Forecasting Government Bond Risk Premia Using Technical Indicators

Transcription

1 Forecasing Governmen Bond Risk Premia Using Technical Indicaors Jeremy Goh Singapore Managemen Universiy Jun Tu Singapore Managemen Universiy Fuwei Jiang Singapore Managemen Universiy Guofu Zhou Washingon Universiy in S. Louis July 28, 2013 Corresponding auhor. Send correspondence o Jun Tu, Lee Kong Chian School of Business, Singapore Managemen Universiy, Singapore ; ujun@smu.edu.sg; phone: We are graeful o paricipans of 2011 Xiamen Universiy Workshop in Fixed Income and Bond Marke, 2012 Peer C.B. Phillips PhD Summer Camp in Financial Economerics, 2012 SMU-ESSEC Symposium on Empirical Finance and Financial Economerics, 2012 China Inernaional Conference in Finance, 2012 SMU Finance Summer Camp, 2012 FMA Annual Meeing, seminar paricipans a Universiy of Houson and Washingon Universiy in S. Louis, Hendrik Bessembinder, Yongmiao Hong, Jaehoon Lee, Michael Lemmon, Neil Pearson, Peer Phillips, Lucio Sarno, Farris Shuggi, and Jun Yu for very helpful commens. Tu acknowledges financial suppor from Sim Kee Boon Insiue for Financial Economics.

2 Forecasing Governmen Bond Risk Premia Using Technical Indicaors Absrac While economic variables have been used exensively o forecas bond risk premia, lile aenion has been paid o echnical indicaors which are widely used by praciioners. In his paper, we sudy he predicive abiliy of a variey of echnical indicaors vis-á-vis he economic variables. We find ha echnical indicaors have significan in boh in- and ou-of-sample forecasing power. Moreover, we find ha using informaion from boh echnical indicaors and economic variables increases he forecasing performance subsanially. We also find ha he economic value of bond risk premia forecass from our mehodology is comparable o ha of equiy risk premium forecass. JEL classificaions: C53, C58, G11, G12, G17 Keywords: Bond risk premium predicabiliy; Economic variables; Technical analysis; Movingaverage rules; Volume; Ou-of-sample forecass; Principal componens

3 I. Inroducion The abiliy o predic ineres raes movemens are imporan o marke paricipans such as bond invesors, policy makers, and financial economiss. For he policy makers, undersanding of he evoluion of fuure ineres raes will aid he fine urning of macroeconomic moneary policies. For he bond invesors, undersanding ineres raes predicabiliy may ranslae ino higher bond reurns performance. There are numerous sudies ha use various financial and macroeconomic variables o predic he excess reurns and bond risk premia on U.S.governmen bonds. For examples, Fama and Bliss (1987) provide evidence ha he n-year forward spread predics n-year bond risk premia. Keim and Sambaugh (1986), Fama and French (1989), and Campbell and Shiller (1991) show ha yield spreads have similar predicive power oo. In he inernaional markes, Ilmanen (1995) find models using macroeconomic variables can forecas bond risk premia. More recenly, based on a linear combinaion of five forward raes, Cochrane and Piazzesi (2005) find much higher predicive power in erms of R 2, beween 30% and 35%. Their sudy focused on risk premia on shor-erm bonds wih mauriies ranging from wo o five years. Ludvigson and Ng (2009) demonsrae furher ha he impressive predicive power found by Cochrane and Piazzesi (2005) can be improved upon using five macroeconomic facors ha are esimaed from a se of 132 macroeconomic variables. In his paper, we sudy he forecasing power of a new se of bond risk premia predicors. We use echnical indicaors (pas price/volume paerns) consruced from boh he bond and sock marke as he se of predicors. Sudies ha use echnical indicaors as predicors of sock reurns dae back o Cowles (1933) and hey are sill being sudied oday. For example, Brock, Lakonishok, and LeBaron (1992), Bessembinder and Chan (1998), Lo, Mamaysky, and Wang (2000), Han, Yang, and Zhou (2012), and Neely, Rapach, Tu and Zhou (2012), among ohers, find evidence supporing echnical indicaors having significan forecasing power on he equiy risk premium. Perhaps, his may be one of he reasons why echnical indicaors are widely employed by raders 1

4 and invesors (e.g., Schwager, 1989, 1992, 2012; Billingsley and Chance, 1996; Covel, 2005; Park and Irwin, 2007; Lo and Hasanhodzic, 2010) o discern marke rends. 1 Despie he voluminous amoun of research in he forecasing power of echnical indicaors in he equiy marke, o he bes of our knowledge, his is he firs paper ha examines he usefulness of echnical indicaors in he bond marke. In bridging his equiy-bond marke gap, we seek o answer wo quesions: (1) Do echnical indicaors provide useful informaion in forecasing bond risk premia? (2) Do combinaions of echnical and economic indicaors, such as forward raes and macroeconomic variables ouperform ha of jus using echnical indicaors alone? In addiion, we exend he findings of earlier sudies by Cochrane and Piazzesi (2005) and Ludvigson and Ng (2009) (on shor-erm governmen bonds) by sudying he predicabiliy of long-erm governmen bond risk premia wih mauriies ranging from 17 o 20 years. In his sudy, we use a oal of 63 echnical indicaors. The firs ype of echnical indicaors is consruced based on moving averages of lagged forward spreads. Cochrane and Piazzesi (2005) provide srong empirical evidence ha lagged forward raes conain informaion abou excess bond reurns beyond ha conained in forward raes of curren period. Their finding suggess ha curren erm srucure does no span all informaion relevan o he forecasing of fuure excess reurns. Given his, we consruc he firs 48 echnical indicaors based on he moving averages of pas forward spreads in he sandard way of rend-following echnical analysis. Technical analyss frequenly use volume daa in conjuncion wih hisorical prices o idenify marke rends. In ligh of his, he second group of echnical indicaor for his sudy will be consruced based on on-balance volume (e.g., Granville, 1963). Since bond marke rading volume daa are unavailable o us, we consruc he nex 15 echnical indicaors based on sock marke rading volume. 2 Hence, we have in oal 63 echnical indicaors. 1 In foreign exchange markes, academic sudies generally find sronger suppor for he predicabiliy of echnical indicaors. For example, Neely, Weller, and Dimar (1997), LeBaron (1999) and Neely (2002) show ha moving averages generae subsanial porfolio gains for currency rading. Moreover, Menkhoff and Taylor (2007) argue ha echnical analysis oday is as imporan as fundamenal analysis o professional currency mangers. 2 Given ha he sock and bond markes are closely relaed (e.g., Fama and French, 1989; Lander, Orphanides and Douvogiannis, 1997; Campbell and Vuolenaho, 2004; Goyenko and Ukhov, 2009; Bekaer and Engsrom, 2010), he sock marke volume echnical indicaors can serve as a reasonable proxy for bond marke volume indicaors. We do no examine he echnical indicaors based on sock price moving averages as hey are dominaed by he same moving 2

