Default and the Maturity Structure in So vereign Bonds ∗ Cristin a Ar ella no † University of Minnesota and Federal Reserve Bank of Minneapolis Ananth Ramanaraya nan ‡ Federal Reserve Bank of Dallas November 2008 Abstract This paper s tu dies the matu rity composition and the term structure of i nterest rate spreads of gove rnm ent debt in emerging mark ets. In the data, wh en interest rate sp reads rise, d eb t matu rity shortens and the spread on short-term bonds is higher than on long-term bonds. To account f o r this pa ttern, w e build a dyn am ic model of intern a tional borrow ing with endogenous default and multiple maturities of debt. Short-term debt can deliver h igher imm ed iate consum ptio n than long-term d eb t; la rge long-term lo an s are not available because theborrowercannotcommittosaveinthenearfuturetowardsrepaymentinthefarfuture. Howeve r, issuin g long -term debt can insure against the need to roll-over short-term debt at high interest rate spreads. T h e trade-off between these two benefits is qua ntitatively importan t for understanding the maturity composition in emerging ma rkets. W hen calibrated to data from Brazil, the model matches the dynamics in the maturity of debt i ssu ances and its como vement with the le vel of spreads across maturities. ∗ We thank V. V. Chari, Tim Kehoe, Patrick Kehoe, Naray ana Kocherlakota, Hanno Lustig, Enrique Mendoza, Fabrizio Perri, and Victor Rios-Rull for many useful comments. The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis, the Federal Reserve Bank of Dallas, or the Federal Reserve System. All errors remain our own. † arellano@econ.umn.edu ‡ anan th.ramanarayanan@dal.frb.org 1 Introduction Em erging markets f ace recurrent and costly financial c rises th at are characterize d by limited access to credit and high interest rates on foreign debt. As crises approac h , not only is d eb t limited but also the maturity of debt shortens, as docum ented by Broner, Lorenzoni, and Schmukler (2007). 1 During these periods, however , the interest rate spread on short-term bonds rises more than the spread on long-term bonds. Why do countries s horten their debt maturity during crises ev en though spreads appear higher for shorter maturity debt? To answer this question, this paper develops a dyna m ic model of the matu rity composition in which debt prices reflect endogenous default risk and debt maturity responds to the prices of short- and long-term debt contr acts. Our model can ration alize shorter debt m a turity during crises as the result of a liquidity advantage in short-term debt contracts; although these contracts carry higher spread s than longer term deb t, they can deliv er la rger resources to the coun try in times of high default risk. We first analyze the dynamics of the maturity composition of in ternational bonds and the term structure of in terest rate spreads for four emerging m arket countries: Arg entina, Brazil, Mexico, and Russia . We use data on prices and issuances of foreign-currency denom inated bonds to estimate spread curves — interest rate spreads over U .S. Treasury bonds across maturit y — as w ell as duration,ameasureoftheaveragetimetomaturityofpaymentson coupon pa ying bonds. We find that governm ents issue short-term d eb t mor e heavily w hen spreads are high and spread curves are down ward sloping, and they issue long-term debt more heavily wh en sprea ds are lo w an d spread curves are upward slo ping. Across these four countries, w ithin periods in which 2-y ea r spreads are belo w their 25th percentile, the average duration of new debt is 7.1 y ears, and the average d ifference bet ween the 10-yea r spread and the 2 -yea r spread is 2.3 percenta ge points. But w hen the 2-year s pread s are abo ve their 75th per centile, the average du ra tion s horte ns to 5 .7 years, while th e ave rage differ en ce bet ween the 1 0-year spread and the 2-year spread is −0.5 percentage points. From this evidence we conclude that the maturity of deb t shortens in tim es of high spreads and do w nwa r d-slo ping spread curves. We then dev elop a dynamic model with defaultable bonds to study the c hoice of debt matu rity and i ts co variation with t he term structure o f spreads. In ou r model, a risk averse bo rrowe r faces persistent incom e sh oc ks an d ca n issue l on g a nd sh o rt d uration bonds. T h e borrowercandefaultondebtatanypointintime,butfacescostsofdoingso. Default 1 Calvo and Mendoza (1996) document in detail how in Mexico during 1994, most of the public debt was converted to 91-day Tesobonos. Bevilaqua and Garcia (2000) document a similar rise in short-term government debt in Brazil during the 1999 crisis. 