Congrès de l Association canadienne d économique Canadian Economic Association Meeting

Transcription

1 Congrès de l Assocaton canadenne d économque Canadan Economc Assocaton Meetng May 2013, HEC Montréal Georges Donne, HEC Montréal Research n collaboraton wth Olfa Maalaou Chun, Kast Graduate School of Fnance, South Korea

2 Our goal s to explan the credt rsk regme shfts of corporate bonds by analyzng n detal default and lqudty regme shfts. By credt rsk, we mean the dfference between corporate bond yeld and government bond yeld. Ths dfference s also labeled corporate yeld spread or credt spread n the fnancal lterature. Ths spread s postve because corporate bond nvestors ask for a hgher yeld than do government bond nvestors snce they are exposed to addtonal rsks and costs. In ths paper, we focus on default rsk and lqudty rsk that are contaned n credt rsk. 1

3 2

4 These questons are mportant because: from an nvestment perspectve, corporate debt s one of the largest asset classes; from a macroeconomc pont of vew, yeld spreads are often lnked to busness and monetary cycles; durng the recent fnancal crss, lqudty rsk became an mportant rsk especally n the bankng ndustry. Durng the recent fnancal crss, lqudty rsk was sgnfcant for many fnancal assets (such as ABCP n Canada) and central banks had to use specal polcy measures to ncrease lqudty nto the fnancal system. 3

5 Before the 2000s, credt spread was assocated to default spread. Then many authors contrbuted to the Credt Rsk Puzzle lterature by showng that only a fracton of the credt spread s explaned by the default rsk. Ths fracton vares between 25% to 50% and s functon of busness cycles. Other factors n the credt spread nclude: rsk averson; taxes; market rsk; lqudty rsk. However, the measure of lqudty rsk s not yet satsfactory, specfcally because data lmtaton before TRACE. 4

6 Yeld curves Yeld (%) BBB curve Government curve 0 Tme to maturty n years Government bond yeld curve Default premum Rsk averson premum Lqudty premum Tax premum Market rsk premum BBB yeld curve 5

7 Another ssue s related to the credt spread cycles. Credt spread cycles do not necessarly correspond to busness cycles (Maalaou Chun, Donne, Franços, 2013, JFQA, forthcomng): hgh level regmes of credt spreads encompass but outlast economc recessons and show persstence after recessons; they occur before economc recessons so they may have some predctve power over a forthcomng recesson. These two features were recently ntroduced n dynamc structural models of default (Chen, JoF, 2010; Bhamra et al, RFS, 2010). Fnally, credt spread regmes are related to monetary Federal Reserve polcy and SLO surveys (Senor Loan Offcer surveys). 6

8 Credt spreads SLO - Survey Fgure 2, Panel A Credt spread BBB BBB - 10 yrs SLO - Survey avr.-87 févr.-89 déc.-90 oct.-92 août-94 jun

9 Credt spreads SLO - Survey Fgure 2, Panel B Credt spread BBB and BB BBB - 10 yrs BB - 10 yrs SLO - Survey janv.-94 nov.-95 sept.-97 jul.-99 ma-01 mars-03 janv.-05 8

10 Credt spreads SLO - Survey Fgure 2, Panel C Credt spread BBB and BB BBB - 10 yrs BB - 10 yrs SLO - Survey Oct-04 Jul-05 Apr-06 Jan-07 Oct-07 Jul-08 Apr-09 Jan-10 9

11 Moreover, volatlty regmes can be detected outsde busness cycles. Ths means that volatlty and level regmes can be lnked to dfferng sets of observable phenomena. For example, we have detected a volatlty regme durng the Asan and LTCM crses n but there was not a level regme durng that perod. 10

12 Credt spreads and Fed Funds rate SLO - Survey Fgure 3, Panel C Mean regmes BBB and BB BBB - 10 yrs BB - 10 yrs Fed Funds Rates SLO - Survey oct.-04 jul.-05 avr.-06 janv.-07 oct.-07 jul.-08 avr.-09 janv

13 Today, we study default rsk and lqudty rsk cycles. CDS premum or default spread In a frst step, we assume that the CDS (Credt Default Swap) premum measures the default spread component of the credt spread. CDS premums can also be affected by lqudty (but contracts). The rsk-neutral default ntensty of the corporate bond follows a square-root dffuson (Cox-Ingersoll-Ross, CIR) process: d dt dz. (1) t t t t where s the ntensty of the Posson process governng the default of the reference ssue, Z t s a standard Brownan moton,,, are CIR parameters estmated usng the Kalman Flter. 12

14 A CDS s lke an nsurance contract. A bondholder or protecton buyer pays a quarterly premum to a protecton seller or nsurer untl ether the default of the bond occurs or the CDS contract comes to maturty. If default occurs, the protecton seller buys the defaulted bond from the protecton buyer at ts face value and receves the recovery value from the bond ssuer. So he loses the non-recovery value of the bond or the loss gven default value. Lets denote 1 w as the recovery rate or w the loss gven default rate. 13

