Macro Factors and Volatility of Treasury Bond Returns

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1 Macro Factors and Volatlty of Treasury Bond Returns Jngzh Huang Department of Fnance Smeal Colleage of Busness Pennsylvana State Unversty Unversty Park, PA 16802, U.S.A. Le Lu School of Fnance Shangha Unversty of Fnance & Economcs Shangha, , Chna Ths verson: March 2009 We would lke to thank Mng Guo and semnar partcpants at the 2008 Chnese Fnance Meetng and the 2008 Chnese Economcs Assocaton Meetng. We acknowledge the fnancal support from the Shangha Pujang Program. Correspondng author. Tel: ; fax: Emal address: (Jngzh Huang), (Le Lu)

2 Macro Factors and Volatlty of Treasury Bond Returns Abstract Ths paper nvestgates the mpact of macroeconomc varables on the volatlty of Treasury- bond returns. By usng prncpal components analyss, we extract the real and monetary macro factors from the real actvtes and monetary varables, respectvely. We fnd that these macro factors have a sgnfcant effect on the volatlty of bond returns. In partcular, the real actvtes affect the volatlty across all maturtes, whle the monetary varables are sgnfcantly related to the return volatlty of short-term bonds but weakly related to the return volatlty of medum-term bonds. The mplcatons of these fndngs are as follows: the monetary authortes can employ macroeconomc polcy to affect the volatlty of Treasury-bond returns; meanwhle, nvestors can mprove ther portfolo management by analyzng the macroeconomc condtons. JEL classfcaton: E44; G12; G17 Keywords: Bond volatlty; Real factor; Monetary factor; Volatlty decomposton

3 1. Introducton Recent emprcal evdence has shown that the volatlty of Treasury bond returns can be predctable. For nstance, Jones et al. (1998), Chrstansen (2000), and Goej and Marquerng (2006) fnd that the announcements of macroeconomc varables sgnfcantly affect the volatlty of Treasury-bond returns. Vcera (2007) fnds that the short-term nomnal nterest rates postvely forecast bond volatlty. Balduzz et al. (2001) and Flemng and Remolona (1999) also study the mpact of macro news on bond volatlty. Usng prncpal-components analyss wth a large number of macroeconomc varables, Ludvgson and Ng (2008) fnd that the macroeconomc fundamentals greatly affect bond returns and bond rsk prema. However, few studes have examned whether macroeconomc fundamentals themselves, rather than ther announcements, predct bondreturn volatlty, whch s the frst queston we wll nvestgate n ths paper. Emprcal evdence has also documented that macro news releases affect the shape of the term structure of nterest rates. For example, Evans and Marshall (1998) fnd that a monetary shock has an mpact on short-term nterest rates, wth a smaller effect on medum-term rates and almost no effect on long-term rates. Goej and Marquerng (2006) fnd that releases of employment data and producer prce ndex affect the medum- and long-term bond volatlty, whle the announcements of monetary polcy only affect shortterm bond volatlty. As such, t s nterestng to nvestgate whether the monetary varables themselves have dfferent effects on the volatltes of bond returns wth dfferent maturtes, whch s the second queston we wll study n ths paper. 1

4 Frst, usng prncpal-components analyss, we extract the real and monetary factors from the macroeconomc varables. We regress the volatltes of bond returns wth maturtes of 1, 5, 10, and 30 years on both the real and monetary factors, and we fnd that the real factor sgnfcantly affects the bond volatlty of all maturtes, whle the monetary factor s only strongly related to 1- and 5-year bond volatlty. Next, to untangle the mpacts of maturty on the volatlty of bond returns from that caused by market rsk, followng Campbell et al. (2001), we decompose the bond volatlty nto market-level volatlty and maturty-dependent volatlty. We fnd that the macroeconomc varables sgnfcantly affect the bond volatlty and ts two components (e.g., market-level and maturty-dependent volatlty). Specfcally, the real actvtes affect the bond volatlty of all maturtes, whle the monetary varables are sgnfcantly related to the volatlty of short-term bonds and weakly related to the volatlty of medum-term bonds. Ths paper dffers from prevous papers n two ways. Frst, many studes (e.g., Jones et al., 1998; Chrstansen, 2000; Goej and Marquerng, 2006) examne the effects of macroeconomc announcements on the volatlty of bond return, but none of them nvestgates the relatonshp between the macroeconomc varables themselves and bond volatlty. In partcular, we fnd that real and monetary factors have dfferent mpacts on the volatlty of bond returns across varous maturtes. Second, as far as we know, ths s the frst paper to use the CAPM to decompose the volatlty of Treasury-bonds nto two components market-level and maturty-dependent volatlty and that examnes the relatonshp wth macroeconomc varables. Ths also makes our paper dfferent from Goej and Marquerng (2006), n whch they examne the mpact of macro announcement 2

