Introduction and summary

Transcription

1 Liquidiy effecs in he bond marke Boyan Jovanovic and Peer L. Rousseau Inroducion and summary Is money neural? Mos economiss would now say ha i is no, a leas no in he shor run. This belief derives parly from he resuls of sudies done decades ago. In heir book on moneary hisory, Friedman and Schwarz (1963) argued ha he Federal Reserve may have caused or prolonged he Grea Depression by a policy of igh money. And in anoher sudy, Phillips (1958) found a negaive relaion beween wage inflaion and unemploymen. In he wo decades ha followed, oher sudies confirmed he view ha money growh raises oupu in he shor run. Since he 197s, however, he Phillips-curve relaion seems o have broken down, and money seems o have no clear effec on real ineres raes eiher. Only if we assume ha some par of money responds o real variables can we conclude ha he exogenous par of money does move ineres raes. Evans and Marshall (1998), for example, describe several scenarios idenifying assumpions under which some par of he money supply can plausibly be said o move real ineres raes. In oher words, wha we infer abou a liquidiy effec on ineres raes depends on wha we believe he Fed reacs o when i ses he money supply. Bu, if we wish o esimae he liquidiy effec on ineres raes, or even if we wish o sudy he ineres rae channel of moneary policy, is money he righ measure of policy? The rae of ineres is he reurn on bonds, which depends mos direcly no on he supply of money bu on he supply of bonds. Using bonds, one can find a liquidiy effec wihou inroducing a hos of oher variables. Wheher we measure money by nonborrowed reserves or more broadly, injecions of money are no he same as wihdrawals of, say, Treasury bills (T-bills). This is because he Fed someimes injecs money by buying long-erm bonds, and his will affec shor-erm raes less han would a purchase of T-bills. Indeed, able 1 shows ha, since 1961, he correlaion beween he real per capia supply of ousanding Treasury securiies (T-secs) and nonborrowed reserves (NBR), which one migh expec o be negaive, has been slighly posiive a The able also shows ha, a leas since 198, growh in nonborrowed reserves has reduced shor-erm raes, bu no as srongly as a conracion of T-secs. Over he whole period, however, growh in boh nonborrowed reserves and T-secs is posiively correlaed wih shor-erm raes which, for nonborrowed reserves, is he wrong sign. These conclusions do no change if we look insead a surprises, as implied in models like Lucas (199) and Chrisiano and Eichenbaum (1995). Table 2 presens he correlaions of ineres raes wih surprises in he growh of NBR and T-secs. 2 For he period, surprises o nonborrowed reserves come in wih he wrong sign, whereas T-sec surprises have he posiive correlaion ha a liquidiy effec implies. Boh correlaions have he wrong sign for he period, bu he correlaion beween surprises o growh in he bond supply and real raes is iny. Tables 1 and 2 sugges ha, a leas in recen decades, bonds have been he beer measure of policy. The remainder of our analysis uses his measure more sysemaically o esimae he degree of risk ha unpredicabiliy in heir supply imposes on he invesor. A nominal bond carries wo kinds of risk. Firs, is Boyan Jovanovic is a professor of economics a he Universiy of Chicago and New York Universiy, a research associae of he Naional Bureau of Economic Research (NBER), and a consulan o he. Peer L. Rousseau is an assisan professor of economics a Vanderbil Universiy and a faculy research fellow of he NBER. The auhors hank he Naional Science Foundaion (NSF) for financial help, Fernando Alvarez and Rober Lucas for useful commens, and Timohy Daniels for assisance in obaining daa. Special hanks go o David Marshall and Helen Koshy for many deailed commens on earlier drafs. 17

2 TABLE 1 Correlaions among monhly growh raes Variable monh real reurn on T-bills and previous monh s real growh in NBR monh real reurn on T-bills and previous monh s real growh in T-secs Real monhly growh in NBR and T-secs.48.7 Noes: NBR = real per capia value of nonborrowed reserves; and T-secs = real per capia value of ousanding Treasury securiies. Sources: See noe 1 on p. 33. real reurn erodes wih inflaion, which may be uncerain. Second, unexpeced changes in he supply of bonds may cause he value of a bond o change. If a large bond issue causes bond prices o fall, hen he reurn on exising bonds is reduced and he cos of purchase is lowered for invesors who are abou o buy bonds. The bond issue herefore ransfers wealh from exising bondholders o fuure bondholders. If such issues are no foreseen, hey give rise o wha we call bond-supply risk. Supply risk can lead o an uncerain price, or (when prices do no clear markes) an uncerain availabiliy. The Fed creaes boh kinds of risk in he primary marke, where i acs as he Treasury s agen in he regular Duch (ha is, single-price) aucions of bonds. The Fed s curren acions affec no only he curren aucion-price resuls, bu also he number of bonds ha will become available in laer aucions. The Fed probably also conribues o price variabiliy in he secondary bond markes, where i conducs open marke operaions. In his aricle, we find ha bondsupply risk remains as imporan as ever, even hough Fed policy has rendered he price level more and more predicable. The lessons from he daa ha we highligh are he following: 1. Surprise sales of T-bills raise real raes: Unanicipaed (monh-o-monh) posiive shocks in he supply of T-bills or oal Treasury securiies available o he public have always had a large posiive effec on he ex pos real reurns earned by hese insrumens. 2. Ineres raes and sock reurns: Popular wisdom holds ha cus in he federal funds rae raise sock prices. This seems o derive from he view ha bonds and socks are close subsiues so ha when he Fed, say, cus ineres raes, sock prices will rise in order o allow price earnings raios o rise and, herefore, sock reurns o fall. Ye he opposie seems o be rue. Overall, if anyhing, T-bill raes are negaively correlaed wih sock reurns. 3. The decline of Treasury finance: The supply of T-bills has decreased seadily over ime, bu his has been neural in is effec on asse prices, including bond prices. 4. Lessons for policy: Supply risk sems from unpredicabiliy in he growh rae of T-secs in he hands of he public ha is, by he unpredicabiliy of changes in his supply relaive o he amoun ousanding. Bu he amoun of T-secs has been declining relaive o he unpredicable rollover demands for hem a aucion by foreign moneary auhoriies and financial insiuions. If he inclusion of a broader range of shor-erm securiies in he Fed s porfolio were o reduce unpredicabiliy in he growh rae of T-secs, supply risk would decline. This is because he risk would be spread across a wider range of asses, many wih deep markes, so ha an unexpeced change in he Fed s overall securiies holdings would impac any one of hese markes minimally relaive o he amoun ousanding. In he nex secion, we provide more deail on how T-bills are sold and how open marke operaions work. Then, we assess he effecs ha bond-supply risk has had over he pas 8 years on he ex pos real reurns obained by purchasing a new hree-monh T-bill and holding i unil mauriy and compare hem o he effecs of bond-supply risk on real sock reurns. We hen consider he role of supply risk under an invesmen sraegy of purchasing a seasoned hree-monh T-bill TABLE 2 Correlaions among growh-rae surprises Variable Unexpeced componens of: 1-monh real reurn on T-bills and previous monh s real growh in NBR monh real reurn on T-bills and previous monh s real growh in T-secs Real monhly growh in NBR and T-secs Sources: See noe 1 on p Q/21, Economic Perspecives

