Seminarios de Matemática Financiera - Instituto MEFF RiskLab-Madrid Madrid, 21 de Enero, 2004

Transcription

1 Cred Dervaves Relave Value Semnaros de Maemáca Fnancera - Insuo MEFF RskLab-Madrd Madrd, 21 de Enero, 24 Cred Dervaves A Relave Value Perspecve Rccardo Galleo Drecor, Cred Dervaves Relave Value Tradng

2 Agenda 1. The Buldng Blocks 2. The Underlyng Model 3. Relave Value Tradng 1

3 Agenda 1. The Buldng Blocks 2

4 Relave Value Approach Tradonal busness model n cred markes: Cash marke Dervaves marke Inegraon n cred markes led o: Relave value opporunes beween varous asse classes Holsc approach owards managng corporae rsk Sandardzaon n he dervaves marke brough lqudy 3

5 Cred Markes Dynamcs Bond vs Cred Defaul Swaps (CDS: LONG CREDIT CDS generally wder han bonds Sell proecon raher han buy bonds (for hose who can SHORT CREDIT Buy proecon avod repo coss CDS o wden more n a marke sell-off (CDS reac more han cash Vrually no lms on sze 4

6 Cred Markes Dynamcs Composon of he nvesor base Buyers vs sellers of proecon Buyers vs sellers of bonds Cheapes o delver opon In a cred even, buyer of proecon has opon o delver he cheapes bond or loan Hgher value n opon for lower raed creds Coupon sep-up language Telecom bonds Converble bonds Generae demand for proecon from converble hedge funds 5

7 Comparng Bonds o Cred Defaul Swaps he Bass Bass defnon: CDS spread mnus spread on a cash nsrumen wh he CDS havng he same Reference Eny, subordnaon and maury Negave bass : arge range 25+ bp Posve carry rades, cred neural, duraon neural Arbrage opporunes beween bonds and CDS Long he bass Look for corporae names lkely o experence sharp cred deeroraons Corporae names n beween hgh grade and hgh yeld Posve bass : arge range 2+ bp on sable cred names Sgnal o ake prof on expensve bond holdngs Swch no CDS/CLNs for spread pck-up Shor he bass Take prof Sop loss 6

8 Example - Telefonca Negave bass for TELEFO $ Sep1 Posve carry Cred neural Telefonca Benchmark bonds and CDS curve, bp Spreads n bass pons as of md January 24 Duraon neural Posve bass for TELEFO Feb13 Bass spread ghenng Negave carry Cred neural Duraon neural LIVE COB 1W 1M 3M $ 7.75% Sep % Feb

9 Bass: how o Trade Telefonca CDS Curves and Bond spreads Spreads n bass pons as of md November 23 Maury mached bass rades Marke sandard Equal nomnals Works well up o 1 year maures Telefonca L+46bp 1Y 42bp FT L+79bp 1Y 8bp LIVE COB 1W 1M 3M 5.125% Feb13 1Y CDS DT L+62bp 1Y 77bp Duraon weghed bass rades Telefonca CDS Curves and Bond spreads Spreads n bass pons as of md November 23 Take advanage of lqudy n 5Y CDS vs long-end of CDS curve Hedge rao 3 : 1 Long daed bond vs 5Y CDS Telefonca L+8bp 5Y 28bp FT L+131bp 5Y 59bp DT L+116bp 5Y 56bp LIVE COB 1W 1M 3M 5.875% Feb33 5Y CDS

10 The Bass Bass radng Negave bass Buy bond and buy maury mached proecon, arge spread ghenng Swches (ou of bonds no CDS Sell bond and sell proecon The bass curve Buyng a he ends vs a he cenre of he rang specrum 9

11 he Curve Curve radng Curve flaeners Long long-daed bond vs duraon weghed 5Y CDS Long CDS forwards Curve seepeners Shor long-daed bond vs duraon weghed 5Y CDS Shor CDS forward Barbells Long shor- and long-daed bonds vs 5Y CDS Box rades FT and DT 33s vs 5Y CDS 1

12 and Beyond Bass - dreconal radng Spread gheners Bull marke rades Sell bass Spread wdeners Bear marke rades Buy bass 11