5 on bond volatlty, whle we nvestgate the effects of macroeconomc varables on both market-level volatlty and maturty-dependent volatlty. The rest of the paper s organzed as follows. Secton 2 descrbes the data used n our emprcal analyss, Secton 3 examnes the mpact of macro varables on the volatlty of bond returns, and Secton 4 concludes. 2. Data 2.1 Bond and stock data We use data on daly returns of constant-maturty bonds of 1, 5, 10, and 30 years for the perod July 1961 through September 2007 from the CRSP Daly Treasury Fxed-term Fle. The excess returns are calculated usng the bond returns n excess of the 3-month Treasury-bll rates, taken from the Federal Reserve Board of Governors. Fgure 1 plots the daly excess returns on the 1-, 5-, 10- and 30-year bonds. The graphs suggest that the daly excess bond returns are qute large for the perod of September 1979 through August Ths s not surprsng because the Federal Reserve s target of monetary polcy swtched from the funds rate to the nonborrowed depostory nsttutonal reserves for ths perod. The graphs also suggest that short-term bond returns have dfferent pattern of evoluton from medum- and long-term bonds as the fluctuaton of 1-year bond returns s hgher than that of 5-, 10-, and 30-year bonds returns, especally for the perod before

6 Table 1 llustrates the descrptve statstcs of daly excess returns. Notced that the average daly excess returns on all maturtes n the sample perod are qute close, whle ther standard devatons are strkngly dfferent. For example, there s a volatlty of 7.5% for 1-year Treasury bonds, and 30%, 45.7%, and 62.6% for the 5-, 10- and 30-year bonds, respectvely. Ths leads us to nvestgate the economc source behnd the obvous dfference n bond volatltes. Followng French et al. (1987) and Schwert (1989), we use the daly bond returns to calculate the realzed monthly volatlty for each maturty, as follows: 2 1/ 2, d = B D B B σ () t = = r () t r () t 1,2,3,4, (1) d 1 B where σ () t s the t-th month volatlty of the excess bond returns on 1-, 5-, 10-, and 30- year bonds; r B, d () t s the excess daly return; and r B () t s the mean of r B, d () t n month t. To calculate the bond-market captalzaton, we obtan the face value of outstandng debt from the CRSP Daly Treasury Master Fle and the bd and ask bond prces from the CRSP Daly Treasury Fxed-term Fle. The market captalzaton of the bond market s calculated by multplyng the debt outstandng by the average prce (of bd and ask). The stock returns are obtaned from the CRSP Daly Stock Indces Fle, whch ncludes the daly returns on the value-weghted portfolo of all stocks traded on the NYSE, the AMEX, and the NASDAQ of the same perod. 2.2 Macroeconomc varables 4

7 The monthly macroeconomc varables are collected from the Global Insght Basc Economcs (GIBE) database for the perod May 1961 through September 2007, and they are classfed nto the two categores of real actvtes and monetary varables. The varables of real actvtes nclude the ndex of Help Wanted Advertsng n Newspaper (LHEL), the unemployment rate (LHUR), the ndustral producton ndex (IPS10), and the Natonal Assocaton of Producton Management (NAPM) producton ndex (PMP). All of these varables except PMP are used by Ang and Pazzes (2003) to reflect the real actvtes. The monetary varables consst of the Federal funds rates (FYFF), nonborrowed reserves (FMRNBA), and M2 (FM2). From October 1979 to August 1982, FMRNBA was chosen as the polcy target, and for the rest of the sample perod FYFF was chosen as the target by the Federal Reserve. Followng Stock and Watson (2002) and Ang and Pazzes (2003), we use prncplecomponent analyss to estmate the common factors for each group of varables, respectvely. Frst, we transform the seres of varables to be statonary, and a code summarzng these transformatons s gven n the Appendx. Second, we standardze each seres separately to have a mean of zero and unt varance. Fnally, we represent the real actvtes and monetary varables as X R = ( LHEL, LUHR, IPS10, PMP) and ( FYFF FMENBA, FM 2) X M =, whch gves X () t = f ( t) + ε ( t) = R, M. β (2) We denote R f and f M as the real and monetary factors, respectvely. The frst real factor accounts for 57% of the varance of real varables. That means that ths 5

