When Do TIPS Prices Adjust to Inflation Information?

Transcription

1 When Do TIPS Prices Adjus o Inflaion Informaion? Quenin C. Chu a, *, Deborah N. Piman b, Linda Q. Yu c Augus 15, 2009 a Deparmen of Finance, Insurance, and Real Esae. The Fogelman College of Business and Economics, The Universiy of Memphis, Memphis, TN b Deparmen of Economics and Business, Rhodes College, Memphis, TN c Deparmen of Finance and Business Law, College of Business and Economics, Universiy of Wisconsin Whiewaer, WI * Corresponding auhor. Fax (901) ; qchu@memphis.edu.

2 When Do TIPS Prices Adjus o Inflaion Informaion? Absrac The rading of Treasury Inflaion-Proeced Securiies (TIPS) provides a unique se of marke price daa o invesigae when securiy prices adjus o inflaion informaion. Afer conrolling for changes in he real rae, changes in he reference Consumer Price Index (CPI), and he weekday effec, he seemingly random flucuaion of daily TIPS holding period reurns sar o reveal he paern of TIPS price adjusmen o inflaion informaion. The sudy finds ha TIPS prices adjus o inflaion informaion during he price survey period, which precedes CPI announcemen by 22 o 42 rading days. TIPS prices also make a significan adjusmen on he CPI announcemen day. The findings are based on regression analysis of ime-series cross-secion daa from hree mauring TIPS. Furhermore, boosrap resuls are used as a benchmark o gauge he robusness of our empirical findings. The empirical evidence presened in his paper is consisen wih a TIPS marke where TIPS price adjusmen is concurren wih he change in consumer price.

3 When Do TIPS Prices Adjus o Inflaion Informaion? 1. Inroducion The adjusmen of Treasury Inflaion-Proeced Securiies (TIPS) prices o he monhly updae of he Consumer Price Index (CPI) is invesigaed using hree maured TIPS wih mauriies occurring in January 2007, January 2008, and January In an efficien marke, securiy prices adjus o new informaion insananeously. TIPS prices are linked o he CPI and are expeced o adjus o inflaion informaion. The Bureau of Labor Saisics follows a monhly cycle lasing for abou 45 rading days o updae he CPI. The monhly cycle includes a price survey period o sample reail prices and an announcemen of CPI abou four weeks afer he price survey period. This sudy asks he quesion when TIPS prices adjus o inflaion informaion. The hypoheses sae ha he adjusmen of TIPS prices occurs concurrenly wih he consumer price survey period as well as TIPS prices reac o he CPI announcemen and make he final adjusmen o inflaion informaion. The rading of TIPS provides a unique se of marke price daa o answer he research quesion. We use a regression model o invesigae he iming of TIPS price adjusmen o inflaion informaion. The regression model uilizes TIPS prices over a hree-year period from each of hree maured TIPS issues. We draw our ime-series cross-secion daa from he las hree years of mauring TIPS prices o reduce he noise associaed wih changing long run real rae expecaions. To avoid he las few monhs when a TIPS issue gradually ransforms from an inflaion hedge securiy ino a Treasury bill, he sudy periods end four monhs before mauriy daes. The regression model

4 invesigaes he impac of marke deermined measures of unexpeced inflaion on TIPS daily holding period reurn (HPR) over a 51-day window, beginning 45 business days prior o a monhly CPI announcemen and coninuing hrough five business days afer he announcemen. Our regression model also includes hree conrol variables ha affec he change in he daily HPR of TIPS: (1) changes in he real rae of ineres (DRY), (2) changes in he hisorical inflaion reference index ha adjuss nominal prices of TIPS for inflaion (DRATIO), and (3) a se of dummy variables (DumDay) o indicae weekday effec on daily HPR. This sudy finds ha TIPS prices do adjus o inflaion informaion during he consumer price survey period, which precedes CPI announcemen by 22 o 42 days. We also find a significan price adjusmen on he announcemen dae. 2. Facors Influencing TIPS Prices The cash flows associaed wih TIPS are direcly ied o he announced inflaion. TIPS prices, which are free from defaul risk and are proeced agains inflaion, provide a unique se of marke daa o observe how securiy prices adjus o inflaion informaion. When TIPS maured on January 15, 2007, he final redempion paymen on he par amoun was adjused for all he inflaion since he TIPS were issued in January This is accomplished by muliplying he saed par amoun by he raio of reference CPI ied o he redempion dae over he reference CPI for he issuance dae. Each semiannual coupon paymen is adjused he same way. Since he cash flow o be paid depends on acual cumulaive inflaion, he TIPS price reacs much differenly over ime han he convenional bond. While he 2

