b ROA ;t þ b 2 SALE ;t þ e ;tþ ; and our focus s the relaton between a frm s CDS spread and ts VRP. 3. Data descrpton and summary statstcs To conduct the emprcal study, we collect data on credt default swap (CDS) spreads, equty opton prces, macroeconomc varables, frm equty, and balance sheet nformaton from varous sources. The summary statstcs of CDS spreads, varance rsk premums, and other market wde or frm-specfc controls, are dscussed here to set the background for examnng the crtcal lnk between CDS spreads and VRPs. 3.. Data sources Under a CDS contract, the protecton seller promses to buy the reference bond at ts par value when a predefned default event occurs. In return, the protecton buyer makes perodc payments to the seller untl the maturty date of the contract or untl a credt event occurs. Ths perodc payment, whch s usually expressed as a percentage (n bass ponts) of the bonds notonal value, s called the CDS spread. By defnton, a credt spread provdes a pure measure of the default rsk of the reference entty. We use CDS spreads as a drect measure of credt spreads. Compared wth corporate bond yeld spreads, CDS spreads are not subject to the specfcaton of the benchmark rsk-free yeld curve and are less contamnated by non-default rsk components (Longstaff et al., 2005; Ercsson et al., 2006). Our sngle-name CDS spreads are obtaned from a database compled by the Markt group. The data set also reports average recovery rates, used by data contrbutors n prcng each CDS contract, whch center around 0.4 wthout much varaton. The sample perod covers January 200 to December 20. We restrct our sample to US dollar-denomnated CDS wrtten on US enttes that are not n the government, fnancal, or utlty sectors. We further elmnate the subordnated class of contracts because of ts small relevance n the database and ts unappealng mplcatons for credt rsk prcng. The maturtes of Markt CDS contracts range ð5þ between 6 months and 30 years. We focus on the most popular and lqud 5-year CDS contracts wth modfed restructurng clauses n our benchmark analyss. CDS spreads of other contract maturtes rangng between and 0 years are relatvely lqud and are used for robustness checks. After cleanng and matchng the CDS data wth relable optons, equty, and balance sheet nformaton, we are left wth 3,4 monthly observatons of 382 enttes n our study. For each entty, the monthly CDS spreads are matched wth the monthly VRPs. The opton data s obtaned from Ivy DB OptonMetrcs. We keep only the optons whose last trade dates match the record dates and whose opton prce dates match the underlyng securty prce dates. We further elmnate the opton prces that volate arbtrage boundares (C 6 S Ke r T T ). Stock dvdend nformaton s acqured from CRSP and taken nto account when applyng the CRR model to extract the mpled volatlty surface. We compute hgh-frequency realzed varances usng nformaton n TAQ database that contans the ntraday equty tradng data spaced by 5 mn durng tradng hours. Followng the method outlned n the prevous secton, we frst calculate the daly varance based on the hgh-frequency data, then aggregate t to construct monthly realzed varance. Next, we estmate expected varance that s of the same maturty as the mpled varance. All types of VRPs are then matched wth CDS spreads on a frm-month bass. Market and frm control varables are the most recently avalable monthly or quarterly varables. Frm quarterly balance-sheet data are acqured from COMPUSTAT. Market varables the swap rates, constant maturty Treasury yelds, and Moody s Aaa and Baa yelds are acqured from the Federal Reserve Board s publc webste. S&P 500 ndex returns come from CRSP. The market VRP s from Zhou (2009). 