ERI Days North America 2013 NYC, October 9, :45-18:00

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2 ERI Days Norh America 2013 NYC, Ocober 9, :45-18:00 Hedging Long-Term Inflaion-Linked Liabiliies wihou Inflaion-Linked Insrumens Lionel Marellini Professor of Finance, EDHEC Business School Scienific Direcor, EDHEC-Risk Insiue Senior Scienific Advisor, ERI Scienific Bea This research has been suppored by Onario Teachers' Pension Plan in he conex of he "Advanced Invesmen Soluions for Liabiliy Hedging for Inflaion Risk" research chair

3 Ouline Inflaion risk versus liabiliy risk Expeced inflaion risk versus realized inflaion risk Diversifying versus hedging expeced inflaion risk 3

4 Inflaion risk versus liabiliy risk Expeced inflaion risk versus realized inflaion risk Diversifying versus hedging expeced inflaion risk 4

5 Inflaion Hedging wihou Inflaion-Linked Bonds The lack of capaciy of inflaion-linked (IL) bond markes, and he increased concern over counerpary risk for derivaives-based soluions, leave mos invesors wih he presence of nonhedgeable inflaion risk. This is a key concern since mos invesors implicily or explicily face IL liabiliies, or more generally consumpion needs. In his conex, a variey of radiional asse classes (socks and bonds) and alernaive asse classes (commodiies or real esae in paricular) have been analyzed in erms of heir abiliy o provide aracive inflaion-hedging benefis. The resuls of such empirical invesigaions have been mixed, wih resuls ha are subjec o subsanial model and parameer uncerainy. 5

6 Inflaion Hedging wih Financial Asses Esimaed correlaion beween asse classes and realized inflaion Socks (S), long erm nominal bonds (B) and commodiies (Com) have an upward-slopping erm srucure of correlaion wih realized inflaion. Socks (S), real esae (RE) and commodiies (Com) have a posiive correlaion wih inflaion (sronger resuls could be obained by increasing granulariy (see for example Ang e al. (2012) for equiy markes); on he oher hand, he shor-erm correlaion beween he reurn on inflaion-linked bonds (I) and inflaion is close o zero (!?). (*) Resuls based on Vasicek model calibraed over he period Q Q

7 Inflaion Hedging wih Financial Asses (Con') Beer resuls could be obained by increasing granulariy (see for example Ang e al. (2012) for equiy markes). Sample (shor-erm) correlaions beween asse classes and realized inflaion (Jan Jun. 2012) 7

8 Inflaion Hedging versus Liabiliy Hedging Wha jusifies he ineres in inflaion-hedging properies of various asse classes is he inuiion ha invesors wih inflaionlinked liabiliies need o inves in asses ha are posiively correlaed wih inflaion. This seemingly sraighforward inuiion is wrong, or a leas severely incomplee (as can be guessed from he virually zero correlaion beween reurn on IL bonds and inflaion). Wha maers is no he inflaion-hedging properies of various asse classes, bu insead heir liabiliy-hedging properies. 8

9 Inflaion Hedging versus Ineres Rae Hedging Liabiliy risk conains ineres rae risk(s) in addiion o inflaion risk(s), so inflaion risk hedging and inflaion-linked liabiliy risk hedging are wo disinc conceps ha coincide only a liabiliy mauriy. For reasonable parameer values, ineres rae risk dramaically dominaes inflaion risk when i comes o he conribuion o shorerm volailiy of he funding raio for long-erm IL liabiliies. From a mahemaical poin, his can be explained as follows: Ineres rae risk affecs liabiliy risk hrough he impac on he discoun facor, an impac ha increases wih ime-horizon. Inflaion risk affecs he value of he liabiliies hrough an impac on he cash-flows, which is no affeced by ime-horizon. I is only in he case of shor ime-o-horizon (say 1 year) ha inflaion risk becomes relaively subsanial wihin oal liabiliy risk. 9

