Sock Reurn Expecaions in he Credi Marke Hans Bysröm * Sepember 016 In his paper we compue long-erm sock reurn expecaions (across he business cycle) for individual firms using informaion backed ou from he credi derivaives marke. Our mehodology builds on previous heoreical resuls in he lieraure on sock reurn expecaions and, empirically, we demonsrae a close relaionship beween credi-implied sock reurn expecaions and fuure realized sock reurns. We also find sock porfolios seleced based on credi-implied sock reurn forecass o bea equally- and value-weighed porfolios of he same socks ou-of-sample. Conrary o many oher sudies, our expecaions/predicions are made a he individual sock level raher han a he porfolio level, and no parameer esimaions using hisorical sock price- or credi spread observaions are needed. Keywords: sock marke; credi defaul swap; implied volailiy; CrediGrades; reurn expecaions JEL classificaion codes: G10; G01 * Hans Bysröm is from he Deparmen of Economics, Lund Universiy, Box 708, 007 Lund, Sweden (hans.bysrom@nek.lu.se). Financial assisance from The Marianne and Marcus Wallenberg Foundaion and Handelsbankens Forskningssifelser is graefully acknowledged. Pars of his paper were wrien when he auhor visied Chulalongkorn Universiy. All misakes in his aricle are he auhor s. 1
The goal of his paper is o demonsrae how one can compue, or explain, long-erm sock reurn expecaions (across he business cycle) using informaion from he credi derivaives marke. We also show how sock porfolios formed based on hese expecaions ouperform simple benchmark sock porfolios. We build our approach on a model suggesed by Marin and Wagner (016) ha links sock reurn expecaions and risk-neural idiosyncraic (or raher individual) sock reurn variances (SVIX indexes). While Marin and Wagner (016) uses opion-implied variances we insead use credi defaul swap (CDS) implied variances backed ou using he mehodology described in Bysröm (015, 016). In addiion o reflecing sock marke expecaions among he marke paricipans in he credi marke raher han hose in he equiy marke, our approach has he advanage of allowing for a much longer-erm focus han he equiy marke. If one uses ordinary call- and pu-opions, like Marin and Wagner (016), he available opion mauriies limi he horizon of he expecaion or forecas o a maximum of welve, or perhaps weny-four, monhs. Marin and Wagner (016), indeed, looks a horizons beween one and welve monhs. If one insead uses credi defaul swaps o back ou he implied sock reurn variances hen he available horizons are much longer. In mos markes here are credi defaul swaps wih mauriies beween one year and en years and his allows us o back ou sock marke expecaions a he same ime horizons. Such long-erm expecaions and forecass are obviously relevan for he sraegic asse allocaion of asse managers wih long invesmen horizons such as pension funds and insurance companies. However, hedge funds and family offices also need o form long-erm expecaions on individual socks. The lieraure on long-erm expecaions of individual sock reurns is very limied hough and he volume does no reflec he pracical relevance and imporance ha reallife invesors aribue o reliable long-erm sock marke forecass.
Since our approach builds direcly on he heoreical resuls in Marin and Wagner (016) i shares he nice feaure of no relying on parameer esimaions. No hisorical sock price- or credi spread observaions are needed. Moreover, he expecaions can be updaed in real-ime and apply o individual socks raher han porfolios. In Marin and Wagner (016), he risk-neural equiyimplied variances are linked o reurn expecaions hrough indexes labeled SVIX indexes. In his paper he risk-neural implied variances come from he credi marke, and o emphasize he differen origins of he expecaions we label our variance indexes C SVIX indexes. According o sandard financial heory i is sysemaic risk, raher han firm-specific or idiosyncraic risk, ha is of ineres o sock marke invesors. The insigh ha only sysemic risk is priced has been challenged in he recen lieraure, however. Goyal and Sana-Clara (003), for insance, claims ha idiosyncraic volailiy can posiively predic excess marke reurns. Fu (009) also finds a posiive relaionship beween expeced reurns and (condiional) idiosyncraic volailiy. Ang e al. (006) insead finds ha socks wih high idiosyncraic volailiy (and high firm-specific volailiy) have low average reurns, a finding ha is subsequenly rebued by Fu (009). Adding o he conflicing empirical evidence, in a recen paper Begin e al. (016) also uses opions daa and shows ha i is ail