15 Hence, gven the stream of quarterly CDS premums, s, that the protecton buyer makes at tmes 0 t1 t2... tn, we can wrte the present value of the premum leg of the CDS, Ps, T as follow, assumng ndependence between r t and t. where 0 D t t tn 0, t ds P s T s t 1 D t E e (2) t t e r ds s the dscount factor, or equvalently: At and t, n Bt 0, (3) P s T s D t A t e t 1 where B t are expressed n terms of the CIR parameters,, n Equaton (1). 14

16 We defne n the same way the protecton leg of the CDS contract: P w T rsds, E 0 we 1 t n (4) where w s the loss gven default of the reference bond, or equvalently: where G t et t n B t 0 0 0, (5) t G t H t w D e dt H t are expressed n terms of the CIR parameters,, n Equaton (1). For estmaton, (5) can be rewrtten as: t G t H t B t 0 tn t 1 0 (6) w D e 15

17 Assumng zero profts at ncepton of the CDS, the actuaral CDS premum of bond can be expressed as follows: s t t G t H t B t w D e n t 1 t B t Dt t 1 A t e n (7) If s not stochastc, s w, the expected loss on the bond. Otherwse, s s the present-value-weghted of 0w and s lower than w because there s negatve correlaton between 0 and e B t 0. 16

18 Lqudty premum We use 8 lqudty measures and two ndexes obtaned from prncpal component analyss. 1) The Amhud llqudty measure For each ndvdual bond, we compute the daly Amhud measure as follows: where Amhud P P, (8) N t 1 1 j, t j1, t t Nt j1 Qj, t Pj 1, t N t s the number of returns n each day t, jt, P (n $ per $100 par) denotes the j th transacton prce of bond n day t and Q jt, (n $ mllon) the j th tradng volume of bond n day t. Ths s the prce mpact of a trade per unt traded. It has a transacton volume component. 17

19 Two measures of bd-ask spread. 2) The unque roundtrp cost (also called mputed roundtrp cost) The unque roundtrp cost (URC) s defned as: max mn URC P P (9) P where P max and P mn denote the maxmum and mnmum tradng prces durng a unque roundtrp trade or sze. max 3) The Roll measure of the bd-ask spread t Pt Pt 1 Roll 2 cov, (10) where P denotes changes n transacton prces. 18

20 4) Frst llqudty rsk measure The frst lqudty rsk measure s equal to the standard devaton of Amhud measure. 5) Second llqudty rsk measure The second lqudty rsk measure s equal to the standard devaton of unque roundtrp costs (URC). 6) The turnover total tradng volume turnover t t amount outstandng (11) The nverse of turnover t can be nterpreted as the average holdng tme of the bond. 19

21 7) Bond zero tradng days number of bond zero trades wthn the rollng wndow bond zero t number of days n the rollng wndow (12) 8) Frm zero tradng days number of frm zero trades wthn the rollng wndow frm zero t number of days n the rollng wndow (13) 20

22 Lqudty premum The lqudty premum s a lnear sum of llqudty measures selected from a prncpal component analyss. We defne the daly measure of the bond specfc llqudty factor as an equally sum of the normalzed llqudty measures retaned from the prncpal component analyss: t? j1 l j t, j j j It where l t s the normalzed measure of llqudty j,. See Dckj Nelsen, Feldhütter and Lando (JFE, 2012) for more detals. 21

23 Default and lqudty regme detecton We present a new regme shft detecton model. The regme shft procedure bulds on sequental t-test for shfts n the mean (level) and sequental F-test for shfts n the varance (or volatlty). Non-parametrc model. The procedure vews regmes as random n the sense that, at each tme t, one cannot predct the exstence or the tmng of any future breakpont. The method allows level and volatlty regmes to have ther own patterns, n contrast to Markov swtchng model. One advantage of the method s ts ablty to account for abrupt changes n a tme seres. 22

24 Ths s a real-tme method, n the sense that possble breaks can be detected as new data arrve and t s free from any assumpton about the number and the tmng of the breaks. The method comes from the lterature of detectng shfts wthn ecosystems and was appled to tme seres data n fnance only recently (Maalaou Chun, Donne, Franços, 2013, forthcomng JFQA). There are two stages for detectng regmes. A frst stage for detectng level regmes and a second stage for detectng volatlty regmes n tme seres. Consder that data s represented by the followng tme seres Y, t 1,..., n. t 23

25 Suppose Y t s descrbed by an autoregressve model: t t t1 t1 t, Y f Y f (14) where f t captures a potentally tme-varyng mean, s the autocorrelaton coeffcent, and 2 0, t N. We defne tme t c as a breakpont where the dstrbuton of the data changes, then the mean level f t can be expressed as: f t 1, t 1,2,..., c1, 2, t c, c 1,..., n. The null hypothess H0 1 2 meanng that we reject a regme shft. Before testng we must estmate ˆ and clean the data of any red nose and work wth the fltered tme seres Y ˆ t Yt 1. (15) 24