5 convenional bond price will respond o changes in he expeced rae of inflaion and changes in he real rae, he TIPS will respond only o changes in pas inflaion and changes in he real rae, assuming conemporaneous adjusmen of he conracual cash flow o he curren CPI. However, he adjusmen of TIPS conracual cash flow is no conemporaneous. The marke relies on repeaed rading o synhesize inflaion informaion and on he announcemen of CPI o make he final price adjusmens. For example, April 2007 CPI measures price level occurring beween March 15, 2007 and April 15, The April 2007 CPI was released on May 15, The reail price survey period for April 2007 CPI covers 22 o 42 business days before he official announcemen of April 2007 CPI on May 15, The sudy window covering 48 days around a CPI announcemen dae is separaed ino four periods. 2 Period I coincides he monhly CPI reail price survey period which covers around 22 days o 42 days prior o a CPI announcemen dae. Period II runs from 21 days o 1 day before a CPI announcemen dae. In period II, Bureau of Labor Saisics processes price daa colleced from he survey period. The CPI announce dae is he period III. Period IV covers he five days afer a CPI announcemen dae. Given he srucure of he TIPS conrac wih he invesor, we expec ha he holding period reurn has a posiive correlaion wih realized inflaion refleced in he change in he reference CPI, and ha i has a negaive correlaion wih he change in real 1 A ypical chronology of monhly CPI announcemen cycle is presened in Schwer (1981), p The observaion window covers 51 days around a CPI announcemen dae, i.e., 45 days before and 5 days afer a CPI announcemen dae. The sudy window is 3 days shorer han he observaion window, i.e., 42 days before and 5 days afer a CPI announcemen dae. 3

6 reurn. The Treasury securiy marke requires one business day o sele a ransacion. The HPR on Friday includes a leas 3-day accrual ineres yield unil he firs business day in he following week. The TIPS daily HPRs are expeced o have a weekly paern in which Friday is expeced o have a larger HPR. Afer conrolling for hese hree facors, we design a regression model o reveal when TIPS prices adjus o inflaion informaion. Specifically, we are asking how much of he TIPS holding period reurns are associaed wih unexpeced inflaion during each of he four observaion periods. 3. Lieraure Review There is a small body of research ha has used marke securiies o invesigae he marke s abiliy o aggregae informaion abou inflaion. Schwer (1981) addressed he informaion aggregaion of inflaion ino he sock prices, and found a weak suppor for he hypohesis ha composie sock prices adjus o new inflaion informaion during he price measuremen period. Huberman and Schwer (1985) used Israeli bonds indexed o is CPI o es wheher announcemens of CPI were already refleced in he indexed bond prices. They find ha 85 percen of he reacion o inflaion informaion occurs from 2 o 5 weeks before he announcemen, i.e., when he inflaion is occurring. They found no significan relaionship beween unexpeced inflaion and indexed bond reurns during he wo weeks afer he monh is ended and before he announcemen is made. On he day afer he announcemen hey made he final 15% adjusmen. Their conclusion is ha index-linked bond prices do absorb mos of he informaion as he price level is changing, bu here is some porion which is missed and is assimilaed only afer public announcemen. 4

