A Supply Story: Emerging Markets, HighYield and Market Closures.

Ana Fostel ∗ †

Abstract

The goal of the paper is to study closures in primary markets ofEmerging Market bonds, stressing the supply (investor) side of theproblem. I use daily data on issuance and spreads covering the period1997-2002 and present three stylized facts. First, Emerging Marketsand High Yield exhibit higher price correlation around primary emerg-ing market closures. Second, although Emerging Market spreads in-crease around primary market closures, the behavior across the creditspectrum within the asset class is not the same: high-rated EmergingMarket spreads increase less than low-rated Emerging Market spreads.Third, during closures the drop in issuance is not uniform: high-ratedEmerging Market issuance drops more than low-rated Emerging Mar-ket issuance. The presence of closures and the three stylized factsare explained by the interaction of several elements: incomplete mar-kets, heterogeneous investors leverage, and adverse selection. I builda multi-period general equilibrium model with incomplete marketsand collateral based on Geanakoplos (2003). The first main result is

∗Yale University. New Haven, USA.†I want to express my gratitude to my advisor John Geanakoplos, for his encouragement

and time invested that made this work possible. Also my other two advisors Andres Velascoand Herb Scarf for extremely helpful comments. Very valuable knowledge I got frommany discussions with market participants, Ajay Teredesai, Francesc Ballcels and ThomasTrebat. I want to thank all the participants of the Mathematical Economics, Micro Theory,Macro Lunch seminars at Yale University. Comments received at the International FinanceSummer Camp at Buenos Aires were crucial for this paper. Financial support from YaleCenter for the Study of Globalization and Cowles Foundation are greatly appreciated. Allerrors remain mine.

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that when rational heterogeneous crossover investors face a liquidityshortage, assets that have independent fundamentals may display cor-related price behavior (explaining Fact 1). The second result showsthat during liquidity shortages high margin asset prices fall more thanlow margin asset prices (explaining Fact 2). The third result showsthat an investor liquidity shortage leads to a severe drop in issuance,in particular that of the good Emerging Market asset, when there isadverse selection (explaining closures and Fact 3).

Keywords: Emerging Markets, High Yield, Market Closures, CreditRatings, Incomplete Markets, Leverage, Collateral Equilibrium, Ad-verse Selection.

JEL Classification:

1 Introduction.

The goal of this paper is to model closures in the primary market of EmergingMarket bonds and to provide empirical evidence and a theoretical explanationof how these closures can be associated with events in mature economies.

A primary market closure is defined as a period of 3 weeks or more duringwhich the primary issuance over all emerging markets is less than 40 percentof the period’s trend. I use daily data on primary issuance from Bondwaredata base covering the period of 1997 to 2002. During this period, I find thatthere were 13 market closures.

That market closures can have extremely serious consequences for Emerg-ing Markets economies is a widely known fact. These sudden stops may trans-form liquidity problems into more serious solvency problems that can easilylead to crises. These closures are not rare; a better understanding of themcan allow emerging markets, and even international financial institutions, totake ex-ante policies that are welfare improving.

There is a huge literature that tries to explain these closures from thedemand side, showing how weak Emerging Markets fundamentals can be re-sponsible for sudden stops of capital flows to these economies. The Sovereign

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Debt literature (as in Bulow-Rogoff (1989)) stresses moral hazard and rep-utation issues.Three “generations” of currency crises models focus on fis-cal deficits (as in Krugman (1979)), current account deficits (as in Obstfeld(1994)) and finally on weaknesses of domestic financial systems and domesticliquidity crises (as in Chang and Velasco (2000)).

In this paper I take a different approach. I look at the supply side ofthe problem and try to understand why certain market closures may beassociated with events in mature markets.

There are many different channels through which mature markets mightinfluence market closures in emerging market bonds. For example, throughmacroeconomic variables such as foreign interest rates (as in Goldfajn andValdes (1997)), shocks to productivity (as in Agenor and Aizenman (1998)),and recessions. Another possible approach is to abstract from macroeconomicelements and to focus exclusively on financial markets and their functioning.In this paper I take this last approach. In particular I focus on the interactionbetween two fixed income sectors: the secondary market of Emerging Marketbonds and US High Yield bonds. I use daily data on spreads for both markets(the JPMorgan index for Emerging Markets, EMBI+, and the Merrill Lynchindex for High Yield) for the period 1997 to 2002. What I find is verysuggestive of a possible supply channel.

I describe three stylized facts. First, Emerging Markets and High Yieldexperience experience higher spreads, higher volatility and higher correlationaround emerging market primary closures, despite the fact that they havedifferent fundamentals. Second, although Emerging Market spreads increasearound primary market closures, the behavior across the credit spectrumwithin the asset class is not the same: high-rated Emerging Market spreadsincrease less than low-rated Emerging Market spreads. Third, during closuresthe drop in issuance is not uniform: high-rated Emerging Market issuancedrops more than low-rated Emerging Market issuance.

I build a general equilibrium model with incomplete markets and col-lateral based on Geanakoplos (2003) that explains market closures and theaforementioned stylized facts. There are some key ingredients in the model.The first one is incomplete markets. Second, conjunction risk. Good newsreduces uncertainty and bad news increases it. The third one is leverage. In-vestors can use assets as collateral to borrow money. The fourth key element

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is the presence of heterogeneous crossover investors. These are investors thathold both types of assets and their opinions become more similar after goodnews than after bad news. The last ingredient is adverse selection. Thereare good and bad emerging countries issuing bonds and these types are notperfectly observed by crossover investors.

The first main result is that when rational crossover investors face a liquid-ity shortage, assets with independent fundamentals may display correlatedprice behavior. In the model, bad news only affects High Yield, yet EmergingMarket prices fall as well. The main reason for this is that, first markets areincomplete. Second, heterogeneous investors react differently after bad news,and therefore make different portfolio decisions. This result explain StylizedFact 1.

The second result is that high margin (low leverage) asset prices fall morethan low margin (high liverage) asset prices. This is quite surprising. Com-mon sense tells us that during crises high leveraged assets are the ones whoseprices crash more. However, this common sense logic relies on the implicitassumption that different assets are held by different investors. The reasonfor the contrary conclusion is that when facing a liquidity shortage, rationalcrossover investors raise cash by selling off the assets which are unencum-bered by loans. Putting it in another way, the price of every asset is the sumof its payoff value and its collateral value. In liquidity crises, the collateralvalue of low margin assets rise, partially offsetting the decline in their payoffvalue. This result explains Stylized Fact 2.

The third main result is that an investor liquidity shortage leads to asevere drop in the issuance, in particular the issuance of the “good” emergingmarket asset, when there is adverse selection. The “good” type has to issueless in order to separate itself from the “bad” type: the greater the pricedifference, the more drastic the quantity reduction. The first spillover from aHigh Yield shock will cause both “good” and “bad” emerging market assetsto deteriorate. But since the “bad” type has higher margins, its price willfall further as we noticed in the second main result. Hence, the gap in pricesbetween different types rises dramatically, creating the quantity reductioncharacterizing closures. This seems to explain why highly rated issuancedrops more during closures. This explains Stylized Fact 3.