3.2. Summary statstcs Table presents the summary statstcs the average across the 382 frms of the 5-year CDS spreads and our benchmark VRP measure (Panel A), model-free mpled varances and expected varances (Panel B). The average Moody s and S&P ratngs of the CDS reference enttes range between AAA and CCC. A majorty of the CDS ratngs are A, BBB, and BB (9%, 37%, and 25% respectvely, n total 8%). The average of CDS spreads n our sample s 49 bass ponts. They ncrease monotoncally from 27 to 589 bass ponts as the credt ratngs of the CDS reference enttes deterorate from AAA to CCC. The dfference between the average CDS spreads for AAA grade and AA grade s 0 bass ponts, whereas the dfference between those for CCC grade and B grade s 89 bass ponts. The CDS spreads dsplay postve skewness of around.27 and leptokurtoss of 5.2. Smlar to the CDS spreads, the VRP dsplays sgnfcant varatons across ratng groups. The average of the benchmark VRP measure for the full sample s 34.73 (monthly percentage squared), ncreasng from 9.43 to 03.50 as CDS reference enttes credt ratngs drop from AAA to CCC. Hgh credt rsk enttes tend to be assocated wth hgh VRPs. The varance rsk prema dsplay postve skewness of.44 and leptokurtoss of 7.7. As shown n Panel B of Table, the means and standard devatons of model-free mpled varances are much hgher than those of expected varances, but the skewness and kurtoss are smlar. The results suggest that mpled varance could contan a larger dosyncratc component than expected varance. The AR() coeffcents for VRP, model-free mpled, and expected varances are 0.75, 0.93, and 0.93 respectvely, suggestng that VRP s less persstent compared wth model-free mpled varances and expected varances. We group our sample nto three sub-samples by CDS ratngs. The frst group contans CDS of AAA, AA and A grades, the second

H. Wang et al. / Journal of Bankng & Fnance 37 (203) 3733 3746 3737 Table Descrptve statstcs CDS spreads, varance rsk premum, mpled varance and expected varance. Ths table presents the summary statstcs average across the 382 frms of the 5-year CDS spreads and our benchmark Varance Rsk Premum (VRP) measure (Panel A), model-free mpled varances and expected varances (Panel B). The CDS spreads are n bass ponts. The VRP s computed as the spread between model-free mpled varance and expected varance. The mpled varance s the model-free mpled varance. The expected varance s the lnear forecast of realzed varance by lagged mpled and realzed varance. The average Moody s and S&P ratngs of the CDS reference enttes range between AAA and CCC. The numbers of frms n each ratng category are reported n the second column n Panel A. AR() denotes autocorrelaton wth one lag. Ratng Frm number CDS spread VRP Mean SD Skew. Kurt. AR() Mean SD Skew. Kurt. AR() Panel A: The means of the statstcs of CDS spreads and VRP across ndvdual frms AAA 7 27.0 2.70 2.07 9.44 0.96 9.43.2.89.2 0.53 AA 7 37.6 22.98.54 6.7 0.98.24 2.40.54 7.29 0.62 A 0 45.53 29.8.46 6.09 0.99 9.86 9.24.72 8.0 0.69 BBB 99 98.77 55.4.23 4.98 0.98 29.72 25.04.38 6.54 0.74 BB 33 25.33 05. 0.90 4.05 0.98 48.70 32.35 0.96 4.97 0.77 B 65 400.04 32.04 0.30 2.8 0.99 67.64 40.83 0.50 3.70 0.8 CCC 4 588.79 37.37 0.64 4.8 0.96 03.50 43.4 0.24 2.49 0.88 Total 382 49.2 79.98.27 5.2 0.98 34.73 28.3.44 7.7 0.75 Ratng Impled varance Expected varance Mean SD Skew. Kurt. AR() Mean SD Skew. Kurt. AR() Panel B: The means of the statstcs of IV and EV across ndvdual frms AAA 46.64 34.84 2.26 9.56 0.90 37.4 26.74 2.53.78 0.92 AA 56.29 40.23.94 7.0 0.9 45.03 32.85.94 7.0 0.9 A 8.85 59.75 2.08 8.38 0.92 6.92 46.20 2.45.8 0.94 BBB.38 73.48.8 7.02 0.92 8.46 55.8.99 8.28 0.93 BB 75.6 9.7.38 5.22 0.95 27.4 72.59.49 5.68 0.94 B 226.28 09.97 0.99 3.53 0.98 56.87 82.72.03 3.84 0.97 CCC 36.37 02.60 0.7 3.26 0.95 2.6 74.88 0.99 4.0 0.94 Total 27.94 84.6.93 7.37 0.93 73.2 64.97 2.2 9.40 0.93 group contans CDS of BBB grade, and the thrd group contans CDS of speculatve grades rangng between BB and CCC. The three subsamples contan 8750,,9, and 680 frm-month observatons, respectvely. Fg. plots the tme-seres of the 5-year CDS spreads of a whole sample and three sub-groups. The CDS spreads decrease gradually from the peaks n late 2002, then ncrease agan as the fnancal crss approaches n md-2007 and reaches peaks n early 2009. The spreads of CDS n year 2009 are hgher than those n year 2002, more so for nvestment grades. Ths pattern hghlghts the systematc nature of the recent fnancal crss, whch s manly fueled by the heghtenng of systematc rsk or economc uncertanty and affects dsproportonately the hgh