13 Agenda 2. The Underlyng Model 12

14 The Underlyng Model - Overvew Relave value compares CDS and bond spreads CDS leg requres probablsc modellng Marke spread Lqudy ssues ousde 5 year maures Newly launched ndces add lqudy o he curve n 1 year maures Bond spreads depend on whch mehodology we use Spread over governmen bonds Par asse swap Z-spread Far value 13

15 Cred Defaul Swaps Paymens unl he earler of he Cred Even rgger or maury: Proecon Buyer Premum* Proecon Seller Paymens afer he Cred Even has occurred and he conrac has been rggered: Proecon Buyer Accrued Premum Noonal Amoun Proecon Seller Delverable Oblgaon** * As a percenage of he noonal amoun and pad on a regular bass ** If Physcal Selemen s specfed. If Cash Selemen s specfed, he payou s (1-R. 14

16 Modellng Approach - Srucural Models Model he asse value of he frm as a log-normal dffuson process Equy s regarded as call opon on he frm s asse value Defaul occurs when he frm s asse value falls below he lables hreshold Defaul me s predcable due o he dffuson process Models ell us o hedge wh equy, may be a good macro hedge Do no use he nal erm srucure of cred spreads 15

17 Modellng Approach - Hazard Rae (or Reduced Form Models Usually, we do no need o know why defaul has happened, jus ha has occurred Defaul me s modeled as he 1s jump of a Posson process assocaed wh a deermnsc/sochasc hazard rae Defaul even s a compleely unpredcable, sudden even Recovery rae s eher consan or sochasc gven by a Bea dsrbuon,.e. flexble shape, deermned fully by s mean & varance Can f cred spread curves o whaever level of deal we choose Can ncorporae neres rae erm srucure models and correlaon 16

18 Presen Value of a Fxed Leg The presen value of a fxed leg* s gven by he sum over all dscouned premum paymens mulpled by he survval probably Example: Sell 5Y proecon on DamlerChrysler a a fxed rae of m Fxed Leg: δ τ n = T Fxed rae paymens are sopped afer rgger of Cred Even Dscounng and mulplyng wh he survval probably yelds he presen value* of he fxed leg: PV Fxed Leg n = m δ df ( p( = 1 PV 1 * Neglecng accrued premum a defaul 17

19 Presen Value of a Floang Leg τ As he occurence of a Cred Even,, s unkown, he presen value of he floang leg has o be wren as he expecaon of he dscouned pay-off a he me of he Cred Even Example: Sell proecon on DamlerChrysler. A he rgger of he Cred Even he proecon seller has o pay 1 and receves he recovery value of a delverable bond denoed by R, e (1-R Floang leg: τ n = T Presen value of he floang leg: 1 R PV Floa Leg (1 R df ( τ 1{ T } = τ As he defaul me s sochasc, he presen value wll be wren as he expecaon PV [ ] Floa Leg = τ E (1 R df ( τ 1{ T } 18

20 Presen Value of a Cred Defaul Swap The presen value s he dfference beween he fxed and he floang legs: PV Defaul Swap n = m δ df ( p( (1 R df ( ρ( d + m acc = 1 T where acc = n = 1 1 ( df ( ρ( d 19

21 Survval Probably I has become marke sandard o assume an exponenal dsrbuon for he survval probably ( Hazard Rae Model wh a lnear nensy funcon p( λ 1 λ p ( = e prob { < τ + } = p( p( + = e λ e λ + ( + τ + Densy Funcon d ρ( = (1 p( = λ' e d λ 2

22 Prcng Process for Cred Defaul Swaps Cred spreads as seen n he CDS marke and explc recovery rae* assumpons are used o value cred defaul swaps Marke Daa Inpu Cred spreads m j as seen n he CDS marke Boosrappng Defaul Probables n T j λ d j = PV j = m j df ( e (1 R λ e for all maures = 1 T j = 1y, 2y,...1y df ( d Defaul nenses λ Defaul & Survval Probables λ u du + m j acc Valung every Defaul Swap Poson PV Defaul Swap n = m δ df ( p ( (1 R df ( ρ ( d = 1 T + m acc P&L *The recovery rae assumpons have o be he same for he boosrappng process as well as for he reprcng of defaul swap posons 21