5 Economerically, including a large number of echnical indicaors in a predicive regression model simulaneously makes in-sample over-fiing a grea concern. In doing so, i will likely resul in poor ou-of-sample forecass. 3 To avoid over-fiing, following Ludvigson and Ng (2007, 2009, 2011), we generae bond risk premia forecass based on a small number of principal componen (PC) facors exraced from he se of 63 echnical indicaors. We analyze he predicabiliy for boh in- and ou-of-sample, because boh approaches have heir relaive srenghs. The use of he enire sample enables in-sample ess o be more powerful for deecing he exisence of reurn predicabiliy. In-sample esimaion also provides more efficien parameer esimaes and hence more precise esimaes of he expeced bond risk premium. On he oher hand, ou-of-sample mehods implicily es he sabiliy of he daa-generaing process and guard agains in-sample overfiing. Moreover, as emphasized by Goyal and Welch (2008), ou-ofsample ess are clearly more relevan for invesors. 4 Employing boh in-sample and ou-of-sample ess help o esablish he robusness of our resuls. In our in-sample analysis, we firs examine he predicive abiliy of sandalone echnical indicaors in a facor-augmened predicive regression framework. Then, we invesigae wheher hese echnical indicaors conain incremenal predicive informaion beyond ha of using CP and LN, he predicors of Cochrane and Piazzesi s (2005) and Ludvigson and Ng s (2009) sudies, respecively. Our in-sample analysis shows ha our se of echnical indicaors has sronger predicive power. For 2- o 5-year shor-erm governmen bonds, over he sample period beween January 1964 and December 2007, boh CP and LN display srong forecasing power, wih he R 2 range of 31 36% and 14 23%, respecively. Consisen wih previous sudies, he R 2 of CP falls o he range of 21 26% when he sample is exended o cover he December 2011 period (which includes he recen financial crisis). In conras, our se of echnical indicaors consisenly generaes high R 2 for boh sample periods, wih he values up o abou 34%. averages based on bond daa. 3 For insance, Hansen (2009) finds ha good in-sample fi is ofen relaed o poor ou-of-sample performance. 4 See Leau and Ludvigson (2009) for a review on in-sample versus ou-of-sample asse reurn predicabiliy. 3

6 I is ineresing o noe ha for he 17- o 20-year long-erm governmen bonds, he in-sample R 2 of LN decreases significanly o abou 5% over 1964:01 o 2007:12 period, bu he R 2 of CP is sill higher han 27%. To our surprise, he se of echnical indicaors consruced o predic he shor-erm bond risk premium, have R 2 of approximaely 45% and 40% over he 1964: :12 and 1964: :12 periods, respecively, for all long-erm mauriies. These resuls are much higher han hose of he shor end of he erm srucure. When uilizing informaion from boh echnical indicaors and economic variables, he resuls are sunning. Forecass from he combinaion of echnical and economic indicaors perform he bes, wih R 2 s up o 50% over he period 1964: :12, for boh shor- and long-erm governmen bonds. We sudy he ou-of-sample predicive abiliy of echnical indicaors based on he Campbell and Thompson s (2008) ou-of-sample R 2 saisic, R 2 OS, which measures he percenage reducion in he mean squared predicive error. Following mehodology from many of he ou-of-sample sudies, we ransform he echnical facors ino bond risk premia forecass using a recursive predicive regression model. We calculae he R 2 OS saisics for he ou-of-sample predicive regression forecass based on echnical indicaor facors relaive o hisorical average benchmark forecas. In he recursive procedure, a any ime, we implemen he predicive regressions wih all predicors, such as echnical indicaor facors, CP, and LN, using informaion available only up o. This mehodology avoids he look-ahead bias or he use of fuure informaion. Our ou-of-sample resuls corroborae ha of he in-sample resuls. Similar o findings for he equiy marke, he bond marke ou-of-sample evidence is generally weaker han he in-sample resuls. For 2- o 5-year shor-erm governmen bonds, he forecass based on CP have R 2 OSs up o 18% over he 1975: :12 ou-of-sample evaluaion periods. The R 2 OS s of CP furher decline o abou 3% over he longer 1975: :12 period. In addiion, LN have R 2 OSs of only 4.7%, 0.1%, 1.4% and 4.2%, respecively, for mauriies varying from 2 o 5 years. Similarly, he R 2 OSs of our echnical indicaors are lower han he corresponding in-sample ones. Neverheless, our echnical indicaors sill perform quie well over boh he 1975: :12 and 1975: :12 ou-of-sample periods, wih he R 2 OS up o 26% and 4

