Modelling US & Australian 10-year bond yields

Transcription

1 Economics & Markes Modelling US & Ausralian 10-year bond yields 23 Ocober 2008 Auhor: Dr. Alex Joiner Economis Alex.Joiner@anz.com Key poins In his noe we provide an economeric analysis of US and Ausralian 10-year bond yields over he pas wo-decades. Firsly, i is found ha he conundrum period of lower han expeced US bond yields in recen years can be explained by aking ino accoun he significan increased in holding of US bonds by foreign eniies. Subsequen o his adjusmen, he relaionship beween US macroeconomic variables and 10-year bond yields is remarkably sable over ime. Using a relaively parsimonious specificaion, he model developed explains around 94% of he variaion of US yields since Secondly, upon developing he model of US bond yields a similar framework is applied o modelling Ausralian bond yields. Despie he decoupling of he US and Ausralia s economic and moneary policy cycles, US bond yields remain an imporan driver of domesic yields. However, i is found he srengh of he relaionship beween he respecive yields has diminished significanly. I is clearly demonsraed ha Ausralian macroeconomic facors and moneary policy sance have become increasingly imporan in explaining movemens in domesic yields. Developing a model based on his framework allows us o explain around 90% of he variance of Ausralian bond yields over he pas decade. The models can be used o anchor forecass of bond yields and o underake scenario analysis for a variey on underlying macroeconomic scenarios. Figure 1: Modelling US bond yields 10 % US 10-year bond yield "Conundrum" period 5 Our Vision: For Economics & Markes o be he mos respeced, soughafer and commercially valued source of economics and markes research and informaion on Ausralia, New Zealand, he Pacific and Asia US 10-year bond yield Un-adjused US 10-year bond yield model Source: Bloomberg, ANZ

2 Modelling US bond yields Modelling US & Ausralian 10 year bond yields The conundrum period of lower han expeced 10-year bond yields ha began o occur around has seen mos radiional economeric models break down. These models employed various saple macroeconomic and financial variables ye were consisenly overesimaing bond yield levels. Despie having successfully explained hisorical movemens in yields (see he un-adjused model in Figure 1). I was no unil modelling began o incorporae variables ha refleced he significanly increased demand for US bonds ha he problem was solved. An example of his, which is adoped in our modelling, is he work of Bandholz, Closermann and Seiz (2007). 1 BCZ focus on explaining he US bond yield conundrum economerically by employing a srucural variable ha accouns for he increased demand for US reasuries by non-us eniies, ha has been driven by: The need o gain a reurn on huge accumulaions of US dollar foreign exchange reserves, paricularly by he cenral banks of curren accoun surplus economies. The wo larges accumulaors of FX reserves, China and Japan are also he wo larges holders of US reasuries. The invesmen of increasing oil revenues by OPEC naions (mos likely in par via he UK and offshore financial cenres) in he relaively high oil price environmen beginning in lae Srong liquidiy growh driven by accommodaive moneary policy. Excluding-Japan (due quaniaive easing) M2 growh (in US$) in he G7 has averaged jus over 9% per year for he pas five years. In Asia, his rae of growh is closer o 14% per annum over he same period acceleraing o close o 20% in recen years. Figure 2: Foreign holdings of US reasuries 3 US$, rillion % of oal deb US Treasuries as % of oal federal deb (RHS) Value of Foreign holdings of US Treasuries (LHS) Source: US Federal Reserve, Daasream, ANZ Once employed, in a modelling conex, his variable acs o srucurally realign bond yields over ime, in his case o a lower level. BCZ presen such a variable as a funcion of foreign demand for reasuries. However, srucurally lower bonds yields generally are mos likely due o a range of facors, including increased foreign demand, ha have prevailed in he marke over he las 20 years. Oher significan facors include increased demand from US insiuional invesors; a reducion of risk aversion due o a less volaile global economic environmen; and generally lower levels of inflaion since he widespread inroducion of inflaion argeing by global cenral banks. In a modelling sense, all hese facors are successfully proxied by he increase demand from foreign holders of US reasuries. 1 Explaining he US Bond Yield Conundrum (2007) Bandholz, H., Closermann, J., Seiz, F. MPRA Paper February This paper in available online: hp://mpra.ub.uni-muenchen.de/2386/ Page 2