nvestment-grade Bass ponts 0 00 200 300 400 500 2000 2002 2004 2006 2008 200 202 Tme All BBB AAA~A BB~CCC Fg.. Tme seres of 5-year CDS spreads. Ths fgure plots the 5-year CDS spreads of full sample and three sub-samples. We group the CDS spreads nto three subsamples by CDS ratngs. The frst group contans CDS of AAA, AA and A grades. The second group contans CDS of BBB grade. The thrd group contans CDS of speculatve grades rangng between BB and CCC. The three sub-samples contan 8750,,9 and 680 observatons respectvely. credt spreads. The dfference between the nvestment-grade and speculatve-grade CDS spreads, however, wdened durng the perod of 2007 2009, potentally because the flght-to-qualty effect durng the fnancal crss that drove up the compensaton for credt rsk. Fg. 2 further llustrates the dynamc relatonshps among CDS spreads, VRP, market VRP, and the leverage rato for a representatve frm n our sample: Aloca. The CDS spread lne and VRP lne resemble each other closely over tme. In partcular, the two lnes move closely n the recent fnancal crss. In addton, the CDS spreads tend to comove wth the frm s leverage rato. A vsual examnaton of the relatonshp between CDS spreads and market VRP suggests that market rsk premum, market VRP n partcular, may not provde a powerful predcton about Alcoa s credt spreads. For nstance, the two lnes move n exactly opposte drectons n late 2009. Table 2 reports the descrptve statstcs for our market- and frm-level control varables; the latter are averaged across 382 enttes. The average monthly market VRP s 6.94 (percentagesquared). The average -year swap rate s 2.88%. The frms n our sample have an average leverage rato of 42% wth a standard devaton of 8%. For smplcty, we omt the dscusson of other control varables, gven that they are smlar to those reported n lterature. Table 3 reports the unvarate correlatons of the regresson varables and shows that the CDS spread s postvely correlated to VRP, mpled varance (IV) and expected varance (EV). VRP s sgnfcantly correlated to IV (0.82), and less correlated to EV (0.63). Such a pattern suggests that VRP and EV may capture dfferent rsk components embedded n IV. Among credt rsk determnants, VRP, and leverage have hgh correlatons wth CDS spreads, whereas other varables exhbt lower correlatons, suggestng that the two varables may possess sgnfcant explanatory power for credt rsk. CDS spreads are postvely correlated wth market VRP (0.30), but the coeffcents of market VRP turn out to be nsgnfcant n the presence of frm-level VRP n the multvarate regressons n the next secton.

3738 H. Wang et al. / Journal of Bankng & Fnance 37 (203) 3733 3746 CDS spreads (bps) 0 200 400 600 800 0 00 200 300 VRP CDS spreads (bps) 0 200 400 600 800 30 40 50 60 70 80 Leverage Rato (%) 2000 2002 2004 2006 2008 200 202 Tme 2000 2002 2004 2006 2008 200 202 Tme CDS VRP CDS Leverage Rato CDS spreads (bps) 0 200 400 600 800 2000 2002 2004 2006 2008 200 202 Tme 0 50 00 50 200 250 VIX Square CDS spreads (bps) 0 200 400 600 800 2000 2002 2004 2006 2008 200 202 Tme 50 0 50 00 Market VRP CDS VIX Square CDS Market VRP Fg. 2. Tme seres of CDS spreads, VRP, leverage rato, MVRP and VIX for General Motor Ltd. Ths fgure llustrates the dynamc relatonshps between CDS spreads and VRP, market VRP, VIX and leverage rato for a representatve frm n our sample: ALCOA. Table 2 Summary statstcs market and frm control varables. Ths table reports the descrptve statstcs of the market- and frm-level control varables. For frm characterstcs, we report the averages of the statstcs across 382 frms. The market VRP s the dfference between mpled varance and expected varance of the S&P 500 ndex as n Bollerslev, Tauchen and Zhou (2009). The S&P 500 return, s the proxy for the overall state of the economy. The one year swap rate s the proxy for the rsk-free nterest rate. The Moody s default premum slope, defned as Baa yeld spread mnus Aaa yeld spread s the default rsk premum n the corporate bond market. The dfference of 5-year swap rate and 5-year Treasury rate s a proxy for fxed ncome market llqudty. Leverage rato s computed as book value of debt over the