Online Appendix Appendix A: The concep in a muliperiod framework Using he reduced-form model noaion proposed by Doshi, el al. (2013), 1 he yearly CDS spread S c,h for a h-year sovereign c CDS conrac can be compued as he rae which equaes he presen value of he paymens (premium leg) o he presen value of he expeced payou (loss leg), premium leg loss leg { [ }} {{ [ }}{ h h E S c,h q+ja c +j ( + j) = E (1 R c ) ( ) q+j 1 c q+j c A ( + j), (1) j=1 j=1 where R c is he recovery rae (as a proporion of he face value of he proecion), q c +j is he survival probabiliy a ime + j, q c +j 1 q c +j is he probabiliy ha he credi even occurs during he inerval ( + j 1, + j) and A ( + j) is he riskless discoun rae ( exp ) h 1 j=0 r +j wih r +j being he risk free rae. In erms of noaion, (1 R c ) is he loss given defaul, λ c +j = (1 R c ) ( q c +j 1 q c +j) and E h j=1 λc +ja ( + j) is he presen value of he expeced loss as a percenage of exposure afer a credi even. From he poin of view of an inernaional invesor based for example in he Unied Saes, if he conrac has a face value of he proecion denominaed in US dollars ($) using (1) hen S c,h,usd = E j=1 λc +ja ( + j) E j=1 qc +j A ( + j), (2) 1 The only difference vis-à-vis Doshi, e al (2013) is ha hey use an indicaor funcion, we use in our noaion he survival probabiliy. 1
if insead he conrac has a face value of he proecion denominaed in euro, hen S c,h,eur = E j=1 XL,c +j λc +ja ( + j) E j=1 XP,c +j qc +j A ( + j), (3) where X P,c +j is he USD/EUR exchange rae coningen upon a credi even no having occurred, X L,c +j is he USD exchange rae versus he euro or he new legal currency coningen upon a credi even having occurred over he period +h and A ( + j) is he riskless discoun rae prevailing in he US dollar money marke. Divide numeraor and denominaor by he curren USD/EUR exchange rae, X P,c, hen S c,h,eur = ( ) E j=1 1 + x L,c +j λ c +ja ( + j) ( ), (4) E j=1 1 + x P,c +j q c+j A ( + j) where x P,c +j = XP,c +j /XP,c 1 is he USD/EUR exchange rae appreciaion coningen upon a credi even no having occurred and x L,c +j = XL,c +j /XP,c 1 is he exchange rae appreciaion of he euro or he new legal currency agains he US dollar coningen upon a credi even having occurred. Assume ha in he absence of a credi even he exchange rae follows a random walk, X P,c +j = XP,c + ε c where ε c is a whie noise (i.e. E ε c = 0, cov(ε c, ε c s) = 0 if s, var(ε c ) = = ( ) XP,c and E h j=1 1 + x P,c +j q+ja c ( + j) = E h j=1 qc +ja ( + j). 2 σ 2 ), hen E X P,c +j Hence, (4) can be wrien as S c,h,eur = ( ) E j=1 1 + x L,c +j λ c +ja ( + j). (5) E j=1 qc +j A ( + j) This implies ha he quano CDS, ha is he difference beween he USD- and he EURdenominaed CDS spreads, can be compued subracing (5) from (2) Q c,h = ( E j=1 λc +ja ( + j) E j=1 E j=1 qc +j A ( + j) ) 1 + x L,c +j λ c +ja ( + j), (6) E j=1 qc +j A ( + j) 2 Similar resuls are obained if he exchange rae is driven by he uncovered ineres pariy condiion: x P,c +j = rusd +j 1 reur +j 1, given ha E h ( j=1 1 + r USD +j 1 +j 1) reur q c h +j A ( + j) E j=1 qc +ja ( + j). 2
which can be rewrien as Q c,h = Credi risk (=0) { [ }}{ h E j=1 λc +ja ( + j) E j=1 λc +ja ( + j) [ E j=1 qc +j A ( + j) h E j=1 qc +j A ( + j) Credi even probabiliy-weighed expeced currency depreciaion (+) { [ }}{ h [ E j=1 λc +ja ( + j) h + E x L,c E j=1 qc +j A ( + j) +j j=1 (7) currency risk associaed wih expeced loss (+) { [ }}{ h COV j=1 xl,c +j, h j=1 λc +ja ( + j) +, E j=1 qc +j A ( + j) By subracing he EUR-denominaed CDS from he USD-denominaed CDS, he credi risk componen becomes nil and wha is lef is he expeced depreciaion and he currency risk componen. Given ha in case of a credi even among euro area counries he US dollar is expeced o appreciae, hen X L,c +i < XP,c and x L,c +i = XL,c +i /XP,c 1 < 0. Therefore, he second componen of (7), namely he credi even probabiliy-weighed counry c s expeced currency depreciaion agains he US dollar, is posiive. Moreover, he larger he expeced loss, he larger he expeced depreciaion; hence he hird componen of (7), namely he currency risk associaed wih he expeced loss, is also posiive: COV j=1 xl,c +j, h j=1 λc +ja ( + j) > 0. Therefore, Q c,h = S c,h,usd E j=1 xl,c +j + COV[ h j=1 xl,c +j, h j=1 λc +j A(+j) E [ h j=1 qc A(+j) > 0. (8) +j Q c,h measures he compensaion demanded by marke paricipans for he risk associaed in holding euro-denominaed asses ha he US dollar appreciaes agains he euro or he new legacy currency afer a credi even. Inra-euro area redenominaion risk, I c,b,h, is defined by subracing from (8) an euro area 3