risk, raher han diffusion risk, ha plays a cenral role in he pricing of idiosyncraic risk. Marin and Wagner (016) looks a he variance of individual socks and suggess a posiive link beween he opions-implied variance of a sock and he expeced (excess) reurn of he sock. They go on o show ha heir heoreical relaionship holds empirically for horizons beween one and welve monhs. In his paper we confirm ha he heoreical relaionship in Marin and Wagner (016) holds also when we replace equiy opions (SVIX) wih credi defaul swaps ( C SVIX). We find a srong link beween risk-neural variances and realized reurns a he much longer horizon of five years. And when we pick socks based on our credi-implied C SVIX 3
indexes he sock-porfolios bea boh equally- and value-weighed porfolios ou-of-sample. While we only forecas sock reurns over a five-year horizon in his paper, in heory, he mehodology lends iself equally well o any forecasing horizon beween one- and en years. In he nex secion we review he Marin and Wagner (016) mehodology and inroduce he C SVIX indexes. Secion wo describes our mehod of backing ou risk-neural sock reurn variances from he credi derivaives marke and secion hree presens he daa and he empirical resuls. Secion four conains some robusness checks and secion five concludes he paper. 1. C SVIX-Indexes and he Expeced Reurn of a Sock Marin and Wagner (016) shows heoreically how he expeced reurn on an individual sock can be expressed in erms of he risk-neural variance of he marke (SVIX), he risk-neural variance of he individual sock (SVIX i ), and a value-weighed average of individual socks' riskneural variances (SVIX average ). Assuming consan fixed effecs across socks, Marin and Wagner (016) ends up wih he following formula for he expeced excess reurn of a sock E R i, 1 R R f, 1 f, 1 SVIX 1 SVIX i, SVIX average, (1) where he SVIX variance indexes are defined as SVIX SVIX i, * R var ( R * Ri, var ( R m, 1 f, 1 1 f, 1 ) ) SVIX average, i w i, SVIX i, 4
and R i,+1 is he (gross) reurn of he individual sock i, R m,+1 is he (gross) reurn of he marke, R f,+1 is he (gross) risk-free reurn and w i is he marke weigh of sock i. Marin and Wagner (016) compues he various SVIX variance indexes using sock reurn variances implied by equiy opions. In his paper we insead use sock reurn variances implied by credi derivaives. Our approach of backing ou variances from credi defaul swap spreads will be described in he nex secion and in order o highligh he differen origin of he variance we name he resuling volailiy indexes C SVIX, C SVIX i, and C SVIX average. The only difference compared o he original SVIX indexes of Marin and Wagner (016) is he source of he implied variance and he resuling formula for he expeced reurn of a sock is herefore E R i, 1 R R f, 1 f, 1 C SVIX 1 C SVIX i, C SVIX average, () Like in Marin and Wagner (016), our implemenaion of he relaionship beween expeced sock reurns and risk-neural sock reurn variances requires no parameer esimaion using hisorical sock prices or CDS spreads.. Sock Marke Volailiy According o he Credi Derivaives Marke Implied sock reurn volailiies (variances) are ypically backed ou from equiy opions. Marin and Wagner (016) follows his pah and compues implied (risk-neural) sock reurn variances using call- and pu opions on individual socks. The mauriies of he opions employed by Marin and Wagner (016) range from one monh o one year. In his paper, we urn o he credi derivaives marke, raher han he equiy derivaives marke, o back ou sock marke variances. We follow Bysröm (015, 016) and compue implied sock volailiies by invering he CrediGrades (00) model. The process is similar o how ordinary implied volailiies are backed ou using he Black-Scholes model, bu wih he equiy opions marke replaced by he 5
credi defaul swap marke. Compared o Marin and Wagner (016) our expeced sock reurns are herefore he expecaions of credi- raher han equiy invesors. Anoher imporan difference is he mauriy of he forecas. As a resul of he long mauriies in he CDS marke, he expecaions generaed using our approach are expecaions over he coming years, i.e. very longerm expecaions, while he expecaions in Marin and Wagner (016) are expecaions over he coming monhs. In his paper we have chosen a five-year forecasing horizon bu we could equally well had chosen any oher horizon beween one and en years, i.e. he available mauriies of he credi defaul swaps in he marke. CrediGrades is normally used o compue sock-marke implied CDS spreads and i relies on sock prices, sock reurn volailiies, deb levels and model assumpions similar o hose in Meron (1974) o do so. The asse value is assumed o follow a sandard geomeric Brownian moion bu, in a generalizaion of he Meron model, CrediGrades also allows he recovery rae o flucuae. In he CrediGrades model he credi defaul swap spread for a cerain mauriy, T, is CDS spread where P() is he survival probabiliy r 1 P(0) e ( G( T ) G( )) r(1 R) (3) rt r P(0) P( T ) e e ( G( T ) G( )) A P( ) N( ln( d) A ) dn( A ln( d) ) A and where d L V 0 e, mean D A, 1 z ln( d) z G( ) d N( z ) d 1 ln( d) N( z ), 6