sum of book value of debt and market value of equty. The asset turnover s computed as sales dvded by total assets. The prce-earnngs rato s the rato of prce over earnngs. The market-to-book rato s the rato of market equty to book equty. The return on assets s computed earnngs dvded by total assets. AR() denotes autocorrelaton wth one lag. Varable Mean SD Skewness Kurtoss AR() Market level Market VRP (%) 6.94 2.73 2.3 2.39 0.53 S&P 500 return (%) 3.45 7.30 0.44 3.2 0.93 Swap ( year, %) 2.88.65 0.20.8 0.99 Baa Aaa (%).3 0.46.94 7.20 0.99 Swap CMT (5 year, %) 0.5 0.25 0.47 3.5 0.9 Frm level Leverage rato 0.42 0.08 0.39 2.90.00 Asset turnover (%) 0.97 0.4 0.0 2.94 0.99 Prce-earnngs rato 5.24 2.80 0.9 7.00 0.86 Market/book rato 2.9 7.29 0.37 3.44 0.99 Return on assets (%) 0.05 0.04 0.49 3.4 0.97 Annualzed sales ($ bllon) 2.85 2.92 0.0 2.92.00 Frm assets ($ bllon) 5.70 3.52 0.2 3.0.00 4. Emprcal results and analyss In ths secton, we show that frm-level VRP dsplays a sgnfcant predctve power for CDS spreads n the presence of all other credt rsk determnants. In partcular, VRP complements the frm leverage rato that has been shown as the leadng explanatory varable for credt spreads by Colln-Dufresne and Goldsten (200) wthn the Merton (974) framework. VRP crowds out the market-level varaton rsk measure market VRP n capturng the systematc varance rsk embedded n CDS spreads. The predctve power of VRP for CDS spreads s unchanged before and after the sub-prme crss, and ncreases as frm credt qualty deterorates. Model-free VRP performs better than the VRP mpled from call or put optons of dfferent moneyness. Further robustness checks suggest that VRP and expected varance are two ndspensable components of the opton-mpled varance n predctng the ndvdual frms credt spreads. In addton, VRP seems to possess more forecastng power at monthly and quarterly horzons whle mpled varance possesses more at weekly horzons, and n aggregate, the market VRP Granger-causes mpled and expected varances. Furthermore, the frm-level VRP measure contans a cleaner systematc factor component than ether mpled varance or expected varance, and the systematc varance rsk seems to be prced by the cross-secton of frm-level VRPs n a stronger way than the market return rsk by frm equty returns. Fnally, our emprcal fndng can be qualtatvely justfable by smulaton evdence from a structural model wth stochastc asset varance rsk.

H. Wang et al. / Journal of Bankng & Fnance 37 (203) 3733 3746 3739 Table 3 Unvarate correlatons of the regresson varables. Ths table reports the unvarate correlatons of the regresson varables. CDS denotes 5-year maturty CDS spread. VRP denotes frm level varance rsk premum constructed wth model free mpled varance IV mnus expected varance EV estmated wth hgh frequency equty returns. MVRP represents market varance rsk premum. S&P and r denote S&P 500 return and swap rate of -year maturty respectvely. DPS represents default rsk premum measured as the spread between Moody s Baa and Aaa rates. STS s the spread between 5-year swap and constant maturty Treasury rates. LEV denotes market leverage. ATO, PE, MB and ROA denote asset turnover, prce-earnngs rato, market-book rato and return on assets respectvely. SALE s the natural logarthm of annual sales. CDS VRP IV EV MVRP S&P r DPS STS LEV ATO PE MB ROA SALE CDS.00 VRP 0.48.00 IV 0.66 0.82.00 EV 0.64 0.63 0.97.00 MVRP 0.30 0.4 0.49 0.46.00 S&P 0.47 0.42 0.65 0.65 0.33.00 r 0.49 0.29 0.29 0.24 0.23 0.04.00 DPS 0.65 0.40 0.73 0.75 0.28 0.73 0.29.00 STS 0. 0.3 0.34 0.39 0.9 0.42 0.33 0.28.00 LEV 0.58 0.33 0.43 0.37 0.8 0.32 0.46 0.43 0.03.00 ATO 0.2 0.06 0.04 0.03 0.02 0.0 0.24 0.03 0.7 0.35.00 PE 0.8 0.09 0.6 0.5 0.06 0.2 0.0 0.7 0.0 0.23 0.0.00 MB 0.43 0.27 0.38 0.33 0.4 0.28 0.32 0.34 0.05 0.79 0.23 0.8.00 ROA 0.30 0.2 0.5 0. 0.07 0.08 0.25 0.06 0.09 0.55 0.45 0.02 0.46.00 SALE 0.04 0.00 0.02 0.04 0.08 0.07 0.02 0. 0. 