8 factor loads much nformaton about the real varables, so we use t to measure the real actvtes. Smlarly, the frst monetary factor accounts for 48.4% of the varance of monetary varables, so we use t as a proxy for the monetary varables. The correlatons between the frst real factor and the four real varables are , 0.725, , and , respectvely. As we antcpated, the sgns of the correlatons ndcate the state of the economy n such a way that when the LHEL, IPS10, and PMP ncrease and the LHUR decreases the economy tends to be healthy. The correlatons between the frst monetary factor wth the three monetary varables are 0.822, 0.74, and Agan, the sgns of these correlatons are ntutve: to mantan a level of total reserves consstent wth the FOMC's target federal funds rate, ncreases n borrowed reserves must generally be met by a decrease n nonborrowed reserves, and therefore the FMRNBA and the FYFF are negatvely correlated. Table 2 reports the correlatons between the macro factors and the bond volatltes, from whch we can gan the prelmnary nformaton about ther relatonshp. We fnd that the real factor s hghly correlated wth the bond volatltes and that the correlatons are almost the same for all maturtes (around 0.25), whle the monetary factor s weakly correlated wth bond volatlty. In partcular, the correlaton of the monetary factor wth 1- and 5-year bond volatlty s much hgher than that wth 10- and 30-year bond volatlty e.g., and vs and Ths suggests that the real factor mght be postvely and sgnfcantly related to the bond volatlty of all maturtes, whle the monetary factor weakly and negatvely affects the bond volatlty and ts effect s not sgnfcant for the volatlty of long-term Treasury bonds. These conjectures wll be further examned and confrmed n the followng secton. 6

9 3. Emprcal Analyss Ths secton examnes whether the volatlty of Treasury-bond returns s related to the macro factors. In partcular, we are nterested n whether the bond volatltes of dfferent maturtes are drven by dfferent macro factors. We frst regress the bond volatlty on the macro factors to see ther relatonshp. Then we decompose the bond volatlty of each maturty nto the bond-market-level (or stock-market-level) volatlty and maturtydependent volatlty, and then we separately regress them on the macro factors. 3.1 Prelmnary analyss We use one-month-lagged real and monetary factors, lagged log nomnal short rate proxed by the 3-month Treasury-bll rate, and lagged volatlty value to forecast the bond volatlty. Because Vcera (2007) fnds that the nomnal short-term nterest rates postvely forecast the bond volatlty, we also nclude ths varable n the regresson models. Table 3 presents the estmated results for the monthly volatlty of 1-, 5-, 10-, and 30- year bonds on the lagged real and monetary factors, the lagged log short rate, and the lagged volatlty value. We fnd that the real factor sgnfcantly affects the 1-, 5-, 10-, and 30-year bond volatlty and that the monetary factor s strongly related to the 1- and 5-year bond volatlty. The results confrm our prelmnary nformaton that the real factor sgnfcantly and postvely affects the bond volatltes of all maturtes, whle the monetary factor s only related to the bond volatlty of short- and medum-term bonds, whch s consstent wth Vcera (2007), who fnds that the nomnal short rate 7