As it was mentioned before, the first three key elements of the model

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are market incompletness, conjunction risk and leverage. In this sense mymodel follows the tradition of modeling credit constraints and collateral ofGeanakoplos(1997), Geanakoplos and Zame (1998) and specially Geanakop-los (2003). When default and limited collateral are explicitly incorporatedinto General Equilibrium Theory, a theory of endogenous contracts, includ-ing endogenous margin requirements arises, making it possible to explain ina general equilibrium framework liquidity and liquidity crises. With “badnews” that makes default more probable, and increases uncertainty, assetprices fall more than the real drop in expected value, due to wealth effectsand feedback from (endogenous) margins requirements.

The third key element is the presence of crossover investors. In this sense,this paper is also related to a big literature on contagion. There are a numberof different theoretical modeling approaches that can explain contagion. Letus mention a few.There are theories that model contagion through wealtheffects. For example Kyle and Xiong (2001) use a continuos-time model toexplain financial contagion in a market with two risky assets and three typesof traders. One of the traders type is a financial intermediary who is fullyrational, and the other two follow rules of thumb. When financial intermedi-aries have reduced capital, they need to liquidate positions in both markets,resulting in reduced market liquidity, increased price volatility and increasedcorrelation. Vayanos (2004) also uses wealth effects to explain contagionin a continuos-time model reaching the same results: the difference in thiscase is that he considers investors as fund managers subject to performance-based (and therefore backward looking) withdrawals, which provides a linkbetween volatility and liquidity. Although in my model wealth effects areexplaining contagion as well, my traders are fully rational and forward look-ing. The aforementioned papers do not consider fully rational agents. Inparticular, the endogenous margins in Vayanos (2004) are not set by supplyand demand, but rather by an ad hoc rule. In Kyle and Xiong (2001) thereare no feedbacks from endogenous margins.1 Another approach to modelcontagion is as information transmission. In this case the fundamentals ofassets are assumed to be correlated. When one asset declines in price be-cause of noise trading, rational traders reduce the prices of all assets sincethey are unable to distinguish declines due to fundamentals from declinesdue to noise trading. Examples of this approach are King and Wadhwani

1In his dynamic model, Geanakoplos(2003) concentrated on the case with a single asset,whereas here we focus on spillovers, which of course requires more assets.

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(1990), Kodres and Pritsker (1998) and Calvo (1999). The first work usesthis information approach to explain the uniformity of price declines in worldstock markets during the 1987 crash. The second paper uses this approachin a multiple asset rational expectation model in order to explain contagionin emerging markets. Finally, the last paper explains liquidation of riskyemerging market assets. My model differs from the last approach because Iconsider uncorrelated assets and there is no information asymmetry amonginvestors.

Finally, the fourth key element of my model is adverse selection (as inRothschild and Stiglitz (1976)) and in this sense the paper is related to thetradition of credit rationing as in Stiglitz and Weiss (1981). But I treat it inperfect competition as in Dubey-Geanakoplos (2002).

The structure of the paper is as follows. Section 2 presents the stylizedfacts present in the data. Section 3 states the problem. Section 4 presents thefirst model of collateral equilibrium. Section 5 presents benchmark cases inwhich the contagion result does not hold. Section 6 adds necessary assump-tion to the model in order to get contagion. Section 7 presents a numericalsimulation. Section 8 presents the first result. Section 9 adds to the previousmodel the primary market of emerging market bonds and adverse selection,presents a simulation and also the second and third results. Section 10 con-cludes. The appendix discusses different equilibrium regimes presented insection 8 and presents formal proofs of propositions.

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2 Stylized Facts.

In this section I describe the data I use in the paper. I also give a precise def-inition of Primary Market Closures and describe some stylized facts presentin the data from 1997 to 2002.

For Emerging Market issuance I use Bondware data base. This consistsof daily Emerging Market issuance of dollar-denominated sovereign bondscovering the period 1997-2002.

With this data I study the presence of market closures during the coveredperiod. A Primary Market Closure is a period of 3 weeks or more duringwhich the primary issuance over all emerging markets is less than 40 percentof the period’s trend. This definition is based on several definitions given bydifferent IMF Global Financial Stability Reports.2 The following table showsthe list of closures.

Market closures are not rare events. In the period 1997-2002 there were13 market closures. From a total number of days of 1587 in the sample,322 correspond to closures. This is, 20.29% of the time primary marketsof Emerging Market bonds are closed. The average duration of a closure is23 days, though there is a big variance, some of them lasting 3 weeks andsome others 12 weeks. Finally, as we can see in the table, while some of theclosures are clearly associated with events in emerging countries, others areassociated with events in mature economies.

As we said in the introduction, in order to understand a possible channelfrom mature economies to primary bond markets in emerging countries, wewill look at the relationship between the secondary markets of EmergingMarkets and US High Yield bonds. The latter are corporate bonds issuedin USA with low credit ratings. These two secondary markets are quite big.The face value of outstanding dollar-denominated Emerging Market bondswas already 217 billion dollars by the end of 2002, and for HIgh Yield was

2In several definitions used by the IMF, a 20% threshold is used instead. Using a40% threshold does not change substantially the results (i.e. the number of closures), andallows me to study issuance during recession periods in which markets are not totally shutdown. The period’s trend is just the accumulative average since the beginning of eachcalendar year. Again, the number of closures is robust to other trend specifications.

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Fig. 1: Market Closures.

288 billion dollars. This last sector includes traditional US corporations, likethe recently downgraded Ford and GM.

To study these secondary markets I use daily data covering the sameperiod 1997-2002. For Emerging Markets spreads I used the JPMorgan indexEMBI+. This index tracks total returns for dollar-denominated externaldebt instruments in the Emerging Markets. For US High Yield I use theMerrill Lynch index for BB and B rated bonds. Figure 2 puts togetherprimary market closures with spreads in these two secondary markets. Thehorizontal axis represents years and the vertical bars the periods of closurein the primary emerging markets. The vertical axis represents basis points.The graph shows historical daily spreads for the two secondary markets, theEMBI+ and the Merrill Lynch High Yield spreads.

Just “eye-balling” the picture gives us an impression that these spreadsare somehow related to the periods of low Emerging Market issuance. I nextdescribe three stylized facts present in the data.

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Fig. 2: Market Closures, EMBI+ and High Yield Merrill Lynch index.

1. Fact 1: Emerging Market and US High Yield Price Correlation.

The first fact is that Emerging Market and High Yield exhibit higherprice correlation around primary market closures. Both Emerging Mar-ket and High Yield present higher spreads and higher volatility aroundclosures.