10 Shor Term Liabiliy Risk Shor erm correlaion beween bond porfolios and liabiliies (%) Mauriy 15 Y 10 Y 5 Y 1 Y Bond porfolios B (10Y) B, I (10Y) The insananeous correlaion beween nominal bonds and IL liabiliies is close o 100 % for mauriies 10Y and 15 Y On he oher hand, for shor liabiliy mauriies (1Y), nominal bonds have lower correlaion wih liabiliies his correlaion falls o 0 for vanishing mauriies (i.e., a mauriy dae). (*) Resuls based on Vasicek model calibraed over he period Q Q

11 Shor Term versus Long Term Liabiliy Risk Hedging There exiss a fundamenal rade-off/conflic beween shor-erm and long-erm IL liabiliy risk hedging: Since real asses (e.g., commodiies) have no well-defined (real) ineres rae hedging properies, heir presence in liabiliy-hedging porfolio would generae high shor-erm volailiy in funding raio levels, and nominal bonds should be clearly preferred as subsiues for IL bonds. A horizon, however, he correlaion beween he (consan) payoff of nominal bonds and he (inflaion-linked) payoff of inflaion-linked liabiliy is zero: nominal bonds have no hedging power for inflaionlinked liabiliy paymens. In pracice, he shor-erm perspecive dominaes, and mos invesors only have fixed-income insrumens in heir liabiliyhedging porfolios, because of heir aracive ineres rae hedging properies. 11

12 Inflaion risk versus liabiliy risk Expeced inflaion risk versus realized inflaion risk Diversifying versus hedging expeced inflaion risk 12

13 Realized versus Expeced Inflaion Risk If realized inflaion risk is no a serious source of shor-erm funding raio volailiy for long-erm consan mauriy IL liabiliies, expeced inflaion risk can be. Nominal bonds are exposed o changes in real raes and expeced or break-even inflaion (*), while IL bonds and IL liabiliies are only exposed o changes in real raes (and realized inflaion). The concern would be a srong increase in expeced inflaion (which would lead o a drop in nominal bond prices), ypically in a conex where realized inflaion is high. (*) Break even inflaion rae = nominal rae real rae; changes in break even raes reflec changes in inflaion expecaions, bu also possible changes in inflaion risk premium as well as spurious effecs relaed o IL bond marke liquidiy facors. 13 Φ Φ ~ ~ d d d d Φ 100 d d d d 100 r r L r L T π π B π r r B r B z σ z σ τ D μ L L PV L z σ τ D z σ τ D μ B B PV B

14 Periods of Large Increases in Expeced Inflaion We consider four relaively shor periods wih high increase in expeced inflaion (from a local minimum o a local maximum). (*) Expeced inflaion is esimaed using he mehodology in Kohari and Shanken (2004, FAJ). 14

15 Reurns on Asses and Liabiliies in These Periods A massive underperformance of nominal bonds wih respec o IL liabiliies is obained on hese periods. Period Jan Aug Nov Oc Oc Mar Jul Dec Absolue increase in expeced inflaion (*) Reurn on GSCI Reurn on 10-year nominal bonds Reurn on 10-year liabiliies (*) (*) Expeced inflaion and liabiliy reurns are esimaed using he mehodology in Kohari and Shanken (2004, FAJ). Acual liabiliy reurns are used afer

16 Inflaion risk versus liabiliy risk Expeced inflaion risk versus realized inflaion risk Diversifying versus hedging expeced inflaion risk 16

17 Inflaion Hedging Ousanding Quesions Hedging IL liabiliies is a key challenge in he absence of IL linked bonds, which are he only (cash) securiies ha have perfec hedging properies for IL liabiliies a all horizons. In his conex, a number of imporan research quesions sand ou, wih a posiive answer already provided for he firs one: Q1: Can we find economic periods/regimes where long posiions in nominal bonds, which are he naural subsiues o IL bonds, are unable o provide saisfacory hedging for IL liabiliies, because of heir inabiliy o hedge agains changes in break-even inflaion? Q2: Can we use real asses in liabiliy-hedging porfolios o compensae for he risk of he poor performance of long posiions in nominal bonds in case of a jump in break-even inflaion? Q3: Alernaively, can we neuralize expeced inflaion risk exposure in nominal bonds so as o generae a beer mach wih respec o he inflaion-linked liabiliy porfolios? 17