10 sgnfcantly affects the stock and bond volatlty up to a 60-month horzon. In our paper, we analyze the 1-month excess bond returns and fnd that the nomnal short rate has sgnfcant mpact on the volatlty of 1-, 5-, and 10-year bonds, whle ts nfluence on the volatlty of 30-year bonds s relatvely lmted. Our fndngs are also consstent wth the fndngs of Evans and Marshall (1998) and Goej and Marquerng (2006). Evans and Marshall (1998) fnd that a contractonary monetary polcy shock nduces a pronounced postve but transtory response n shortterm nterest rates and has a smaller effect on medum-term rates and almost no effect on long-term rates. Goej and Marquerng (2006) fnd that the announcements of monetary polcy only affect the volatlty of short-term bonds. However, ths paper focuses on the connecton between bond volatlty wth monetary varables. 3.2 Volatlty decomposton based on value-weghted bond-market ndex Campbell et al. (2001) decompose the stock volatlty nto three components marketlevel, ndustry-level and frm-specfc volatltes, and they fnd that these three components have dfferent patterns over tme. Followng ther method, we decompose the volatlty of government bonds nto bond-market-level and maturty-dependent volatltes. Maturty s denoted by subscrpt, and the excess bond return wth maturty s denoted by r B. For smplcty, we assume that the total bond-market captalzaton s calculated on the bass of 1-, 5-, 10-, and 30-year bonds. The weght of maturty n the B B total bond market s denoted by w, and the excess bond-market return s r = = w 1 r. 8 4

11 In the next step, we decompose the excess bond return on each maturty by usng the CAPM gven by r B B B () t = + β ( t) r ( t) v ( t). α (3) B + Because r B () t and v () t are orthogonal, the varance of bond returns s therefore Var B B B where Var ( ), ( r ) r B B B ( r () t ) Var ( t) r ( t) ( ) Var v ( t) = β ( ), (4) + Var β, and ( ) v Var are called bond varance, rsk-adjusted varance of the bond-market, and maturty-dependent bond varance, respectvely. To dfferentate B from the rsk-adjusted varance of the bond market, we call ( r ) Var the varance of the bond market. Moreover, we denote the bond volatlty of maturty, the rsk-adjusted volatlty of the bond-market-level, the volatlty of the bond-market-level, and the B B B B B maturty-dependent volatlty by σ Var( r ), σ β B B Var( β r ), Var( r ) v and σ Var( v ), respectvely. σ, In decomposng the stock volatlty, Campbell et al. (2001) assume that the CAPM beta of ndustry wth respect to the stock market s constant over tme. Followng ther methodology, we also assume that the beta n Eq. (3) s constant over the sample perod. Pcture 2 shows plots of the bond volatlty of each maturty, σ, and ts two components: the bond-market-level volatlty, σ βb, and the maturty-dependent volatlty, v σ. We fnd that the bond volatltes of 5, 10 and 30 years are much hgher than that of 1 B 9

12 year, whle the maturty-dependent volatlty s emboded by the bond volatlty of 1 year more effectvely than by 5, 10, and 30 years. Ths means that the maturty-dependent volatlty s more mportant n explanng the volatlty of short-term bonds than of medum- and long-term bonds. In the prevous secton, we studed the mpact of real and monetary factors on bond volatlty of each maturty. The next step s to nvestgate the mpacts of real and monetary factors on the two components of total volatlty: the bond-market-level B v volatlty, σ, and the maturty-dependent volatlty, σ. Table 4 presents the regresson results of real and monetary factors on the bondmarket-level volatlty. For all combnatons of explanatory varables, the coeffcents of the real factor are postve, and the t-values demonstrate that the real factor sgnfcantly affects the bond-market-level volatlty. It s not surprsng to fnd that the monetary factor s not sgnfcant, although t s stll negatvely correlated wth the bond-market-level volatlty. The reason s that the effect of the monetary factor on the maturty-dependent volatlty has been removed leavng the effect of the real factor on the volatlty of bond-market-level. Moreover, when the real factor s excluded from the regressons, the nomnal short rate s stll sgnfcant n affectng the bond-marketlevel volatlty. Table 5 presents the estmates of real and monetary factors on the maturtydependent volatlty. Smlar to the analyss of the bond volatlty of each maturty and the bond-market-level volatlty, the real factor sgnfcantly affects the maturtydependent volatlty of all maturtes, whle the monetary factor only affects the 10