3 Modelling US & Ausralian 10 year bond yields This srucural decrease of bond yields has had a profound impac on all asse classes. The fall in he benchmark risk-free rae has lowered he hurdle for reurns in oher asse classes, serving o push he prices of hese asses ever higher. This was seen paricularly in equiies, commercial and residenial propery prices in he pre-credi crisis period. Wih oher bond yields priced off US yields his effec spread hroughou global financial markes. Model esimaion - US 10-year bond yields We simplify he general approach of BCZ, who esimae a vecor error correcion model, o esimae an ordinary leas squares model. In his way, he focus is on he medium o long erm relaionships beween economic variables and bond yields and fied esimaes reflec a fair value of bond yields over ime. The variables used in he model follow wha is a common specificaion of bond yield models in academic lieraure, wih he addiion of he variable o accoun for foreign holdings of bonds. The long-erm bond yield is modelled as a funcion of he shorerm ineres rae, inflaion and a proxy for business-cycle condiions. Specifically, he variables are: US 10-year bond yields, US 3-monh LIBOR (%), he annual rae of US core inflaion (%), he ISM manufacuring index and he raio of Foreign held US Treasuries o he oal amoun of foreign deb ousanding (%). 2 The period of esimaion is January-1986 o Augus The esimaed equaion akes he following form: i US 10 year = α + β i + φπ + λy + ψ reasuries + ε 3m libor core ism The resuls of he OLS esimaion of he above equaion gives: Table 1 OLS resuls US 10-year bond yields Esimae s.e. -sa P-val. consan (α ) monh LIBOR (β ) Core inflaion (φ ) ISM (λ ) Treasuries (ψ ) R S.D. dependen var 1.62 S.E. of regression DW saisic This parsimonious specificaion explains over 94% of he variaion of US 10-year bond yields (see Figure 1). All coefficiens are saisically significan and are correcly signed (having he expeced economic inerpreaion). We find ha: a 100 bps increase in he 3-monh LIBOR resuls in a 28bps increase in 10-year bond yields. In line wih he expecaion ha he yield curve will flaen/seepen wih higher/lower yields a he shor end, largely wih moves in moneary policy. a core inflaion rae ha is 1% higher will raise 10 year bond yields 52bps. Ineresingly, his esimae is slighly lower han hisorical sudies, which may indicae inflaion expecaions have become beer anchored in he las decade, reflecing a period of relaive moneary sabiliy. a 1.0 poin move in he ISM index (which is roughly equivalen o a 0.2pp move in real GDP growh) will raise 10 year bond yields 7bps. This indicaes ha yields are pro-cyclical and will rise on he expecaion ha he economy will ener an expansionary phase. a 100 bps increase in proporion of US Treasuries held overseas resuls in a 9bps decrease in 10-year bond yields. The fall in yields reflecs srong foreign demand for reasuries. 2 Financial variables are end-monh raher han monh average, sourced from Bloomberg. 3 Firs order serial correlaion is inheren in models ha adop he fair value approach as aken here. This can be solved by applying a lag of he dependen variable in he specificaion (refleced in a DW much closer o 2). Doing his does no change he raio of he variables o each oher and i is herefore concluded ha he presence of serial correlaion is no having a significan negaive impac on he saisical qualiy of he parameer esimaes in he fair value model. Page 3