3 wih wo monhs unil mauriy and selling i one monh laer. Nex, we documen he recen decline of Treasury finance in he conex of he Fed s hisory and show ha supply risk is unrelaed o his decline. Wha causes bond-supply risk? Bond-supply risk arises when agens commi funds o he bond marke before hey know he price a which hey will buy he bonds or he price a which hey will be able o sell hem aferwards. Such risk arises because asse markes are incomplee and, in he sense of Grossman and Weiss (1983), segmened. Some agens and some fracion of heir resources are ready o rade in he bond marke and his exposes hem o he risk ha comes from randomness in he supply of bonds. Buyers are in luck when a bond-supply shock is posiive because bond prices are hen lower han expeced and he rae of reurn is higher han expeced. These agens ge a good deal, and any real consequences are disribuional because he shock has favored some agens a he expense of ohers. To ake par in he bond marke, insiuions mus commi liquid asses o he new-issue and secondary markes. Primary dealers, who make compeiive bids in he course of heir direc ineracions wih he New York Fed in he conduc of Treasury aucions, pay for heir winning bids when he new bonds are issued on he Thursday following he Monday aucions. Cerain deposiory insiuions and oher broker/dealers may also pay for heir winning bids on he dae of issue. Oher compeiive bidders pay a he ime of submission and are eiher refunded excess balances or called upon o remi addiional funds based upon he final aucion price and securiy allocaions. A majoriy of secondary dealers, however, acquire new issues from primary dealers, and presumably pay for hem upon delivery, hough he bonds rade acively prior o heir issue in a when-issued marke. Noncompeiive enders, or offers o purchase bonds a he final aucion price, whaever ha may be, are paid upfron on he aucion day. 3 Noncompeiive bids a T-bill aucions are currenly limied o $1 million per accoun, and hey have accouned for only 1.4 percen of oal aucion sales since July Thus, even hough many bidders can delay paymen unil issue, hey mus be ready o purchase heir enire bid if won, and, in he even of an unsuccessful bid, mus ac quickly o reinves liquid asses ha had been se aside. A closer look a how hese markes work shows how he winning bids can become quie uncerain. By supply risk, in some cases, we mean residual supply risk. A large chunk of he demand for T-bills comes from he decisions of foreign financial insiuions and inernaional moneary auhoriies (FIMA) regarding wheher o roll over heir subsanial and various holdings of bonds, and hese rollover decisions affec he residual supply ha will be available o he remaining raders because hey coun agains he issue quaniy saed in he aucion announcemen. Furher, when FIMA make rollovers, hey do so a he single aucion price as noncompeiive bidders. 5 Many individuals also bid noncompeiively, bu, as menioned above, he quaniies of such bids are resriced and hus more predicable. All of his means ha supply risk can arise a he aucion sage, even hough he Treasury announces he face value of he T-bills ha i inends o issue. Since he public knows only he mauring quaniy and no he rollover plans, he randomness in hese plans, from he perspecive of he dealer, makes he final aucion price less predicable. The Fed iself mus also decide wheher o roll over porions of is own porfolio of mauring bonds a he final noncompeiive price. The securiies ha he Fed rolls over do no coun agains he oal offered o he public in ha week s aucion and, hus, have a bes a minimal impac on he final aucion price, bu hey will affec he size of subsequen aucions. For example, if he Fed rolls over only half of he bills ha i could have in a given aucion, o mainain a consan deb level he Treasury would need o arrange a larger issue for he nex week. I seems, however, ha he Fed s rollovers, a leas in recen years, have been quie predicable he Fed rolls over is enire holdings unless ha would exceed is self-imposed limi on individual securiies holdings, in which case i redeems enough o mee ha limi. The Treasury has changed is usual procedures wice recenly wih regard o foreign rollovers, and he naure of hese changes suggess ha i may be rying o reduce supply risk. In early 1999, aucion announcemens sill specified ha he Treasury could, a is discreion, issue addiional securiies for foreign accouns whenever he oal of new bids from hese sources exceeded heir oal holdings of mauring bills. Beginning wih he T-bill aucions of March 29, 1999, however, he Treasury usually placed an explici limi of $3 billion on he amoun of foreign rollovers ha would be couned agains he public s oal, agreeing o make addiional issues auomaically if rollover bids were o exceed his amoun. This pracice became more common as 1999 progressed. The change signaled a more accommodaive sance by he Treasury ha would have reduced residual supply risk by limiing he degree o which unexpeced noncompeiive rollover decisions could affec he final aucion price. As of February 1, 21, however, he Treasury has allowed 19