18 Managing Expeced Inflaion Risk: Possible Approaches Diversifying away expeced inflaion risk (Q2) Saic approach: he sraegy here would consis in holding a all imes a saic mix of nominal bonds and real asses problem here is ha he allocaion o real asses will be much oo low in case of a surge in expeced inflaion, and much oo high in all oher marke condiions. Dynamic approach: he sraegy here would consis in holding a all imes a dynamic mix of he opimal LHPs under each paricular regime; he weighs assigned o each LHP are aken o be a funcion of he filered probabiliies for each regime o prevail looking forward. Hedging away expeced inflaion risk (Q3 ) Mach he expeced inflaion exposure (ha is neuralize i) and he real rae exposure wih respec o he liabiliies. In principle, his can be achieved hrough a suiably-designed dynamic long-shor porfolio sraegy in nominal bonds; in pracice, we need o analyze wheher his approach would work ou-of-sample. 18

19 A Formal Model We use he model of Munk, Sørensen and Vinher (2004) which allows for a sochasic expeced inflaion process ha evolves as: dπ and he price index follows: dφ π Φ d σ φ π π π d σ dz This model accouns for he fac ha neiher expeced inflaion risk nor real rae risk is enirely spanned by nominal bonds. Φ d z Φ π The abiliy of nominal bonds o hedge IL liabiliies depends on: Magniude of expeced inflaion risk (volailiy s p, speed of mean reversion j), The magniude of realized inflaion risk (volailiy s F ). 19

20 Preview of Resuls Using a wo-sae Markov regime swiching model, we find ha: Sae 1 corresponds o he larger uncerainy on expeced and realized inflaion, wih higher volailiies for boh processes; i does no disinguish however beween increases and decreases in expeced inflaion ; Sae 2 corresponds o he lower uncerainy: boh processes have lower volailiies, alhough expeced inflaion has lower speed of mean reversion. The esimaed speed of mean reversion is no lower in regime 1 han in regime 2, bu i is very imprecisely esimaed, wih a sandard error ha represens a leas half he esimae. Filered and smoohed probabiliies allow one o clearly idenify he wo inflaion regimes. 20

21 Esimaed Parameers and Probabiliies All parameers are sae-dependen. 21

22 Dynamic Hedging Sraegies The presence of regime swiches moivaes he use of dynamic liabiliy-hedging porfolio sraegy, by swiching from a 100% nominal bond LHP o a LHP conaining some allocaion o commodiies when i is recognized ha he high expeced inflaion regime has maerialized, for some crierion o be defined: Nom. Bonds Commodiies 1 x x In wha follows, we ake x = 25%, 50% or 75%, and he porfolio is hen lef buy-and-hold unil exi from he regime. We consider an idealized shifing sraegy wih no lag, and a sraegy wih a shif ha occurs wih a 6 monhs lag. 22

23 Dynamic Diversificaion Sraegies No Lag 1972 o 1989 Period Jan Aug Absolue increase in expeced inflaion (*) Absolue increase in Michigan Survey Absolue increase in 20 year break-even rae Reurn on GSCI Reurn on 20 year nominal bonds Reurn on 20 year liabiliies Reurn on dynamic sraegy wih x = 25% and no lag Reurn on dynamic sraegy wih x = 50% and no lag Reurn on dynamic sraegy wih x = 75% and no lag Reurn on dynamic sraegy wih x = 100% and no lag Nov Oc Feb May NA NA NA NA NA NA Nov Mar Ouperformance w.r.. liabiliies. Underperformance w.r.. liabiliies. (*) Before April 1999, expeced inflaion and liabiliy reurns are esimaed using he mehodology in Kohari and Shanken (2004, FAJ). 23