, z 1 4 r. L mean and is he mean and sandard deviaion, respecively, of he global recovery rae while R is he issue-specific recovery rae. r is he risk-free ineres rae and, he asse volailiy, is normally calculaed from he equiy volailiy, E, since asse values are non-observable. CrediGrades uses he linear approximaion V = E + L mean D, where E and D is he firm s equiy and deb, respecively, and his implies ha = ( E E) / (E + L mean D). For a more deailed descripion of he CrediGrades model we refer o he CrediGrades TM Technical Documen (CrediGrades (00)). Now, in his paper we follow Bysröm (015, 016) and inver he CrediGrades model (numerically) in order o ge sock reurn volailiies, E, implied by he observed credi defaul swap spreads in he marke. These volailiies are hen used o compue he C SVIX indexes ha we use o esimae he expeced sock reurns. The CrediGrades model requires esimaes of he mean global recovery rae, L mean, he sandard deviaion of he global recovery rae,, as well as he issue-specific recovery rae, R. We follow he CrediGrades Technical Documen (CrediGrades, 00) when choosing he global recovery rae; i.e. we le L mean = 0.5. We hen le he issue-specific recovery rae R be equal o he global recovery rae for all firms. When i comes o, however, we rea non-financial and financial firms differenly. As discussed in Bysröm (015), he CrediGrades Technical Documen acknowledges ha is likely o be lower for financial firms han for non-financial firms. We herefore follow Bysröm (015) and le =0.3 for non-financial firms and =0.03 for financial firms. In oher words, he CrediGrades 7
benchmark -value is used for non-financial firms while a -value one enh he size of he benchmark value is used for financial firms. This choice is based on he difference in leverage beween non-financial firms and financial firms. We also follow Bysröm (015) in reaing financial firms deb differen from non-financial firms. In he ligh of he discussion on governmen bank suppor and effecive leverage raios in he CrediGrades Technical Documen, Bysröm (015) adjuss financial firm deb by muliplying he acual deb levels by one half o beer reflec he acual defaul risk. In his paper, we also calculae effecive deb levels for financial firms in his way. 3. Daa and Empirical Resuls In his secion, we empirically examine he performance of he credi defaul swap marke in predicing fuure sock reurns using he heoreical relaionship derived by Marin and Wagner (016) beween a sock s expeced reurn and he risk-neural variance of he marke, he individual sock's risk-neural variance, and he value-weighed average risk-neural variance across all individual socks. We have chosen o focus on he expeced sock reurns of he 15 firms in he itraxx Europe CDS index (Series 5). The European CDS marke is one of he mos maure CDS markes and he credi defaul swaps included in he itraxx index are among he mos liquid CDS conracs around. The 15 European firms come from five indusry secors (Auos & Indusrials, Consumers, Energy, Financials and TMT). Due o missing observaions, firms no having publicly raded socks or (a few) non-converging numerical volailiy esimaions (when keeping he L mean and values unchanged) he final sample consiss of 91 firms, among which 68 are non-financial firms and 3 are financial firms. 8
The overall ime-period of he sudy, December 14, 007 o December 31, 015, is deermined by daa availabiliy. We are focusing on long-erm (five-year) sock reurn expecaions and forecass, and our credi-implied expeced sock reurns are consequenly only compued from December 14, 007 o December 31, 010, since a five-year long ou-of-sample period is needed for forecas evaluaion purposes. The mauriy of he (Euro-denominaed) CDS conracs is five years and all daa, excep he leverage raios, is available on a daily basis and downloaded from Daasream. The leverage raios are available on a yearly basis and are from he web page of Professor Damodaran a New York Universiy. They are ransformed o daily deb levels using a linear inerpolaion beween year-end observaions. All values are denominaed