4 only $1 billion in oal foreign noncompeiive enders, and ha limi canno be exceeded. 6 Foreign insiuions seeking o purchase large amouns of T-secs a aucions mus now bid compeiively. Even hough his change migh ameliorae disurbances ha would impede he sysemaic paying down of he federal deb, i is also likely o raise residual supply risk. Cammack (1991, p. 11) repors ha he Fed and FIMA combined o buy 43 percen of all T-bills ha were sold a aucion beween 1973 and By examining he press releases of aucion resuls, we have found ha his porion has risen o 44.8 percen since mid The risk associaed wih rollover decisions exceeds boh he spread in he disribuion of bids and he ime-series variaion of he winning bids, because he losing bidders (of which here are more eiher immediaely or in fuure aucions when he Fed absorbs is limi) mus end up holding cash or a lowerreurn subsiue. Bond-supply risk and ineres raes How much do bond supplies vary from monh o monh? Figure 1 shows he sandard deviaion of he monhly per capia real growh of he moneary base, T-bills and T-noes, and all markeable T-secs, including bills, noes, bonds, and cerificaes of indebedness since The Treasury quaniies reflec securiies ha are ousanding and in he hands of he public (ha is, excluding he Fed s holdings). 8 The sriking feaure of figure 1 is he high monho-monh variabiliy of oal T-secs in he hands of he public. This variabiliy was paricularly high in he early 194s due o large issues of securiies of all mauriies o finance he Second World War. We also observe large rolling sandard deviaions for he T-bills and T-noes subse in he mids of he Depression and again from 1942 o Ineresingly, variabiliy in he supply of T-secs is much larger han ha of he moneary base iself, which suggess ha a considerable porion of wha we call supply risk may have served o sabilize money growh. How srongly do bond-supply surprises affec he real rae of ineres? We use he effecs of inflaion surprises as a sandard of comparison and compare he wo kinds of risk, firs for he enire period and hen for hree subperiods. Here is how we proceed: The nominal reurn a dae on a one-period zerocoupon bond mauring a dae + 1 is R 1, 1 µ P 1, percen FIGURE 1 Sandard deviaion of monhly growh of T-secs and moneary base where P is he price of he bond a dae. The ex pos real reurn on his bond is 1 1, 1 µ P 1Q ª, 1 ¹ r 1, where Q, 1is he rae of inflaion of goods prices beween daes and + 1. Rearranging and aking logs, ln(1 r ) ln P ln(1 Q ),, 1, 1 for any small number FÁln É1 F z F Using his, we approximae he above equaion by r,, 1 zi, 1 Q, 1 where i y, 1 1/ P 1. Le he superscrip e denoe an expeced value given informaion from he previous period, which we shall denoe I 1, so ha, for insance, e r, 1 E\ r, 1 I 1 ^. 9 Le he superscrip u denoe he surprise componen of a random variable so ha, for insance, e u r, 1 r, 1 r, 1and so on. Then o a firs approximaion, 1) r i. u u u, 1, 1 Q, 1 T-bills and T-noes Markeable T-secs Moneary base Noe: Figure displays rolling sandard deviaions of monhly growh raes of real per capia supplies of T-secs and he moneary base, The firs erm is he bond-supply risk and he second is inflaion risk. 2 4Q/21, Economic Perspecives

5 Now assume a liquidiy effec of bond-supply surprises on he price of bonds as in, say, Lucas (199). Tha is, assume ha 2) i Bg, u u, 1 1, u where, once again, g 1, is he surprise growh in he number of bonds a given I 1. Subsiuing ino equaion 1 leads o 3) r g. u u u, 1 B 1, Q, 1 The noaion may sugges ha he surprises in he above hree variables are formed a differen daes and are based on differen informaion ses, bu his is no he case. The dependen variable and he regressors all derive from he informaion se I 1 ha we describe in noe 9 on page 33. To reierae, a he sar of dae, agens know he realizaion of p 1,. Bu he presence of bond-supply risk means ha he agens do no know he dae supply of bonds when hey form heir expecaions of P and, hence, of i,+1. This means ha hey canno ye know g 1,, since is realizaion comes oo lae o be included in he dae informaion se. Therefore, in spie of he daing differences in he u u subscrips, rˆ ˆ, 1, g 1,, and Q ˆ u, 1, are surprises based on he same informaion se, I 1. We esimae equaion 3 wih he regression 4) rˆ a a gˆ a ˆ, u u u, 1 1 1, 2 Q, 1 ˆ u u u where rˆ ˆ, 1, g 1,, and Q, 1are surprises of he hree variables. In pracice, we obain hese surprises using de-seasonalized monhly observaions as he one-sep ahead forecas errors from a se of vecor auoregressions (VARs) wih a rolling esimaion window. To be more precise, he variables in he forecasing equaions are: 1. g, he growh rae of real per capia T-secs in he hands of he public, 2. r, he ex pos real reurn on T-bills, 1 3. p, he rae of growh of he consumer price index, 11 and 4. he ex pos real reurn on he S&P Thus, all four variables in he sysem are dimensionless. We hen pool he forecass and errors from he VARs over he sample period and use hem o esimae equaion 4. The monhly daa represen he highes frequency ha is available coninuously for he pas 8 years of Fed hisory. The T-bill reurn is he monhly average of daily raes for he curren (ha is, on he run ) hree-monh T-bill, from which we subrac realized inflaion over he nex hree monhs. The reurns ha we consider firs, and he only ones ha can be consruced going back o 192, correspond o an invesmen sraegy of buying he curren hree-monh T-bill and holding i unil mauriy. Laer we consider onemonh holding period reurns on seasoned T-bills since Box 1 describes in deail he mehods we used o prepare he daa for analysis and o compue he surprises. Supply risk Using monhly daa from January 192 hrough December 1999 and forecasing equaions wih a 36-monh rolling window and hree lags, figure 2 shows he effecs of one-sandard-deviaion surprises o boh he price level and he supply of markeable T-secs available o he public on he annualized ex pos real reurn on T-bills. 13 Pooling he surprises across periods, we obain he following esimaes for equaion 4 (wih -saisics in parenheses): 5) rˆ gˆ 1.82 ˆ e. u u u, 1 1, Q, 1 (.6) (7.45) ( 17.31) The superscrip u in equaion 5 denoes a variable s deviaion from is one-sep-ahead forecas from he rolling VAR. As limied paricipaion models would sugges, gˆ u 1, raises ex pos real T-bill reurns because a release of T-bills lowers T-bill prices. This in urn conribues o beer-han-expeced reurns for hose who have commied funds o he T-bill marke. Unanicipaed inflaion eners wih, essenially, a uni coefficien, ˆ u which suggess ha Q, 1 is indeed a rue surprise. To obain he series ploed in figure 2, we muliply he coefficiens gˆ u 1, and Qˆ u, 1by he cenered values of heir rolling 12-monh sandard deviaions and compound he resul over 12 monhs o annualize. This measures he effecs of he surprises on annualized real T-bill reurns. 14 The figure indicaes ha boh sources of risk have always maered, wih inflaion risk a imes quie large, especially a he heigh of he Grea Depression in 1933 and in he year immediaely following he end of he Second World War. The relaive imporance of inflaion risk has declined dramaically over he pas wo decades, however, as he price level has sabilized. The effec of supply risk in hree subperiods The mehod used o consruc figure 2 assumes ha he seasonal adjusmen coefficiens applied o he raw daa and he responses of he T-bill rae o unexpeced inflaion and T-sec growh are sable across he period. One way o examine he 21