7 22%, respecively. When all he predicors are combined ogeher, he R 2 OSs improve subsanially o abou 33% during 1975: :12. For long-erm bonds, he resuls qualiaively he same, wih he R 2 OS range of 20 24%. Saisically, boh he in- and ou-of-sample resuls are highly significan. The quesion ha remains o be answered is, wheher he saisical significance is of economic value for he invesors. To assess he economic value of he ou-of-sample bond risk premia forecass, we follow he sraegy oulined by Kandel and Sambaugh (1996) and Pásor and Sambaugh (2000) and many ohers. As wih hese sudies, we examine he uiliy gains from an asse allocaion perspecive. To be more specific, we consider an invesor who opimally allocaes a porfolio beween an n-year Treasury bond and one-year risk-free Treasury bill. We assume a mean-variance uiliy funcion for simpliciy as in Campbell and Thompson (2008) and ohers. We calculae he average uiliy gain of he invesor when he/she forms porfolios using he ou-of-sample excess bond reurn forecass generaed by our proposed predicors. The uiliy gain is calculaed by comparing uiliy generaed by our predicors versus one ha is generaed wihou any models. This mehod of calculaion is similar o boh he Zhu and Zhou (2009) and Neely, Rapach, Tu and Zhou (2011) sudies, in he conex of assessing he economic value of echnical analysis. One way of looking a he uiliy gain is o hink of i as he porfolio managemen fee ha he invesor would be willing o pay o have access o he predicive regression models. Anoher advanage of his approach is ha i uses a uiliy funcion, which capures invesor s risk aversion. Our mehodology, which is o calculae invesors uiliy gain addresses he criicism ha many sudies peraining o profiabiliy of echnical indicaors are ad hoc in naure. As an example, suppose he risk aversion coefficien of an invesor is hree, hen from our resuls, his invesor will be willing o pay an annualized porfolio managemen fee up o 2.77%, over he ime period 1975: :12, in order o have access o he 5-year governmen bond reurn forecas uilizing echnical indicaors. The fee can be as high as 3.06% when uilizing informaion conained in he combined echnical and economic predicors. If he indicaors were excluded, he fee drops o 0.69%. Over he exended 1975: :12 period, he fee for having access o 5-5

8 year bond forecass uilizing all he predicors falls o 2%. In his case, he imporance of echnical indicaors becomes more apparen because wihou hem, he fee would furher drop o an economically undesirable level of 1.23%. For he 17- o 20-year long-erm governmen bonds, he economic values are relaively large, abou 3% for he 1985: :12 and 1985: :12 periods. The economic value assessmen is imporan as i sheds ligh on why he bond marke is much more predicable han he sock marke in erms of R 2 (e.g., Della Core, Sarno, and Thornon, 2008; Thornon and Valene, 2012). In he equiy marke, as repored in a recen sudy by Neely, Rapach, Tu and Zhou (2011), he maximum monhly ou-of-sample R 2 OS is 1.79%, and he maximum annual ou-of-sample uiliy gain is 4.94%. Using his measure, i appears ha he bond marke is abou 10 imes more predicable han he sock marke in erms of R 2 OS. Bu our economic value assessmen reveals ha he bond marke is no 10 imes more predicable han he sock marke. This resul suggess ha across he financial markes, he economic value of forecasing is likely o be capped a similar levels. One possible reason could perhaps be due o arbirage aciviies across various markes or iner-marke efficiency. Given he impressive predicive performance of our bond marke echnical indicaors, a naural quesion one would ask is: Are here any heoreical reasons? A survey of pas lieraure may provide some insighs ino he quesion. For example, Wacher (2006) shows ha Campbell and Cochrane s (1999) habi-formaion model can be adaped o explain ime-varying bond risk premia. Brand and Wang (2003) develop a model in which ime-varying bond risk premia are driven by inflaion as well as by aggregae consumpion. Bansal and Shaliasovich (2010) provide an explanaion on he predicabiliy of bond risk premia based on long-run risks. In addiion, in an economy when invesors receive fundamenal informaion a differen imes or process informaion a differen speeds, Treynor and Ferguson (1985) show ha echnical analysis is valuable for assessing wheher he informaion has been priced in. Hence rading will be more profiable when combining fundamenals wih echnicals han oherwise.. In a relaed sudy, Brown and Jennings (1989) argue ha when invesors receive fundamenal 6

9 informaion a he same ime, bu are heerogeneously informed, pas price can help invesors o make more precise inferences abou heir signals. Moreover, Grundy and McNichols (1989) and Blume, Easley, and O Hara (1995) demonsrae ha, as long as raders rade muliple rounds or hey receive signals wih differing qualiy, rading volume can provide useful informaion beyond prices. In a series of recen sudies, Cespa and Vives (2012) and Guo and Xia (2012) show ha, in a marke wih liquidiy raders, prices can deviae from heir fundamenals and echnical analysis can be used o capure price rends. Inuiively, echnical indicaors may capure informaion beyond ha measured by he macroeconomic variables. This is because he se of he macroeconomic variables ha are used in many sudies are clearly no exhausive, and hey ignore imporan variables such as unexpeced governmen policy changes and large shocks in he world economy. 5 However, any persisen reacion of he bond marke o he laer variables may be capured by marke echnical indicaors. One can argue ha echnical indicaors may be forward looking and perhaps be an effecive ool in helping invesor predic fuure evens. For example, in he recen Fed QE3 exercise on January 13, 2012, prices of he long-erm bond fuures dropped 6 days ou of 7, wih one day virually unchanged. The reason, as pu forh by Aneiro in Barron s is, Marke had priced in expecaions of some form of a hird round of quaniaive easing ahead of he Fed s policy-commiee meeing. 6 This example illusraes ha echnical indicaors may be forward looking and may capure marke expecaions of fuure macroeconomic daa or evens. In conras, macroeconomic variables ha are used in predicive regression sudies emphasize he marke impac of heir realized values. The predicabiliy of sock marke rading volume based echnical indicaors is poenially relaed o he negaive correlaion beween sock and bond reurns during periods of high uncerainy (e.g., Connolly, Sivers, and Sun, 2005; Beber, Brand, and Kavajecz, 2009; Baele, Bekaer, and Inghelbrech, 2010). I is suggesed ha bond reurns end o be high (low) relaive o sock reurns during days when sock rading volume and volailiy increase (decrease) subsanially. The nega- 5 For example, Pásor and Veronesi (2012a, 2012b) poin ou ha poliical news do impac asse prices, and hey also find ha uncerainy abou poliical policy changes do raised he equiy risk premia. 6 See Michael Aneiro, Curren yields, Barron s, M12, Sepember 17, I is of ineres o noe ha he marke dropped furher on he announcemen day and he day afer. 7