in Euro and as a proxy for he risk-free ineres rae we use he Euro 3M deposi rae. The expeced five-year excess reurns compued from equaion () are ploed in Figure 1 (averaged across firms). The expecaions are based on five-year credi defaul swap spreads and herefore correspond o long-erm (five-year) forecass. As shown in Figure 1, and in line wih he shor-erm expecaions in Marin and Wagner (016), our long-erm expecaions are boh high and volaile. A he beginning of he sample, he credi marke expecs European sock reurns over he coming five years (007-01) o be around 10% annually. During he crisis, he expecaions seadily rise unil he expecaions of fuure five-year reurns (009-014) reach a maximum of 30% around he ime of he sock marke boom in March 009. From hen on, he expecaions flucuae beween 0% and 35% wih an all-ime-maximum for he average firm of 36% in May 010. Among he various indusry secors, he only secor ha sands ou is he financial secor where, from he sar of he financial crisis in Ocober 008 onwards, he expecaions are much lower han in he oher indusry secors. This is probably as expeced considering ha he crisis had is epicener in he financial indusry, and i is also consisen wih 9
he, ex pos, much lower observed sock reurns from 008 o 010 in he financial secor, compared o in he oher non-financial secors. 3.1 Correlaion Resuls Before we urn o regressions beween expeced excess reurns and (subsequen) realized excess reurns we look a simple pair-wise correlaions beween he wo. We calculae average correlaions in wo ways; (i) he ime-series average of daily cross-secional correlaions among he firms in he sample (for a given day, how similar are he disribuions of expeced and realized reurns among he firms) and (ii) he cross-secional average across he firms of (firm by firm) ime-series correlaions beween expeced and realized reurns (for a given firm, how similar are he ime-series movemens for expeced and realized reurns). High correlaions of he ype labelled cross-secional correlaion opens up for sock picking while high correlaions of he ype labelled ime-series correlaion opens up for marke iming. Now, for our paricular sample of firms, and for our choice of ime-period, he average crosssecional correlaion is found o be quie high a 0.41 and he average ime-series correlaion is found o be even higher a 0.75. I.e. he numbers are high enough o imply a srong link beween C SVIX-implied expeced reurns and subsequen realized reurns. The high correlaions also indicae ha C SVIX indexes possibly could be used boh for sock picking and for marke iming. 3. Regression Resuls We will now es, more formally, wheher equaion () holds or no, empirically, when we replace he SVIX indexes of Marin and Wagner (016) wih our C SVIX indexes, i.e. when we replace equiy-derivaives implied variances wih credi-derivaives implied ones. 10
Like Marin and Wagner (016) we sar wih a preliminary analysis of wheher ime-series averages of socks excess reurns line up wih C SVIX, C SVIX i and C SVIX average as posulaed by equaion (). Since we rely on five-year credi defaul swaps, all he C SVIX indexes represen he credi derivaives marke s forecass of sock reurn variances over he nex five years. Equaion () predics ha for each percenage poin change in C SVIX i - C SVIX average he expeced excess sock reurn should change half a percenage poin. In he empirical analysis we replace he expeced excess reurn wih he realized excess reurn and in OLS regressions of excess reurns on 0.5 ( C SVIX i - C SVIX average), averaged across he ime-period Dec. 14, 007 o Dec. 31, 010, he esimaed slope value is 1.14 (-value = 4.67 and R = 0.0). This is close o he value prediced by heory (1.0) and close o he value of 1.1 in Marin and Wagner (016) for heir longes mauriy (one year). The esimae of he inercep is no significanly differen from zero and he relaionship beween excess reurns and risk-neural variances suggesed by Marin and Wagner (016) holds up well, a leas when we look a ime-series averages, when equiy-opion implied variances are replaced by credi defaul swap implied variances (like Marin and Wagner (016) we require full-sample period coverage of all firms). The nex sep is o perform a condiional analysis, using monhly daa, where we es if he relaionship in () holds by pooling all our panel observaions and run he regression R i, 1 R R f, 1 f, 1 C C SVIX i, SVIX average, i, 1 C SVIX (4) We expec α = 0, β = 1 and γ = 0.5, and he resuls for he full sample of firms are found in Table I. We find α = -0.16, β = 0.94 and γ = 0.38 and all he regression coefficiens are saisically significan (R = 0.6). The wo slope coefficiens β and γ are close o he heoreically expeced values bu he inercep erm α is differen from zero (negaive). The inerpreaion of his is ha while here indeed is a srong posiive relaionship beween socks 11