2 occ urs in equ ilibrium in low-income, high-debt times be cau se the cost of coupon paym ents outweighs the co sts of default when con su m ption is low. Interest rate sp reads on lon g and short bonds compensa te foreign len ders for the expected loss from future d efau lts. T hu s, t he supply of credit is more string ent in time s of lo w income and high outstanding debt, becau se the probability of default is high. In fact, cou nte rcyclica l default risk su bsta nt ially limits the degree of risk sh aring, and the model can generate cap ital outflows in r ecession s, when in terest rate spreads are at t heir highest. The model generates the observ ed dynamics of spread curv es because the endogenous probab ility of default is persistent, yet mean rever ting, as a result of the dynamics of deb t and income. Wh e n debt is lo w and income is h ig h, default is unlikely in th e near future, s o spreads are lo w . H owe ver, long-terms spreads are higher than short-term spreads because default m ay become likely in the far future if t he borrower receives a sequence of bad shoc ks and accum ulates debt. On the other hand, when income is low a nd debt i s high, default is lik ely i n t he near future, so spreads are h igh . Lo ng-term spreads, ho wever, increa se by l ess than short-term spread s becau se the borrowe r’s lik elihood of repa yin g may rise if it receives a sequence of good shocks and red u ces its debt. Although cumu lative d efault p roba bilities on long-ter m debt are a lways larger th an o n sh ort-term debt, the long spread can be lower than the short spread because it reflects a lowe r a verage future default probability. The m odel can rationalize the covariation observ ed in th e data between the maturit y structure of debt issuances and the term structure of spreads as reflectingatrade-off bet ween insurance benefits of long-term debt and liqu i d it y benefits of short-term debt, both due to the presence of default. Long-term deb t provides insurance against the uncertaint y o f short- term interest rate spreads. Since short-term spreads rise during periods of low income, w hen default risk is high, issuing long-term d eb t allow s the borro we r to avo id rollin g over sho rt- term debt at high spreads in states when con sum p tion is low . Moreove r, long-term d eb t insures against futur e periods of limite d credit availabilit y ; in particular, the borrowe r can a void capital outflows in recessions by i ssuin g long-term debt. Ev en though long debt dom inates short debt in term s of insurance, it is not as effective in delivering high i mmediate consumption; hence the l iquidity benefit of sh ort-term debt. Short- termdebtallowstheborrowertopledgemoreofhisfutureincometowarddebtrepayment becau se in eac h subseq uent period the threat of default punishm ent gives him incentives for repayment before an y further short debt is issued. Long-term debt contr acts do not allo w suc h large transfers because the borrowe r is unable to commit to saving in the near fu ture to ward repa ym en t in the further future. Effectively, th e threat of default pu nish m ent is lowe r with long-te rm debt given th at it w ill be relevant o nly in the fu tu re, when the lon g-te rm d eb t 3 is due. This greater efficacy of short-term debt in alleviating commitmen t problems for debt repa yment is reflected in more lenien t price sc hedules and smaller drops in short-term prices with in creases in the lev el of debt issues. In th is sen se, sho rt d ebt is a more liqu id a sset, and consum ptio n can alw ays be margin ally increased b y more with short-term debt than with long-term deb t. The time-varying maturity structure responds to a time-varying valuation of the in surance benefit of long-term debt and the liquidity benefitofshort-termdebt.Periodsoflowdefault probabilities and upward spread curves correspond to states when the borrower is wealthy and values insurance. Thus, the portfolio is shifted to wa rd long debt. Periods of high defa ult probabilities and inverted sprea d cur ves correspond to states when the borrower is poor and credit is limited. Th ese are times when liquidity is most va lua b le , an d thus the portfolio is shifted to ward shorter-term debt. We can therefore rationalize higher short-term debt po sitions in times of crises as an optimal response to the illiquidity of long-ter m d ebt, and the tigh t er availability of its supply. W hen calibra ted to Brazilia n dat a, the mod el quantitatively m a tches the dyna m ics of the matu rity compo sition of new d ebt issuances an d its co variation w ith spreads observe d in the data. In connecting our model to the data, a me thodological contribution of the p aper is to develop a tractable fram ewo rk with bonds that have empirically releva nt duration. Bonds in our model are perpetuity contra cts w ith non-state-contingent cou pon pa ym ents that decay at differe nt rates. B ond s with paym ent s that decay quick ly have more of their va lu e paid early, and so have short dura tion. This gives a recursive structure to debt a ccu mu lation that allows the model to be cha ra cteriz ed in t e rm s of a sm a ll nu mber of state variables although decisions at any date are contingent on a long sequence of future expected payments. Our findings indicate that the insurance benefits of long-term debt and the liquidity benefits of short-term debt are quantitatively