10 ive sock and bond reurn correlaion is ofen referred o as he fligh o qualiy and/or fligh o liquidiy effecs. Theoreically, Vayanos (2004) shows ha risk averse invesmen managers prefer liquid asses during volaile periods. Meanwhile, as heir risk aversion also increases, i leads o higher risk premiums and resuling in driving down he prices of risky asses. Caballero and Krishnamurhy (2008) show ha Knighian uncerainy may lead agens o shed risky asses in favor of safe asses when aggregae liquidiy is low, hereby provoking a figh o qualiy. Brunnermeier and Pedersen (2009) show ha margin requiremens can rigger a liquidiy spiral following a large bad shock, where liquidiy deerioraes sharply for he high margin and volaile asses, leading o fligh o qualiy or liquidiy. These research aricles collecively provide a heoreical underpinning as o why our bond marke echnical indicaors perform so well as predicors. I also lends suppor o he use of equiy rading volume as a componen in our forecasing models. The res of he paper is organized as follows. Secion II oulines he consrucion of echnical indicaors, as well as he esimaion and evaluaion of he in-sample and ou-of-sample bond risk premia forecass. Secion III repors he empirical resuls and Secion IV concludes. II. Economeric Mehodology This secion describes our economeric framework, which includes he consrucion of echnical indicaors, as well as he esimaion and evaluaion of boh in-sample and ou-of-sample excess bond reurn. The forecass are based on all he echnical, financial and economic indicaors. A. Technical indicaor consrucion We follow Cochrane and Piazzesis (2005) noaion of excess bond reurns and yields. p (n) is he log price of n-year discoun bond a ime. Then, he log yield of n-year discoun bond a ime is y (n) n 1 p(n). The n-year bond price a ime is f s (n) f (n) y (1), where f (n) p (n 1) p (n) is he forward rae a ime for loans beween ime + n 1 and + n. The excess log reurn on 8

11 n-year discoun bond from ime o + 1 is rx (n) +1 r(n) +1 y(1), where r (n) +1 p(n 1) +1 p (n) is he log holding period reurn from buying an n-year bond a ime and selling i as an n 1 year bond a ime + 1. The average excess log reurn across mauriy is defined as rx n=2 rx(n) +1. Two groups of echnical indicaors are considered. The firs is a forward spread moving average rading rule MA f s ha generaes a buy or sell signal (S = 1 or S = 0, respecively) a he end of period by comparing wo moving averages of n-year forward spreads: 7 S = 1 if MA f s,(n) s, 0 if MA f s,(n) s, > MA f s,(n) l, MA f s,(n) l,, (1) wih MA f s,(n) j, = (1/ j) j 1 k=0 f s (n) k/12, for j = s,l, (2) where f s (n) k/12 is he n-year forward spread a ime k/12, and s (l) is he lengh of he shor (long) forward spread moving average (s < l). 8 We denoe he forward spread moving average rule wih mauriy n and lenghs s and l as MA f s,(n) (s,l). Inuiively, he MA f s rule is designed o deec he changes in rends of he bond prices. 9 For example, recenly when he n-year forward raes have been falling relaive o he one-year bond yields, he shor forward spread moving average will end o be lower han he long forward spread moving average and hence will generae a sell signal. If he n-year forward raes begin rending upward relaive o he one-year bond yields, hen he shor moving average ends o increase faser han he long moving average, evenually exceeding he long moving average and hence generaing a buy signal. In Secion III, we analyze he monhly MA f s,(n) (s,l) rules wih n = 2,3,4,5, s = 3,6,9 and l = 18,24,30,36. Technical analyss frequenly use volume daa in conjuncion wih pas prices o idenify marke 7 Noe ha forward rae is he log-ransformed bond price. 8 The ime indexaion reflecs he fac ha, while he mauriies of he Fama-Bliss discoun bonds are from one year o five years, our daa are sampled a a monhly frequency. Following Cochrane and Piazzesi (2005), we se he uni period o a year so ha i maches he holding period of rx (2) +1,..., rx(5) +1. The monhly sampling inerval is hen denoed as 1/12 of a year. 9 Noe ha forward raes are ransformed from log bond prices, hus he forward spread moving average echnical indicaors are funcions of bond prices. We can also consruc rading rules using he lagged excess bond reurns, we leave hese exensions for fuure research. 9

12 rends. In view of his, he second ype of echnical indicaors are consruced based on onbalance volume (e.g., Granville, 1963). Since bond rading volume daa (over he 1964 hrough 2011 period) are no available o us, we compue he volume indicaor using sock marke rading volume. Formally, we firs define OBV = 12 1 VOL k/12 D k/12, (3) k=0 where VOL k/12 is a measure of he sock marke rading volume beween period (k + 1)/12 and k/12 and D k/12 is a binary variable ha akes a value of 1 if P k/12 P (k+1)/12 0 and 1 oherwise. We hen form a rading volume-based buy or sell signal from OBV as S = 1 if MA OBV s, 0 if MA OBV s, MA OBV l, > MA OBV l,, (4) where MA OBV j, = (1/ j) j 1 k=0 OBV k/12, for j = s,l. (5) We denoe he rading volume-based rading rule as MA OBV (s,l), where s (l) is he lengh of he shor (long) moving average of on-balance rading volume (s < l). Inuiively, relaively high recen sock marke volume ogeher wih recen sock price decrease indicaes a srong negaive sock marke rend, and hence generaes a buy signal for bond marke. The sock marke rading volume based echnical indicaor migh be relaed o fligh o qualiy or fligh o liquidiy. In a siuaion wih a high degree of uncerainy and risk aversion, bond reurns end o be higher relaive o sock marke reurns and invesors may shif heir porfolios from a risky sock marke owards safer shor-erm governmen bonds (Connolly, Sivers, and Sun, 2005; Caballero and Krishnamurhy, 2008; Beber, Brand, and Kavajecz, 2009; Brunnermeier and Pedersen, 2009; Baele, Bekaer, and Inghelbrech, 2010, among ohers). In Secion III, we compue monhly MA OBV (s,l) signals for s = 1,2,3 and l = 9,12,15,18,21. The wo ypes of echnical indicaors ha we consider (bond price and rading volume-based) 10