6 BOX 1 Esimaing he impac of price and T-sec supply risk on real T-bill reurns The mehodology underlying figures 2 9 begins wih adjusing he raw daa o make he iming of monhly observaions consisen across variables. Since he nominal quaniy of T-secs in he hands of he public (X ) is available a he end of each monh, while he consumer price index (CPI ) and populaion (pop ) are compued as annualized monhly averages, we derive he real quaniy of Treasury securiies a he end of monh as: X x 4 s, ÉCPI CPI ( pop pop ) 1 s 1 which amouns o averaging he consumpion deflaor and populaion across periods o cener hem wih X. To approximae he ex pos real reurn on T-bills (r,+1 ) associaed wih he buy-and-hold sraegy discussed in his aricle, we sar wih he annualized yields o mauriy on hree-monh (91-day) T-bills ha are compued by he Fed as averages of daily yields over he course of a calendar monh (R ) and subrac he annualized inflaion rae implied by he change in he CPI over he nex hree monhs. Since he CPI is a monhly average and R is annualized, we have CPI3 CPI z R µ µ CPI µ ª ¹ ª ¹ r, This is he monhly real reurn ha an invesor would receive by buying a hree-monh T-bill and holding i unil mauriy, assuming ha he inflaion rae is seady across he hree monhs. The nominal reurn on he S&P 5 (S ) covers an acual calendar monh, so we derive an ex pos reurn by subracing he growh rae of he consumer price index (CPI ), CPI CPI 1 S µ CPI 1 ª CPI ¹ s 1, which amouns o compuing inflaion as he growh in he CPI afer averaging across periods. Before using he series derived above (as well as CPI inflaion iself), we de-seasonalize by regressing each on monhly dummy variables and an adequaely high-order polynomial in ime. We include he ime polynomial o reduce he degree o which he esimaes of he monhly effecs reflec cyclical and rend componens. Afer subracing he coefficiens on he monhly dummy variables from he raw series, we add he mean of he derended series back in o complee he seasonal adjusmen. See Johnson (1984, pp ) for a clear exposiion of his mehod along wih is advanages and drawbacks. The VAR equaions used o compue he surprises o growh in he supply of T-secs (g) and inflaion (p) have he form k k k 1, k k 1, kqk 1, k k i1 i1 i1 k h1, ks k e1, i1 g c g d f r k k k c2, kgk d2, k k f2, krk i1 i1 i1 k h2, ks k e2,, i1 Q Q where k is he lag lengh and is a linear ime rend. The ime subscrips refer o he informaion ses I k from which he variables derive. To allow he forecass o reflec recen economic condiions, we allow he VAR samples o roll wih ime, choosing esimaion windows of 36 monhs (figure 2) or 3 monhs (figures 3 9). This implies ha each successive onesep ahead forecas and forecas error is compued wih an informaion se ha overlaps he previous one in all bu he laes and earlies periods. Using he coefficiens from he ime regression, we compue he forecass for ime + 1 as fied values obained wih he informaion se from ime. In esimaing equaion 4, we pool he monhly surprises across he sample period o obain a single se of regression coefficiens. robusness of our resuls o hese assumpions is o repea he analysis over subperiods. We do his for , , and , and display he resuls in figures 3 5. We spli he poswar period ino pre-198 and pos-1979 segmens because of he shif in Fed argeing policy ha occurred in To accommodae he shorer sample periods, we limi he underlying VAR models o wo lags and shoren he lengh of he esimaion periods o 3 monhs. Table 3 includes regression resuls for equaion 5. Figure 3 reaffirms he imporance of inflaion risk in he pre-1947 period, including he 1933 and 1946 episodes. The effecs of supply risk on T-bill reurns rise a hese same imes and average Q/21, Economic Perspecives

7 FIGURE 2 Effec of surprises in T-sec supply on T-bill reurns, percenage poins % in 1946 Inflaion risk Supply risk Noe: Figure illusraes effecs, in percenage poins, of one sandard deviaion surprises in inflaion and growh in he supply of T-secs on annualized real T-bill reurns. percen over he period, bu are always less imporan han he effecs of inflaion risk, which average 5.31 percen. In figure 4, he narrower scaling reflecs he overall decline in inflaion risk ha occurred from 1947 o 1979, during which i averaged only 1.35 percen. Even hough supply risk also fell o.12 percen over his same period, he decline is considerably less in percenage erms han ha of inflaion risk. Figure 5, on he oher hand, shows ha supply risk has if anyhing become more imporan over he pas 2 years, averaging o.14 percen, while inflaion risk has coninued o decline, averaging.99 percen. By 198, he Treasury had compleed a long-erm shif in financing away from T-bonds and ino shorererm T-bills and T-noes (see figure 15 on page 3). I is herefore possible ha flucuaions in he quaniy of T-bills and T-noes are more precise measures of supply risk for he pos-198 period han he oal of ousanding markeable T-secs. To see if his preference shif has influenced our resuls, we compue supply shocks o T-bills and T-noes only afer 198, and in figure 6 once again display heir effecs on real T-bill reurns. The resuls are similar o hose observed for all T-secs, wih average real effecs of.16 percen and 1. percen, respecively. Once again, supply risk grows in relaive imporance over ime. Tha bond-supply risk, which arises from commiing funds o he T-bill marke before supply is revealed, should even approach inflaion risk in imporance is quie sriking. Afer all, if inflaion surprises are measured over he enire erm of he T-bill, hey should affec ex pos yields virually poin for poin. 15 To generae bond-supply risk, however, i is necessary for open marke operaions or variaions in aucion quaniies o have large effecs on ineres raes, and his in urn suggess some degree of marke segmenaion. Oherwise, in he absence of segmenaion, invesors could offse T-sec supply shocks wih ransacions in he markes for subsiue asses. Bond-supply risk and real sock reurns Theory leads us o expec a posiive relaion beween sock reurns and real bond reurns. If socks and bonds were perfec subsiues and if hey raded TABLE 3 Ineres rae regressions for buy-and-hold sraegy g = T-bills g = Markeable T-secs and noes Consan (.6) (1.4) (.1) (.24) (.29) ˆu g 1, (7.45) (1.97) (1.42) (2.37) (2.66) Q ˆu, ( 17.31) ( 9.43) ( 6.4) ( 6.54) ( 6.79) R 2 /(DW) (1.98) (1.19) (1.7) (1.81) (1.77) N u Noes: The dependen variable is he unanicipaed real reurn on a hree-monh T-bill, ˆ r, 1. The able presens coefficien esimaes for equaion 5 over he subperiods included in figures 2 6, wih T-saisics in parenheses. The R 2 and Durbin-Wason (DW) saisics and number of observaions (N) for each regression appear in he final wo rows. 23