7 Chu (1991) used he shor-lived inflaion fuures prices ( ) o examine he iming and speed wih which inflaion fuures prices absorb inflaion informaion. The research measures he expeced and unexpeced componens of he inflaion rae by idenifying a ime series inflaion rae model based on pas inflaion raes. The imeseries model is used o predic inflaion of he nex monh. Any difference beween he prediced inflaion and he acual inflaion which was subsequenly announced is reaed as he unexpeced inflaion. Chu (1991) found ha inflaion fuures prices reflec 71 percen of unexpeced inflaion abou 25 business days prior o he CPI announcemen, which coincides wih he end of he inflaion measuremen period. The remaining 29 percen occurs on and shorly afer he CPI announcemen dae. Boh sudies conclude ha while he markes involved are no perfecly aggregaing informaion, hey are efficien in absorbing a grea deal of inflaion informaion ino he price of he underlying securiy far in advance of he announcemen dae. Previous sudies using Israeli indexed bond price daa have several problems. Some of he Israeli bonds are only parially indexed wih respec o principal and none of he coupon paymens are indexed, rendering he bonds less effecive as an inflaion hedge securiy. Also here is a defaul premium in he Israeli bonds reurns which may bias resuls of he es. Moreover, he Israeli governmen does inervene in he bond marke (Huberman and Schwer, 1985), wih indexed bonds represening he 67% of governmen bonds ousanding in The inflaion fuures conrac used by Chu (1991) overcomes hese problems, bu he conrac had a relaively shor rading hisory and never enjoyed a large rading volume. 5

8 Our sudy is he firs aemp o documen when TIPS prices adjus o inflaion informaion. In a survey paper, Thomas (1999) indicaes ha proxies for expecaions of inflaion are problemaic, and ha here is no consensus on wheher surveys or ime series models or macroeconomic models are he bes esimaor. This sudy uses a markegeneraed measure of inflaion expecaions jus as Kandel, Ofer, and Sarig (1993) did. The expeced inflaion on a specific dae is measured by he breakeven inflaion rae, i.e. he nominal yield o mauriy on a consan five-year convenional Treasury bond minus he real yield o mauriy on a consan five-year TIPS. 4. The Regression Model and Hypoheses The dependen variable in he regression model is he ime-series of daily holding period reurn (HPR) from hree individual TIPS issues. To fully uilize all hree mauring TIPS issues (TIPS2007, TIPS2008, and TIPS2009), he regression model analyzes a pooling of ime-series cross-secion daa. Table 1 summarizes he ime-series crosssecion HPRs. The sudy covers a ime span of 1,268 rading days saring Sepember 2, 2003 hrough Sepember 12, TIPS2007 has 767 rading days covering Sepember 2, 2003 hrough Sepember 15, TIPS2008 has 765 rading days covering Sepember 1, 2004 hrough Sepember 14, TIPS2009 has 763 rading days covering Sepember 1, 2005 hrough Sepember 12, In oal, he pooling daa se has 2,295 rading day records. The oal 1,268 rading days are separaed ino five cross-secion periods. TIPS2007 was he sole TIPS securiy raded in period 1 (Sepember 2, 2003 hrough Augus 31, 2004, 252 rading days). Two TIPS securiies, TIPS2007 and TIPS2008 were 6

9 raded in period 2 (Sepember 1, 2004 hrough Augus 31, 2005, 253 rading days). All hree TIPS issues were raded in period 3 (Sepember 1, 2005 hrough Sepember 15, 2006, 262 rading days). TIPS2008 and TIPS2009 were raded in period 4 (Sepember 18, 2006 hrough Sepember 14, 2007, 250 rading days). Finally, TIPS2009 was he sole TIPS issue raded in period 5 (Sepember 17, 2007 hrough Sepember 12, 2008, 251 rading days). The following regression model is used o idenify he iming of TIPS price adjusmen o inflaion informaion. HPR 5 = α ( + δ U + μ 4 Yr, + β DRY ) + γ (DRATIO ) + θ i i ( DumDay 1 i, ) = k = 45 k k, Yr, where = 1,2,...,1268, Yr = 2007, 2008, (1) HPR Yr, : DRY : DRATIO : he daily nominal holding period reurn for TIPS Yr issue on he -h dae; daily change in real ineres rae, a conrol variable; daily change in he raio of reference CPI over base CPI, a conrol variable; DumDay i, : dummy variables o indicae weekday for he -h dae, a conrol variable; U : he monhly inflaion surprise if he -h dae is k days away from a CPI k, announcemen dae; zero oherwise; k: a negaive number means k days prior o a CPI announcemen dae; a posiive number means k days afer a CPI announcemen dae; and zero means a CPI announcemen dae; μ : a disurbance erm for he TIP Yr issue on he -h dae; Yr, α β, γ, θ 's : he regression coefficiens for conrol variables;, i 7