4 Modelling US & Ausralian 10 year bond yields Imporanly, he inclusion of he Treasuries(ψ ) variable significanly improves he explanaory power of he model in he boh he conundrum period bu also hroughou he hisorical sample. The variable also significanly ou performs he use of dummy variables, especially as a saisically significan srucural break canno be found. Modelling Ausralian bond yields Many developed economy bond yields can be priced-off US yields and i is found in his noe ha his remains rue for Ausralia. This is despie divergen economic performance and moneary policies in recen years as he Ausralian economy becomes ever more relian on faser growing developing counries in he Asian region. However, i is found ha he link beween US and Ausralian bond yields has weakened significanly in he recen decade. The modelling approach is similar o ha above wih he specificaion including shor erm domesic ineres raes, core inflaion 4 as well as he US shor erm ineres rae and US 10 year bond yield. The model is esimaed from March-1986 o Augus- 2008, aking he following form: i Aus 10 yr = α + ξi + χπ + ωi + β i + υ US 10 year RBAcore 90 daybbsw 3m libor The resuls of he OLS esimaion of he above equaion gives: Table 2 OLS resuls Ausralian 10-year bond yields Esimae s.e. -sa Prob. consan (α ) US 10-year yield (ξ ) RBA core inflaion (χ ) day bank bill (ω ) US 3-monh LIBOR (β ) R S.D. dependen var 2.95 S.E. of regression DW saisic 0.47 The model successfully accouns for 97% of he variance of Ausralian bond yields (see Figure 3 overleaf) over he period wih all variables saisically significan and correcly signed. a 100 bps increase in he US 10-year bond yield resuls in a 120bps increase in Ausralian 10-year bond yields. This reflecs boh he reliance of domesic yields on he US, as well as he risk premium aached o Ausralian bonds over he period. Alhough modelled as separae variables, he US LIBOR and 90-day bill rae are inerpreed as he difference in moneary policy sance. As such, a widening of his differenial resuls in a 9bps increase in domesic bond yields. a core inflaion rae ha is 1% higher will raise 10 year bond yields 7bps. This esimae seems quie low and may be explained by much of he domesic expeced inflaionary impac on yields being explained by nominal US yields which are a funcion of US inflaion. Ineresingly, domesic business cycle condiions (as proxied by real GDP growh amongs oher variables esed) were found o be non-significan o Ausralian bond yields over he period. Similar o inflaion, given he high correlaion beween he US and Ausralian economies, especially over he firs half of he sample, he US bond yield co-efficien is mos likely masking domesic economic facors. 4 Core inflaion is defined as he average of he Reserve Bank s saisical measures of inflaion. Quarerly observaions are exrapolaed o consruc a monhly series. Page 4

5 Modelling US & Ausralian 10 year bond yields In he same vein, rends in he holding of Ausralian Treasuries has followed wha has aken place in he US wih a significan increase in he proporion of foreign ownership. In he lae 1980 s around 20% of domesic Treasuries were held offshore. As of he end of lae-2007, his proporion had jumped o 65%. However, his impac of his demand in he model is capured he srucural shif downwards of US bond yields. Figure 3: Modelling Ausralian bond yields % p.a Acual Aus. bond yields 10 8 Aus. bond yield model Source: Bloomberg, ANZ Despie he presence of heeroscedasiciy (non-consan variance of residuals) no being deeced saisically in he model, an ocular examinaion of he acual and fied values in Figure 3 does raise some concerns. The fied value consisenly over- or under-shoos he acual value in he second-half of he esimaion period. This occurs due o he variance of yields in he second-half of he period being considerably less han in he firs. This decrease in variance has aken place in many macroeconomic variables and is a consequence of well-anchored inflaion expecaions in he inflaion argeing period of Ausralian moneary policy. In his case, his invies he use of an alernae mehodology o ake accoun of non-consan variance or o more simply re-esimae he model over a shorer period, which is wha is done here. The sample period is biseced, o begin in 1998 around five years ino he Reserve Bank of Ausralia s formal inflaion argeing period. The sandard deviaion of yields is 270bps in he period 1986 o 1997, bu only 45bps from 1998 onwards confirming ha a re-esimaion of he model should be able o provide improved resuls. Table 3 demonsraes his improved performance of he model. Table 3 OLS resuls Ausralian 10-year bond yields shor sample Esimae s.e. -sa Prob. consan (α ) US 10-year yield (ξ ) RBA core inflaion (χ ) day bank bill (ω ) US 3-monh LIBOR (β ) Real GDP growh (λ ) R S.D. dependen var S.E. of regression DW saisic The variables used explain 89% of he variance in yields which is slighly less han he longer sample model. However, he sandard error of he regression is only 17bps as opposed o he 49 bps of he previous model. This provides a significan improvemen in he cerainy around, and robusness of, he poin esimaes which also is beneficial for producing projecions wih he model. Page 5

6 Modelling US & Ausralian 10 year bond yields Anoher significan change in he model esimaes is he diminished influence of US bond yields on Ausralian yields in favour of domesic macroeconomic variables. The deail of his occurrence is as follows: a 100 bps increase in he US 10-year bond yield resuls in a 77bps increase in Ausralian 10-year bond yields. This esimae is much lower han he 120bps found in he longer sample model, reflecing less reliance of domesic yields on US yields. Tha being said, he hisorical pricing behaviour remains he key driver Ausralian yields (having he larges coefficien esimae). Similarly, he difference in moneary policy sance has become more imporan wih a widening of shor end yields resuling in a 15bps increase in domesic bond yields. Domesic inflaion has become significanly more imporan in explaining movemens in yields due o he increased ransparency of moneary policy over he las decade. A core inflaion rae ha is 1% higher will raise 10 year bond yields 33bps, more han four imes he previous esimae. Domesic business cycle condiions are also now included in his framework, afer being found o be saisically non-significan in he previous model. A rae of real GDP growh ha is 1% higher adds 8bps o yields. This is around he same impac as he US business cycle has, as proxied by he ISM index, has on US yields. Figure 4: Modelling Ausralian bond yields Sep % p.a. Acual Aus. bond yields % confidence inerval Aus. bond yield model Source: Bloomberg, ANZ Conclusion The economeric models developed here ake a relaively simple approach o producing fair value esimaes for US and Ausralian 10-year bond yields. The cenral conclusion of his exercise has been ha he hisorical, and empirically proven, relaionship beween Ausralian and US yields remains relevan despie he decoupling of moneary policy and macroeconomic cycles. I is clearly demonsraed ha alhough he relaionship remains imporan, Ausralian macroeconomic facors and moneary policy sance have become increasingly imporan in explaining movemens in domesic yields. Page 6