8 in he same marke, heir real raes of reurn would always be equal. In such a world, an open marke operaion of he Fed or, indeed, any oher even ha changed he reurn on bonds would change he reurn on socks by he same amoun. For example, a cu in he federal funds rae would cause bond prices and sock prices boh o rise and he holding rae of reurn on each asse o fall. The presence of inflaion risk on bonds and dividend risk on socks would, perhaps, weaken he conemporaneous correlaion beween he ex pos real reurns on he wo asses, bu would no eliminae i enirely. One implicaion of his logic is ha if he Fed s acions can affec he sock marke, we should expec o find a posiive correlaion beween bond reurns and sock reurns. Surprisingly, we find no evidence of a posiive correlaion beween he wo ex pos reurns. We proceed as we did wih T-bill reurns, bu now he dependen variable in equaion 5 is he unanicipaed componen of he real reurn on he S&P 5, sˆ u : 6) sˆ a a gˆ a ˆ e. u u u, 1 1 1, 2 Q, 1 Table 4 presens our findings using surprises from he same VAR models ha we used o examine T-bill reurns. Ineresingly, T-sec surprises never affec real sock reurns. Inflaion surprises, on he oher hand, ener wih he expeced negaive and significan coefficiens in he and subperiods, FIGURE 3 Effec of surprises in T-sec supply on T-bill reurns, percenage poins Inflaion risk T-sec supply risk Noe: Figure illusraes effecs, in percenage poins, of one sandard deviaion surprises in inflaion and growh in he supply of T-secs on annualized real T-bill reurns FIGURE 5 Effec of surprises in price level and T-sec supply on T-bill reurns, percenage poins 2. T-sec supply risk Inflaion risk Noe: Figure illusraes effecs, in percenage poins, of one sandard deviaion surprises in he price level and T-sec supply on annualized real T-bill reurns. FIGURE 4 Effec of surprises in T-sec supply on T-bill reurns, percenage poins 5 FIGURE 6 Effec of surprises in supply of T-bills and T-noes on T-bill reurns, percenage poins Inflaion risk Inflaion risk T-sec supply risk Noe: Figure illusraes effecs, in percenage poins, of one sandard deviaion surprises in inflaion and growh in he supply of T-secs on annualized real T-bill reurns.. T-bill and T-noe supply risk Noe: Figure illusraes effecs, in percenage poins, of one sandard deviaion surprises in inflaion and growh in he supply of T-bills and T-noes on annualized real T-bill reurns. 24 4Q/21, Economic Perspecives

9 bu wih a posiive and significan coefficien for The laer resul may be driven by a few exraordinary evens, such as he sharp deflaion and decline of equiy values associaed wih he Grea Depression and he inflaion and rising marke values of he immediae poswar period. In all, he evidence suggess ha he sock marke has been relaively unaffeced by Fed policy. In able 5, we repor conemporaneous correlaions among he variables in our VARs (ha is, he variables hemselves and no heir surprises) and for he moneary base over he period and he hree subperiods. 16 Once again, links beween sock reurns and growh in bond supplies are weak and inconsisen across subperiods. For example, correlaions beween real growh in he T-sec supply and sock reurns never exceed.5 and have he expeced negaive sign only for T-bill reurns vary inversely wih sock reurns in all bu he period, bu in all cases he correlaions are small. As i urns ou, he mos consisen correlaions are posiive ones beween growh in T-sec quaniies on he one hand and real T-bill reurns on he oher. This is rue for he full sample period and for all of he subperiods. I is also as we migh expec, since more T-secs in he hands of he public require higher ineres raes o induce invesors o hold hem. Since a rise in T-bills and T-noes in he hands of he public usually implies bond sales and, hence, a moneary ighening, i is surprising ha growh in he real moneary base a moneary loosening seems o go hand in hand wih bond sales (and he higher ineres raes ha hey imply) in all bu he period. To explore his furher, we compue he correlaions using growh in real per capia nonborrowed reserves, which is probably a closer indicaor of policy sance han growh in he moneary base, for he period over which we have a series for nonborrowed reserves. We find in his case ha a moneary loosening, as measured by growh in nonborrowed reserves, also has an unexpeced posiive correlaion wih T-bill reurns and T-sec growh, and ha his resul obains for boh he and subperiods. 17 This may again reflec imporan differences beween indicaors of policy sance ha are based on moneary aggregaes and our bond supply measures. An alernaive measure of real T-bill reurns Unil now, we have considered he effecs of bondsupply risk on T-bill reurns under a buy-and-hold sraegy. This, of course, is only one sraegy ha a T-bill invesor migh follow, as i is easy for an invesor o liquidae a T-bill, and in paricular afer a supply or price shock has been realized. To analyze such a holding sraegy, we now esimae equaion 5 using surprises o he ex pos real one-monh holding period reurn on a seasoned T-bill as he dependen variable. The effecs of supply risk should be differen under his shorer-erm sraegy. This is because he invesor now faces wo sources of supply risk one ha occurs jus before he bond is purchased and anoher ha occurs over he holding period. A posiive shock afer commimen bu before purchase will lower he bond price and raise he real reurn, ye a similar TABLE 4 Sock reurn regressions g = T-bills g = Markeable T-secs and noes Consan (.55) (.5) (.57) (.6) (.19) ˆu g 1, (1.2) (.42) (.36) (.76) (.53) Qˆu, (.16) (1.92) (2.81) ( 1.53) ( 1.61) R 2 /(DW) (1.76) (1.96) (1.84) (1.78) (1.77) N u Noes: The dependen variable is he unanicipaed real reurn on a one-monh invesmen in he S&P 5 porfolio, ˆ s, 1. The able presens coefficien esimaes for equaion 6, wih T-saisics in parenheses. The R 2 and Durbin-Wason (DW) saisics and number of observaions (N) for each regression appear in he final wo rows. 25