13 maturty-dependent volatlty of 1-year bonds. Ths s dfferent from the results n Table 3, n whch the monetary factor sgnfcantly affects the bond volatlty of 1- and 5-year bonds. Fama and French (2005), Ang and Chen (2007), and other papers suggest that the CAPM betas vary over tme. Next, we wll take the tme-varyng CAPM betas nto account and reproduce the regressons of maturty-dependent volatlty on the real and monetary factors. To calculate the tme-varyng CAPM betas for each month of the sample perod, we regress the daly excess bond returns of maturty on the daly bondmarket returns lke Eq. (3) to gan the seres of monthly betas. Pcture 3 plots the bond volatlty of each maturty and ts two components for the case of tme-varyng betas. Smlar to the case for constant betas, the bond volatltes of 5-, 10-, and 30-year maturtes are much hgher than that of 1-year bonds, whle the maturty-dependent volatlty explans the bond volatlty of 1 year more effectvely than those of 5, 10, and 30 years. Therefore, the maturty-dependent volatlty s more sgnfcant for the shortterm bonds than for the medum- and long-term bonds. Table 6 presents the estmates of real and monetary factors on the maturtydependent volatlty for the case of tme-varyng betas. The results are nterestng because they are more smlar to those n Table 3 than to the ones n Table 5. The real factor sgnfcantly affects maturty-dependent volatlty of all maturtes, whle the monetary factor only affects the 1- and 5-year maturty-dependent volatlty. In summary, when we decompose bond volatlty nto market-level volatlty and maturty-dependent volatlty, we fnd that the macro factors sgnfcantly affect the 11

14 maturty-dependent bond volatlty. In partcular, the real factor affects the bond-return volatlty across all maturtes, whle the monetary varables are sgnfcantly related to the return volatlty of short-term bonds, weakly related to the return volatlty of medum-term bonds, and have no nfluence on the volatlty of the long- term bonds. 3.3 Volatlty decomposton based on value-weghted stock-market ndex In the prevous secton, we used the CAPM to decompose the bond return nto bondmarket return and maturty-dependent bond return. In ths secton, we wll calculate the CAPM beta between the bond return of each maturty and the stock-market return by employng the value-weghted stock-market ndex, whch has been used by Vcera (2007) to proxy for the bond rsk. By usng the same methodology as n the prevous secton, we can express the bond return on each maturty as follows: r S S S () t = + β ( t) r ( t) u ( t), α (5) B + where S r s the stock return n excess of the 3-month Treasury-bll rates, and Var B S S ( r () t ) Var ( t) r ( t) ( ) Var u ( t) = β ( ). (6) + Fgures 4 and 5 plot the bond volatlty of each maturty and ts two components of market-level and maturty-dependent volatlty of bond return. Much lke n Fgures 2 and 3, the maturty-dependent volatlty s more mportant n explanng the volatlty of short-term bonds than that of medum- and long-term bonds. 12

15 Tables 7 and 8 llustrate the estmates of maturty-dependent volatlty for the cases of constant and tme-varyng betas when we use the daly stock returns on the valueweghted portfolo as the market portfolo. Consstent wth the results n Tables 5 and 6, the regresson results n Tables 7 and 8 show that the real factor sgnfcantly affects the volatltes of bond return of all maturtes, whle the monetary factor s only sgnfcantly related to the return volatltes of short-term bonds. Therefore, the results from the analyss presented n ths secton provde further evdence that the macro factors sgnfcantly affect the bond volatlty. In partcular, the real factor affects the bond volatlty of all maturtes whle the monetary varables are sgnfcantly related to the volatlty of short-term bonds and weakly related to the volatlty of medum-term bonds. 4. Concluson Ths paper nvestgates the mpact of macro varables on the volatlty of government bond returns. We extract the real and monetary factors from the real actvtes and monetary varables, respectvely. Then we examne the two factors mpact on the daly volatlty of the 1-, 5-, 10- and 30-year U.S. Treasury bonds. We fnd that both real and monetary factors sgnfcantly affect the bond return volatlty. In partcular, the real factor affects the volatlty across all maturtes, whle the monetary varables are sgnfcantly related to the volatlty of short-term bonds and weakly related to the volatlty of medum-term bonds. 13

16 Through all of the above dscussons and fndngs, we can conclude that the monetary authortes can employ macroeconomc polcy to affect the volatlty of Treasury bonds. At the same tme, nvestors can mprove ther portfolo management by analyzng macroeconomc condtons. 14