0.05 0.60 0.08 0.37 0.34.00 4.. The benchmark regressons Table 4 reports the regresson results of the relatonshp between 5-year CDS spreads and benchmark VRP computed wth model-free mpled varance mnus expected varance estmated from lagged mpled and realzed varances (see Secton 2). Regresson reports that CDS spreads are postvely related to VRP n the unvarate regresson. The t-statstc s a sgnfcant 4.0. In terms of economc sgnfcance, one standard devaton ncrease n VRP (28.3) wll ncrease CDS spreads by 60.76 bass ponts. Regresson 2 shows that leverage rato s ndeed hghly sgnfcant, as the leadng determnant of credt spread levels and changes (Colln-Dufresne and Goldsten, 200; Colln-Dufresne et al., 200); however, ncludng leverage rato n the regresson stll preserves the hgh sgnfcance of the VRP measure (regresson 3). Regresson 4 ndcates that market VRP postvely predcts CDS spreads. However, regresson 5 shows that the relatonshp between CDS spreads and VRP remans ntact n the presence of market VRP. More mportant, market VRP s nsgnfcant, suggestng frm VRP subsumes market VRP n terms of capturng the exposure to systematc varance rsk n predctng CDS spreads. Ths fact remans true wth the control of leverage rato (regresson 6). As ndcated n Zhou (2009) and Burasch et al. (2009), market VRP predcts a sgnfcant postve rsk premum n market credt spreads, whch s consstent wth our frm level evdence here. Regresson 7 reports the full-scale regresson results after ncludng all control varables. The coeffcent of VRP decreases slghtly from 2.6 n the unvarate regresson to.38 but remans statstcally sgnfcant at the % level wth a robust t-statstc of 9.08. Among the market level control varables, the S&P 500 return, Table 4 The CDS spreads and VRP. Ths table reports the regresson results of 5-year CDS spreads on the VRP computed wth model free mpled varance IV mnus expected varance EV estmated wth hgh frequency equty returns. Regresson () s the unvarate regresson of VRP; regresson (2) s the unvarate regresson of leverage; regresson (3) shows the relatonshp between CDS spreads and VRP n the presence of leverage only; regresson (4) s the unvarate regresson of market VRP; regresson (5) shows the relatonshp between CDS spreads and VRP n the presence of market VRP; regresson (6) further ncludes leverage nto regresson (5); and regresson (7) ncludes all other control varables. We adjust two-dmensonal (frm and tme) clustered standard errors n the regressons as n Petersen (2009). The numbers n the brackets are t-statstcs. Independent varable Regresson () (2) (3) (4) (5) (6) (7) VRP 2.6.64 2.6.63.38 (4.0) (.56) (3.66) (.25) (9.08) Leverage 4.69 3.62 3.63 3.30 (.90) (.6) (.59) (9.73) Market VRP 0.83 0.0 0.06 0.06 (3.25) (0.03) (0.22) (0.28) S&P 500 return 0.94 (4.36) Swap rate ( year).98 (.08) Baa Aaa 37.88 (4.2) Swap CMT (5 year) 39.8 (3.3) Asset turnover rato 7.78 (.36) Prce-earnngs rato 0.0 (.2) Market/book rato 0.00 (2.56) Return on assets 90.2 ( 3.63) Log sales 9.84 ( 5.38) Adjusted R 2 0.29 0.3 0.47 0.02 0.29 0.47 0.5

3740 H. Wang et al. / Journal of Bankng & Fnance 37 (203) 3733 3746 the spread between Baa and Aaa ndexes, and the market llqudty measure are statstcally nsgnfcant. For frm-level controls, return on assets and log sales are statstcally sgnfcant at the % level. The results support the ntuton behnd the structural-form credt rsk models n that frms wth hgher proftablty tend to have a relatvely smaller chance of default, hence a lower credt rsk premum. The adjusted R 2 for the unvarate regresson of VRP ndcates that 29% of the varaton n CDS spreads can be accounted for by the frm-specfc VRP, whch may capture a frm s exposure to systematc varance rsk. In comparson, the adjusted R 2 for the unvarate regresson of leverage s 3%, whle the adjusted R 2 for market VRP s 0.02. Addng market VRP to the regresson has no effect on the adjusted R 2, whch remans at 29%. Ths result suggests that frm-level varaton rsk measure has much stronger explanatory power for ndvdual frm s CDS spreads compared wth the well-documented market-level varaton rsk measure. Includng leverage rato n the regresson ncreases the adjusted R 2 to 0.47, possbly capturng the frm-specfc default rsk on top of systematc rsk n the sprt of Merton (974). Addng all other control varables ncreases the adjusted R 2 sghtly to 0.5. It appears that, among all