10 δ k 's : he regression coefficiens revealing he adjusmen of TIPS prices o inflaion informaion. Holding period reurn measures daily realized reurn if an invesor purchases TIPS on day -1 and sell he same TIPS on day. Daily HPR for an issue of TIPS is compued as follows: where HPR = P P + 1 (nomial coupon paymen on ex - coupon day, zero oherwise) P 1 (2) P repored clean price + I = c days beween selemen dae and he las coupon paymen dae I 2 days beween coupon paymen daes B (3) P is nominal invoice price of a TIPS issue on observaion dae ; c is annual coupon in eal erm; I is he reference CPI for he observaion dae; and I B is he reference CPI for he original daed issue dae. DRY is measured by daily change in 5-year consan mauriy real rae. The monhly unexpeced inflaion rae is obained by subracing he monhly expeced rae from he acual monhly rae. The monhly expeced rae is measured by he breakeven inflaion rae divided by 12. The breakeven inflaion rae is defined as he yield spread beween 5-year consan mauriy nominal and real raes. We use observaion dae July 20, 2007 for TIPS issue mauring on January 15, 2008 as an example o explain he 51-day observaion window and he srucure of independen variables U k, ' s. The observaion dae on July 20, 2007 is 42 rading days before he announcemen of Augus 2007 CPI on Sepember 19, The U 42, for observaion dae on July 20, 2007 is he acual monhly inflaion rae for Augus

11 minus he expeced inflaion measured by he one welfh of he breakeven inflaion rae observed on July 20, Similarly, July 20, 2007 is 18 rading days before he announcemen of July 2007 CPI and 2 rading days afer he announcemen of June 2007 CPI. U 18, and U 2, are compued according o he same procedure for observaion dae on July 20, According o he definiion of unexpeced inflaion, he res of 48 U k, ' s. for observaion dae on July 20, 2007 are se o zero. We examine a observaion window of 45 days before and 5 days afer a CPI announcemen dae. The regression coefficiens for he hree conrol variables are expeced o be significanly differen from zero. The regression coefficien for he conrol variable DRY is expeced o be significanly less han zero, i.e., β < 0. The TIPS HPR is negaively relaed o changes in he real ineres rae. An increase in he real ineres rae resuls in a decrease in real and nominal prices of TIPS and subsequenly a negaive HPR. The nominal price of TIPS increases as he reference CPI increases. HPR is expeced o be posiively relaed o an increase in he raio of reference CPI over base CPI. The regression coefficien for he conrol variable DRATIO is expeced o be significanly greaer han zero, i.e., γ > 0. The regression coefficiens for he se of dummy weekday variables (DumDay i s) are used o reflec weekday effec due o he selemen procedure used in he TIPS marke. The specificaion of he regression model enables us o es iming hypoheses linked o he four sudy periods. Firs, if he TIPS HPR reflecs new flow of informaion abou inflaion during he reail price survey period, he summaion of regression coefficiens for unexpeced inflaion over he price survey period should be significanly differen from zero. The monhly price survey period covers around 22 o 42 business 9