17 References [1] Ang, A, Chen, J., CAPM over the long run: Journal of Emprcal Fnance 14, [2] Ang, A, Pazzes, M., A no-arbtrage vector autoregresson of term structure dynamcs wth macroeconomc and latent varables. Journal of Monetary Economcs 50, [3] Balduzz, P., Elton E. J., Green, T.C., Economc news and bond prces: evdence from the U.S. treasury market. Journal of Fnancal and Quanttatve Analyss 36, [4] Campbell, J., Lettau, M., Malkel, B., Xu, Y., Have ndvdual stocks become more volatle? an emprcal exploraton of dosyncratc rsk. Journal of Fnance 56, [5] Chrstansen, C., Macroeconomc announcement effects on the covarance structure of government bond returns. Journal of Emprcal Fnance 7, [6] Evans, C.L. Marshall, D.A., Monetary polcy and the term structure of nomnal nterest rates: evdence and theory. Carnege-Rochester Conference Seres on Publc Polcy 49, [7] Fama, E.F. French, K.R., The value premum and the CAPM. Journal of Fnance 61, [8] Flemng, M. J., Remolona, E.M., Prce formaton and lqudty n the U.S. treasury market: the response to publc nformaton. Journal of Fnance 54, [9] French, K. R., Schwert, G.W., Stambaugh, R.F., Expected stock returns and volatlty. Journal of Fnancal Economcs 19, [10] Goej, P. and W., Marquerng, Macroeconomc announcements and asymmetrc volatlty n bond returns. Journal of Bankng & Fnance 30, [11] Jones, C.M., Lamont, O., Lumsdane, R.L., Macroeconomc news and bond market volatlty. Journal of Fnancal Economcs 47, [12] Ludvgson, S.C., Ng, S., Macro factors n bond rsk prema. forthcomng Revew of Fnancal Studes. [13] Schwert, G.W., 1989, Why does stock market volatlty change over tme?. Journal of Fnance 44, [14] Stock, J.H., Watson, M.W., Macroeconomc forecastng usng dffuson ndexes. Journal of Busness and Economc Statstcs 20,

18 [15] Vcera, L.M, Bond rsk, bond return Volatlty, and the term structure of nterest rates. Workng paper. 16

19 Appendx Descrpton of Macroeconomc Varables Ths table descrbes the real actvtes and monetary varables used n our analyss. In the transformaton column, lv denotes the level of the seres, lv denotes the dfference of the level, ln denotes the frst dfference of logarthm, and 2 ln denotes the second dfference of logarthm. Data on all seven seres are from the Global Insght Basc Economcs database. Seres Mnemonc Descrpton Real actvtes 1 LHEL 2 LHUR Index of Help-Wanted Advertsng n Newspapers (1967=100; SA) Unemployment Rate: All Workers, 16 Years & Over (%, SA) Trans 3 IPS10 Industral Producton Index Total ndex ln 4 PMP NAPM Producton Index (Percent) lv Monetary varables ln lv 1 FYFF 2 FMRNBA 3 FM2 Interest Rate: Federal Funds (Effectve) (% Per Annum, NSA) Depostory Inst Reserves: Nonborrowed, Adjusted Reserve Requrement Changes (Ml$, SA) Money Stock: M2 (M1+O'NITE RPS, EURO$, G/P&B/D MMMFS & Sav & SM Tme Dep (Bl$, SA) lv 2 ln 2 ln 17

20 Table 1 Descrptve statstcs of daly excess bond returns ( ~ ) Ths table presents the sample statstcs of daly returns on 1-, 5-, 10-, and 30- year Treasury bonds n excess of the 3-month Treasury-bll rates. The bond returns are obtaned from the CRSP Daly Treasury Fxed-term Fle. The 3-month Treasure-bll rates are taken from the Federal Reserve Board of Governors. 1-year 5-year 10-year 30-year Mean Medan Std dev Table 2 Correlatons among (real and monetary) factors and bond return volatlty ( ~ ) Ths table presents the correlatons between the realzed volatlty of 1-, 5-, 10-, and 30- year bonds and the one-month-lagged real and monetary factors. The correlatons among bond volatltes are also presented n the followng table. 1-year 5-year 10-year 30-year Real Money year year year