10 TABLE 5 Correlaions of real asse reurns and real per capia quaniies T-bills Moneary S&P 5 T-bills and noes T-secs base Real reurn on S&P 5 1. Real reurn on T-bills Growh in real T-bills and noes Growh in real T-secs Growh in real moneary base Real reurn on S&P 5 1. Real reurn on T-bills Growh in real T-bills & noes Growh in real T-secs Growh in real moneary base Real reurn on S&P 5 1. Real reurn on T-bills Growh in real T-bills & noes Growh in real T-secs Growh in real moneary base Real reurn on S&P 5 1. Real reurn on T-bills Growh in real T-bills & noes Growh in real T-secs Growh in real moneary base shock over he holding period will lower he resale value of he bond. Thus, i is deviaions of resale values from invesor expecaions ha were formed prior o purchase ha impar risk o he sraegy. To derive he equivalen of equaion 4 for muliperiod bonds, we again define he cos of such a bond 1 a dae as P unis of real consumpion. The bond s nominal reurn over he holding period is i P P 1, 1, P where we inroduce aserisks o reflec he change from he buy-and-hold invesmen sraegy discussed earlier o he seasoned one-monh holding sraegy considered here. The ex pos real reurn is again r i Q and as in equaion 1,, 1, 1, 1, r u u u., 1 i, 1 Q, 1 Now we need o be quie precise abou he daing of u informaion. Le 1 z y he surprise componen of a random variable z given I 1, and suppose ha u u P 1 u u, 1 1 BÉ 1 1, µ É 1, 1 P 7) i 1 g b g. The righ-hand side of equaion 7 is based on he logic behind equaion 2. The firs erm deals wih he denominaor of he lef-hand side; i is he one-sepahead surprise and is he same as in equaion 2. The second erm deals wih he numeraor, P +1, and is a wo-sep-ahead surprise o growh in he bond supply. We compue his erm as a VAR forecas using I. 1 Isolaing he reurn surprises on he lef-hand side, we have he holding-period analog of equaion 3: u u u u, 1 r, 1 zbé 1g1, b É 1 g, 1 É 1 Q, 1 or, roughly, he linear relaion ha we esimae: 8) rˆ a gˆ a gˆ a ˆ. u u u u 1, 1z 1 É 1 1, 2 É 1, 1 3 É 1 Q, 1 The final erm in equaion 8 is inflaion risk over he holding period. Under he buy-and-hold sraegy ha we considered earlier, we subraced realized inflaion over he hree-monh erm of he T-bill and, assuming monhly 26 4Q/21, Economic Perspecives

11 compounding, convered o a monhly reurn. The resul here refleced an average of inflaion over he nex hree monhs. Here we proceed slighly differenly: For he one-monh holding sraegy, we subrac he one-monh inflaion rae ha corresponds o he acual holding period. Our analysis of one-monh invesmens in seasoned hree-monh T-bills is limied o 1961 o 1999 he period for which daily secondary marke prices on U.S. Treasury securiies are available from he New York Fed and he Wall Sree Journal. 18 Using he composie quoe shees, we colleced he annualized yield-o-mauriy on he final rading day of he monh for he T-bill wih closes o 6 days unil mauriy and hen recorded is yield on he final rading day of he nex monh. We hen compued a synheic annualized 3-day holding period yield as R 6 1 R2 µ 365 2,1 6 1 R 1 µ 365 ª ¹ where R 2 is he annualized yield-o-mauriy on he reference T-bill wih approximaely 6 days unil mauriy, and R 1 is he annualized yield on he same T-bill a monh laer. Due o weekends, holidays, and he monhly calendar, we do no always observe prices 3 days apar, so our compuaion assumes ha R 1 whenever observed also applies on he 3h and final day of he holding period. This ignores changes in secondary marke yields ha migh arise for a seasoned T-bill over a mos a wo-day period, bu does no generae any sysemaic bias. We conver o real erms by subracing Consumer Price Index (CPI) inflaion. Afer again obaining surprises o T-bill reurns, inflaion, and growh of he T-sec supply from a series of 3-monh rolling VARs wih wo lags and he S&P 5 reurn as a conrol, we use he coefficien esimaes from equaion 8 o compue he overall effecs of supply risk over he course of a monh (ha is, boh pre-purchase and holding period risk) as he square roo of 1, u 2 u É ˆ É ˆ É ˆ 1, , 2 u Éaˆ2 Var É ˆ 1 g, 1 Var r a Var g 2 aacov ˆ ˆ gˆ gˆ, u u 1 2 É1 1,, 1, 1 where he Var( ) erms are variances and Cov( ) he covariance. The effecs of inflaion risk are he produc of a 3 and he sandard deviaion of he forecas errors for inflaion. We obained he series of variance covariance marices from 12-monh rolling samples of he forecas errors. Figure 7 presens our resuls for he period, which have been annualized by compounding over 12 monhs. We repor he corresponding esimaes for equaion 8 in able 6. In figure 7, an inflaion surprise of one sandard deviaion lowers he holding period yield by 1.77 percen on average. Like he resuls in figures 2 and 5 for he buy-and-hold sraegy, inflaion risk rises o nearly 4.5 percen in he mid-197s afer flucuaing a abou 1 percen o 2 percen hroughou he 196s. Supply risk, hough no significan in equaion 8, averages.1 percen, which is only slighly smaller han ha observed under he buy-and-hold sraegy for Figure 8 and he wo oher columns of able 6 cover he period and offer a direc comparison wih figures 5 and 6. Wheher we use all T-secs in he hands of he public (figure 8) or only T-bills u and T-noes (figure 9) in forming g ˆ, he effecs of supply risk on one-monh yields are similar o hose obained under he hree-monh buy-and-hold sraegy, averaging.16 percen and.21 percen in figures 8 and 9, respecively. The coefficiens on he pre- and pos-purchase surprises o growh in he T-sec supply variables also have he expeced and opposie signs, bu are saisically significan only when T-bills and u T-noes are included in g ˆ 1,. This differs from he resuls under he buy-and-hold sraegy, where our analysis of pre-purchase risk in isolaion showed significan effecs of supply surprises for oal T-secs as well. Inflaion risk is larger on average wih he FIGURE 7 Effec of surprises in T-sec supply on one-monh T-bill reurns, percenage poins Inflaion risk T-sec supply risk Noe: Figure illusraes effecs, in percenage poins, of one sandard deviaion surprises in inflaion and growh in he supply of T-secs on annualized real one-monh reurns on T-bills. 27