varables, frm-level VRP and leverage rato are the two most powerful explanatory varables affectng CDS spreads. The 2007 2008 sub-prme credt crss sgnfcantly changed the landscape of the CDS markets. We, therefore, dvde our sample nto pre- and post-sub-prme crss perods to examne whether the predctablty of VRP on CDS spreads holds strong durng both perods. Table 5 reports that durng both perods, VRP postvely and sgnfcantly predcts subsequent CDS spreads. Its predctve power s pretty much unchanged, evdenced by the t-statstcs and R 2 s reported n Columns () and (4). The results reported n (3) and (6) confrm VRP s strong predctve power on credt spreads n the presence of the control varables. Interestngly, some of the control varables become sgnfcant after the sub-prme crss. For example, the S&P 500 return, the aggregate credt prce ndex (Baa Aaa), and the market llqudty measure swtch to be sgnfcant. The result adds evdence to contagon n fnancal markets after the sub-prme crss and echoes that noton that the ncrease n the perceved systemc rsk was manly drven by the heghtened rsk averson and the squeezed lqudty (Longstaff, 200; Huang et al., 202). 4.2. Robustness checks It s an mportant fndng that VRP explans a sgnfcant porton of credt rsk premum, whch may be orthogonal to the asset return rsk that s already beng captured by the leverage rato. In ths secton, we conduct a seres of robustness checks that such a fndng s relable f we consder dfferent credt ratng enttes and s robust to dfferent CDS contract maturtes, mpled varances constructed from dfferent optons and moneyness. The credt spreads of low-qualty ssuers are lkely to respond more to underlyng varance rsk shocks captured by VRP. Therefore, we regress 5-year CDS spreads on VRP for three sub-samples respectvely: AAA-A (hgh nvestment grade), BBB (low nvestment grade), and BB-CCC (speculatve grade), based on the average CDS ratngs of Moody s and S&P. Table 6 presents both the bvarate regresson results on frm VRP and leverage rato and the multvarate regresson results on VRP wth all control varables. In both sets of regressons, the coeffcents of VRP are hghly sgnfcant and ncrease monotoncally as the CDS ratngs deterorate. VRP exhbts much stronger predctablty on the credt spreads of the CDS wrtten on bonds ssued by low-credt-qualty enttes. The coeffcents of VRP for the lowest ratng group BB-CCC are almost fve to seven tmes larger than those for the hghest ratng group AAA-A and at least twce larger than those for the mddle ratng group BBB. Consstent wth the benchmark regressons, leverage rato plays a sgnfcant role n affectng CDS spreads. The lower the credt qualty of ssung enttes, the larger postve effect the leverage rato has on the CDS spreads. We examne the relatonshp between CDS spreads and VRP for dfferent CDS maturtes. Table 7 reports the regresson results by CDS maturty terms:, 2, 3, 5, 7, and 0 years. In all of these regressons, CDS spreads are correlated postvely and sgnfcantly wth Table 5 Before and after the fnancal crss. Ths table reports the regresson results of 5-year CDS spreads on VRP before and after the 2007 2008 sub-prme crss. We defne year 200 2006 as the pre-crss perod and year 2007 20 as the crss and post-crss perod. Two-dmensonal (frm and tme) clustered standard errors n the regressons are adjusted as n Petersen (2009). The numbers n the brackets are t-statstcs. Year 200 2006 Year 2007 20 () (2) (3) (4) (5) (6) VRP 2.29 2.03.85 2.6.63.38 (.9) (.35) (9.4) (4.0) (.25) (9.08) Leverage 2.69 2.48 3.63 3.30 (9.58) (7.57) (.59) (9.73) Market VRP 0.87 0.65 0.06 0.06 ( 4.06) ( 3.72) (0.22) (0.28) S&P 500 return 0.08 0.94 (0.42) (4.36) Swap Rate ( year) 2.42.98 (.78) (.08) Baa Aaa 7.42 37.88 (.44) (4.2) Swap rate CMT (5 year) 3.80 39.8 ( 0.4) (3.3) Asset turnover rato 0.85 7.78 ( 0.6) (.36) Prce-earnngs rato 0.0 0.0 (.05) (.2) Market/book rato 0.00 0.00 (2.56) (2.56) Return on asset 86.90 90.20 ( 2.88) ( 3.63) Log sales 2.29 9.84 ( 3.26) ( 5.38) Adjusted R 2 0.34 0.50 0.53 0.29 0.47 0.5