risk-neural variances and excess reurns, as posulaed by heory, he consan erm α shifs he enire relaionship downwards. This negaive shif is mos likely caused by our paricular choice of ime-period, wih he large negaive (realized) reurns during he ime of he financial crisis dominaing he picure. In fac, his is confirmed in secion 4 below when we perform our analysis on a year-by-year basis. In sum, however, he heoreical relaionship in Marin and Wagner (016) seems o hold also when we replace shor-erm (<1Y) equiy opions-implied variances wih long-erm (5Y) credi defaul swap-implied ones. 3.3 Porfolio Selecion and Simple Trading Schemes The saisically significan relaionship beween curren risk-neural variances and fuure excess reurns in he previous sub-secion opens up for he possibiliy of using credi defaul swaps when making long-erm predicions in he sock marke. We will now look ino he economic significance of his opporuniy using a simple invesmen (porfolio selecion) scheme based on he predicive abiliy of he C SVIX indexes. Forecass of individual firms excess sock reurns are made using conemporaneous daa. Neiher fuure- nor hisorical daa is used and he resuling ou-of-sample porfolio selecion scheme closely resembles a real-life rading exercise. Our invesmen sraegy is essenially he same as ha in Marin and Wagner (016) and, like hem, we consruc sock porfolios wih weighs based on he model-implied expeced reurns and hen compare hese porfolios wih naïve equally-weighed and value-weighed porfolios of he same socks. Like Marin and Wagner (016) we build on Asness e al. (013) and choose weighs in our model-implied porfolios based on he ranks of he firms expeced five-year excess reurns a ime 1
rank rank E R wi, (5) rank E R i i, 1 i, 1 where θ > 0 is a measure of he aggressiveness of he sraegy. This porfolio selecion sraegy ensures ha he weighs allocaed o he socks are all posiive, ha hey increase wih he socks expeced reurns and ha hey sum o one, i.e. our hypoheical invesor behaves like a fully invesed long-only invesor wih equally- and value-weighed porfolios of he same socks as naural benchmarks. Like Marin and Wagner (016) we vary he aggressiveness in he sock selecion by seing θ = 1 or θ = in our empirical analysis. The higher he θ-value he more emphasis is pu on he model s ranking of socks expeced reurns when choosing he porfolio weighs. Wih θ = 1 or θ = we avoid exreme over- or under-weighing of socks and ensure ha he model-implied porfolio is always well diversified. We eiher le he invesor form a buyand-hold porfolio on he firs day of he sample, Dec. 31, 007, or rebalance he porfolio once a year (on Dec 31), i.e. four imes over he 007-010 period covered by our C SVIX indexes. We do no allow for more frequen (daily or monhly) rebalancing for he simple reason ha i would be inconsisen wih our forecass being long-erm five-year forecass raher han one-day or onemonh forecass. Table II presens mean reurns, sandard deviaions, skewness, kurosis and Sharpe raios for he four porfolio sraegies: (i) he model-implied porfolio wih θ = 1, (ii) he model-implied porfolio wih θ =, (iii) an equally weighed porfolio and (iv) a value-weighed porfolio. The wo model porfolios clearly perform beer han he wo naïve porfolios. While boh he equally weighed- and he value weighed porfolios lose money, each of he wo model-implied porfolios make a profi, regardless of wheher we rebalance or no. The annualized excess reurns of he model porfolios vary beween 1.09% and.10% while he annualized excess 13
reurns of he equally weighed and he value weighed porfolio is -1.07% and -.38%, respecively. The more aggressive model sraegy dominaes he less aggressive sraegy bu rebalancing he porfolio once a year does no improve he performance significanly. The laer finding is in accordance wih wha one would expec, considering ha he forecass are very longerm (five years) and ha hey (in heory) should no change oo much from one year o he nex. Finally, i should be added ha here are (essenially) no ransacion coss o consider for our invesmen sraegies since even he rebalanced porfolio is raded only once a year. The day-oday movemens of he cumulaive porfolio value, wih and wihou rebalancing, is ploed in Figures and 3 and i is clear ha he ou-performance by he model porfolios is no caused by a single significan even