12 TABLE 6 Ineres rae regressions for he one-monh holding sraegy g = T-bills g = Markeable T-secs and noes Consan..1.1 (.17) (1.12) (1.3) g (1.2) (1.28) (1.77) ˆu 1 1, g (.83) ( 1.36) ( 1.76) ˆu 1, 1 1 ˆu, 1 Q ( 27.1) ( 2.54) ( 21.32) R 2 /(DW) (2.9) (1.5) (1.5) N u Noes: The dependen variable is he unanicipaed real reurn on a T-bill ˆ 1 r, 1. The able presens coefficien esimaes for equaion 8, wih T-saisics in parenheses. The R 2 and Durbin-Wason (DW) saisics and number of observaions (N) for each regression appear in he final wo rows. one-monh holding sraegy han wih he buy-andhold. The closeness of he coefficiens on he inflaion surprises o uniy is also good news for our specificaion, as inflaion should affec he real reurn poin for poin when he ime periods for he inflaion and reurn observaions coincide. Nex, we again place he unanicipaed componen of he real S&P 5 reurn (s u ) on he lef-hand side of equaion 8 o obain 9) sˆ a gˆ a gˆ u u u 1, 1z 1 É 1 1, 2 É 1, 1 u a3 É ˆ 1 Q, 1. The resuls, which we repor in able 7, indicae ha surprises o ĝ do no generae subsanive supply risk for invesors who are abou o buy he S&P porfolio, bu ha posiive shocks afer purchase raise one-monh sock reurns for he period. This runs couner o he sandard view ha socks lose when he Fed ighens and gain when he Fed cus raes. The lack of significance on he coefficien for he pre-purchase surprise could simply sugges ha he Fed canno direcly and consisenly affec he sock marke. The posiive and significan coefficien on he holding period supply shock, on he oher hand, is consisen wih a policy of passive responses by he Fed o changing condiions in oher asse markes. For example, when he sock marke is surging, he Fed may ry o slow i down a bi by injecing bonds and raising ineres raes. Since any relaionship beween Fed policy and he sock marke is probably loose, however, he bond sale ofen seems o have lile effec, and he marke coninues o push ahead. The effecs of foreseen policy changes: The secular decline of Treasury finance The relaive imporance of T-bills and oher markeable T-secs in he aggregae porfolio has declined FIGURE 8 Effec of surprises in T-sec supply on one-monh T-bill reurns, percenage poins 2.4 FIGURE 9 Effec of surprises in supply of T-bills and T-noes on one-monh T-bill reurns, percenage poins Inflaion risk Inflaion risk.6.6. T-sec supply risk. T-bill and T-noe supply risk Noe: Figure illusraes effecs, in percenage poins, of one sandard deviaion surprises in inflaion and growh in he supply of T-secs on annualized real one-monh reurns on T-bills Noe: Figure illusraes effecs, in percenage poins, of one sandard deviaion surprises in inflaion and growh in he supply of T-bills and T-noes on annualized real one-monh reurns on T-bills. 28 4Q/21, Economic Perspecives

13 TABLE 7 Sock reurn regressions for he one-monh holding sraegy g = T-bills g = Markeable T-secs and noes Consan ( 1.89) (1.12) (1.7) g (.37) (1.17) (1.12) ˆu 1 1, g (.81) (1.93) (2.3) ˆu 1, 1 1 ˆu, 1 Q ( 1.913) (.24) (.5) R 2 /(DW) (1.93) (1.71) (1.73) N Noes: The dependen variable is he unanicipaed real reurn on he u S&P 5, ˆ 1 s, 1. The able presens coefficien esimaes for equaion 9, wih T-saisics in parenheses. The R 2 and Durbin-Wason (DW) saisics and number of observaions (N) for each regression appear in he final wo rows. over he poswar period. This should no maer for real ineres raes if i is only surprises o he growh of bond supplies ha maer. Indeed, mos raional expecaions models wih money and no nominal rigidiies specify no real effecs for expeced changes in he money or bond supplies. One such change is he gradual decline in ousanding T-secs, since his is probably well undersood by agens in he bond and money markes. Bu his change may no be neural, or a leas may begin o maer soon if he rend coninues. This is because flucuaions in bond supplies semming from rollover risk and oher sources FIGURE 1 T-secs in hands of public and moneary base, have become larger relaive o he quaniy of ousanding T-secs. Figures 1 and 11 sugges ha such a rend may be emerging. Figure 1 shows ha he amoun of T-secs in he hands of he public has fallen since he mid-199s. Figure 11, on he oher hand, indicaes ha he sandard deviaion of he growh rae surprises (he cause of supply risk) has increased a lile. 19 In his secion, we documen long-run rends in Treasury financing over he Fed s hisory and argue ha heir effecs on supply risk up unil now have probably been small. The size of he bond marke can be measured by he share of hese securiies in he aggregae porfolio. This share will decline if, because of a policy change, he quaniy of Treasury securiies made available o he public begins o shrink. The share will also decline as more individuals gain access o insrumens oher han bank deposis for lodging heir surplus balances. Figures 12 and 13, which include he raios of federal deb, commercial and corporae deb, and corporae equiies o gross domesic produc and he aggregae porfolio, respecively, indeed show subsanial declines in he share of markeable federal deb from is poswar high in The growing imporance of financial asses in he U.S. economy and he rapidly rising share of equiy in oal finance are also apparen. Figure 14 provides addiional deail on he rising share of equiy in oal business finance, wih boh he corporae bond and bank lending componens of business deb falling o FIGURE 11 Sandard deviaion of surprises o monhly growh of T-secs and moneary base percen 5 rillions of 1999 dollars 4 4 T-bills and T-noes Markeable T-secs 2 1 Markeable T-secs M-base T-bills and T-noes M-base Noe: Figure displays rolling sandard deviaions of surprises o monhly growh raes of real per capia supplies of T-secs and he moneary base,