important in understanding the dynamics of the m aturity structure o b served i n Brazil. Importantly, the m a turity s tructur e in the model responds to the underly in g dy na mics of default pr ob a bilities re flected in spread curves, wh ich ma tch the data well. Rela ted L itera tur e This paper is related to the literature on the optimal maturity structure of government debt. Angeletos (2002), B uera and Nicolini (2004) and Shin (2007) show that, when debt is not state contingent, a rich m aturity structure of gov ernm en t bonds can be used to replicate the allocations obtained w ith state-co nting ent deb t in econ om ies w ith distortiona ry taxes as in Lucas a nd Stok ey (1983). In th ese closed econo my mod els, s hort- and long-ter m inter est 4 rate dynamics reflect the variation in the representative a gent’s margin al rate o f substitutio n, which changes with the state of the economy. Thus, ha ving a ric h enough maturity structure is equivalent to ha vin g assets with state-contin gent pa yo ffs. 2 Our paper shares with these papers the message that man aging th e m atu rity com position of debt can provide benefits to the governm ent because of uncertain ty over fu tu re in terest rates. The message is particularly relevant for the case of emergin g m arket econo mies. As N eum eyer a nd Pe rri (2005) have sho wn, fluctuations in c ountry specific i nterest rate sp rea ds play a major r ole in a ccountin g for the large business cycle fluctuations in emerging markets. T h e lesson th at our paper prov id es in this con text is that the volatility of the maturity composition of debt in these countries is an optimal response to these int erest rate fluctuatio ns. Ho wever, in c ontra st to these papers, the fluctuation s in interest rates in o ur model reflect time variation in the endogenous country’s o wn prob ability of default. 3 The maturity of d ebt in e m erg ing coun tries is also of interest because of the general view that coun tries could alleviate their vulnerability to v er y costly crises by c h oosing the appropriate maturity structure. For example, Cole and Kehoe (1996) argue that the 1994 Mexican debt crisis could ha ve been a voided if the maturit y of go vernm ent debt had been longer. Long er mat urity debt would allow count ries to better man age external shocks and sudden stops. Broner, Lorenzoni, and Schmu kler (2007) formalize this idea in a model where the govern ment can avoid a crisis in th e s hort term by is suing l ong -term debt. In their model, with risk a ver se lenders w h o face liquidit y s h oc ks, lon g -term debt is more expensive, s o the maturity com position is the result of a trade-off between safer long -term d eb t and cheaper short-term debt. In line with their paper, w e a lso find that short-term debt provid es larger liquidit y benefits. In c ontrast to Bron er, L orenzoni, and Schmu kler, in our m odel the time- varying availabilit y of short- a nd long-term deb t is a n equilibriu m respons e to compensate fo r the economy’s default r isk, rath er th an to compensate for foreign lenders’ shock s. Moreover, our paper is the first to develop a dynamic framework with defaulta ble debt and m ultiple matu rities with which these questions can be analyzed and assessed quantitative ly. The larger liquidity benefits of short-term debt relativ e to lon g -term debt arise in our model because short-term contracts are more effectiv e in solving the commitm ent prob lem of the borrower in term s of future debt and default policies. In this regar d, o u r paper is related to Jeanne’s (2004) model where short-term deb t gives m ore incentive s for the gover nm ent 2 Lustig, Sleet, and Yeltekin (2006) develop a general equilibrium model with uninsurable nominal frictions to study the optimal maturity of government debt. They find that higher interest rates on long-term debt relative to short-term debt reflect an insurance premium paid by the government, for the benefits long-term debt provides in hedging against future shocks. 3 The idea that credit risk makes longer term debt attractive is also present in Diamond (1991) in a three period model of corporate debt where firms have private information about their future credit rating. 5 to implement better policies. Wh en short-term debt needs to be rolled o ver, creditors can discipline the go vern ment b y rolling over the debt only after desired polic ies are implement ed . 