21 Table 3 Estmates of real and monetary factors on bond volatlty ( ~ ) Ths table presents monthly regressons of realzed volatlty of 1-, 5-, 10-, and 30- year bonds on the lagged real factor Real -1, the lagged monetary factor Money -1, the lagged log short rate r -1, and the lagged bond volatlty. The t-values are reported n the brackets. Real -1 Money -1 r -1 Vol -1 R 2 1-year (3.71) 0.51 (13.947) (-3.467) (15.982) (5.536) (12.787) (4.068) (-3.847) (14.328) (3.225) (5.211) (11.723) (-3.265) (5.404) (13.165) (3.574) (-3.61) (5.032) (12.096) year (3.875) (11.509) (-1.966) (12.708) (3.729) (11.529) ( (-2.415) (11.555) (3.359) (3.191) (10.739) (-1.909) 4.64 (3.696) 0.44 (11.605) (3.605) (-2.312) (3.112) (10.794) year (3.622) (11.545) (-1.082) (12.734) (2.604) (12.182) (3.757) (-1.473) 0.44 (11.567) (3.229) (2.033) 0.43 (11.261) (-1.033) (2.582) (12.212) (3.364) (-1.398) (1.978) (11.286) year (2.732) (17.064) (-1.219) (18.447) (1.868) (18.043) (2.883) (-1.528) (17.061) (2.444) (1.42) (16.901) (-1.189) (1.848) (18.068) (2.596) (-1.478) (1.365) (16.9)

22 Table 4 Estmate of real and monetary factors on bond-market-level volatlty Ths table presents monthly regressons of bond-market-level volatlty on the lagged real factor Real -1, the lagged monetary factor Money -1, the lagged log short rate r -1, and the lagged bond volatlty. The t-values are reported n the brackets. Real -1 Money -1 r -1 Vol -1 R (2.946) (17.21) (-1.124) (18.411) (2.258) (17.834) (3.088) (-1.455) (17.21) (2.603) (1.792) (16.902) (-1.087) (2.238) (17.784) (2.744) (-1.392) (1.741) (16.907)

23 Table 5 Estmates of real and monetary factors on maturty-dependent volatlty wth value-weghted bond-market ndex and constant beta Ths table presents monthly regressons of maturty-dependent volatlty (for the case of value-weghted bond-market ndex and constant CAPM betas) on the lagged real factor Real -1, the lagged monetary factor Money -1, the lagged log short rate r - 1, and the lagged bond volatlty. The t-values are reported n the brackets. Real -1 Money -1 r -1 Vol -1 R 2 1-year (3.882) (10.632) (-2.28) (12.338) (6.131) (9.437) (4.117) (-2.658) (10.828) (3.334) (5.783) (8.458) (-2.043) (6.037) (9.621) (3.553) (-2.383) (5.651) (8.65) year (4.103) (6.439) (-1.018) (7.491) (4.851) (6.184) (4.234) (-1.463) (6.458) (3.441) (4.297) (5.494) (-0.923) (4.827) (6.213) (3.565) (-1.311) (4.243) (5.519) year (3.888) (5.461) (1.125) (6.32) (4.233) (5.417) (3.789) (0.743) (5.451) (3.266) (3.667) (4.795) (1.238) 4.57 (4.262) (5.371) (3.149) (0.9) (3.7) (4.779) year (3.003) (3.773) (-0.56) (4.345) (2.244) (4.099) (3.079) (-0.884) (3.776) (2.628) (1.716) (3.651) (-0.522) (2.233) (4.107) (2.702) (-0.82) (1.683) (3.656)

24 Table 6 Estmates of real and monetary factors on maturty-dependent volatlty wth value-weghted bond-market ndex and tme-varyng beta Ths table presents monthly regressons of maturty-dependent volatlty (for the case of value-weghted bond-market ndex and tme-varyng CAPM betas) on the lagged real factor Real -1, the lagged monetary factor Money -1, the lagged bond volatlty, and the lagged log short rate r -1. The t-values are reported n the brackets. Real -1 Money -1 r -1 Vol -1 R 2 1-year (3.668) (12.047) (-2.678) (13.898) (6.041) (10.75) (3.91) (-3) (12.358) (3.149) (5.725) (9.749) (-2.368) 1.41 (5.899) (11.015) (3.376) (-2.663) (5.545) (10.038) year (4.732) (13.193) (-2.763) 0.55 (15.459) (4.367) (13.594) (5.018) (-3.222) (13.488) (4.259) (3.854) (12.109) (-2.615) 1.51 (4.271) (13.864) (4.542) (-3.05) 1.3 (3.709) (12.398) year 0.67 (3.678) 0.62 (18.76) (1.27) (20.417) (5.129) (17.397) (3.566) (0.918) 0.62 (18.75) (3.218) (4.8) (16.314) (1.464) (5.178) (17.326) (3.082) (1.144) (4.846) (16.29) year 1.15 (4.007) (9.557) (-1.611) (11.062) (3.648) (10.065) (4.18) -0.7 (-2) (9.672) (3.508) (3.095) (8.999) (-1.511) (3.601) (10.168) (3.679) (-1.872) (3.011) (9.113)