7 Conacs ANZ Economics & Markes Saul Eslake Fiona Allen Chief Economis Business Manager Saul.Eslake@anz.com Fiona.Allen@anz.com Tony Pearson Mark Rodrigues Julie Toh Paul Deane Depuy Chief Economis, Indusry and Sraegic Senior Economis, Indusry and Sraegic Senior Economis, Indusry and Sraegic Rural and Regional Economis Tony.Pearson@anz.com Mark.Rodrigues@anz.com Julie.Toh@anz.com Paul.Deane@anz.com Warren Hogan Kaie Dean Riki Polygenis Dr. Alex Joiner Head of Ausralian Economics and Ineres Raes Senior Economis, Ausralian Economics and Ineres Raes Economis, Ausralian Economics and Ineres Raes Economis, Ausralian Economics and Ineres Raes Warren.Hogan@anz.com Kaie.Dean@anz.com Riki.Polygenis@anz.com Alex.Joiner@anz.com Paricia Gacis Jason Hill Sraegis, Markes Credi Analys Ausralian Economics and Ineres Raes Paricia.Gacis@anz.com Jason.Hill@anz.com Amy Auser Tony Morriss Jasmine Robinson Amber Rabinov Head of Foreign Exchange and Inernaional Economics Senior Currency Sraegis, Foreign Exchange and Inernaional Economics Senior Economis, Foreign Exchange and Inernaional Economics Economis, Foreign Exchange and Inernaional Economics Amy.Auser@anz.com Tony.Morriss@anz.com Jasmine.Robinson@anz.com Amber.Rabinov@anz.com Mark Pervan Amber Rabinov Doug Whiehead Naalie Roberson Head of Commodiies Economis, Commodiies Sof Commodiy Sraegis Graduae Analys Mark.Pervan@anz.com Amber.Rabinov@anz.com Doug.Whiehead@anz.com Naalie.Roberson@anz.com Paul Braddick Ange Monali Dr. Alex Joiner Sephanie Wayne Head of Propery and Financial Sysem Senior Economis, Propery and Financial Sysem Economis, Propery and Financial Sysem Analys, Propery and Financial Sysem Paul.Braddick@anz.com Ange.Monali@anz.com Alex.Joiner@anz.com Sephanie.Wayne@anz.com Paul Gruenwald Ivy Tan Tamara Henderson Joshua Saldanha Chang Wei Liang Head of Asian Economics, Singapore Associae Direcor, Credi, Markes Asia Direcor, Currency and Raes Sraegy, Markes Asia Associae Direcor, Macroeconomics, Markes Asia Inern, Markes Asia Paul.Gruenwald@anz.com Ivy.Tan@anz.com Tamara.Henderson@anz.com Joshua.Saldanha@anz.com WeiLiang.Chang@anz.com & Informaion Services Mary Yaxley Marilla Rough Manesha Jayasuriya Head of & Informaion Senior Informaion Officer, R&IS Informaion Officer, R&IS Services Mary.Yaxley@anz.com Marilla.Rough@anz.com Manesha.Jayasuriya@anz.com ANZ New Zealand Cameron Bagrie Khoon Goh Philip Borkin Seve Edwards Kevin Wilson Chief Economis Senior Economis Economis Economis Rural Economis Cameron.Bagrie@anz.com Khoon.Goh@anznaional.co.nz Philip.Borkin@anznaional.co.n seve.edwards@anznaional. TKevin.Wilson@nbnz.co.nz z co.nz David Croy Sraegis, Ineres Rae Sraegis David.Croy@anz.com Page 7

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