bu is building up quie seadily over he eigh-year long ime-period. As an addiional example of how informaion from he credi derivaives marke (he C SVIX indexes) could be used o ouperform he overall sock marke Figures and 3 also show he performance of wo small equally-weighed porfolios conaining he hree highes- and he hree lowes ranked socks, again ranked according o heir expeced fuure five-year excess reurn as of Dec. 31, 007. The significan difference in performance of hese wo porfolios adds some evidence o he predicive abiliies of he credi marke; while a porfolio made up of he boomhree socks loses more han 30% across he sample period he porfolio made up of he op-hree socks gains more han 5%. Furher evidence of his predicive abiliy of he credi-implied expeced reurns is shown in Table III where we show he cumulaive porfolio performance of he op-n as well as he boom-n porfolios for n = 1 o 10 (wihou rebalancing). For mos n, he porfolios conaining he n socks wih he n highes expeced reurns perform very well over he eigh-year long sample period while he porfolios wih he n lowes ranked socks perform much worse. In fac, a simple long/shor sraegy going long he op-10 ranked socks and shoring he boom-10 socks, as of Dec. 31, 007, in his sample of 91 European socks across he ime- 14
period 007 o 015, a period ha is dominaed by he financial crisis, would generae a reurn of around 55%. Again, his indicaes how gains could be made from using credi derivaives marke informaion when predicing sock reurns. 4. Robusness Checks The resuls in he previous secion indicae a srong relaionship beween individual socks riskneural volailiy and subsequen excess sock reurns. The resuls are all averaged-ou resuls across he enire sample, however, and i is possible ha a few exreme episodes, perhaps linked o he sock marke correcion around he collapse of Lehman Brohers, drive he resuls. I is also possible ha he resuls differ among he indusries in he sample. For robusness, and o invesigae he sabiliy of he resuls over ime and across firm-ype, we herefore presen he correlaion, regression- and rading resuls above for sub-periods as well. We look a each year from 008 o 015 individually o ge some indicaions on he sabiliy of he resuls and o ell wheher he crisis years 008 and 009 differ from he oher years. In addiion o his year-byyear reamen we will also rea socks from each of he five indusries separaely. The correlaions in Table IV show ha, regardless of how we compue he correlaion beween expeced- and realized reurns, he link beween he wo is srong also when we divide he sample ino one-year long sub-periods. The cross-secional correlaion measure is very sable over ime and he correlaion coefficien is essenially he same every year (around 0.40) while he imeseries correlaion measure is somewha higher in 008 (0.80) han in 009 and 010 (0.36 and 0.50, respecively). As for he regressions, in Table V we show he regression resuls year-by-year and he resuls for 008 and 009 are essenially he same as hose for he enire sample; all he regression 15
coefficiens are saisically significan and he slope coefficiens β and γ are close o he heoreically expeced values while he inercep erm α is negaive. The year 010 differs from 008 and 009, however, wih he relaionship beween reurns and volailiies being somewha weakened bu wih slopes ha are sill saisically significan and a consan erm ha, in correspondence wih heory, is no significanly differen from zero. This parly suppors our hypohesis ha he negaive α esimae found for he full sample could be due o he Lehman Brohers crash and is dramaic and long-lasing effec on he sock marke no only in 008 bu in 009 as well. As for he porfolio sraegies, we presen year-by-year mean reurns, sandard deviaions and Sharpe raios for he four porfolio sraegies in Table VI. Excep for he wo years 008 and 014, he model porfolios perform beer han he naïve porfolios every year (and even in 008 and 014 he wors sraegy is one of he wo naïve sraegies). The resuls do no seem o be driven by one or wo freak evens and our simple invesmen sraegy based on informaion from he CDS marke seems o work in urbulen years (perhaps o a slighly lesser degree) as well as in less urbulen years. Overall, he suppor of he heoreical relaionship in Marin and Wagner (016) beween expeced long-erm sock reurns and long-erm variances found in he previous secion seems o hold also when we look a each year separaely. To furher invesigae he robusness of our resuls we also look a each indusry separaely. The number of firms in each indusry is quie low (beween 14 and 6 firms), however, and we herefore focus solely on correlaions. Each indusry is reaed separaely, wih all analysis redone on an indusry-by-indusry basis and wih he firms in he paricular indusry making up he marke in he compuaion of expeced reurns of individual socks. Table VII shows ha he correlaion resuls above, indeed, are robus across indusries. All he correlaions are posiive, saisically significan and of similar size, excep for 16