14 heir lowes levels in recen years. The marke for commercial paper has also grown rapidly over he pas hree decades, bu i remains a small par of oal finance. (See boxes 2 and 3 for descripions of how we consruced he series for ousanding corporae equiies and he componens of ousanding deb ha are presened in hese figures.) Figure 15, which provides a breakdown of markeable Treasury securiies by ype, shows ha longerm bonds dominaed governmen finance beween 1915 and 196, bu ha medium-erm T-noes and shor-erm T-bills have risen o preeminence more recenly. These shifs sugges ha a broad measure of governmen bond aciviy, such as he sum of all markeable Treasury securiies in he hands of he public, may be bes for evaluaing he effecs of supply shocks relaed o he Fed s open marke policies over he long erm, bu ha he quaniies of T-bills and T-noes migh be more relevan in recen years. These consideraions more precisely explain our choices of variables for quanifying supply risk earlier in his aricle. Ineresingly, and in keeping wih mos raional expecaions models, we found in mos cases ha he choice of supply variable did no maer. Figures 12 and 13, when combined wih he effecs of changes in he supply of T-secs presened in figure 2, sugges ha he decline in he share of hese securiies in he aggregae porfolio has had lile effec on he disribuion of r he real reurn on T-bills. This sands in sharp conras o he implicaions ha such a decline would have in he limied paricipaion model of Alvarez e al. (21), in which he ineres rae effecs of moneary injecions depend inversely on he fracion of agens ha ake par in he bond marke. FIGURE 12 Federal and business securiies as share of GDP, raio of securiies o GDP Markeable Treasury securiies Corporae equiies Business deb percen Corporae bonds FIGURE 14 Corporae financing in he 2h cenury Corporae equiies 2 Commercial paper Bank loans FIGURE 13 Ousanding federal and business securiies, FIGURE 15 Markeable Treasury financing, percen 1 percen 1 Oher 8 Corporae equiies T-bonds T-noes 4 Business deb 2 Markeable Treasury securiies T-bills Q/21, Economic Perspecives

15 BOX 2 Esimaing he marke value of ousanding corporae equiy To esimae he marke value of ousanding corporae equiy, we exend he Federal Reserve Board s Flow of Funds series (able L.4) backwards, using he available daa on capializaion for he New York Sock Exchange (NYSE), he regional exchanges, and overhe-couner (OTC) markes. We work backwards no from 1945 (which is when he Flow of Funds daa series begins) bu, raher, from 1949 because he closes overlapping observaions of OTC aciviy are for The Flow of Funds repors $117 billion for ousanding corporae equiies in 1949, which we divide ino he value of NYSE-lised firms, he value of firms lised exclusively on The American Sock Exchange (AMEX) and he regional exchanges, and he value of firms raded exclusively in OTC markes. Friend (1958) esimaes he sum of NYSE and regional capial in 1949 a $95 billion. We know from he Cener for Research on Securiies Prices (CRSP) daabase ha NYSE capializaion was $68 billion. This implies a regional capializaion of $27 billion and OTC capial of $22 billion in Assuming ha he capializaions of NYSE lised and regionally lised firms are proporional o heir ransacion values, which are available from various issues of he Annual Repor of he Securiies and Exchange Commission for , we muliply NYSE capial by he raio of regional o NYSE ransacions o approximae movemens in capializaion on he regional exchanges. We hen adjus he resuling regional series o mach he $27 billion ha we esimae for To esimae regional capial for , we observe ha he raio of regional o NYSE ransacion value was seady a.18 for and again use NYSE capial o derive regional capial from 192. The OTC marke presens a double-couning problem. Friend esimaes ha, in 1949, 25 percen of quoed OTC issues were also lised on a regisered exchange. Our measure of OTC capial mus exclude such firms. To derive esimaes for , we use Friend s couns of he number of OTC-quoed firms over a hree-monh window surrounding hree benchmark daes in 1949, 1939, and There were 5,3 such OTC firms in 1949, of which 75 percen were no lised on regisered exchanges. The median marke value of hese unlised firms was $2.4 million. Therefore, we approximae exclusive OTC capial a $9.54 million (.75 5,3 ÿ$2.4) in Assuming ha he real median size of unlised OTC firms did no change over , we nex use he gross domesic produc (GDP) deflaor o conver he median size ino nominal erms a he oher benchmark daes. Nex, we observe ha he $9.47 million for 1949 is oo small by a facor of 2.3, given our comparable esimae from he Flow of Funds, and adjus he OTC benchmark esimaes by his facor. Finally, we inerpolae beween he benchmarks o obain an annual OTC series for To obain OTC capial for , we coninue o assume ha capial on he exchanges is proporional o relaive ransacion values. Since we know NYSE capializaion and now have esimaes for he regional and OTC markes in 1929, we can esimae he share of he OTC in oal marke value in Using Friend s (1958, p. 19) esimaes of his share for 1926 and 192, we can esimae OTC capial for hese years given he values of NYSE capializaion from CRSP and our earlier esimaes of regional capial. We inerpolae beween he benchmarks once again o obain OTC capial for FIGURE 2A Esimaes of ousanding equiy, share of GDP Flow of funds and backcas CRSP By adding NYSE, regional and OTC capializaions, we obain a series for oal marke value for ha is consisen wih he Flow of Funds in he sense ha he wo segmens coincide in Our final esimaes of equiy capial ousanding, displayed in figure 2A, are obained by splicing our series wih he Flow of Funds in The figure also includes he series for equiy capial ha would resul from he use of CRSP ( ) and our NYSE lisings (19 24) daa alone. The imporance of equiies ha were no lised on he NYSE from he end of he Firs World War o he sar of Nasdaq in 1971, as depiced by he verical disance beween he black and colored lines in he figure, is considerable. Since we wish o use marke value from 19 in figures 12 and 13, for he purpose of compuing he share of equiy in oal finance, we raio splice he value of NYSE capial for 19 2 (obained from individual issues of he New York Times Co. s The Annalis, Dana & Company s Commercial and Financial Chronicle, he New York Times, and Bradsree s) o our resul for