12 days prior o he announcemen dae. The priori hypohesis of he iming of TIPS price adjusmen saes ha ( k = 42 o 22) δ is greaer han zero. k Second, he ime period beween 21 days o one day before a CPI announcemen dae, Bureau of Labor Saisics processes reail price daa colleced from he survey period. In a marke ha processes inflaion informaion efficienly, a priori hypohesis saes ha ( k = 21 o 1) δ is insignificanly differen from zero. k Third, he regression coefficienδ 0 measures he reacion of TIPS price o he CPI announcemen. Excep for he case of perfec foresigh abou inflaion, he CPI announcemen is expeced o carry new inflaion informaion and TIPS price adjusmen. A priori hypohesis saes ha δ 0 is greaer han zero. Finally, in an efficien marke, no addiional TIPS price adjusmen is expeced afer he CPI announcemen. We hypohesize ha ( k = 1 o 5) δ k is insignificanly differen from zero. Table 2 summarizes he four priori hypoheses. 5. Economeric Issues and Mehodology Two economeric issues are in order. Firs, he regression model uses ime-series cross-secion daa o esimae regression coefficiens and perform hypohesis ess. For each rading day, here may be one, wo, or hree TIPS issues in he panel daa. If he number of TIPS issues are greaer han one, TIPS prices are subjec o conemporaneous marke disurbance across TIPS issues and heir regression disurbance erms a an observaion dae, μ ', are highly correlaed. Ordinary leas squares esimaors are Yr, s unbiased bu heir variance-covariance marix is inefficien. In esimaing an efficien 10

13 covariance srucure, Whie (1980) heeroscedasiciy consisen esimaor is applied o conrol for boh conemporaneous correlaion and heeroscedasiciy. The correlaion among various TIPS residual erms on an observaion dae is allowed o change over ime. The variance-covariance marix is esimaed by ( X X ) X 1 ' ' 1 ( X ˆ ˆ X )( X ) μ μ, where X is he regression design marix, X is he cross-secional explanaory variables for he -h dae, and μˆ is residual vecor esimaed from separae auoregressive model applied o individual TIPS ime series daa. Second, afer conrolling for he presence of cross-secional correlaion among TIPS issues, he ime-series cross-secion daa are sill subjec o he auocorrelaion problem. We apply nonparameric boosrapping mehods o examine he robusness of hypohesis ess using Whie heeroscedasiciy consisen variance-covariance esimaor. Davison and Hinkley (2006) describe he deails of boosrapping mehod o resample regression error erms. To mainain he original srucure of ime-series cross-secion daa, he resampling error erms are resriced o same weekday and same ime period specified in Table 1 panel B. 6. Daa and Resuls We invesigae hree mauring issues of TIPS wih mauriies on January (TIPS 2007), January (TIPS 2008), and January (TIPS 2009). When he hree Treasury securiies were issued, all of hem had 10 years mauriy. Daily real clean price series for TIPS, 5-year consan mauriy real and nominal ineres raes are 11

14 rerieved from Daasream daabase. 3 Hisorical ime series CPI and announcemen daes are available a he Bureau of Labor Saisics websie. Reference CPI and base CPI for a specific issue of TIPS are rerieved from he TreasuryDirec websie. Our sudy periods include hree years of rading hisory before each TIPS mauriy daes. The TIPS have a hree-monh lag in indexing heir coupon and principal paymens. The inflaion hedging propery of a TIPS issue expires hree monhs before he mauriy dae. To avoid he las few monhs when a TIPS issue gradually ransforms from an inflaion hedge securiy ino a Treasury bill, he sudy periods end four monhs before mauriy daes. Table 3 summarizes he mean and sandard deviaion values for he variables used in he regression models. The average daily HPRs for he hree TIPS issues are %, %, and %. In erms of nominal annual yields, he hree average HPRs are equivalen o 3.73%, 3.43%, and 4.99%, respecively. The average 5-year consan mauriy real raes for he hree TIPS sudy periods are 1.49%, 1.89%, and 1.84%. The average real raes are relaively low compared wih convenional esimaes beween 3% and 4% using annual growh rae of real gross naional produc. The average 5-year consan mauriy nominal raes for he hree TIPS issues are 3.93%, 4.35%, and 4.19%. We also repor summary saisics for daily changes in real raes (DRY), daily changes in he raio of reference CPI over base CPI (DRATIO), and acual monhly percenage change in CPI. The HPR is calculaed based on TIPS nominal invoice price and he accrued nominal coupon paymen. Figure 1 shows he ime series paern of holding period reurn 3 Federal Reserve compiles and publishes daily 5-year consan mauriy real and nominal ineres raes. Daasream includes he ime series in is daabase. 12