he small negaive, and saisically insignifican, cross-secional correlaion among he firms in he consumers indusry. 5. Conclusions In his paper we have demonsraed how one can compue sock reurn expecaions using informaion from he credi derivaives marke. Our mehodology builds on work by Marin and Wagner (016) bu insead of using ordinary call- and pu opions o impue risk-neural sock variances we use credi defaul swaps. One advanage of his approach is ha very long-erm forecass of sock reurns can be made (across he enire business cycle if needed). In he empirical par of he paper we show ha he heoreical relaionship beween expeced excess reurns and risk-neural variances in Marin and Wagner (016) holds also when we replace shor-erm (<1Y) equiy opions-implied variances wih long-erm (5Y) credi defaul swap-implied variances. We also examine he performance of he credi defaul swap marke in making long-erm (5Y) sock marke predicions and, ou-of-sample, we find sock porfolios seleced based on credi-implied sock reurn forecass o bea boh equally- and value-weighed benchmark porfolios. The empirical resuls in he paper are robus across years, across indusries and o varying sample-sizes. References Ang, A., R. J. Hodrick, Y. Xing, and X. Zhang. 006. The Cross-Secion of Volailiy and Expeced Reurns. Journal of Finance 61 (1), pp. 59-99. Bysröm, H. 015. Credi-Implied Volailiy: Long-Term Forecass and Alernaive Fear Gauges. Journal of Fuures Markes 35 (8), pp. 753-775. 17
Bysröm, H. 016. Sock Prices and Sock Reurn Volailiies Implied by he Credi Marke. Journal of Fixed Income 5 (4), pp. 3-54. CrediGrades. 00. CrediGrades. Technical documen, RiskMerics Group. Fu, F. 009. Idiosyncraic Risk and he Cross-secion of Expeced Sock Reurns. Journal of Financial Economics, 91 (1), pp. 4-37. Goyal, A., and P. Sana-Clara. 003. Idiosyncraic Risk Maers! Journal of Finance, 58 (3), pp. 975-1008. Marin, I. and Wagner, C. 016. Wha is he Expeced Reurn on a Sock? Working Paper, London School of Economics. Meron, R. 1974. On he Pricing of Corporae Deb: The Risk Srucure of Ineres Raes. Journal of Finance, 9 (), pp. 449 470. 18
Table I Pooled Regression Resuls In his Table we presen resuls from OLS regressions, using monhly daa, beween realized five-year excess reurns and five-year risk-neural variances pooled across all 91 firms. Values in square brackes are p-values and he regressions are based on 3367 monhly observaions from December 31, 007 o December 31, 010. α β γ F Ȓ -0.160 0.941 0.380 60.1 0.64 [0.000] [0.000] [0.000] [0.000] [0.000] 19
Table II Porfolio Performance In his Table we presen he performance of our model porfolios for wo differen levels of aggressiveness (θ) compared o naïve equally-weighed and value-weighed porfolios wih and wihou yearly porfolio rebalancing. The porfolio holding period is from December 31, 007 o December 31, 015 and he porfolios are made up of long posiions in all he 91 firms in he sample. The reurns and sandard deviaions are annualized. Buy-and-Hold Model (θ=1) Model (θ=) Equally weighed Value weighed Mean reurn (%) 1.1 1.94-1.07 -.38 Sandard deviaion (%).14.3 3.03 1.61 Skewness -0.13-0.13-0.10-0.07 Kurosis 5.55 5.63 5.7 5.38 Sharpe raio 0.051 0.087-0.047-0.110 Yearly Rebalancing Model (θ=1) Model (θ=) Equally weighed Value weighed Mean reurn (%) 1.09.10-1.07 -.38 Sandard deviaion (%).48.94 3.03 1.61 Skewness -0.1-0.11-0.10-0.07 Kurosis 5.6 5.07 5.7 5.38 Sharpe raio 0.049 0.091-0.047-0.110 0
Table III Porfolio Performance Highes and Lowes Ranked Socks In his Table we presen he cumulaive performance of equally-weighed porfolios of he op-n and boom-n ranked socks wihou yearly porfolio rebalancing. The porfolio holding period is from December 31, 007 o December 31, 015 and he numbers are cumulaive percenage reurns. n op-n boom-n 1 +11.9 +9.4 +18.3 -. 3 +5.3-31. 4 +1.3-3.4 5-0.6-4. 6-1.1-8.8 7 +5.4-3.1 8 +31.3-39.4 9 +7.8-4.9 10 +8. -45.5 1