26 Detecton of the level regme We start by defnng the sample mean Z cur of the frst sequence of the data of length m. Let be the dfference between the mean values of two subsequent sequences: t 2 s m, (16) 2m2 2 m mean where m s the ntal cut-off length of regmes smlar to the cut-off 2 pont n low-pass flterng, s m s the sample varance, and value of the two-taled t-dstrbuton wth 2 2 freedom at the gven probablty level mean. 2m 2 t s the mean m degrees of 25

27 26

28 The shft n the level occurs f the current value tested Z cur s outsde the crtcal threshold Zcrt, Z crt, Z Z crt crt Z Z cur cur,, (17) where Z crt s the crtcal mean f the shft s upward and Z crt s the crtcal mean f the shft s downward. We must then test f the shft s the startng pont of a new regme or smply an accdent. Defne RSI that represents a cumulatve sum of normalzed anomales relatve to the crtcal mean Z crt: 1 RSI Z Z j t t t m ms j crt, cur, cur 1,..., cur 1. (18) m t cur 27

29 If at any tme durng the testng perod from tcur to tcur m 1 the RSI turns negatve when Zcrt Z crt or postve when Zcrt Z crt, the null hypothess s not rejected. Detecton of the volatlty regme The detecton of the volatlty regme shfts s performed n the same way as for the level regme, except t s based on the F-test nstead of the Student t-test. At ths stage, we purge our ntal data of level regmes, thus obtanng the tme seres of the resduals. I wll not go nto the detals of the volatlty tonght. 28

30 The TRACE database The TRACE database reports hgh frequency data and contans nformaton about almost all trades n the secondary over-thecounter market for corporate bonds, accountng for 99% of the total tradng volume. Data covers the perod July 2002 to December We use the Dck-Nelson flter for the duplcates and the Han and Zhou flters for the prces. 29

31 The CDS database Data for CDS contracts are obtaned from Markt. Ths ncludes all North Amercan Fnancal CDS for whch we can match data from TRACE. Maturtes are from 6 months to 10 years. The data has a daly frequency and covers the perod from 2001 to We use the whole term structure to extract the λ-ntensty of each ssuer. Snce we have many maturtes, we use the flterng approach of Duan and Smonato (2004). Tradng days are defned by the tme schedule of the NYSE. 30

32 31

33 Statstcs for lqudty measures Fgure 1: Dynamcs of the eght lqudty varables Panel A: Dynamcs of lqudty varables durng the to NBER recesson 32

34 Panel B: Dynamcs of lqudty varables durng the to fnancal crss 33

35 Statstcs for default measure The CDS and the mpled ntensty of default durng the to NBER recesson λ 34

36 Prncpal component analyss of the lqudty varables Table 4: Prncpal component analyss of the lqudty varables Panel A: Egenvalues of the eght prncpal components 35

37 Panel B: Egenvectors of the eght prncpal components 36

38 Regmes detected wth respect to the fnancal crss perod and last recesson Default regmes Fgure 2: Dynamcs of the default factor Panel A: Default factor durng the to NBER recesson 37

39 Panel B: Default factor durng the to fnancal crss 38

40 Lqudty regmes Fgure 3: Dynamcs of the frst lqudty factor Panel A: Frst lqudty factor durng the to NBER recesson 39

41 Panel B: Frst lqudty factor durng the to fnancal crss 40

42 Fgure 4: Dynamcs of the second lqudty factor Panel A: Second lqudty factor durng the to NBER recesson 41

43 Panel B: Second lqudty factor durng the to fnancal crss 42

44 The prelmnary results are very encouragng. They ndcate that the ratng and the prcng of bonds must ntroduce a lqudty factor n ther analyss, not only a default factor. They ndcate that the new regme detecton methodology adequately captures the shfts n default and lqudty rsks. It seems that durng the two crses, the bd-ask spread measures of lqudty rsk were the most mportant ones. The llqud measure of Amhud seems beng more mportant after the two crses for measurng the low volume of tradng. We stll try to fnd an nterpretaton but t s well known that the tradng actvty n fnancal markets was very low after the fnancal crss. 43

45 44

46 45

47 46

48 Credt spreads and Fed Funds Rate SLO - survey Fgure 3, Panel A Mean regmes BBB BBB - 10 yrs Fed Funds Rates SLO - Survey avr.-87 févr.-89 déc.-90 oct.-92 août-94 jun

49 Credt spreads and Fed Funds rate SLO - Survey Fgure 3, Panel B Mean regmes BBB and BB BBB - 10 yrs BB - 10 yrs Fed Funds Rates SLO - Survey janv.-94 nov.-95 sept.-97 jul.-99 ma-01 mars-03 janv