15 for he hree mauring TIPS during heir respecive ime spans. Similar o oher risky securiies, he HPR for TIPS flucuaes over ime o reflec he changes in real rae and inflaion informaion. As a general rend, he flucuaion in HPR aenuaes as a TIPS issue approaches is mauriy dae. The aenuaion paerns reflec he decrease in duraion as he ime o mauriy of a TIPS issue decreases. Table 4 repors regression coefficiens for conrol variables. For an individual TIPS, SAS AUTOREG procedure is applied o esimae regression coefficiens for conrolling variable. The AUTOREG procedure specifically recognizes he presence of auocorrelaion in individual TIPS ime-series residual erms. Consisen wih our prior expecaion he β coefficien for he conrol variable DRY is significanly less han zero. The TIPS HPR is negaively relaed o changes in he real ineres rae. An increase in he real ineres rae leads o a decline in TIPS prices and subsequenly a negaive HPR. On he oher hand, TIPS nominal price increases as reference CPI increases and vice versa. Consisen wih our expecaions, we found a posiive and saisically significan relaionship beween TIPS prices and reference CPI. The coefficien esimaes for he conrol variable DRATIO varies from o The saisically significan regression coefficiens for β and γ are observed for all hree issues. The esimaed regression coefficiens for weekday dummy variables show ha Friday consisenly has he highes HPRs, which reflec he selemen procedure used in he TIPS marke. The esimaed firs order auoregressive parameer, ˆ φ 1, is significanly greaer han zero for all hree TIPS ime-series regression models. Afer adjusing for he firs order auocorrelaion, he regression models for individual TIPS issues are free from auocorrelaion problem as indicaed by he repored Durbin-Wason saisics in Table 4. 13

16 Table 4 also repors he pooling ime-series cross-secion resuls for conrol variables. Ordinary leas squares mehod is used o esimae regression coefficiens for conrol variables. The esimaed sandard errors are seleced from Whie (1980) heeroscedasiciy consisen variance-covariance esimaor o conrol for boh conemporaneous correlaion and heeroscedasiciy. The resuls for pooling daa are robus wih respec o resuls from individual TIPS ime-series daa. TIPS HPRs are negaively relaed o change in real ineres rae, posiively relaed o he daily change in he raio of reference CPI over base CPI, and a larger HPR on Friday due o he TIPS selemen procedure Four priori hypoheses summarized in Table 2 es when TIPS prices reflec new flow of informaion abou inflaion during he four sudy periods. We calculae a ime series of he cumulaive sum of he esimaed regression coefficiens ˆ' δ s over a 51-day observaion window. The window runs from 45 days before hrough 5 days afer a CPI announcemen dae. Figure 2 plos he cumulaive sum of he esimaed coefficiens for he 2007, 2008, and 2009 mauring TIPS and he pooling ime-series cross-secion daa wih he horizonal axis represening number of days before or afer an announcemen day. All four ime-series of cumulaive sum of coefficiens show similar paern. The paern reveals a significan porion of he unexpeced inflaion has been refleced in TIPS prices 22 days prior o CPI announcemen. The sum of esimaed coefficiens for δ 42 hrough δ 22 reflecs new flow of informaion abou informaion during he price survey period. A saisically significan posiive ( k = 42 o 22) ˆ δ indicaes new informaion abou inflaion is being incorporaed k ino TIPS prices as hey occur. Our pooling daa show ha he esimaed 14