23 22 Presen Value of a Cred Defaul Swap Presen Value of a Cred Defaul Swap The PV of a defaul swap can be deermned quckly hrough he dfference of he fxed rae and marke rae and he PV1 ( ( (1 ( ( 1 = + = = acc m d df R p df m PV T n OnMarke ρ δ acc m p df m d df R n T + = =1 ( ( ( ( 1 ( δ ρ 1 ( ( ( ( ( ( ( ( ( ( (1 ( ( PV m m acc p df m m acc m p df m acc m p df m acc m d df R p df m PV n n n T n Swap Defaul = + = + = + = = = = = δ δ δ ρ δ

24 Presen Value & Rsk of a Cred Defaul Swap The prof and loss of an open poson can easly be deermned from he cred spread change and he PV1 Example: We sell 5Y proecon on $1mm DamlerChrysler a 125bp PV = ( m m PV 1 1 Mllon Day Marke Cred Spread PV1 PV Daly P&L , -43, ,5 64,5 P&L = Change of PV accordng o marke spread move = m x PV1 x Noonal + (m -m x PV1 x Noonal m x PV1 x Noonal small Cred Spread Sensvy* = Change of PV f marke spread moves 1bp PV1 x Noonal PV PV = PV 1 + ( m m 1 m m * 23

25 Hedgng Corporae Bonds wh Cred Defaul Swaps In general, we have o hedge an amoun equal o 1 + (Px 1/(1-R where Px s he marke value of he bond and R s he assumed recovery rae For example, assumng a 5% recovery rae: If he bond rades a par, we hedge $1m of bonds wh $1m of CDS If he bond rades a premum.e.11%, we hedge $1m of bonds wh $12m of CDS If he bond rades a dscoun.e. 9%, we hedge $1m of bonds wh $8m of CDS Imporanly, he bond prce no only mpacs he sze of he CDS hedge bu also he spread evaluaon We need o address hs ssue 24

26 Bond Prcng Mehodologes Spreads over Governmen Bond US$ Bond yelds vs US$ yeld curve Spreads n bass pons as of md January 24 7 US$ Treasures YTM US$ Denomnaed bonds YTM Spread over benchmark governmen bond Wdespread marke sandard n U.S. Hgh lqudy, low bd/offer spread DT $5.25% Jul13 F $5.625% Oc8 Dageo $3.375% Mar8 TI $6.375% Nov33 Approxmae neres rae hedge 2 Shell $5% Jul7 fals o accoun for prce Deermnsc framework 1 FT $7.2% Mar Years 25

27 Bond Prcng Mehodologes Asse Swap Spreads US$ Bond ASW vs US$ ASW curve Spreads n bass pons as of md January 24 7 US$ ASW US$ Denomnaed bonds ASW Par asse swap spread Wdespread marke sandard n Europe Sus asse swap nvesors Spread reflecs blended rsk, mpac of bond prce no capured n he spread Probablsc framework Take no accoun he prce of he bond Theorecal measure 6 TI $6.375% Nov33 5 F $5.625% Oc8 DT $5.25% Jul13 4 Dageo $3.375% Mar8 3 2 Shell $5% Jul7 1 FT $7.2% Mar Years 26

28 Bond Prcng Mehodologes Z-spreads and Far Value Bond ASW vs ASW curve Spreads n bass pons as of md January 24 Z-spread Bul over zero swap curve ASW Denomnaed ASW F 5.5% May6 DCX Jan7 KPN 4.75% Nov8 Repsol 5% Jul13 DT 7.5% Jan33 Spread ndcaes cred rsk 4 Easly avalable on BBG Assumes fla rsky curve Semens 5.75% Jul11 EdP 5% Mar8 Far value Compare o CDS spread curve Years Measure pure cred rsk for bonds 27