Emerging Market Spreads increase before and during market closures,even if there is no Emerging Market specific problem. Figure 3 (left)shows the average Emerging Market spreads from 20 days before aclosure starts until 20 days after the closure starts. (The vertical linerepresents the beginning of a closure for all the pictures that follow).We can clearly see the increasing behavior. In 10 out of the 13 closuresEmerging Market spreads are higher 20 days after the closure beginsthan it was 20 days before the closure started. For 2 closures EmergingMarket spreads increase for the window -10 to +10, for one closure allthe increase is done strictly before the closure starts.

Surprisingly, US High Yield spreads also increase before and during

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Fig. 3: EM and HY Spreads around closures

Emerging Market closures. Figure 3 (right) shows the average behaviorof High Yield spreads from 20 days before until 20 after the beginning ofan Emerging Market closure. The increase in spreads is again evident.And it is also robust across closures. For 10 out of the 13 closures,High Yield spreads were higher 20 days after the closure started than20 days before the beginning of a closure. For one closure the behavioris true for the window -20 to +10. For other the same is true but forthe window -10 to +20. Finally, for one last closure all the increase isdone before the beginning.

Moreover, Emerging Market and US High Yield volatility increases dur-ing Emerging Market closures. Figures 4 shows the average EmergingMarket (left) and High Yield (right) 20-day rolling volatility starting 10days before a closure. Again this is a robust behavior across closures.

Emerging Market bonds and High Yield bonds are asset classes thathave, in principle, different fundamentals and therefore their prices (orspreads) should not be very correlated. However, Fact 1 shows thataround closures in the primary market of Emerging Market bonds,

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Fig. 4: EM and HY volatility around Closures

these two asset classes display higher price correlation. In the tablein figure 5, we show average covariance and correlation during normaltimes (days that do not correspond to closures) and during closuresfor different rolling windows. The average covariance and correlationduring closures is always bigger than during normal times regardless ofthe rolling window used to calculate the statistics.3

3In fact the two spreads exhibit almost no correlation before 1997 and very high corre-lation even outside closures after 2002. Clearly, these two asset classes have become morecorrelated even during normal times due to the presence of different investors or differentinvestors’ portfolio strategies. I will not explain this fact in the paper, although I think itis something should be explained.

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Fig. 5: Covariance, correlation and closures.

2. Fact 2: Credit Rating and Emerging Market Spreads

The second stylized fact is that although Emerging Market spreadsincrease around primary market closures, the behavior across the creditspectrum within the asset class is not the same: high-rated EmergingMarket spreads increase less than low-rated Emerging Market spreads.4

For this fact I use weekly data on Emerging Market spreads for differentcredit ratings from the Merrill Lynch data base. Figure 6 shows theaverage weekly percent change in spreads around closures for the BBB-and higher rated Emerging Market bonds and for all the sub-investmentgrade 5 weeks before and after the beginning of a typical closure.

It can be clearly seen that average low-rated spreads increase more thanhigh-rated spreads, and this behavior is robust across closures as well.

4By low-rated I mean everything below BB, BBB- being the lowest rating among thehigh ratings.

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Fig. 6: Percentage Changes in EM around closures.

3. Fact 3: Credit Rating and Emerging Market Issuance

Finally, the last fact I want to draw attention to is that during primaryMarket Closures the drop in issuance is not uniform across the creditspectrum: high-rated Emerging Market issuance drops more than low-rated Emerging Market issuance. In fact we see that, the behavior inissuance is the opposite as the behavior in prices presented in Fact 2.Figure 7 shows that the percentage of total issuance done by investmentgrade emerging countries during normal times is bigger than duringclosures. In fact, this percentage drops in almost 43%.

These facts involve the interaction among three different markets: theprimary market of Emerging Market bonds, (the market in which bonds areissued by countries for the first time), the secondary market of EmergingMarket bonds (the market in which outstanding bonds are traded), and theUS High Yield secondary market. The modeling strategy will proceed asfollows. First, we will model the interaction between the secondary EmergingMarket and the High Yield market and explain Fact 1. Finally, in a secondstep, we will add the primary Emerging Market and explain Facts 2 and 3.

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Fig. 7: Percentage of high ratings issuance.

3 The Problem

We consider a world with a High Yield asset H and one or more EmergingMarket assets E, possibly of differing quality EG and EB. The output of theassets is uncertain. We shall suppose that news arrives which makes everyonebelieve that H is less likely to be productive, but which gives no informationabout E. In this sense, we are considering only idiosyncratic risk. Naturallythe price of H falls. But we ask, why should the price of E also fall, and whyshould the new issuance of E drop, specially of EG?

Consider for example the following tree in figure 8. After U, (with prob-ability q) the ouput of H is 1 for sure, but after D the output of H can beeither 1 or H < 1. The output of E is either 1 or E < 1 irrespective ofwhether U or D is reached. Why should the price of E be less at D than atU or at 1?

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Fig. 8: Economy and Assets Payoffs.

4 Collateral Equilibrium

In this section we will present the formal general model that will be used asthe main basic theoretical framework in all the examples and simulations.

4.1 Uncertainty

Uncertainty is represented by a tree of date-events or states s ∈ S, includinga root s = 1. Each state s 6= 1 has an immediate predecessor s∗, and eachnon-terminal node s ∈ S\T has a set S(s) of immediate successors. Eachsuccessor t ∈ S(s) is reached from s via a branch σ ∈ B(s); we write t = sσ.We denote the time of s by the number of nodes τ(s) on the path from 1 tos.

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4.2 Assets and Leverage

Each asset j ∈ J delivers a dividend of goods Dsj in each state s ∈ S. The setof assets J is divided into those assets j ∈ J c that can be used as collateraland those assets j ∈ J\J c that cannot. Holding collateralizable asset j ∈ J c

in state s permits an agent to issue φs ≤ mint∈S(s)[pjt + Dtj] promises to

deliver one unit of the consumption good in each immediate successor statet ∈ S(s).

The collateral capacity of an asset j at s is thus endogenous, depending onthe equilibrium prices pj

t , t ∈ S(s).5 There is no risk of default, and thereforethe price of a loan is just given by the riskless interest rate.

Finally, notice that buying 1 unit of j on margin at state s means: sellinga promise of mint∈S(s)[p

jt + Dtj] using that unit of j as collateral, and paying

(pjs − 1

1+rs·mint∈S(s)[p

jt + Dtj])

in cash. The margin at s is, therefore,

mjs = (pj

s − 11+rs

·mint∈S(s)[pjt + Dtj])/p

js

4.3 Agents.

4.3.1 Utilities

Each agent i ∈ I has von Neumann Morgenstern utility ui(x) for consumptionof x units of the consumption good in each state s ∈ S. With discountingthis brings utility δ

τ(s)i ui(x) Agent i assigns subjective probability qs to the

transition from s∗ to s. (Naturally q1 = 1). Letting qs be the product of allqs′ along the path from 1 to s, the utility to agent i of consumption x ∈ RS

+

can be written as

U i(x) =∑

s∈S qsδτ(s)i ui(xs)

5Geanakoplos (2003) showed that with heterogeneous priors, even if agents were allowedto use j to collateralize any promise of the form λ · (1, 1), they would choose exclusivelyλ = mint∈S(s)[p

jt + Dtj ]. It is worth mentioning that we will find inefficiencies arising in

equilibrium even when default is not present in equilibrium.