4 Moreo ver, when defaulted debt is renegotiated, Bi (2007) shows th at long-term debt is more expe nsive also to co m pensate for debt dilution. Absent explicit sen iority clau ses, issuin g short-term debt can dilute the reco very of long-term debt in case of default. The theoretical model in this p aper builds o n t he work of A guiar and Gopinath (2006) a nd Arellan o (2008), w ho mode l e q uilibriu m default with incomplete marke ts, a s in the seminal paper on sovereign debt b y Eaton and G erso vitz (1981). This paper extends this framework to incorporate lon g debt of multip le maturities. In recen t wo rk, Chatterjee and Eyigun gor (2008) and Hatchondo and Martinez (2008) show that long-term defaultable debt allow s a better fit of emerging market data in terms of the v olatility and mean of the coun try spread as well as debt levels . All t hese models ge nerate a time - varyin g probability of d efault that is linked to the dynamics of debt and income. The dynamics of the spread curv e in o ur model reflect the time-varying default probab ility, in t he sam e way that Merton (1974) derived for credit spread curves on defau ltable corporate bond s. In Merton’s model, w h en the exo genou s default probability is low, the credit spread curve is up wa rd sloping, and w hen the default probabilit y is hi gh, credit spread curves are downward sloping or hump shaped. The s pread curve dyn am ics in t his p aper follow Merto n’s resu lts. Howe ve r, our framework d iffers from Merton’s in that the probability of default and the level and maturity composition of debt issuances are endogen ous variables. The outline of the paper is as f o llows. Sect io n 2 documen ts the dynamics of the spread curve and matu rity composition for four emerging markets: Argentina , Brazil, Mexico, a nd Russia. Section 3 p resents the theor etical model. Section 4 presents so m e examp les t o illustrate the mech anism for the optima l deb t portfolio. Section 5 p res ents all the quan titat ive results, and Section 6 c onclu des. 2 Emerging M ark ets Bond Data We examine data on sovereign bon ds issued in in terna tional financial mark ets b y four emerging- market countries: A rgentina, Brazil, M exico, and Russia. We look at th e behavior of th e in terest rate spreads over d efa ult-free bond s, across di fferen t maturities, and at the w a y the matu rity of n ew debt issued covaries with spreads. We find that when spread s are low, g overn - ments issue long-ter m bonds m ore heavily an d lon g-term spreads are higher than short-term 4 Commitment problems have been shown to reduce the level of sustainable debt in the literature of optimal policy without commitment, as in Krusell, Martin, and Rios-Rull (2006). 6 spreads. When spreads rise, the maturity of bond issuances shortens a nd short-term spr eads are higher than long-term spreads. Our findin gs also confirm the earlier results of Broner, Lorenzon i, and Schmu kler (2007), who showed in a samp le o f eight emerging eco nom ies tha t debt maturit y shortens when spreads a re v ery high. 5 2.1 Spread Curv es We define the n-year sp read fo r an emerging market count ry as the difference between the yield o n a d efaulta ble, zer o-coupon bond maturing in n years i ssu ed by the count ry and on a zero-coupon bo nd of the same matu rity with negligible default risk (for example, a U.S. Treasury note). The spread is the implicit interest rate premium required b y investors to be willing to purchas e a defaultable bond of a given ma tur ity. 6 The spre ad curve depicts spreads as a function of maturity. We denote the ann ually com pounded yield at date t on a zero-coupon bond issued b y country i,maturinginn years, as r n t,i . The yield is related to the price p n t,i of an n-y ea r zero-coupon bond, wi th face value 1, through p n t,i =(1+r n t,i ) −n . (1) We define country i’s n-year spread as the differ ence in zero-coupon yields betwe en a bo nd issued b y country i relative to a default-free bond. The n-year spread for coun try i at date t is given by: s n t,i = r n t,i − r n t,rf ,wherer n t,rf is the yield of a n-year defau lt-free bon d . 7 Since governments do not issue zero-coupon bonds i n a wide range of maturities, we estimate a country’s spread curve by using secondary market data on the prices at whic h coupon-bearing bonds trade. The estimation procedure, described in the Appendix, follows Svensson (1994) and Broner, Lorenzon i, and Schmukler ( 2007 ). We comp ute spread s starting in M arch 19 96 at the earliest and e nding in M ay 2 004 at th e latest, dependin g on th e availability of data for each co untry. Figure 1 displays the estim ated spreads f or 2-year and 1 0-y ear bonds for A rgentina, Brazil, Mexico, and Russia. 5 Broner, Lorenzoni and S chmukler (2007) focus on the relationship betw een the term structure of risk premia (compensation for risk aversion) and the average maturity of debt. In this section we construct measures of the t erm structure of yield spreads and t he average duration of debt because these statistics prov ide the basis for the quantitative assessment of our model. 6 Yield spreads on bonds issued by emerging markets could also arise due to risk premia or liquidity differences. However, g iven the incidence of sovereign defaults in emerging markets, in o ur model we abstract from these other factors and examine the extent t o which default risk can rationalize t hese spread dynamics. 