benchmark counry b quano CDS: I c,b,h = Q c,h Q b,h. (9) Given ha he expeced probabiliy of a credi even in he benchmark counry is negligible, we expec The proposiions ha Q c,h characerise he daa. I c,b,h λ c,h > 0 and I c,b,h > λ b,h λ c,h >λ b,h 0. (10) 0 are key feaures ha should Appendix B: Descripion of he Variables This appendix provides deails abou he definiion, sources and iming of he daa used in he sudy. Panel A: Main Variables of he single counry VAR X1 = US governmen bond yield a 5-year mauriy. The US governmen bond yield a 5-year mauriy is Unied Saes 5-year governmen benchmark bond yield in US dollar provided by Bloomberg. X2 = he US sock marke index. The US sock marke is he Thomson DaaSream Global Equiy Index for he Unied Saes provided by Thomson Reuers. X3 = US volailiy premium. The US volailiy premium is calculaed as he difference beween he square of VIX index (obained from Thomson Reuers) and he square of condiional volailiy for he US sock marke obained as a GARCH(1,1) on he daily US sock marke reurns. X4 = US invesmen grade. The US invesmen grade is he spread beween he Unied Saes corporae BBB and AAA 7-10-year (USD) Merrill Lynch Bond Index provided by Thomson Reuers. X5 = EUR depreciaion versus USD 5-year forward. The euro depreciaion versus USD 5-year forward is compued using he covered ineres rae pariy condiion as a difference beween he euro area and he US OIS risk free raes a 4
5-year mauriy. The Euro and USD Overnigh Ineres Swaps (OIS) rae a 5-year mauriy are provided by Bloomberg. X6 = EUR depreciaion versus USD. The exchange rae is expressed as unis of euro per US dollar and is obained from he ECB. X7 = 10-dela EUR/USD 1-monh implied volailiy (skew). The 10-dela dollar-euro opion implied volailiy skew is he difference in he US Dollar/Euro 1-monh Black-Scholes implied volailiies of an ou-of-he-money 10-dela call opion and an ou-of-he-money 10-dela pu opion for OTC currency opion markes provided by Bloomberg. A dollar-euro pu (call) opion is a European opion of selling (buying) euro a he conracual opion srike price in an exchange of US dollars a he opion mauriy. X8 = Break-even inflaion rae 5-yr forward. The break-even inflaion rae 5-yr forward is he five-year forward break-even inflaion rae five years ahead provided by he ECB. X9 = German 5-yr CDS. The German CDS spreads are obained from Bloomberg. They are midmarke indicaive prices for five-year sovereign CDS conracs. X10 = EA 5-yr OIS. The EA 5-yr OIS is he Euro OIS rae a 5-year mauriy provided by Bloomberg. X11 = Euro area sock marke volailiy. The euro area sock marke volailiy is he realised volailiy for he euro area sock marke obained as a GARCH(1,1) on he daily euro area sock marke reurns provided by Thomson DaaSream. X12 = Euro area invesmen grade. The euro area invesmen grade is he spread beween he European Moneary Union corporae BBB and AAA 7-10-year (Euro) Merrill Lynch Bond Index provided by Thomson DaaSream. X13 = KfW-Bund spread. The KfW-Bund spread is he difference beween he 5-year KfW ( Krediansal für Wiederaufbau ) bond and he German sovereign bond (i.e. Bund). They are boh guaraneed 5