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4.3.2 Endowments

Agent i begins with an endowment of the consumption good eis in each state

s ∈ S, and an endowment of assets at the beginning yi1∗ ∈ RJ

+. We supposethat all assets are present,

∑i∈I yi

1∗ >> 0.

4.3.3 Budget Set.

Bi(p, r) = {(x, y, φ) ∈ RS+ ×RSJ

+ ×RS : ∀s

(xs − eis) +

∑j∈J

pjs(ysj − ys∗j) ≤ 1

1 + rs

φs − φs∗ +∑j∈J

ys∗jDsj

φs ≤∑j∈Jc

ysj mint∈S(s)

[pjt + Dtj]}

The first line of the budget set says that expenditures in consumptionminus endowments of the good, plus total expenditures on assets minus en-dowments of assets, has to be less or equal than the money borrowed sellingpromises, minus the payments due at s from promises done in the previousperiod, plus the total asset deliveries. The second line says that the totalamount of promises made at s cannot exceed the total collateral capacity ofall collateralizable asset holdings.

Finally, agents have rational expectations and foresee asset prices andthe interest rate. They solve the problem that consists of maximizing theirutility function over the budget set just described.

4.4 Collateral Equilibrium.

A Collateral Equilibrium in this economy is a set of prices and holdings suchthat

((p, r), (xi, yi, φi)i∈I) ∈ RSJ+ ×RS

+ × (RS+ ×RSJ

+ ×RS)I : ∀s∑i∈I

(xis − ei

s) =∑i∈I

∑j∈J

yis∗jDsj

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∑i∈I

(yisj − yi

s∗j) = 0∑i∈I

φis = 0

(xi, yi, φi) ∈ Bi(p, r)

(x, y, φ) ∈ Bi(p, r) ⇒ U i(x) ≤ U i(xi)

Markets of the consumption good, assets and promises clear in equilib-rium, and agents optimize their utility constrained to their budget set asdefined above.

It is worth noticing that depending on which constraints (that define theagents budget set) are binding, we get different regimes. Of greatest impor-tance is when an asset is not held, ysj = 0. Next in importance is when the col-lateral constraint (i.e. the borrowing constraint) φs ≤

∑j∈Jc ysj mint∈S(s)[p

jt +

Dtj] is binding. We will come back to this point later in the discussion ofequilibrium in the paper.

Finally, a Collateral Equilibrium always exists in this model. For thiswe rely on a theorem by Geanakoplos and Zame (1998). As it is known,this result is not true for the standard General Equilibrium model with in-complete markets. Hart (1975) showed that an equilibrium may fail to existwithout a bound on short sales, and the best result in the standard modelis only generic existence. The reason why equilibrium always exists in thismodel is because the requirement that assets sales be collateralized placedan endogenous bound on short sales.

5 Two Benchmark Cases

Let us now go back to our problem described in section 3. Suppose we havetwo assets E and H as described before in figure 7. Intuitively, since E andH are independent assets, one would expect uncorrelated price behavior inequilibrium. And in fact this intuition is confirmed by the following twoexamples.

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5.1 Representative Agent Model.

Suppose we had a model, like the one just described, with a representativeinvestor that holds all the assets and the consumption good in equilibrium.In figure 9 we show equilibrium prices for an agent with logarithmic utilities,no discounting, and parameters of E = .1, H = .2, e = 2020 and probabilitiesq = .9.

Fig. 9: Equilibrium with a representative agent.

The prices are actually slightly negatively correlated. The reason for thisis very simple. At D future consumption is lower (since H is less productive)and so the marginal utility for future output like from E is slightly higher.

5.2 Complete Markets Model.

Now consider a model like the one described but with complete markets. Inthis case, again we will not have a strong case for price correlation either.Suppose we have an economy with heterogeneous agents, an optimist that

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assign probability qO = .9 to good news about H and a pessimist that assignsprobability qP = .5 to the same event. The rest of the parameters are asbefore, E = .1, H = .2. Finally, endowments are eO = 20, and eP = 2000.Figure 10 shows the equilibrium prices for this Arrow-Debreu Economy.

Fig. 10: Equilibrium with complete markets.

The prices exhibit almost no correlation at all. The reason for the slightlypositive correlation is that naturally, with complete markets, agents transferwealth to the states which they think are more probable. Therefore, at Dprices reflect more the pessimist preferences (and therefore may be slightlylower than at U). However, as we make the pessimist richer and richer,he will become sort of a representative agent and all prices will reflect hispreferences. In the limit the correlation will be zero. As we will see laterin the paper, making pessimists richer will not kill the contagion in a modelwith incomplete markets.

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6 Correlated Prices with Uncorrelated Fun-

damentals

As the the two benchmark cases illustrate, price correlation without corre-lated fundamentals is not a general phenomenon. We need assumptions inorder to get the result.

6.1 Incomplete Markets.

In our model markets are incomplete, this is, at any equilibrium, there isa node at which agents, at equilibrium prices, cannot create all the Arrowsecurities that span the dimension of the set of future states.

6.2 Heterogeneous Crossover Investors

Agents in the model are heterogeneous crossover investors: they may differ inbeliefs, utilities and endowments, and can hold different assets in equilibrium.We will think basically about two types of crossover investors: Optimists,who attach higher probability of U than the Pessimists, so qO > qP . Finally,we call investors crossovers, since they can (and will) in equilibrium partici-pate in both asset markets. This last assumption will play a very importantrole in our results, and it is not unrealistic. By 2002, crossover investorscounted for more than 50% of the investor base in emerging markets.6

6.3 Conjunction Risk.

The tree described in figure 7 represents what we call Conjunction Risk. Theidea is very simple: when good news arrives, uncertainty declines. H paysfully 1 unless two independent pieces of bad news (D) occur. As a result,each bad news generates more volatile posterior beliefs about H fully paying.Suppose that q = .9. Then the probability of H fully paying at 1 is 99/100;the posterior beliefs due to the first piece of information are 1 and 9/10. At

6For this see IMF (2003).

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D the probability is 9/10, and the posterior beliefs due to the second pieceof bad news are 1 and 0.

Finally, leverage permits optimists to afford to buy all of an asset despitesmall wealth. But it also jacks up asset prices. It causes a transfer of wealthfrom s = 1 to states where the asset pays higher than its minimum; since itmeans less money carried over than would have been, it effectively transferswealth of optimists from D to U. On the other hand, in a crisis it also permitsthe optimist to borrow his way out of trouble. Therefore, it is not necessarilythe case that leverage creates more problems, and as we will see later, itis not necessary for the correlation result. It will be crucial though in thesecond part of this paper jointly with the presence of adverse selection.