13 convenienly capure he rend-following idea ha is a he hear of echnical analysis. These are represenaive of he echnical indicaors ha are ofen analyzed in he academic lieraure (e.g., Brock, Lakonishok, and LeBaron, 1992; Sullivan, Timmermann, and Whie, 1999). In his paper, we sudy wheher echnical indicaors provide useful informaion in forecasing excess bond reurns. Furhermore, we also aim o assess wheher echnical indicaors could generae beer excess bond reurn forecass han hose conained in economic predicors. To invesigae he laer quesion, we include Cochrane and Piazzesi (2005) forward rae facor CP and Ludvigson and Ng (2009) macroeconomic variable facor LN as conrol variables. Cochrane and Piazzesi (2005) find ha he predicive power of a large number of financial indicaors including forward raes and yields spreads is subsumed by heir single forward-rae facor. Ludvigson and Ng (2009) show ha real and inflaion facors are more imporan han he Cochrane and Pizzesis forward-rae facor when i comes o predicive power for excess bond reurns on U.S. governmen bonds. B. In-sample forecas We use he sandard predicive regression framework o analyze he in-sample predicive power of echnical indicaors for excess bond reurns rx (n) +1. However, analyzing he predicive power of a large number of poenial echnical predicors raises an imporan economeric issue. Including all of he poenial regressors simulaneously in a muliple regression model can produce a very good in-sample fi, bu i also can resul in in-sample over-fiing. Hence, will likely leads o very poor ou-of-sample forecasing performance. To be able o incorporae informaion from all of he echnical indicaors while avoiding over-fiing, we follow Ludvigson and Ngs (2007, 2009) recommendaion and use a principle componen approach. Le x = (x 1,,...,x N, ) denoe he N- vecor of poenial echnical predicors. Le ˆf = ( ˆf 1,,..., ˆf J, ) represen he vecor comprised of he firs J principal componens of x, where J N. The number of common facors, J, is deermined by he informaion crieria developed in Bai and Ng (2002). Inuiively, he principal componens convenienly deec he key comovemens in x, while filering ou much of he noise in individual echnical predicors (e.g., Connor and Korajczyk, 1986, 1988; Ludvigson and Ng, 2007, 2009, 11

14 2011). Since he pervasive facors in ˆf may no be relevan in predicing excess bond reurns rx (n) +1, following Ludvigson and Ng (2009), we selec he preferred se of echnical analysis PC facor ˆF from he differen subses of ˆf using he Bayesian informaion crierion (BIC), which provides a way of selecing echnical indicaors facors wih addiional forecasing abiliy for excess bond reurns among he facors in ˆf. 10 Specifically, we firs form differen subses of ˆf. We hen regress rx (n) +1 on his candidae subse and conrolling economic predicors, and compue he corresponding BIC for each candidae subse of facors. The preferred subse of echnical indicaors facors ˆF is deermined by minimizing he BIC. We hus uilize he facor-augmened predicive regression o analyze he in-sample predicive power of echnical indicor PC facor ˆF for excess bond reurns rx (n) +1 : rx (n) +1 = α + β ˆF + ε +1, for n = 2,3,4,5, (6) which analyzes he uncondiional predicive power of echnical indicaors for excess bond reurns. The null hypohesis is ha β = 0, and he echnical indicaors have no uncondiional predicive abiliy for excess bond reurns. The alernaive hypohesis is ha β 0, and he echnical indicaors are useful in predicing excess bond reurns. We are also ineresed o sudy wheher he echnical indicaors can be used in conjuncion wih economic predicors o furher improve excess bond reurns predicabiliy as compared o jus using economic predicors alone. To analyze he incremenal predicive power of echnical indicaors, we include an economic predicor Z in he regression model as condiioning variable: rx (n) +1 = α + β ˆF + η Z + ε +1, for n = 2,3,4,5, (7) where Z includes economic predicors like CP and LN, which subsume he forecasing informa- 10 BIC crierion is an asympoic approximaion o Bayesian poserior probabiliies, and i asympoically selecs he bes model wih he mos parsimonious parameerizaion among nesed models (Schwarz, 1978). Neverheless, we obain similar resuls using alernaive model selecion crierion such as AIC. 12

15 ion in forward spreads, yield spreads, and a large number of macroeconomic variables. Thus (7) allows us o assess he incremenal predicive power of echnical indicaors beyond ha of economic predicors. Under he null hypohesis, β is equal o zero, and he echnical indicaors have no addiional predicive power for excess bond reurns once he economic predicors are included in regression model. Under he alernaive hypohesis, β is differen from zero, and he echnical indicaors are sill useful in predicing excess bond reurns even wih he presence of economic predicors. In boh (6) and (7), he sandard errors of he regression coefficiens are correced for serial correlaion using Newey and Wes (1987) wih 18 lags, which is necessary since he annual log excess bond reurns have an MA(12) error srucure induced by overlapping observaions. The Newey and Wes (1987) covariance marix is posiive definie in any sample, however, i underweighs higher covariance. Following Cochrane and Piazzesi (2005) and Ludvigson and Ng (2009), we use 18 lags o beer ensure he correcion for he MA(12) error srucure. C. Ou-of-sample forecas Alhough in-sample analysis may have more esing power, Goyal and Welch (2008), among ohers, argue ha ou-of-sample ess seem o be a more relevan sandard for assessing genuine reurn predicabiliy in real ime. Therefore we also conduc analysis on he ou-of-sample predicive abiliy of echnical indicaors for he excess bond reurns. To avoid look-ahead bias and he use of fuure daa, we generae ou-of-sample forecass of excess bond reurns using recursive predicive regression, wih all facors, including echnical indicaor facors F, forward rae facor CP, and macroeconomic facor LN, and parameers esimaed jus using informaion available up o he monh of forecas formaion,. 11 Firs, we generae an ou-of-sample forecas of excess bond reurn rx (n) +1 based on he echnical 11 Noe ha, while he echnical indicaor facor ˆF used in he in-sample analysis is esimaed using he full-sample informaion, he ou-of-sample echnical indicaor facor F is esimaed using informaion available hrough he curren ime. 13