Table IV Robusness: Year-by-Year Correlaion Resuls In his Table we presen average correlaions beween expeced five-year excess reurns and subsequen realized fiveyear excess reurns for wo differen ways of calculaing average correlaions on a year-by-year basis; (i) he imeseries average of daily cross-secional correlaions among he firms in he sample and (ii) he cross-secional average across he firms of ime-series correlaions beween expeced and realized reurns. The correlaions are compued using 91 firms and daily reurn observaions from 008, 009 and 010, respecively. 008-010 008 009 010 Cross-secional correlaion 0.41 0.41 0.44 0.38 Time-series correlaion 0.75 0.80 0.36 0.50
Table V Robusness: Year-by-Year Pooled Regression Resuls In his Table we presen resuls from OLS regressions beween realized monhly excess reurns and monhly riskneural variances pooled across all 91 firms on a year-by-year basis. Values in square brackes are p-values and all regressions are based on 109 monhly observaions from, respecively, 008, 009 and 010. 008 α β γ F Ȓ -0.187 1.113 0.508 19.6 0.19 [0.000] [0.000] [0.000] [0.000] [0.000] 009 α β γ F Ȓ -0.191 1.178 0.339 76.7 0.13 [0.000] [0.000] [0.000] [0.000] [0.000] 010 α β γ F Ȓ -0.005 0.44 0.33 48.6 0.08 [0.174] [0.00] [0.000] [0.000] [0.000] 3
Table VI Robusness: Year-by-Year Porfolio Performance In his Table we presen he performance of our model porfolios for wo differen levels of aggressiveness (θ) compared o naïve equally-weighed and value-weighed porfolios wih yearly porfolio rebalancing on a year-byyear basis. The porfolio holding period is always one year and he porfolios are made up of long posiions in all he 91 firms in he sample. The reurns and sandard deviaions are annualized. 008 Model (θ=1) Model (θ=) Equally weighed Value weighed Mean reurn (%) -60.73-59.45-65.96-51.63 Sandard deviaion (%) 36.36 36.73 37.07 34.64 Sharpe raio -1.67-1.6-1.78-1.49 009 Mean reurn (%) 6.77 7.3 6.0 16.0 Sandard deviaion (%) 7.0 8.18 7.89 5.19 Sharpe raio 0.99 0.97 0.93 0.64 010 Mean reurn (%) 14.37 16.58 9.70 4.65 Sandard deviaion (%) 18.56 19.09 19.08 17.6 Sharpe raio 0.77 0.87 0.51 0.6 011 Mean reurn (%) -1.35-11.9-17.10-11.9 Sandard deviaion (%) 4.79 5.31 5.54 3.38 Sharpe raio -0.50-0.45-0.67-0.48 01 Mean reurn (%) 15.96 16.7 15.7 9.94 Sandard deviaion (%) 16.73 17.1 17.49 15.84 Sharpe raio 0.95 0.97 0.87 0.63 013 Mean reurn (%) 17.84 18.86 17.0 14.4 Sandard deviaion (%) 1.68 13.03 1.93 1.58 Sharpe raio 1.41 1.45 1.33 1.13 014 Mean reurn (%) 1.60 1.65 1.80 0.09 Sandard deviaion (%) 13.77 13.98 13.93 14.18 Sharpe raio 0.1 0.1 0.13 0.01 015 Mean reurn (%) 5.41 6.53 4.64-0.97 Sandard deviaion (%) 19.60 19.58 19.73 0.59 Sharpe raio 0.8 0.33 0.4-0.05 4
Table VII Robusness: Indusry-by-Indusry Correlaion Resuls In his Table we presen average correlaions beween expeced five-year excess reurns and subsequen realized fiveyear excess reurns for wo differen ways of calculaing average correlaions on an indusry-by-indusry basis; (i) he ime-series average of daily cross-secional correlaions among he firms in he sample and (ii) he cross-secional average across he firms of ime-series correlaions beween expeced and realized reurns. The cross-secional correlaions are compued using 91 firms (or less, for he indusries) and he ime-series correlaions are compued using 796 daily reurn observaions from December 14, 007 o December 31, 010. All Firms Auo. & Ind. Consumers Energy Financials TMT Cross-secional correlaion 0.41 0.38-0.14 0.54 0.37 0.39 Time-series correlaion 0.75 0.76 0.65 0.53 0.74 0.7 5
Figure 1. Average Expeced Excess Reurns. This graph shows he average daily expeced five-year excess reurn (annualized) for he firms in he sample, divided ino indusries, across he ime period December 14, 007 o December 31, 010. 6
Figure. Porfolio Performance: Buy-and-Hold. This graph shows he cumulaive porfolio performance of our model porfolios for wo differen levels of aggressiveness (θ) wihou yearly porfolio rebalancing compared o naïve equally-weighed and value-weighed porfolios and wo equally-weighed porfolios conaining he hree highes- and he hree lowes ranked socks, respecively. The porfolio holding period is from December 31, 007 o December 31, 015 and he porfolios are made up of long posiions in all he 91 firms in he sample. 7
Figure 3. Porfolio Performance: Yearly Rebalancing. This graph shows he cumulaive porfolio performance of our model porfolios for wo differen levels of aggressiveness (θ) wih yearly porfolio rebalancing compared o naïve equally-weighed and value-weighed porfolios and wo equally-weighed porfolios conaining he hree highes- and he hree lowes ranked socks, respecively. The porfolio holding period is from December 31, 007 o December 31, 015 and he porfolios are made up of long posiions in all he 91 firms in he sample. 8