7 Simulation

We numerically solve the equilibrium in the case in which all investors havelogarithmic utilities. The parameters values are:

• H = .2, E = .1,

• δ = 1.

• q0 = .9, qP = .5.

• eOs = 20 and eP

s = 2000, for all s.

For simplicity we will assume that E is more leveraged than H, in partic-ular that H cannot be used as collateral for any promise. The result does notdepend on this assumption at all: the presence of price correlation does notdepend on margins. However, as we will see in the second part of the paper,different margins will have important quantitative consequences. Moreover,it is not an unrealistic assumption. High Yield bonds tend to have betterrecovery than Emerging Markets: this tend to make their margins lower.However, they are a very illiquid class, less liquid than Emerging Markets:this tend to make High Yield margins higher. In reality “haircuts” tend tobe around 15% for High Yield bonds, 10% for high rated Emerging Marketsbonds and 20% or more for low rated Emerging Markets bonds.

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We are assuming that H’s recovery value is bigger than E’s recovery.The results do not hinge on this either, but we think it is realistic to assumethat the recovery value of a domestic company is bigger than the recoveryvalue of a foreign country, since there are not such things as internationalbankruptcy courts. Optimists are indeed optimists, since q0 = .9, qP = .5.Finally, we are assuming that pessimists are richer than optimists. What wehave in mind here, is that optimist will be the class of natural investors inEmerging Markets (dedicated investors maybe), whereas pessimists are the“normal” public who invest say in the US Stock Market. As we said before,while the Emerging markets accounts for a hundred billions of dollars, theUS Stock Market accounts for ...... The portfolio and consumption decisionsin each node are shown in figure11. Prices are shown in figure 12.

Fig. 11: Real allocations.

In equilibrium it turns out that the prices of E and H rise at U and fallat D. Since optimists think U is more likely, they will tend to hold the assetsand borrow to buy them. Optimists never lend in equilibrium, and pessimistsnever borrow. Optimists hold all assets and leverage to the max in nodes 1and D. In node U they only hold E and still leverage to the max on it, butpessimists hold all of H. At this node the optimists are bullish on E, but

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Fig. 12: Equilibrium prices.

both investors agree on the future of H. Finally, we can see that the optimistsconsume much less along the path 1 − D. These portfolio allocations andconsumption decisions will have a profound effect on asset prices.

In figure 10 we can see asset prices in equilibrium. Along the path ofbad news about H, 1 to D, the price of H falls. It goes from .93 to .74,falling 21.5%. There are several surprising things in this equilibrium. First,the price of E falls as well from 1 to D, even when there was no specific badshock to it. It goes from .85 to .74, a decline of 12.8%. Second, the price ofE at U is bigger than at D. Third, the gap in the price of H between U andD is bigger than the gap in the prices of E between the same states, evennet of the fall in the productivity of H. The explanation of the third fact isthat E is more leveraged than H. We discuss it later in the paper.

Notice also that the interest rate is always nearly zero, since the pessimists(the lenders in equilibrium) are very rich and do not discount the future.

The simulation should remain the reader of Stylized Fact 1. Let us exploremore this result.

24

8 Why Contagion?

Our explanation for contagion relies on the dependence of portfolio regimeson news about H and on the redistribution of wealth the news creates. Whatis crucial is that optimists are richer at U than at D, and they hold less Hafter good news than after bad news. When this portfolio reallocation failsto occur, contagion may disappear as well.

Leverage is not indispensable for contagion. But it may strengthen it.With leverage an agent who is optimistic about good news can transferwealth from 1 exclusively into U , thus increasing his wealth advantage atU compared to D. Leverage can also reduce contagion, because it allows thepoor optimist at D to borrow his way into investing in E. But we shall seethat leverage will not eliminate contagion.

8.1 Asset Prices and Collateral.

Asset prices not only reflect their future return, but also their ability to beused as collateral to borrow money.

Consider a collateral equilibrium in which an agent i∗ holds an asset j atstate s ∈ S, yi∗

sj > 0. If the asset j cannot be used as collateral, then

pjs =

∑σ∈B

qi∗sσ [psσj+Dsσj ]dui∗ (xi∗

sσ)/dx

dui∗ (xi∗s )/dx

where B = B(s) is the set of branches leaving s. The expected marginalutility of its payoff next period must be equal to the marginal utility of itsprice today. This equation remains true if j can be used as collateral but thecollateral constraint for i∗ is not binding at s. In that case we have that thefirst order condition for borrowing also holds,

( 11+rs

)(1/xi∗s ) =

∑σ∈B

qi∗sσdui∗ (xi∗

sσ)/dx

dui∗ (xi∗s )/dx

When an asset can be used as collateral, and the collateral constraint isbinding, the situation for holding of j and for loans is quite different. Theagent i∗ cannot take out a loan unless he holds collateral. Thus even if the

25

marginal disutility of repaying the loan is less than the marginal utility ofthe money borrowed, it may be impossible to borrow more money. Similarly,by buying j, i∗ makes it possible to take out a loan, hence he may buy j onmargin even when the expected marginal utility of j is less than its price.Then we might well get

psj >∑

σ∈Bqi∗sσ [psσj+Dsσj ]dui∗ (xi∗

sσ)/dx

dui∗ (xi∗s )/dx

The traditional first order condition for holding j does not hold. Similarly,the price of a unit of consumption owed might be less than the marginalutility of the price such a promise fetches:

( 11+rs

)(1/xi∗s ) >

∑σ∈B

qi∗sσdui∗ (xi∗

sσ)/dx

dui∗ (xi∗s )/dx

Denote this last difference (LHS-RHS) by the Liquidity Preference of i∗ ats, LP i∗

s . Agent i∗ might well prefer to have cash immediately rather than thecash plus interest next period, simply because he cannot borrow against thefuture without collateral. In fact, when yi∗

sj > 0 and the collateral constraintis binding, the first order condition that holds shows that the marginal utilityof the cash payment necessary to buy j is equal to the expected marginalutility of the unencumbered payoff, i.e. the return on j less the repaymentof the debt.

Let us define the debt of agent i backed by a marginal unit of asset j as

φi∗sj ={

0 if j 6∈ J c or if the collateral constraint is not biding at s for i∗

mint∈S(s)[pjt + Dtj] otherwise

Then in equilibrium we must have

psj − 11+rs

φi∗sj =

∑σ∈B

qi∗sσ [psσj+Dsσj−φi∗

sj ]dui∗ (xi∗sσ)/dx

dui∗ (xi∗s )/dx

A useful way of rewriting the last equality is

pjs(dui∗(xi∗

s )/dx) ==

∑σ∈B qi∗

sσ[psσj + Dsσj]dui∗(xi∗sσ)/dx+

+{( 11+rs

φi∗sj)(dui∗(xi∗

s )/dx)− [∑

σ∈B qi∗sσ[φi∗

sj]dui∗(xi∗sσ)/dx]} =

= PV js + CV j

s

26

where PV js is i∗’s expected marginal utility of j′s payoff after s, the Payoff

Value, and CV js is the Collateral Value of j, where CV j

s = LP i∗s · φi∗sj.