17 ( k = 42 o 22) ˆ δ is The -saisics for esing he null hypohesis δ = 0 k ( k = 42 o 22) is 4.79, which is significanly greaer han zero a he 1% level. Similar sum of coefficien esimaes and suden- saisics are compued o es priori hypoheses for he k oher hree sudy periods. The esimaed ( k = 21 o 1) ˆ δ k, ˆ δ, and ˆ 0 ( = 1 5 δ ) k k o are 0.034, 0.092, and 0.009, respecively. The corresponding suden- saisics for Period II, III, and IV are 0.43, 4.50, and 0.24, respecively. The error erms used o compue he Whie heeroscedasiciy consisen variancecovariance marix are exraced from individual auoregressive regression models for hree TIPS issues. As he Durbin-Wason saisics repored in Table 4, he exraced error erms from he firs order auoregressive regression model are free from he auocorrelaion problem. As an alernaive approach o examine he robusness of he repored -saisics for esing he four hypoheses, we apply boosrap mehod by resampling regression residual erms wih replacemen. The boosrap resampling procedure permues he regression error erms. Ordinary leas squares mehod is used o compue regression residual erms and subsequenly he esimaion of he variancecovariance marix. Based on 1,000 simulaion runs, Table 5 shows he comparison beween sample esimaes and boosrap resuls. The sample esimaes are close o he benchmark resuls derived from he boosrap mehod. Our empirical resuls are robus wih respec o auocorrelaion problem observed in he TIPS regression models. 7. Conclusions We analyze he iming o incorporae inflaion informaion ino TIPS prices. Four or five weeks afer he change in consumer price for a paricular monh has been 15

18 measured, he CPI is announced. The cash flow of he TIPS is impaced by he inflaion, and his securiy provides a rare opporuniy o observe direcly, hrough a marke-based daily measuremen, when he TIPS prices adjus o inflaion informaion. The iming of adjusmen of TIPS prices o monhly updae of CPI was revealed for mauring TIPS prices once we conrol for changes in he real rae, changes in he reference CPI and he weekday effec. Three overlapping hree-year sudy periods are drawn from hree mauring issues of TIPS, and a regression model idenifies when TIPS holding period reurns are correlaed wih daily inflaion surprise. The inflaion surprise is measured by he acual inflaion minus he expeced inflaion. Previous research in his area has used ime series models o predic he expeced inflaion series. In conras, his sudy obains inflaion expecaions from he yield spread beween he nominal Treasury securiies and he TIPS of he same mauriy, i.e. breakeven inflaion using acual marke prices. Our resuls indicae ha he TIPS marke is efficien in aggregaing inflaion informaion. Using he pooling ime-series cross-secion daa from hree maured TIPS issues, TIPS prices sar reacing o inflaion during he price survey period. A significan porion of unexpeced inflaion has been incorporaed ino TIPS prices by he end of he price survey period. TIPS prices adjus any misinerpreaion abou inflaion on he CPI announcemen dae. Boosrap resuls are used as a benchmark o gauge he robusness of -saisics for hypohesis ess. This paper presens he empirical evidence and conribues o he undersanding of when informaion abou inflaion is incorporaed ino TIPS whose fuure cash flows are linked o inflaion. The empirical evidence presened in his paper is consisen wih a TIPS marke where TIPS price adjusmen is concurren wih he change in consumer price. 16

19 References Chu, C., 1991, Fuures prices and inflaion informaion. Review of Quaniaive Finance and Accouning 1, Davison, A. C. and Hinkley, D Boosrap mehods and heir applicaions, Cambridge: Cambridge Series in Saisical and Probabilisic Mahemaics. Huberman, G. and G. W. Schwer, 1985, Informaion aggregaion, inflaion, and he pricing of indexed bonds. Journal of Poliical Economy 93, Kandel, Shmuel, A. R. Ofer, and Oded Sarig, 1993, Learning from rading, The Review of Financial Sudies, 6:3, Schwer, G. W., 1981, The adjusmen of sock prices o informaion abou inflaion. Journal of Finance 36, 1, Thomas, L. B., Jr., 1999, Survey measures of expeced U.S. inflaion. Journal of Economic Perspecives 13, 4, Whie, H A heeroscedasiciy consisen covariance marix esimaor and a direc es for heeroscedasiciy. Economerica, 48,