16 indicaor facor F, Equaion (6), and informaion available hrough period as rx (n) +1 = α + β F, (8) where α and β are leas squares esimaes of α and β in (6) by regressing {rx (n) k/12 }12( 1) 1 k=0 on a consan and { F 1 k/12 } 12( 1) 1 k=0. For each forecas formaion period, we firs esimae he ou-of-sample echnical indicaor PC facors { f k/12 } 12 1 k=0 from a large number of poenial individual echnical indicaors {x k/12 } 12 1 k=0 using informaion available hrough period. Then, he preferred subse of ou-of-sample echnical indicaor facors { F k/12 } 12 1 k=0 is seleced from differen subses of { f k/12 } 12 1 k=0 using he BIC crierion. Dividing he oal sample of lengh T ino m firs period sub-sample and q second period sub-sample, where T = m+q, we can calculae a series of ou-of-sample principle componen forecass of rx (n) +1 based on F over he las q ou-ofsample evaluaion periods: { rx (n) m+k/12 }12q k=1.12 Second, o analyze wheher including echnical indicaors wih economic variables could furher improve he ou-of-sample forecasing gains for excess bond reurns, we generae an ou-ofsample forecas of excess n-year bond reurn rx (n) +1 based on boh he echnical indicaor PC facor F and he economic predicor Z, and informaion hrough forecas formaion period : rx (n) +1 = α + β F + η Z, (9) where Z includes CP or LN. α, β and η are leas squares esimaes of α, β and η in (7) from regressing {rx (n) k/12 }12( 1) 1 k=0 on a consan, { F 1 k/12 } 12( 1) 1 k=0 and {Z 1 k/12 } 12( 1) 1 k=0, respecively. We hen can compue a series of condiional ou-of-sample excess bond reurn forecass based on F and Z over he las q ou-of-sample evaluaion periods: { rx (n) m+k/12 }12q k=1. In addiion, o 12 Observe ha he forecass are generaed using a recursive (i.e., expanding) window for esimaing α, β and η in (8). Forecass could also be generaed using a rolling window (which drops earlier observaions as addiional observaions become available) in recogniion of poenial srucural insabiliy. Pesaran and Timmermann (2007) and Clark and McCracken (2009), however, show ha he opimal esimaion window for a quadraic loss funcion can include prebreak daa due o he familiar bias-efficiency radeoff. Moreover, we obain similar resuls using rolling esimaion windows of various sizes. 14

17 assess he incremenal forecasing power of echnical indicaors over economic variables, we also generae ou-of-sample forecass uilizing he informaion in he economic predicor Z alone: rx (n) +1 = α + η Z, (10) where α and η are leas squares esimaes based on informaion available hrough. The hisorical average of excess bond reurns, rx (n) +1 = k=0 rx (n) k/12, is he naural forecas benchmark for (8), (9), and (10) corresponding o he he consan expeced excess reurn model (β = η = 0). Goyal and Welch (2008) show ha he hisorical average forecas is a sringen benchmark in he sock marke. Forecass based on economic variables frequenly fail o ouperform he hisorical average forecas in ou-of-sample ess. We use wo merics for evaluaing he ou-of-sample bond risk premia forecass based on echnical indicaors or economic variables. The firs is he Campbell and Thompson (2008) R 2 OS saisic, which measures he reducion in mean square predicion error (MSPE) for a compeing predicive regression model which includes echnical indicaors or economic variables relaive o he hisorical average forecas benchmark, R 2 OS = 1 12q k=1 (rx(n) m+k/12 rx(n) m+k/12 )2 12q k=1 (rx(n) m+k/12, (11) rx(n) m+k/12 )2 where rx (n) m+k/12 represens he excess log reurn on n-year governmen bond from ime m 1+k/12 o m + k/12, rx (n) m+k/12 represens a compeing ou-of-sample forecas for rx(n) m+k/12 based on echnical indicaors or economic variables, and rx (n) m+k/12 represens he hisorical average benchmark. Thus, when R 2 OS > 0, he compeing forecas ouperforms he hisorical average benchmark in erm of MSPE. We also employ he Clark and Wes (2007) MSPE-adjused saisic o es he null hypohesis ha he compeing model MSPE is greaer han or equal o he resriced predicive benchmark MSPE, agains he one-sided alernaive hypohesis ha he compeing forecas has 15

18 lower MSPE, corresponding o H 0 : R 2 OS 0 agains H A : R 2 OS > 0.13 Clark and Wes (2007) develop he MSPE-adjused saisic by modifying he familiar Diebold and Mariano (1995) and Wes (1996) saisic so ha i has a sandard normal asympoic disribuion when comparing forecass from nesed models. 14 Comparing he compeing predicive regression forecas wih he hisorical average benchmark enails comparing nesed models. R 2 saisics are ypically large for bond risk premia forecass, bu a relaively large R 2 may imply lile economic significance for an invesor (e.g., Della Core, Sarno, and Thornon 2008; Thornon and Valene, 2012). From an asse allocaion perspecive, however, uiliy gain iself is he key economic meric. As a second meric for evaluaing ou-of-sample excess bond reurn forecass, we compue uiliy gains for a mean-variance invesor who opimally allocaes across n-year governmen bond and 1-year risk-free bill, as in, among ohers, Kandel and Sambaugh (1996), Marquering and Verbeek (2004), Campbell and Thompson (2008), Della Core, Sarno, and Thornon (2008), Neely, Rapach, Tu and Zhou (2011), and Thornon and Valene (2012). As discussed in he inroducion, his procedure addresses he weakness of many exising sudies of echnical indicaors ha fail o incorporae he degree of risk aversion ino he asse allocaion decision. In paricular, we compue he average uiliy for a mean-variance invesor wih risk aversion coefficien of hree. Every monh, he invesor allocaes beween n-year governmen bond and 1- year risk-free bill. The invesmen decision is based on using an ou-of-sample excess bond reurn forecas generaed by a predicive regression model including echnical indicaors or economic variables as predicors versus a hisorical average forecas benchmark corresponding o he consan 13 The sandard error in MSPE-adjused saisic is adjused for serial correlaion using Newey and Wes (1987) wih 18 lags. 14 While he Diebold and Mariano (1995) and Wes (1996) saisic has a sandard normal asympoic disribuion when comparing forecass from non-nesed models, Clark and McCracken (2001) and McCracken (2007) show ha i has a complicaed non-sandard disribuion when comparing forecass from nesed models. The non-sandard disribuion can lead he Diebold and Mariano (1995) and Wes (1996) saisic o be severely undersized when comparing forecass from nesed models, hereby subsanially reducing power. 16