H. Wang et al. / Journal of Bankng & Fnance 37 (203) 3733 3746 374 Table 6 CDS spreads and VRP by CDS ratng. Ths table reports the regresson results of CDS spreads on VRP for three sub-samples: AAA-A, BBB, BB-CCC. The ratngs are the average of Moody s and S&P ratngs. Two-dmensonal (frm and tme) clustered standard errors n the regressons are adjusted as n Petersen (2009). The group AAA-A has 8750 observatons. The group BBB has,9 observatons. The group BB-CCC has 680 observatons. The frst three regressons are the regressons of VRPs and leverage. The second three regressons are the multvarate regressons wth all the control varables. The numbers n the brackets are t-statstcs. Independent varable Regresson by ratngs AAA-A BBB BB-CCC AAA-A BBB BB-CCC VRP 0.66 0.94.28 0.37 0.66.0 (5.98) (8.80) (8.36) (3.97) (6.46) (6.05) Leverage 0.89.57 5.89 0.9.23 5.83 (5.6) (7.75) (2.) (5.40) (5.40) (0.43) Market VRP 0.2 0.4 0.43 (.4) (.3) (.28) S&P 500 return 0.29 0.07 0.63 (2.74) (0.3) (.59) Swap rate ( year) 4.22 7.39 9.23 ( 5.3) ( 5.0) ( 2.57) Baa Aaa 29.77 30.86 35.92 (5.9) (3.23) (2.3) Swap CMT (5 year) 2.59 24.89 98.20 (3.44) (2.89) (5.03) Asset turnover rato.30 6.80 3.72 (0.63) (.39) (.00) Prce-earnngs rato 0.00 0.0 0.0 ( 2.04) (.54) ( 0.69) Market/book rato 0.00 0.00 0.00 (3.95) (0.4) (2.37) Return on assets 5.07 59.42 73.40 (2.29) ( 0.94) ( 2.7) Log sales 2.63 2.73 7.46 ( 2.22) ( 0.76) ( 0.80) Adjusted R 2 0.26 0.24 0.47 0.43 0.32 0.5 Table 7 The CDS spreads of dfferent maturty terms and VRP. Ths table reports the regresson results of CDS spreads of all maturtes on the VRP computed wth model free mpled varance IV mnus expected varance EV estmated wth hgh frequency equty returns. We adjust two-dmensonal (frm and tme) clustered standard errors n the regressons as n Petersen (2009). The numbers n the brackets are t-statstcs. Independent varable CDS spreads -year 2-year 3-year 5-year 7-year 0-year Panel A: Unvarate regressons VRP.64.85 2.03 2.6 2.9 2.8 (4.5) (4.6) (4.43) (4.0) (3.66) (3.20) Adjusted R 2 0.28 0.29 0.30 0.29 0.29 0.29 Panel B: Multvarate regressons VRP 0.96.3.28.38.4.40 (8.56) (8.60) (8.90) (9.08) (8.98) (8.82) Leverage.88 2.32 2.7 3.30 3.36 3.47 (8.6) (8.43) (9.00) (9.73) (9.5) (9.7) Market VRP 0.02 0.03 0.03 0.06 0.09 0. (0.3) (0.5) (0.3) (0.28) (0.45) (0.54) Controls Yes Yes Yes Yes Yes Yes Adjusted R 2 0.46 0.48 0.50 0.5 0.5 0.5 frm-level VRP and leveraged rato. The t-statstcs confrm that the frm-level VRPs perform much better than the market-level VRP n predctng ndvdual frm credt spreads. 6 In general, the longer the maturty of a CDS contract, the more sgnfcant the economc effect of frm-level VRP on CDS spreads wth larger slope coeffcents and hgher adjusted R 2 s. It s ntutve that a CDS contract of longer maturty s relatvely more exposed to the varance uncertanty rsk and hence requres a larger spread compensaton. 6 In another robustness check, we substtute VIX (monthly squared n percentage) for the market-level VRP n the regressons. The unreported results show that the strong predctablty of VRP on CDS spreads remans ntact n the presence of VIX. Importantly, CDS spreads are negatvely correlated to VIX wth near zero adjusted R 2. Ths result s dfferent from prevous research that fnds a postve relatonshp between CDS spreads and VIX (Ercsson et al., 2006) n the absence of frm-level VRP. To check the extent to whch the sgnfcance of the explanatory power of VRP on credt spreads depends on dfferent methods of constructng VRP, we carry out a regresson analyss of CDS spreads on VRPs constructed wth varous opton features. Besdes the benchmark model-free mpled varance, we use mpled varances computed from out-of-the-money, at-the-money, and n-themoney put/call optons. As reported n Table 8, all VRP measures dsplay consstently sgnfcant predctablty for CDS spreads n the presence of other credt rsk predctors. Among them, the VRPs constructed wth model-free mpled varance dsplays the strongest predctng power on CDS spreads, reflected n both t-statstcs and adjusted R 2 s. The model-free mpled varance s nformatonally more effcent than the mpled varance from at-the-money (out-of-the-money or n-the-money) optons alone, as t ncorporates by constructon the opton nformaton across all moneyness.