24 Dynamic Diversificaion Sraegies 6 Monhs Lag 1972 o 1989 Period Jan Aug Absolue increase in expeced inflaion (*) Absolue increase in Michigan Survey Absolue increase in 20 year break-even rae Reurn on GSCI Reurn on 20 year nominal bonds Reurn on 20 year liabiliies Reurn on dynamic sraegy wih x = 25% and 6 M lag Reurn on dynamic sraegy wih x = 50% and 6 M lag Reurn on dynamic sraegy wih x = 75% and 6 M lag Reurn on dynamic sraegy wih x = 100% and 6 M lag Nov Oc Feb May NA NA NA NA NA NA Nov Mar Ouperformance w.r.. liabiliies. Underperformance w.r.. liabiliies. (*) Before April 1999, expeced inflaion and liabiliy reurns are esimaed using he mehodology in Kohari and Shanken (2004, FAJ). 24

25 Dynamic Diversificaion Sraegies No Lag 1992 o 2009 Period Jan Dec Absolue increase in expeced inflaion (*) Absolue increase in Michigan Survey Absolue increase in 20 year break-even rae Reurn on GSCI Reurn on 20 year nominal bonds Reurn on 20 year liabiliies Reurn on dynamic sraegy wih x = 25% and no lag Reurn on dynamic sraegy wih x = 50% and no lag Reurn on dynamic sraegy wih x = 75% and no lag Reurn on dynamic sraegy wih x = 100% and no lag Oc Mar Jan Sep NA NA Jul Dec Ouperformance w.r.. liabiliies. Underperformance w.r.. liabiliies. (*) Before April 1999, expeced inflaion and liabiliy reurns are esimaed using he mehodology in Kohari and Shanken (2004, FAJ). 25

26 Dynamic Diversificaion Sraegies 6M Lag 1992 o 2009 Period Jan Dec Absolue increase in expeced inflaion (*) Absolue increase in Michigan Survey Absolue increase in 20 year break-even rae Reurn on GSCI Reurn on 20 year nominal bonds Reurn on 20 year liabiliies Reurn on dynamic sraegy wih x = 25% and 6 M lag Reurn on dynamic sraegy wih x = 50% and 6 M lag Reurn on dynamic sraegy wih x = 75% and 6 M lag Reurn on dynamic sraegy wih x = 100% and 6 M lag Oc Mar Jan Sep NA NA NA NA NA NA Jul Dec Ouperformance w.r.. liabiliies. Underperformance w.r.. liabiliies. (*) Before April 1999, expeced inflaion and liabiliy reurns are esimaed using he mehodology in Kohari and Shanken (2004, FAJ). 26

27 Expeced Inflaion Risk: Diversificaion vs. Insurance In he absence of IL bonds, commodiies are useful addiions o nominal bonds provided ha we have a subsanial allocaion o hem when needed, as opposed o a small allocaion o hem all he ime (dynamic vs. saic approach). In he end, he problem is no so much abou diversificaion (minimizaion of he volailiy of he funding raio over long periods of ime) han i is abou insurance (geing proecion in some very few specific economic condiions). We need o calibrae a parsimonious model o swich o he commodiies-dominaed LHP (before i is oo lae?) Which model o use is unclear: using a formal MRS model would no really help since i may no disinguish beween increases and decreases in expeced inflaion; perhaps a model based on observable sae variable would do beer? 27

28 Expeced Inflaion Risk: Diversificaion versus Hedging All he afore-menioned challenges could be avoided if one could neuralize he exposure o unexpeced inflaion in nominal bond porfolios, while maching he real rae exposure wih respec o he liabiliies. In principle, his can be achieved hrough a suiably-designed porfolio sraegy involving long/shor porfolios of nominal bonds (a shor posiion in nominal bonds would generae a profi in case of a large increase in expeced inflaion, wihou he need for iming he regime). In pracice, we need however o analyze he ou-of-sample robusness of he approach in he presence of parameer uncerainy. 28