19 expeced excess bond reurn model. A he end of period, he invesor allocaes w (n) +1 = 1 γ rx (n) +1 σ 2 n,+1 (12) of his wealh o an n-year bond during period + 1, where γ is he coefficien of risk aversion, rx (n) +1 is a ou-of-sample forecas for excess n-year bond reurn, and σ n,+1 2 is a forecas of he excess n-year bond reurn variance. We assume ha he invesor uses a four-year moving window of pas excess bond reurns o esimae he variance (e.g., Campbell and Thompson, 2008). Following recen sudies such as Campbell and Thompson (2008) and Thornon and Valene (2012), we consrain he porfolio weigh on he n-year bond o lie beween -1 and 4 o preven exreme invesmens and limi he impac of esimaion error. 15 The average uiliy for he invesor who incorporaes informaion conained in echnical indicors or economic variables ino he predicive model of excess n-year bond reurn is given by ˆν (n) = ˆµ n 0.5γ ˆσ 2 n, (13) where ˆµ n and ˆσ 2 n are he sample mean and variance, respecively, for he he porfolio formed on Equaion (12) using he sequence of forecass rx (n) +1 periods. over he las q ou-of-sample evaluaion We hen calculae he average uiliy for he same invesor who insead uses he hisorical average forecas o predic he excess n-year bond reurn. A he end of period, he invesor allocaes w (n) +1 = 1 γ rx (n) +1 σ 2 n,+1 (14) o he n-year Treasury bond during period + 1, where rx (n) +1 is he hisorical average forecas for 15 Our resuls are robus o alernaive porfolio weigh consrains. Uiliy gains could be even larger when moderaely relaxing he porfolio weigh consrains. 17

20 rx (n) +1. The invesor hen realizes an average uiliy of ν (n) = µ n 0.5γ σ 2 n, (15) during he ou-of-sample evaluaion period, where µ n and σ 2 n are he sample mean and variance, respecively, for he he porfolio formed on Equaion (14) using he sequence of hisorical average forecass rx (n) +1. The uiliy gain is he difference beween (13) and (15), ˆν(n) ν (n), which can be inerpreed as he annual percenage porfolio managemen fee ha an invesor would be willing o pay o have access o he bond risk premium forecas rx (n) +1 using echnical indicaors or economic variables relaive o he hisorical average benchmark rx (n) +1 corresponding o he consan expeced excess bond reurn model (no predicabiliy). III. Empirical Resuls This secion describes he daa, and repors he in-sample es resuls and ou-of-sample resuls for he R 2 OS saisics. Resuls on he average uiliy gains from using echnical indicaors in forecasing excess bond reurns are also repored in his secion. A. Daa We obain he shor-erm zero coupon U.S. Treasury bond prices wih mauriies from onehrough five-years from Fama-Bliss daase available a he Cener for Research in Securiies Prices (CRSP) spanning he period 1964: :12. The long-erm U.S. Treasury bond daa wih mauriies from seveneen- o weny-years are from he Federal Reserve s websie, which provides updaed daa from Gürkaynak, Sack, and Wrigh (2007) beginning in 1981: We compue he yields, forward raes, forward spreads, and annual log excess bond reurns a a monhly frequency 16 The Gürkaynak, Sack, and Wrigh (2006) daase is available a hp:// Noe ha he differences beween Gürkaynak, Sack, and Wrigh (2006) and Fama-Bliss daase are quie small on mos daes (e.g., Cochrane and Piazzesi, 2008). 18

21 as described in Secion II. The macroeconomic fundamenal daa are obained from Sydney C. Ludvigson s web page and used in Ludvigson and Ng (2009, 2011). 17 The macroeconomic daase includes 132 monhly macroeconomic ime series over he period 1964: :12. We use he monhly forward spreads when compuing he forward spread moving average echnical indicaors in Equaion (1). In addiion, we use monhly S&P 500 index and sock marke rading volume daa from Google Finance o compue he rading volume-based echnical indicaors in Equaion (4). Table 1 repors summary saisics for he firs hree forward spread moving average echnical indicaor PC facors, ˆf f s, and rading volume echnical indicaor PC facors, ˆf OBV, which are esimaed from 48 forward spread moving average echnical indicaors MA f s and 15 rading volume echnical indicaors MA OBV, respecively. 18 The number of facors is deermined using he informaion crierion developed by Bai and Ng (2002). These echnical PC facors during period are esimaed using full sample of ime-series informaion from 1964:01 o 2011:12. These in-sample PC facors are used o es he in-sample predicive power of echnical indicaors. 19 Column R 2 i of Table 1 shows ha a small number of echnical PC facors describe a large fracion of he oal variaion in he daa. 20 R 2 i measures he relaive imporance of he ih PC facor, which is calculaed as he fracion of oal variance in hose echnical indicaors explained by facors 1 o i. 21 Column R 2 i of Table 1, Panel ˆf f s i, shows ha he firs PC facor accouns for 68% of he oal variaion in he 48 MA f s echnical indicaors, and he firs hree PC facors furher increase he R 2 i o 79%. Column R 2 i of Table 1, Panel ˆf OBV i, presens ha he firs PC facor alone explains up o 83% of he oal variaion in he 15 MA OBV echnical indicaors, and he firs hree 17 The daa are available a hp:// 18 An alernaive se of echnical PC facors can be esimaed on he panel of 63 echnical rading rules (pooling he MA f s rules and MA OBV rules ogeher). However, we do no repor he resuls for his mehod since he resuls are similar. In addiion, he facors esimaes from his mehod are ofen criicized for being difficul o inerpre. Grouping daa ino wo groups based on rading rules o be moving-average or rading volume permis us o easily name and inerpre he facors. 19 We also conduc analysis on he ou-of-sample predicive power of he echnical indicaors, in which he ou-ofsample PC facors f f s and f OBV are esimaed recursively using daa only available o forecas formaion period, as described in Secion II. 20 The firs facor explains he larges fracion of he oal variaion in hose echnical indicaors, and he ih facor explains he ih larges fracion of he oal variaion. The oal variaion is defined as he sum of he variance of he individual echnical indicaors. The PC facors are muually orhogonal. 21 R 2 i is calculaed by dividing he sum of he firs i larges eigenvalues of he marix xx, he sample covariance marix of he echnical indicaors, o he sum of all eigenvalues. 19