25 Table 7 Estmates of real and monetary factors on maturty-dependent volatlty wth value-weghted stock-market ndex and constant beta Ths table presents monthly regressons of maturty-dependent volatlty (for the case of value-weghted stock-market ndex and constant CAPM betas) on the lagged real factor Real -1, the lagged monetary factor Money -1, the lagged log short rate r -1, and the lagged bond volatlty. The t-values are reported n the brackets. Real -1 Money -1 r -1 Vol -1 R 2 1-year (3.723) (13.834) (-3.436) (15.88) (5.389) (12.853) (4.075) (-3.814) (14.213) (3.236) (5.053) (11.765) (-3.239) (5.259) (13.229) (3.58) (-3.583) (4.876) (12.136) year (3.846) (11.306) (-1.946) (12.523) (3.341) (11.58) (4.088) (-2.385) (11.361) (3.367) (2.781) (10.744) (-1.891) (3.207) (11.662) (3.608) (-2.291) (2.7) (10.807) year (3.603) (11.301) (-1.023) (12.512) (2.162) (12.145) (3.729) (-1.406) (11328) (3.27) 2.95 (1.561) (11.154) (-0.983) (2.142) (12.175) (3.397) (-1.347) 2.85 (1.508) (11.182) year (2.656) 0.58 (16.598) (-1.1) (17.992) (1.348) (17.804) (2.791) (-1.396) (16.597) (2.444) 1.76 (0.87) (16.562) (-1.078) (1.33) (17.826) (2.582) (-1.363) (0.818) (16.562)

26 Table 8 Estmates of real and monetary factors on maturty-dependent volatlty wth value-weghted stock-market ndex and tme-varyng beta Ths table presents monthly regressons of maturty-dependent volatlty (for the case of value-weghted stock-market ndex and tme-varyng CAPM betas) on the lagged real factor Real -1, the lagged monetary factor Money -1, the lagged log short rate r -1, and the lagged bond volatlty. The t-values are reported n the brackets. Real -1 Money -1 r -1 Vol -1 R 2 1-year (3.867) (12.971) (-3.507) (15.004) (5.862) (11.695) (4.224) (-3.896) (13.375) (3.367) 1.66 (5.531) (10.648) (-3.276) (5.718) (12.089) (3.714) (-3.631) (5.34) (11.042) year (3.962) (10.546) (-2.128) (11.724) (4.091) (10.391) (4.226) (-2.582) (10.619) (3.403) (3.551) (9.654) (-2.059) (4.052) (10.49) (3.664) (-2.465) (3.465) (9.736) year 2.42 (3.916) (10.665) (-1.21) 0.45 (11.876) (2.893) (11.227) (4.064) (-1.625) (10.711) (3.487) (2.29) (10.318) (-1.151) 4.98 (2.867) (11.273) (3.633) (-1.538) (2.228) (10.366) year (3.281) 0.53 (14.698) (-1.299) (16.128) (2.041) (15.709) (3.44) (-1.659) 0.53 (14.722) (2.971) (1.594) (14.537) (-1.263) (2.018) (15.75) (3.131) (-1.604) (1.444) (14.563)

27 Fgure 1: Daly excess returns on 1-, 5-, 10-, and 30-year Treasury bonds 25

28 Fgure 2: Volatlty decomposton wth value-weghted bond-market ndex and constant beta 26

29 Fgure 3: Volatlty decomposton wth value-weghted bond-market ndex and tme-varyng beta 27

30 Fgure 4: Volatlty decomposton wth value-weghted stock-market ndex and constant beta 28

31 Fgure 5: Volatlty decomposton wth value-weghted stock-market ndex and tme-varyng beta 29

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