3742 H. Wang et al. / Journal of Bankng & Fnance 37 (203) 3733 3746 Table 8 CDS spreads and VRPs of dfferent mpled varances. Ths table reports the regresson results of CDS spreads on VRPs computed from dfferent measures of mpled varances. Besdes the benchmark VRP computed from model-free mpled varance, we use VRP constructed from mpled varances of out-of-the-money (OTM), at-the-money (ATM) and n-the-money (ITM) put optons, together wth those of out-of-the-money (OTM), at-the-money (ATM) and n-the-money (ITM) call optons. We adjust two-dmensonal (frm and tme) clustered standard errors n the regressons as n Petersen (2009). The numbers n the brackets are t-statstcs. Independent varable Regresson () (2) (3) (4) (5) (6) (7) VRP.38 (9.08) VRP Put OTM 0.93 (8.42) VRP Put ATM.64 (8.56) VRP Put ITM 0.67 (6.39) VRP Call OTM 0.85 (4.96) VRP Call ATM.47 (8.57) VRP Call ITM 0.53 (6.28) Leverage 3.33 3.29 3.35 3.65 3.58 3.42 3.53 (9.73) (9.06) (9.44) (9.36) (9.06) (9.50) (9.0) Market VRP 0.06 0.07 0.3 0.28 0.30 0.08 0.06 (0.28) (0.42) (0.67) (.95) (.58) (0.37) (0.30) Controls Yes Yes Yes Yes Yes Yes Yes Adjusted R 2 0.5 0.49 0.50 0.45 0.45 0.49 0.46 Table 9 VRP vs. mpled varance and expected varance. Ths table compares the predctablty of VRP on CDS spreads to that of model-free mpled and expected varances for 5-year maturty CDS spreads. Regressons () (3) report the multvarate regresson results for VRP, mpled and expected varances, along wth all control varables. Regressons (4) (6) report the regresson results of CDS spreads on each pars of VRP, mpled and expected varances respectvely, along wth all control varables. We adjust two-dmensonal (frm and tme) clustered standard errors n the regressons as n Petersen (2009). The numbers n the brackets are t-statstcs. Independent varable () (2) (3) (4) (5) (6) VRP.38 0.7 0.93 (9.08) (.28) (7.47) MFIV 0.8 0.77 0.88 (3.63) (2.43) (7.65) EV 0.94 0.0 0.78 (2.48) ( 0.80) (2.35) Leverage 3.30 2.7 2.89 2.7 2.7 2.70 (9.73) (8.93) (8.43) (9.03) (8.99) (9.0) Market VRP 0.06 0.3 0.20 0.30 0.30 0.32 (0.28) (.92) (.46) (.87) (.88) (.97) Controls Yes Yes Yes Yes Yes Yes Adjusted R 2 0.5 0.59 0.56 0.59 0.59 0.59 4.3. Impled varance, expected varance, and VRP Prevous studes fnd that an ndvdual frm s CDS spread s strongly related to the opton-mpled volatltes, whch s consstent wth the nformaton effcency argument for the optons market (see, e.g., among others Cao et al., 200). However, n ths subsecton, we try to argue from several emprcal angles that the explanng power of VRP for credt spread comes manly from capturng a systematc rsk component and tends to be long run. Also on the market level, VRP Granger causes mpled varance but not the other way around. To nvestgate ths ssue, we frst carry out regressons n whch VRP competes aganst mpled varance and expected varance. Table 9 reports the results of regressng CDS spreads on those varables. The results of regresson () (3) ndcate that wth all control varables, VRP, mpled varance, and expected varance explan 5%, 59%, and 56% of the varatons n CDS spreads, respectvely. In regresson (4) and (5), we test the predctablty of VRP or expected varance on CDS spreads n the presence of mpled varance. The coeffcent of VRP remans postve, whle that of expected varance turns negatve. In regresson (6), we regress CDS spreads smultaneously on VRP and expected varance. The coeffcents of both VRP and expected varance are postve and statstcally sgnfcant at the % level, suggestng that VRP and expected varance are two mportant components n mpled varance that help to explan ndvdual frm credt spreads. If VRP better captures a systematc rsk factor than mpled varance, we mght observe that the explanatory power of VRP on CDS spreads ncreases as data frequency becomes lower, snce systematc rsk tends to be long term yet nformaton shocks to the optons market tend to be short lved. Panel A of Table 0 confrms such ntuton by showng that, n unvarate regressons, the t-statstcs of VRP ncreases monotoncally from 6.44 to 0.4 as the sample frequency changes from weekly to monthly then to quarterly. In the presence of mpled varance, the t-statstcs of VRP ncrease consstently, whle the t-statstcs of mpled varance keep decreasng as the samplng frequency lowers. In both sets of regressons, the adjusted R 2 ncreases for lower data frequency. Fnally, at weekly frequency, mpled varance mproves the predctablty of VRP by 2 percentage ponts; but at monthly and quarterly frequences, the mprovement s only 5 percentage ponts.