22 PC facors describe 93% of he oal variaion. Column AR1 i of Table 1 displays he firs-order auoregressive coefficiens of AR(1) model for each facor. Significan differences in persisence are found among PC facors. The auoregressive coefficiens for forward spread moving average echnical indicaor PC facors ˆf f s of , and rading volume-based echnical indicaor PC facors ˆf OBV coefficiens range of 0.01 o are in he range have auoregressive Following Ludvigson and Ng (2009, 2011), we deermine he preferred subse of echnical indicaor facors from all of he possible combinaions of he esimaed echnical PC facors using shor-erm governmen bonds and following he BIC crierion. Wih Cochrane and Piazzesi (2005) facor CP and Ludvigson and Ng (2009) facor LN included as condiioning variables, hree echnical indicaor facors, ˆF T I = ( ˆF f s 1,, ˆF f s 3,, ˆF OBV 1, ), are seleced based on full sample informaion, where he wo-facor subse ˆF f s = ( ˆF f s 1,, ˆF f s 3, ) ˆf f s and one-facor subse ˆF OBV = ˆF OBV 1, ˆf OBV. 23 In unrepored resuls, we show ha ˆF f s 1, is a level forward spread moving average echnical indicaor facor wih correlaion of abou 0.70 o 0.90 wih he 48 individual forward spread moving average echnical indicaors; ˆF f s 3, is a slope forward spread moving average echnical indicaor facor, which is posiively correlaed wih he individual forward spread moving average echnical indicaors consruced on wo- o four-year bonds bu negaively correlaed wih he individual echnical indicaors consruced on five-year bond; and ˆF OBV 1, is a level rading volume echnical indicaor facor wih correlaion of abou 0.80 o 0.95 wih he 15 individual rading volume echnical indicaors The relaively high persisence of echnical indicaor facors are consisen wih rend following idea of echnical analysis, ha are designed o deec he rending paerns in he marke. 23 The same se of hree echnical indicaor facors will be seleced when conrolling for CP and LN over he 1964: :12 period or conrolling for CP alone over he 1964: :12 period. 24 Noe ha he ou-of-sample facors F f s, F, OBV, and F, T I are deermined recursively using daa only available hrough forecas formaion period. 20

23 B. In-sample analysis Table 2 repors regression slope coefficiens, heeroskedasiciy and serial correlaion robus - saisics, and adjused R 2 for in-sample predicive regression of log excess reurns of shor-erm n- year governmen bonds, rx (n) +1, wih n = 2,...,5 on lagged echnical indicaor facors over he period 1964: : To examine he incremenal predicive power of echnical indicaor facors beyond ha conained in he financial and economic variables, we include CP and LN, which are he Cochrane and Piazzesi (2005) facor and Ludvigson and Ng (2009) facor, respecively, as condiioning variables. We repor in-sample forecasing resuls of using CP or LN alone as forecas benchmark. Table 3 repors for he period of 1964: :12, which includes he recen financial crisis and laer periods. Since he macroeconomic daase of Ludvigson and Ng (2009) is only available up o December 2007, we hence only conrol for CP alone over he laer sample period. Following Cochrane and Piazzesi (2005) and Ludvigson and Ng (2009), he sandard error of he regression coefficiens are correced for serial correlaion using he Newey and Wes (1987) echniques wih 18 lags. We use 18 lags because he annual log excess bond reurns have an MA(12) error srucure ha are induced by overlapping observaions. According o Row 1 of he op panel of Table 2, consisen wih Cochrane and Piazzesi (2005), he forward rae facor CP generaes huge in-sample forecasing power for excess reurns on woyear governmen bond, rx (2) +1, over he 1964: :12 period, wih adjused R2 of 31%. In addiion, Row 2 of he op panel of Table 2 presens ha he macroeconomic variable facor LN produces sizable in-sample adjused R 2 of 23% over he 1964: :12 period. In his websie, John Cochrane suggess ha he predicive power of CP seems o be weak during he recen financial crisis. Consisen wih his finding, Row 1 of he op panel of Table 3 shows ha he R 2 of CP is only of 21% over he 1964: :12 period. 26 Nex, Rows 3 5 of he op panel of Table 2 show ha echnical indicaor facors have sizable in-sample forecasing power over he 1964: :12 period, which is comparable o ha of 25 We find similar resuls for simple raw excess reurns. 26 Recen sudies such as Duffee (2012) and Thornon and Valene (2012) also find similar resuls. 21

24 economic variables CP and LN in erm of R 2. The wo forward spread moving average echnical indicaor facors, ˆF f s = ( ˆF f s 1,, ˆF f s 3, ), explain 28% of he wo-year excess bond reurn variaion; and boh ˆF f s 1, and ˆF f s 3,, which are he firs and hird PC facors esimaed from 48 forward spread moving average rading signals, are saisically significan a he 1% or beer level. In addiion, he rading volume echnical indicaor facor, ˆF OBV = ˆF OBV 1,, produces adjused R 2 of 10%, wih saisical significance for ˆF OBV 1,, he firs PC facor esimaed from 15 rading volume echnical indicaors. Row 5 of Table 2 furher shows ha ˆF T I, which combines informaion from ˆF f s and ˆF OBV ogeher, generaes highes adjused R 2 of 32%, wih all echnical facors saisically significan a he convenional level. 27 Rows 2 4 of he op panel of Table 3 repor he in-sample forecasing resuls of echnical indicaor facors for rx (2) +1 over he 1964: :12 period. In conras o CP, for his longer sample period, echnical indicaor facors generae consisenly srong forecasing power wih R 2 of 30%; all of he hree echnical indicaor facors are saisically significan a convenional level. When combining informaion in echnical indicaors and economic variables including ˆF T I, CP, and LN ogeher, he predicive regression forecass perform he bes. The forecass remarkably ouperform he corresponding forecass based on economic variables or echnical indicaors alone, and generae he highes in-sample R 2 of 47% during 1964: :12 period, as shown in Row 6 of Panel rx (2) +1 of Table 2. All hree echnical indicaor facors are saisically significan a reasonable level. For he 1964: :12 sample period, he same conclusion holds qualiaively. For example, Row 5 of Panel rx (2) +1 of Table 3 shows ha forecass based on ˆF T I and CP ogeher ouperform he forecass based on eiher alone, oo. Following Ludvigson and Ng (2009), we find ha all hree echnical indicaor facors are relaively economically imporan by inspecing he absolue value of regression coefficiens. In summary, our findings sugges ha echnical indicaors conain addiional forecasing informaion beyond ha conained in forward raes, yields, and macroeconomic variables. The remaining hree panels of Tables 2 and 3 show ha boh he forward spread moving 27 Following Cochrane and Piazzesi (2005), we find ha a single-facor predicor which is a single linear combinaion of he hree echnical indicaor facors in ˆF T I conains almos he same predicive power. 22