by he German governmen and, herefore, carry he same defaul risk. Any differences beween agency and governmen bond yields should reflec inernaional invesors preference for asses wih he lowes liquidiy risk. X14 = Greek sovereign spread. The Greek sovereign spread is he difference beween he 10-year Greek sovereign bond and he 10-year Euro OIS provided by Bloomberg. X15 = Sovereign yield bid-ask spread. The sovereign bid-ask spread is he difference beween he 5-year bid and ask EURdenominaed sovereign yield provided by Bloomberg. X16 = Redenominaion risk. Redenominaion risk is defined as a difference beween he quano CDS of Ialy, Spain or France and he quano CDS of Germany. The USD- and EUR-denominaed CDS a 3-year mauriy are provided by Thomson Reuers. X17 = Domesic sock marke. The domesic sock marke is he Thomson DaaSream Global Equiy Index for he counry provided by Thomson Reuers. X18 = Sovereign yield spreads. The sovereign yield spreads are he difference beween he 5-year EUR-denominaed sovereign bond of Ialy, Spain and France and he 5-year Euro OIS rae provided by Bloomberg. They are midmarke prices for five-year sovereigns. Panel B: Main Variables of he FAVAR X1 = US 1s PC US 1s PC is he firs principal componen of US governmen bond yield a 5-year mauriy, he US sock marke index, US volailiy premium and US invesmen grade. X2 = FX 1s PC FX 1s PC is he firs principal componen of EUR depreciaion versus USD 5-year forward, EUR depreciaion versus USD and 10-dela EUR/USD implied volailiy. X3 = EA 1s PC is he firs principal componen of break-even inflaion rae 5-yr forward and he EA 5-yr OIS. X4 = German 5-yr CDS 6
The German CDS spreads are midmarke indicaive prices for five-year sovereign CDS conracs. X5 = EA risk 1s PC EA risk 1s PC is he firs principal componen of euro area sock marke volailiy, euro area invesmen grade and KfW-Bund spread. X6 = Greek sovereign spread The Greek sovereign spread is he difference beween he 10-year Greek sovereign bond and he 10-year Euro OIS rae. X7 = CDS bid-ask spread 1s PC CDS bid-ask spread 1s PC is he firs principal componen of Ialian, Spanish and French CDS bid-ask spread. X8 = Sovereign yield bid-ask spread 1s PC Sovereign yield bid-ask spread 1s PC is he firs principal componen of Ialian, Spanish and French sovereign yield bid-ask spread. X9-11 = IT/ES/FR redenominaion risk Redenominaion risk is defined as a difference beween he quano CDS of Ialy, Spain or France and he quano CDS of Germany a 3-year mauriy. X12 = Domesic sock marke 1s PC Domesic sock marke 1s PC is he firs principal componen of Ialian, Spanish and French domesic sock markes X13-X15 = IT/ES/FR CDS spreads The CDS spreads for Ialy, Spain and France are midmarke indicaive prices for five-year USD-denominaed sovereign CDS conracs. X16-X18 = IT/ES/FR Sovereign yield spreads. The sovereign yield spreads are he difference beween he 5-year EUR-denominaed sovereign bond of Ialy, Spain and France and he 5-year Euro OIS rae. They are midmarke prices for five-year sovereigns. Variables used as robusness check: The US price-earnings raio is based on he Thomson DaaSream Global Equiy Index for he Unied Saes provided by Thomson Reuers. 7
The ne flows (inflows minus ouflows) ino muual funds are obained from EPFR Global. The CDS spreads for he Unied Saes are provided by Bloomberg. They are midmarke indicaive prices for five-year CDS conracs. The CDS conrac references he sovereign. The credi spreads of oher sovereigns is compued as an average of CDS spreads all he oher euro area counries. The EUR/USD implied volailiy provided by Bloomberg. The 10-dela dollar-euro opion 1-year implied volailiy provided by Bloomberg. The local expeced budge defici o GDP raio is compued as a raio beween he expeced budge balance and he expeced nominal GDP; he laer in urn compued using expeced inflaion and GDP growh. The daa provider is consensus forecas. The observaions are monhly. The German sovereign spread is he difference beween he 5-year Bund and he 5-year Euro OIS rae provided by Bloomberg. They are midmarke prices for five-year sovereigns. The commodiy prices are gold and oil provided by Thomson Reuers. The redenominaion risk a 5-year mauriy is defined as a difference beween he quano CDS of Ialy, Spain or France and he quano CDS of Germany a 5-year mauriy. The USD- and EUR-denominaed CDS a 5-year mauriy are provided by Thomson Reuers. The firs wo principle componens exraced from he global and exchange rae variables specifically for he FAVAR. The firs wo principle componens exraced from he regional variables specifically for he FAVAR. 8