29 Model-Free Bond Prices In general, nominal bond prices can be wrien as funcion of real yields and break-even expeced inflaion: B B 1 B exp r, T p 1, T T 1 1 T1 B r, T p 1, T1 2 2 exp B B B r, p 2, T 2 2 T2 B r, T p 2, T2 2 2 T T Inflaion-indexed bond prices wrien as funcion of mauriydependen real ineres rae and CPI level: I I F expr, L L L I r, L 29

30 Esimaion wih OLS Assumpion on shifs in real ineres rae and break-even expeced inflaion: T2, T1 L, T1 dr b d r ; dr b dr, T, T,, T 2 1 L 1 d T2, T1 p, T dp 2, T1 Inuiion suggess ha long-erm inflaion expecaions are less volaile han shor-erm inflaion expecaions (i.e., β(t 2,T 1 ) <1). Nominal and real yields are observed, and break-even expeced inflaion inferred from observed yields: p, T y 1, T r 1, T1 p, T y 2, T r 2, T2 Regression equaion: T2, T1 T2, T1 p p 2 1, T 0, T T T 2, 1 30

31 Replicaing Sraegy L : consan-mauriy liabiliy porfolio A : replicaing porfolio consiued by wo nominal bonds and cash 1 2 da db db w1 w w1 w2 rd A B B Main idea: maching he exposures o changes in he real ineres rae and break-even expeced inflaion. We obain he following sysem (o which can poenially be added leverage consrains): w T w T b b T2, T1 w1 T1 w2 T2 0 T, T, T L 2 1 L 1 31

32 Long-Shor Porfolio The soluion is a long-shor porfolio sraegy: Expression of weighs: w w 1 T, T T, T T1 b T, T T, T T1 b b L, T T, T L L b 1 2 1, T L 1 Expeced sign ( T 1 < T 2 ): + Expeced signs are based on he inuiion ha: β T, T bt T 2 1 2, Decreasing in T We use T 1 = 5Y, T 2 = 20Y, L = 10Y, and we esimae he beas over 2-year rolling windows. 32

33 Backes of Replicaing Sraegy The sraegy deviaes from liabiliies in November 2008, when here was a subsanial drop in ineres raes (+100 bps). Accuracy of he sraegy could be improved by adding a convexiy adjusmen. (*) (*) I can also be poenially improved by seeking o neuralize changes in he shape of he yield curve using a parsimonious model such as he Nelson-Siegel model. 33

34 Consraining Parameers b(t 2,T 1 ) and b( L,T 1 ) Anoher idea is o se b(t 2,T 1 ) = b( L,T 1 ) =1 so as o reduce he number of parameers o esimae and o limi he volailiy of he weighs. This has a negaive impac on he long-erm performance. Sraegy wih 150% oal leverage consrain. 34

35 Forward-Looking Esimaes Coefficiens are no consan over ime! Idea is hus o generae forward-looking esimaes for b and by regressing rolling-window esimaes ono a se of predicive variables. 35

36 Predicive Regression of Coefficiens We run he following predicive regression for each coefficien: β T2, T1 1 κ0 κ1' X ε 1 where X is a vecor of predicors ha conains he curren esimaed coefficiens (T 2,T 1 ), b(t 2,T 1 ) and b( L,T 1 ), as well as wo macro-economic predicors (2Y break-even rae and unemploymen rae - Ang and Piazzesi (2003)). 36

37 Backes of Replicaing Sraegy As before, we impose a 150% oal leverage consrain. The replicaion is more accurae han wih rolling-window esimaes for he coefficiens. 37

38 Main Conclusions Liabiliy risk hedging is differen from inflaion risk hedging: Ineres rae risk srongly dominaes (realized) inflaion risk wihin shor-erm liabiliy risk, excep a liabiliy mauriy. Nominal bonds appear as a good subsiue for IL bonds, excep in case of a surge in expeced inflaion. This concern can be addressed in wo possible ways: Add real asses o provide diversificaion if and when needed bu hey probably belong o he PSP, no LHP. Implemen L/S nominal bond allocaion sraegies so as o hedge away exposure o expeced inflaion. Boh mehods suffer from a number of shorcomings when feasible, using IL bonds is he only opion ha always works. 38