29 Agenda 3. Relave Value Tradng 28

30 Relave Value Tradng BAT (Baa1/BBB+ Overvew CDS Curves Spreads n bass pons as of md November 23 Trade dea: BAT 13s looked cheap vs 5Y CDS BAT 13s L+93bp Par ASW 5Y 68bp md Poson analyss Long duraon, BAT mprovng cred sory LIVE 4.25% Apr4 BAT 9s neg bass wdenng COB 1W 1M 3M 4.875% Feb % Jul13 Real money accs exendng duraon 5s/1s curve flaenng Curve flaener rade Bull marke rade Exend duraon Swch ou of BAT 9s no BAT 13s BAT 9s vs 5Y CDS bass sable Par ASW vs 5Y CDS Spreads n bass pons as of md November 23 Bass Bass Brsh Amercan Tobacco plc 4.875% Feb9 Tradng sraegy Take prof on BAT 13s and swch no BAT 9s, whle beng long 5Y proecon BAT 9s bass vs 5Y CDS as becomes more negave BAT 9s neg bass wdenng 21Aug 11Sep 2Oc 23Oc 13Nov 29

31 Relave Value Tradng FORD (A3/BBB- Overvew CDS Curves Spreads n bass pons as of md November 23 Trade dea: Long 2Y forward sarng n 3Y Poson analyss Long duraon If oulook sable > prof If oulook negave > curve nverson Curve flaener rade Seep curve o 3Y 1Y forward rollng curve hghlghs value Curve ghenng Long duraon Curve flaened CDS radng wde relave o bonds Posve bass across he curve Swch ou of bonds no long rsk va CDS LIVE 5.5% May6 6% Feb5 COB 1W 1M 3M $ 5.625% Oc $ 7% Oc13 3

32 Relave Value Tradng FT (Baa3/BBB vs DT (Baa3/BBB+ Overvew CDS Curves Spreads n bass pons as of November 23 Box Trade: 12bp spread dfferenal Long FT L+81bp Par ASW vs Buy Proecon 1Y 83bp Shor DT L+63bp Par ASW vs Sell Proecon 1Y 77bp FT DT FT 7.25% Jan13 DT $ 5.25% Jul13 Cred neural 2 Duraon neural Par ASW vs Maury Mached CDS Spreads n bass pons as of November 23 Par ASW vs Maury Mached CDS Spreads n bass pons as of November 23 Bass Bass France Telecom 1y CDS 7.25% Jan13 Bass Deusche Telekom AG 1y CDS $ 5.25% Jul Aug 26Aug 16Sep 7Oc 28Oc 18Nov Aug 26Aug 16Sep 7Oc 28Oc 18Nov 31

33 Relave Value Tradng Bayer (A3/A+ Overvew CDS Curves Spreads n bass pons as of md January 24 Bass packages: range radng beween fla and -25bp BYIF L+64bp vs 8Y 47bp Posve carry of 17bp Negave bass rade Currenly n lne wh radng range BYIF L+36bp vs 3Y 32bp LIVE COB 1W 1M 3M 6% Apr % Apr Fla carry (posve carry of 4bp Par ASW vs Maury Mached CDS Spreads n bass pons as of md January 24 Bass Bass Bayer AG 3y CDS 5.375% Apr Aug 25Sep 23Oc 2Nov 18Dec 2Jan 32

34 Relave Value Tradng Wes LB (Aa1/AA Overvew Par ASW vs Maury mached CDS Spreads n bass pons as of md December 23 Suppor mechansm unl md 25 Bearsh radng sraegy Shor cred Buy 1Y proecon Cover acual cred rsk Buy proecon 8Y FWD sarng n 2Y Moderae fundng Cover expeced cred rsk Buy proecon 5Y FWD sarng n 5Y Hgher fundng Expecng exenson of ranson perod Wach for S&P announcemen on 24 November regardng sandalone credworhness LIVE COB 1W 1M 3M