Thus, letting MU i∗s = dui∗(xi∗

s )/dx, we can write

pjs = PV j

s

MU i∗s

+ CV js

MU i∗s

8.2 Contagion

It is evident that pHs will be higher in up nodes than in down nodes, and

that pH1 > pH

D , since down moves lower the fundamental value of H. Thefundamental value of E is not affected by down moves before period 3, yet,in the equilibrium shown in the simulation, pE

s behaves the same way. Herewe explain why.

Our simulation is not just a fluke. In fact the contagion property isquite robust to other choices of the parameters. To show this, let us fix theparameters

• H = .2, E = .1,

• δ = 1.

• q0 = .9,

• eOs = 20

this is, parameters describing assets, preferences and beliefs and wealthof the optimist investor. Now define q = qO − qP as the difference in beliefsor the degree of disagreement among agents. Also define w = eP − eO, as thedifference in wealth among investors.

Figure 13 shows different equilibrium regimes depending on these two lastvariables. The vertical axis measures disagreement, q, and the horizontal axisthe difference in wealth, w.

All the red area, all the regions numbered from 1 to 12, are regions inwhich contagion holds in equilibrium. The different regions correspond todifferent regimes in terms of asset holdings and whether collateral constraints

27

Fig. 13: Equilibrium Regimes for qO = .9 and eO = 20.

are binding or not. In the appendix each regime is precisely described as wellas the amount of contagion that prevails in each of them. The simulationpresented in section 7 corresponds to region 1. As we can see, contagionholds almost everywhere. The only region in which it does not hold is in theorigin and in the two lower regions painted in blue. Of course, at the originwe are back to the case of complete markets with a representative agent. Forlower enough disagreement, contagion may fail to hold as well. In fact, forthese parameter values shown in the figure it breaks down for qP = .8999.

Once again, we clearly see that incompleteness and some degree of dis-agreement is crucial for contagion to hold in equilibrium. We could showa similar plane for different values of qO and eO, and of course the regimeswould be different, but the same idea would be true.

Notice that in all the regimes in which contagion holds, it is true thatthe optimist consume more at U than at D and consume less at those statesfollowing U than in those following D. Of course, this consumption allocationis due to the portfolio holdings in equilibrium, this is, the optimist in allthese regimes, buy more assets in D than in U . Proposition 1 relates this

28

consumption allocation (which of course is endogenous) with the desired priceproperty.

Proposition 1: Price Correlation.

Consider a model with states U and D spawning branches B(U) = B(D) =B. Assume that for some agent O, qO

Uσ = qODσ for all σ ∈ B. Suppose that in

equilibrium an asset E satisfies pUσE + DUσE ≥ pDσE + DDσE for all σ ∈ B,and yO

DE > 0. Suppose that rU = rD , xOU > xO

D and xOUσ ≤ xO

Dσ,∀σ ∈ B.Then pE

U > pED.

Moreover if r1 = 0, and U and D are the only successors of 1, then pE1 > pE

D.

Proof: Follow from Lemma 1- Lemma 4 and Corollary presented inappendix.

The proposition also relies on several more hypotheses. The general risk-less interest rate should not change with the news about H. And for theconclusion that the price of E falls over time, we naturally require the inter-est rate to be zero. More generally, we would need to make an assumptionabout the interest rate and the dividend yield of E in order to avoid trivialcases where the price of E falls because it pays a low dividend. In the propo-sition, the price of E falls no matter what the dividends are, assuming theycan never be negative. Note finally, that the proposition holds whether ornot E or H can be used as collateral.

A way of thinking about this proposition is the following. If bad newsabout H causes some E investor to increase their holdings of H, while re-ducing their present consumption, then the price of E must go down. Thesimulation capture an explanation for how this might happen. If bad newsabout H causes some (perhaps dedicated) investors to flee H (even at itslower price), this will create an opportunity for crossover E investor to holdmore H. If they are also poorer, this will force them to reduce their in-vestment in E, pushing its price down as well. They are indeed likely tobe poorer if they had been investing in H as well as in E, since bad newsabout H will drive its price down. The scenario depicted in the simulationdepends critically on heterogeneous investors responding differently to newinformation.

Finally, the proof of the first part of the proposition without leverage issimple. Higher xO

U and lower xOUσ means lower marginal utility at U and

29

higher marginal utility in the future, raising all asset values. The only sub-tlety in the proof comes from showing that this conclusion is not changed byleverage.

9 Adverse Selection and Market Closures.

In this section we extend the first model to incorporate the primary marketof Emerging Market bonds. Now we will explicitly model the supply ofthe Emerging Market asset. Two elements are going to be crucial in thisextension of the two results: leverage and adverse selection.

9.1 Emerging Countries.

In each state, s, two emerging countries k = G, B supply assets. To avoidreputation issues, we assume that in each state different countries enter themarket.

9.1.1 Utilities

Each country ks has von Neumann Morgenstern utility uks(x) for consump-tion of x units of the consumption good in state s and in states t ∈ T (s),where T (s) is the set of terminal nodes that follow s. This is, countries con-sume only at the period of issuance and at the end. With discounting, thisbrings utility from consumption xα in any state α ∈ {s}∪T (s) to δ

τ(α)ks uks(xα).

Country ks assigns subjective probability qksα to the transition from any state

α∗ to α. (Naturally q1 = 1). Letting qα be the product of all qα along thepath from 1 to α, the utility to country ks of consumption can be written

Uks(x) =∑

α∈{s}∪T (s) qksα δ

τ(s)ks uks(xα)

9.1.2 Endowments

Each country ks has an endowment of the consumption good only at eachterminal node, and has 1 unit of asset to sell to investors at its issuance dates. We denote the issuance at s by zks. The asset of country ks deliversdifferently depending on k, but not on s. So Dks

α = Dkα,∀αs ∈ S.

30

9.2 Heterogeneous crossover investors

Investors are described by the same characteristics as before, except for theirendowments. In this model they do not have initial endowments of theemerging market asset and they have 1 unit of H in each period (not only atthe beginning).

9.3 Types and Asymmetric Information.

In each state there are two types of countries, “good”, G, and “bad”, B,countries. For tractability purposes we assume that the payoffs of all thecountries are perfectly correlated. These two types differ in their deliveries.The good type always pay at least as much as the bad type. So, DsG ≥DsB,∀s. We assume that the deliveries of countries of the same type are thesame (even if they were issued at different states). Thus, the payoffs of allexisting good assets are identical, and will trade at the prices psG, while thepayoffs of all the existing bad assets are identical, and will trade at the sameprices psB. The prices psG and psB may or may not be the same.