20 Table 1. Time-Series Cross-Secion Holding Period Reurns Panel A: Time-Series Daa TIPS Issue Time Span Number of Trading Day TIPS /02/2003 ~ 09/15/ TIPS /01/2004 ~ 09/14/ TIPS /01/2005 ~ 09/12/ Toal 2,295 Panel B: Cross-Secion Periods Time Number of Number of Trading TIPS Time Span Period Trading Days Records Issues 1 09/02/2003 ~ 08/31/ TIPS /01/2004 ~ 08/31/ TIPS2007, and TIPS /01/2005 ~ 09/15/ TIPS2007, TIPS2008, and TIPS /18/2006 ~ 09/14/ TIPS2008, and TIPS /17/2007 ~ 09/12/ TIPS2009 Toal 1,268 2,295 Sudy Period I II III IV Table 2. Summary of Hypoheses Time span relaive o a CPI Descripion Prior hypohesis announcemen dae 22 days o 42 days prior o a CPI reail price δ > 0 ( k = 42 o 22) k CPI announcemen dae survey period 1 day o 21 days prior o a δ = 0 ( k = 21 o 1) k CPI announcemen dae CPI announcemen Day zero δ 0 > 0 dae 1 day o 5 days afer a CPI = 0 ( 1 5) announcemen dae k = o δ k 18

21 Table 3. Summary Saisics (All numbers are in percenage.) Panel A: TIPS 2007 (Mauriy dae January 15, 2007; Real coupon rae 3-3/8%) Sudy Period: 09/02/2003 hrough 09/15/2006, 767 Trading Days Mean Sandard Maximum Minimum Deviaion HPR DRY DRATIO Real Rae Nominal Rae Monhly change in CPI Panel B: TIPS 2008 (Mauriy dae January 15, 2008; Real coupon rae 3-5/8%) Sudy Period: 09/01/2004 hrough 09/14/2007, 765 Trading Days Mean Sandard Maximum Minimum Deviaion HPR DRY DRATIO Real Rae Nominal Rae Monhly change in CPI Panel C: TIPS 2009 (Mauriy dae January 15, 2009; Real coupon rae 3-7/8%) Sudy Period: 09/01/2005 hrough 09/12/2008, 763 Trading Days Mean Sandard Maximum Minimum Deviaion HPR DRY DRATIO Real Rae Nominal Rae Monhly change in CPI

22 Table 4. Regression Coefficiens for Conrol Variables Individual TIPS Time-Series Model: HPR 4 5 = + β ( DRY ) + γ (DRATIO ) + θ i i ( DumDayi + δ k ku = 1, ) = 45 k, α + μ where μ = φ μ + ε, = 1,2,..., T. 1 1 Pooling Time-Series Cross-Secion Model: 4 5 HPR Yr, = α + β ( DRY ) + γ (DRATIO ) + θ i i ( DumDayi, ) + δ k ku 1 45 k, + μ = =, = 1,2,...,1268, Yr = 2007, 2008, Yr Individual TIPS Time-Series Model Pooling Time-Series Cross-secion Model Coefficien 2007 Esimae Sandard Error 2008 Esimae Sandard Error 2009 Esimae Sandard Error Panel Esimae Sandard Error α 0.012* β ** ** ** ** γ 0.605** ** ** ** θ 1 (Tuesday) θ 2 (Wednesday) θ 3 (Thursday) θ 4 (Friday) ** Num. of Records ,295 φ ** ** ** R Durbin-Wason ** Significanly differen from zero a he 1% level. * Significanly differen from zero a he 5% level. The coefficien esimaes and heir sandard errors are based on ime-series regression models wih auoregressive error erms. The coefficien esimaes are esimaed from he ordinary leas squares mehod. The sandard errors come from Whie (1980) heeroscedasiciy consisen esimaor o conrol for boh conemporaneous correlaion and heeroscedasiciy. 20

23 Table 5. Sample Esimaes and Boosrap Resuls Sudy Period Sample -saisics Boosrap Resuls (1,000 simulaion run) Mean Median Sandard Deviaion I II III IV

24 Figure 1. Holding Period Reurns 22

25 Figure 2. Cumulaive Sum of Coefficiens 23