7 Our data include bonds denominated in U.S. dollars and European currencies, so we take U.S. and Euro-area government bond yields as default-free. 7 96 97 98 99 00 01 02 03 04 0 5 10 15 20 25 30 date spread (%) Argentina 96 97 98 99 00 01 02 03 04 0 5 10 15 20 25 30 date spread (%) Brazil 96 97 98 99 00 01 02 03 04 0 5 10 15 20 25 30 date spread (%) Mexico 96 97 98 99 00 01 02 03 04 0 5 10 15 20 25 30 date spread (%) Russia 2 year 10 year Figure 1: Tim e series o f 2-year and 10-year spreads. Spreads are v ery v olatile, and the difference between long-term and short-term spr eads va ries substan tially over time. W hen spreads are low, long-term spreads are generally h igher than short-term spreads. Howe ver, w h en the level o f spreads rises, the gap betwe en long and short-term spreads tends to n arrow and sometimes reve rses; the spread curv e is flatter or inverted. The tim e series in Figure 1 show sharp in crea ses in interest ra te spreads associated with R u ssia ’s de fault in 1998, Argentin a’s default in 2001, and Braz il’s financial crisis in 2002. 8 The expectation that the countries w o uld default in these episodes is reflectedinthe high spreads charged on de faultable bonds. To em ph asize the pattern observed in the time series that sho rt-term spreads tend to rise more than long-term spreads, in Figure 2 we display spread curv es a veraged across different 8 For Argentina and Russia, we do not report spreads after d efault on external debt, unless a restructu ring agreement was largely completed at a later date. We use dates taken from Sturzenegger and Zettelmeyer (2005). For Argentina, we report spreads until the last week of December 2001, when the country defaulted. The restructuring agreement for external debt was not offered until 2005. For Russia, we report spreads un til the second week of August 1998 and beginning again after August 2000 when 75% of external debt had been restructured. 8 time periods for each country: the overall avera ge, the a vera ge w ithin periods with t he 2-yea r spread belo w its 1 0th percentile, and the a ve rage within periods with t he 2 -year sp read above its 9 0th percen tile. When spreads are lo w, the spread curve is up ward sloping: long-term spreads are higher than short-term spreads. Wh en spreads are high, short-term spreads rise more than l ong-term spreads. For A rgen tina, Brazil, a nd R ussia, the spread curve becomes do wnward sloping in these tim es. For M exico, which had relatively smaller in creases in spreads during this time period, the spread curv e flattens as short spreads rise more than long spreads. 9 2.2 The Maturity Composition of Debt and Spreads We no w examine the maturity of new debt issued by the four emerging mark et economies during the s ample period, and relate t he changes in t he maturity of debt to changes in spreads. 10 In each week in the sample, we measure the m atu rity of debt as a q u antity-we ighted a verag e maturity of bonds issu ed that week. We measure the maturity of a bond using two alternativ e statistics. T h e first is simply the number of y ears from the issue date until the maturity date. The second is the bond’s duration,defined in M acaulay ( 1938) as a weighted a verage o f the nu mber of years until each of the bond’s future payments. A bond issued at date t by country i,payingannualcouponc at dates n 1 ,n 2 , n J years into the future, and face value of 1 has d uration d t,i (c) defined by d t,i (c)= 1 p t,i (c) Ã J X j=1 n j c(1 + r n j t,i ) −n j + n J (1 + r n J t,i ) −n J ! , (2) where p t,i (c) is the coupon bond’s price, and r n t,i is the zero-co upon yield curve. Th e time until each future p ay m e nt is weig hted by the discounted value of that pay m ent rela tive to th e price of the bond. A zero-coupon bond has duration equal to the number of years until its maturity da te, but a coupon-paying bond m aturing on t he s ame d ate h as shorter dura tion. We consid er duration as a measure of m atu rity because i t is m ore comparable a cross bonds 9 The findings are similar to empirical findings on spread curves in corporate debt markets. Sarig and Warga ( 1989), for example, find that highly rated corporate bonds have low levels of spreads, and spread curves that are flat or upward-sloping, while low-grade corporate bonds have high levels of spreads, and average spread curves that are hump-shaped or downward-sloping. 10 In addition to external bond debt, emerging countries also have debt obligations with multilateral institutions and foreign banks. However, marketable debt constitutes a large fraction of the external debt. The average marketable debt from 1996 to 2004 is 56% of total external d ebt in Argentina, 59% in Brazil, and 58% in Mexico (Cowan et al. 2006). 