There is asymmetric information: investors cannot perfectly observe thetype of credit they are trading. It is important to understand that the in-formation asymmetry is between investors and countries and not among in-vestors.

Now let us go back to our original problem described in figure 8 andsee how that example is extended. The time and uncertainty structure isthe same as before. In each period three assets are traded: good EmergingMarket, G, bad Emerging Market, B, and High Yield, H. The final payoffsof any Emerging Market bond and the High Yield bonds are completelyindependent, and occur in period 3.

The Emerging Market bonds are perfectly correlated; either they all pay1, or else they all pay a recovery value. The two types differ in their recoveryvalue. The good type pays G < 1 whereas the bad type pays B < G < 1.Figure 14 describes emerging countries issuance and asset payments.

31

Fig. 14: Countries issuance and asset payoffs.Payoffs B < G < 1, H < 1.

9.4 Adverse Selection and Perfect Competition.

At this point we face a problem: how can we make compatible the adverseselection problem arising from the asymmetric information with a perfectcompetition framework described in the previous sections?

In order to solve this we will follow closely the modeling strategy used byDubey-Geanakoplos (2002). In that paper they used a competitive frame-work to study insurance. Here I will use the same strategy to study creditmarkets and rationing. The results in that paper extend to this frameworkas well.

In each state, there are many different debt markets, each characterizedby a quantity and its associated market clearing price:

{(zs, ps(zs)); zs ∈ (0, 1] and ps ∈ <+}.

All agents take the price schedule as given and emerging countries andinvestors decide in which of these debt markets they will participate. We

32

further assume that countries can issue (sell) in only one debt market at anygiven time, that is, they must choose a quantity zs to sell and then acceptthe corresponding clearing market price ps(zs). Investors who buy assetsin market zs get a pro rate share of the deliveries of all assets sold in thatmarket. Thus if only one country type chooses to sell at the quantity zs,then it reveals its type, and from then on, its asset payoffs are known to bethe corresponding type.

Now we are able to describe precisely the budget set of country ks

Bks(p) = {(x, z) ∈ R1+T (s)+ ×R+ :

xs ≤ ps(z)zz ≤ 1

∀α ∈ T (s) : xα = eksα + (1− z)Dαk}

The first line of the budget set says that expenditures in consumption atthe period of issuance has to be less or equal than the income from issuanceof quantity z. The second line says that the issuance at s cannot exceed thetotal endowment of the asset k, that is 1. The third line says that the totalconsumption at each terminal node that follows s has to be less or equal thanthe endowment of the consumption good plus the deliveries on the remainingof the asset that was not sold at s.

With this interpretation there is room for adverse selection since coun-tries, by publicly committing to small quantity markets, may signal morereliable deliveries.

The quantities characterizing each market are exogenous and the asso-ciated prices are set endogenously as in any traditional competitive model.However, it may occur that in equilibrium only a few debt markets are ac-tive, even when all the markets are priced in equilibrium. In this sense, thequantities are set endogenously as well, without the need of any contractdesigner. Market clearing and optimizing behavior are enough.

The equilibrium is pooling if at any state s two countries of differenttype decide to sell the same amount. The equilibrium is separating whendifferent types, ks and k′s, always issue different amounts in the same state.

33

The model in this paper exhibits a unique7 equilibrium. It is a separatingequilibrium.

9.5 Separating Collateral Equilibrium

With this in mind we will give a precise definition of separating equilibrium.In such an equilibrium, an Incentive Compatibility Constraint needs to hold:the bad type prefers the quantity it chose in equilibrium to the one chosenby the good type. So it prefers to sell zsB unit of its asset B at a lower pricepB

s than to sell zsG of its asset at price pGs . Analogously, the good type must

prefer (strictly perhaps) to sell zsG at a good price psG than more at the badprice pB

s . In equilibrium it will turn out that the incentive compatibility ofthe bad type will be the only binding one.

More formally, a Separating Collateral Equilibrium is defined by a stan-dard collateral economy consisting of agents I = {O,P,G1, B1, GU,BU, GD,BD},with assets J = {H, G1, B1, GU,BU, GD,BD}. Assets G1, GU and GD payidentical dividends of 1 or G, while assets B1, BU and BD pay identicaldividends of 1 or B.

A Separating Collateral Equilibrium is defined as a standard CollateralEquilibrium ((p, r), (xi, yi, φi)i∈I) with the following extra requirements:

1. agents i ∈ I\{O,P} are not free to choose their yi. Agent i = ks mustpick yi

αks = 1 − zks for all α equal to s or non-terminal followers of s.For all other αks, he must set yi

αks= 0.

2. A separating equilibrium must satisfy the separating property, zks 6=zk′s, if k′ 6= k.

3. yiαBs = 1 − zB

s would be the optimal portfolio choice of B if he couldsell all he wanted at the the price pB

s = p(zBs ).

4. Finally, incentive compatibility constraint have to hold for every type.

7Actually a refinement of the equilibrium is needed, but we do not give details here.We simply look only for a separating equilibrium.

34

Finally, let us stress why this definition is so important. The fact thatwe know that the model exhibits a unique and separating equilibrium is ofextreme importance from a computational point of view. If we didn’t knowthis fact we had to calculate a whole set of quantities and prices which ofcourse has infinite dimension. Now we reduce the problem to calculate afinite set of variables as we had before. So let us now proceed with thesimulation.

9.6 Simulation

We numerically solve the equilibrium in the case in which all investors havelogarithmic utilities. As before we assume that H cannot be used as collat-eral, whereas G and B can. The parameters values are:

• Asset payoffs, H = G = .2, B = .05

• δ = 1

• q0 = .9, qP = .5

• Endowments for the optimists are eOs = 50; for all s.

• Endowments for the pessimists are ePs = 2000, for all s.

• Countries utilities are quadratic : Uks = (xs−βx2s)+

∑s′∈T (s)(xs′−βx2

s′),β = 1/650.

• Endowments for all countries are ekss′∈T (s) = 50.

• Countries have the same beliefs as optimists: qks = .9. (Results do notdepend on this)

The results can be seen in figure 15 and 16.

The regime is the same as in the first model: optimists hold all assets andleverage to the max in nodes 1 and D. In node U they only hold G and Band still leverage to the max, and pessimists hold all of H. These portfolioreallocations and consumption decisions will have, again, profound effects onasset prices.

35

Fig. 15: Investors portfolios and consumption.

The price behavior described in sections 7 and 8 is still present here:contagion holds. The prices of both types, G and B fall even if the bad newsis only for H. However there are two new things in this equilibrium.