35 Relave Value Tradng Endesa (Baa1/A vs Iberdrola (A2/A+ Overvew Spread dfference n he 5y CDS conrac of 13bp, around he maxmum for he las 6 monhs Posve carry of 13bp Sell Proecon on Endesa 5Y 34 Buy Proecon on Iberdrola 5Y 21 Trade DV1 neural Lan Amerca exposure no an ssue as s a posve cred hsory Endesa 5y CDS vs Iberdrola 5y CDS Spreads n bass pons as of md January Iberdrola Endesa Aug 1Sep 21Sep 11Oc 31Oc 2No 1Dec 3Dec 2Jan Iberdrola Spreads n bass pons as of md January 24 Endesa Spreads n bass pons as of md January 24 4 LIVE COB 1W 1M 3M 6 LIVE COB 1W 1M 3M % Oc % Feb

36 Bass Radar European Telecoms Secor TELDAN Jan1 TELEFO Feb33 VOD May9 VOD Jan8 BRITEL Feb BRITEL $ Dec1 BRITEL Feb11 DT Feb8 DT Jan33 TELEFO Feb13 TELEFO $ Sep1 OLIV $ Nov FRTEL $ Mar6 FRTEL Jan33 KPN Apr6 OLIV Jan33 KPN $ Oc1 OLIV Jan13 PORTEL Apr9 OLIV Apr12 OLIV Feb12 OLIV Jan8 TI $ Nov33 TI Jan33 TI Apr12 TI Jan13 TI Feb12 TI Jan8 35

37 Bass Radar European Auos Secor VLVV Jan1 VLOF Jul6 MICH Apr12 MICH Apr9 VW May13 F Feb F May6 F Jun6 F $ Oc8 F $ Oc13 DCX $ Jun8 SCANIA Dec8 DCX $ Jun1 RENAUL May1 DCX $ Nov13 CONTI Dec8 GM Jul8 BMW Aug18 GM $ Aug12 36

38 Relave Value Opporunes 14 January 24 Top negave bass Bond deals Prce Mod Dur Par ASW Z-Spread Conrac Ma. Mach CDS Par Bass 1 Damlerchrysler AG USD 8.% Jun y France Telecom EUR 8.13% Jan y Telecom Iala SpA EUR 7.75% Jan y Olve Spa EUR 7.75% Jan y Deusche Telekom AG EUR 7.5% Jan y France Telecom USD 8.45% Mar y Telefonca, S.A. EUR 5.88% Feb y Damlerchrysler AG USD 6.5% Nov y Brsh Telecommuncaons plc USD 8.38% Dec y Brsh Telecommuncaons plc EUR 6.38% Feb y Ford Moor Cred Company EUR 5.63% Jun y Ford Moor Cred Company EUR 6.% Feb y Ford Moor Cred Company EUR 5.5% May y Royal KPN NV USD 8.% Oc y Pearson plc EUR 6.13% Feb y Bayer AG EUR 6.% Apr y VNU NV EUR 6.75% Oc y Casno Guchard-Perrachon EUR 6.% Mar y Dxons Group plc GBP 6.13% Nov y EADS EUR 5.5% Sep y Telefonca, S.A. USD 7.75% Sep y General Moors Accepance Corp USD 6.88% Aug y Arcelor EUR 5.13% Sep y Imperal Tobacco Group plc EUR 6.25% Jun y GUS PLC EUR 4.13% Jul y J Sansbury plc EUR 5.63% Jul y Scana AB EUR 6.% Dec y Telecom Iala SpA EUR 7.25% Apr y Olve Spa EUR 7.25% Apr y Hlon Group plc EUR 6.5% Jul y 6-14 Top posve bass Bond deals Prce Mod Dur Par ASW Z-Spread Conrac Ma. Mach CDS Par Bass 1 Fa SpA EUR 5.75% May y Fa SpA EUR 6.75% May y Shell Peroleum NV EUR 3.25% Dec y General Elecrc Capal Corp EUR 3.% Feb y General Elecrc Capal Corp EUR 4.13% Dec y Telecom Iala SpA USD 5.25% Nov y Olve Spa USD 5.25% Nov y General Elecrc Capal Corp EUR 3.75% Apr y Deusche Telekom AG USD 5.25% Jul y Damlerchrysler AG EUR 7.% Mar y

39 Conclusons Fas-growng Cred Dervaves Marke Prcng Mehodologes n Cred Modellng Relave Value Tradng Opporunes 38

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