9 5 10 15 20 0 5 10 15 20 25 Argentina years to maturity spread (%) 5 10 15 20 0 5 10 15 20 25 Brazil years to maturity spread (%) 5 10 15 20 0 5 10 15 20 25 Mexico years to maturity spread (%) 5 10 15 20 0 5 10 15 20 25 years to maturity spread (%) Russia average high short spread low short spread Figure 2: Av erage s pread c urves: over all, and w ith in periods in th e h igh est an d lowest deciles of the 2 -year spread. with differen t coupon rates. We calculate the a vera ge ma tur ity and avera ge dur ation of new bonds issued in each week b y eac h country. Table 1 displays eac h country’s averages of th ese weekly maturit y and duration series within periods of high (above median) and low (below med ia n) 2-y ea r spreads. First, the table shows that duration tends to be much shorter than maturity. Because the yield on an e m erg ing market bond i s ty p ically high, the p r incipa l pay m e nt at the matu rity date is severely d iscou nted, and much o f the bond’s value comes fr om coupon payments made soon er in the future. This weig ht o n coupon pa ym ents shortens th e d uratio n measure relative 10 [...]... bL , y) is the value associated with not defaulting and staying in the contract and v d (y) is the value associated with default Since we assume that default costs are incurred whenever the borrower fails to repay its obligations in full, the model will only generate complete default on all outstanding debt, both short and long term When the borrower defaults, output falls to y def , and the economy... yet 2 the borrower issues long-term debt The lower discount price on long debt is the insurance premium the borrower is willing to pay for insurance against the variation in bond prices in period 1 This insurance mechanism is the same as that emphasized in Kreps (1982), Angeletos (2002) and Buera and Nicolini (2004) in their models of the optimal maturity structure of debt with incomplete markets The. .. model contains a dynamic portfolio problem where the borrower chooses holdings of two defaultable bonds of shorter and longer duration Below, we show how movements in the probability of default generate time-varying differences in the prices, and in the liquidity and insurance benefits of these two assets, which rationalize the movements in spread curves and maturity composition observed in the data 5.2.1... is low The economy borrows a large amount at low interest rate spreads, so that in states where the economy is hit by a bad shock, default becomes more likely further in the future In contrast, when the likelihood of imminent default is high, the economy avoids default in the next period only in states with high output Conditional on not defaulting, then, output is expected to remain high, and the probability... in our model is that the variation in bond prices comes from the government’s inability to commit to repaying, rather than from variation in the lender’s marginal rate of substitution 4.3 Summary In a standard incomplete markets model with fluctuating output and without default, a borrower would find the portfolio of long and short debt indeterminate if the risk-free rate were constant across time; the. .. of default further in the future falls The persistence and mean reversion of default and repayment probabilities driven by the dynamics of debt and income therefore rationalize the dynamic behavior of the spread curve observed in the data 5.2.2 Maturity Composition We now present the quantitative predictions for the maturity composition of debt It is important to note that we analyze the optimal maturity. .. On the other hand, when wealth is low, the short spread is on average 10.84% and the long spread is on average 2.43% below the short spread In summary, through the lens of our model, the maturity structure of defaultable debt in emerging markets and its covariation with spread curves and levels can be rationalized by two factors: hedging advantage of long-term debt for insuring against fluctuations in. .. high and low short spreads, as well as the difference in volatilities of the two spreads The model also matches quantitatively the volatility of the long spread The model’s overall average short and long spreads, however, are both pinned down by the average probability of default, so the average spread curve is quite flat Underlying the time-varying spreads is the interaction of the dynamics of income and. .. when the two-period loan is due does not induce the borrower to repay, because the borrower discounts the future, so that reducing consumption in period 1 is worse than facing the punishment for default in period 2 At the same time, the threat of punishment for default in period 1 is irrelevant, because none of the debt is due in period 1, and the threat of punishment cannot be used to induce savings... 2 b1 = 0 1 In this example the borrower faces risk because of the variation in bond prices across states in period 1 due to differences in default risk in period 2 Using long-term debt in period 0 allows the borrower to avoid the risk involved with rolling over short-term debt in period 1 The borrower benefits from this insurance with smoother consumption and higher utility 1 2 Note that in period 0 . iven the incidence of sovereign defaults in emerging markets, in o ur model we abstract from these other factors and examine the extent t o which default. defaulting and sta yin g in the contra ct and v d (y) is the value associated with default. Since we assume that default costs are incurred w henever the