The first one is that the price of B falls more than the price of G: Bfalls 9.46% and G only 7.68%. So the spreads between types goes from .0234at 1 to 0.0367 at D. Contagion makes both prices to fall, and as we willexplain, different leverage make the fall different. Of course, this shouldremind the reader of Stylized Fact 2. As we said before margins are 10% forhigh-rated Emerging Markets bonds and 20% or more for low-rated EmergingMarkets bonds. As we will see now, this difference in leverage is what maybe explaining Fact 2.

The second new thing is the drop in issuance of the good type.8 Thebad type issuance is always equal to 1 and the good type issuance goes from

8In fact in equilibrium the issuance of the bad type does not drop, but for differentparameter values it may be that the unconstrained optimal quantity of issuance is lessthan one

36

Fig. 16: Equilibrium prices and Issuance.

zG1 = .79 all the way to zG

D = .07. Of course this result, should remind us ofstylized fact 3.

Finally, let us notice, that as in the previous model, the simulation isrobust to parameters. We will save the reader from the discussion of differentregimes that produce the result since there is nothing conceptually new.

9.7 Why Closures?

Our explanation is twofold.

First, leverage will now play the shinning role.We show that in standardcollateral equilibrium, the prices of high margin (or low leverage) assets fallmore than the prices of low margin (high leverage) assets in liquidity crises,i.e. under conditions given for contagion in proposition 1. This explains whythe price spread between G and B increases at D.

Second, adverse selection enters. With increasing spreads, in order tosatisfy the incentive compatibility constraint at D “good” issuance has to

37

decrease: with pGs so much bigger than pB

s , good countries need to choosezGs < zBs to prevent bad countries from imitating them.

Proposition 2: High margin asset prices fall more.

Consider a standard collateral model with states U and D such that B(U) =B(D) = B and that for some agent O, qO

Uσ = qODσfor all σ ∈ B. Suppose that

in equilibrium there are two assets G and B such that for both l ∈ {G, B},pUσl+DUσl = pDσl+DDσl for all σ ∈ B, and such that yO

GD > 0, yOBD > 0 and

yOGU > 0. Suppose in equilibrium rU = rD, xO

U > xOD, xO

Uσ ≤ xODσ, ∀σ ∈ B,

and (pBUσ + DBUσ − φO

BU) ≥ (pGUσ + DGUσ − φO

GU)Then pB

U − pBD > pG

U − pGD.

Moreover if r1 = 0 and O is fully leveraged at 1 on G and B, then pB1 −pB

D >pG

1 − pGD.

Proof: Follows from Lemma 5, Lemma 6.

The prices of both types, B and G, fall because of spillovers from the Hmarket as we saw before. However, the price of B falls more than the price ofG. The reason for this is that margins for B are higher in equilibrium thanmargins for G. Hence the net delivery of G, which is 1− .2 = .8 or .2− .2 = 0is less than the net deliveries of B, which is 1− .05 = .95 or .05− .05 = 0.

We can also understand this phenomenon via collateral value as presentedin section 8. When the optimists suffer a liquidity problem, the collateralvalue of G is bigger than the collateral value for B. We can see this effect veryclearly in our simulation. While CV G/MUO goes from .0188 in 1 to .0311 inD (increases), CV B/MUO goes form .0179 in 1 to .0075 in D (decreases!). Itis this difference in collateral value that explains the increasing gap in prices.

Corollary: Type-Issuance differential.

Under all the conditions of Proposition 2, zB1 − zG1 < zBD − zGD.

Proof: The statement about the decrease in issuance of the good typefollows from the standard adverse selection argument. Note that the utilityfunction satisfies the single crossing property and in equilibrium the incentivecompatibility condition for the bad type is the one binding.

38

The greater the price difference between types the more drastic the quan-tity reductions. With the increase in the gap between prices of B and G, theincentive for the bad type to pretend to be the good type is bigger, there-fore the cost of separation increases. The quantity, zGs, of G issuance thatsatisfies the incentive compatibility constraint becomes much smaller whenthe gap in prices increases, creating the quantity reduction characterizingclosures.

10 Conclusion

The goal of this paper is to model closures in the primary market of EmergingMarket bonds and to provide empirical evidence and a theoretical explana-tion of why these closures can be associated with events in mature economies.A primary market closure is a period of 3 weeks or more during which theprimary issuance over all emerging markets is less than 40 percent of theperiods trend. There is a huge literature that tries to explain these clo-sures stressing the demand aspect of them, i.e., how weak emerging marketfundamentals can be responsible for sudden stops of capital flows to theseeconomies. In this paper I take a different approach. I look at the supplyside of the problem and try to understand why certain market closures maybe associated with mature market events. Since 1997, the data reveal somepuzzling stylized facts that seem to suggest this connection. I describe threestylized facts. First, Emerging Markets and High Yield experience experiencehigher spreads, higher volatility and higher correlation around emerging mar-ket primary closures, despite the fact that they have different fundamentals.Second, although Emerging Market spreads increase around primary marketclosures, the behavior across the credit spectrum within the asset class is notthe same: high-rated emerging market spreads increase less than low-ratedemerging market spreads. Third, during closures the drop in issuance is notuniform: high-rated Emerging Market issuance drops more than low-ratedEmerging Market issuance.

The first main result is that when rational crossover investors face a liq-uidity shortage, assets that have very different fundamentals may displaycorrelated price behavior. In the model, bad news only affects High Yield,yet Emerging Market price falls as well. There are two reasons for this.Crossover investors hold H as well as E, so with bad news about H they

39

suffer a negative wealth shock. Moreover, after bad news about H, pes-simists abandon their holdings of H, giving optimists an opportunity in theH market that distracts them from fully investing in E.

The second results states that high margin asset prices fall more thanlow margin asset prices. The reason is that when facing a liquidity shortage,rational investors raise cash by selling off the assets which are unencumberedby loans. Putting it in another way, the price of every asset is the sum of itspayoff value and its collateral value. In liquidity crises, the collateral valueof low margin assets rises, partially offsetting the decline in its payoff value.

The third main result is that an investor liquidity shortage leads to asevere drop in the issuance of the “good” emerging market asset, when thereis adverse selection. The “good” type has to issue less in order to separateitself from the “bad” type: the greater the price difference, the more drasticthe quantity reduction. The first spillover from a High Yield shock will causeboth “good” and “bad” emerging market assets to deteriorate. But since the“bad” type has higher margins, its price will fall further as we noticed in thesecond main result. Hence, the gap in prices between different types risesdramatically, creating the quantity reduction characterizing closures. Thisseems to explain why highly rated issuance drops more during closures.

11 Appendix

11.1 Description of Regimes in Figure 13.

Here we describe the different regimes presented in figure 13. We describeat each mode what are the asset holdings for each type of investor. Alsowhether they borrow or lend and if the borrowing constraint is binding ornot. Regimes 1 to 12 exhibit price correlation (or contagion) in equilibrium.

• Regime 1.

– Node 1.

Optimist: E, H. Borrows. Borrowing Constraint Binding.Pessimist:–. Lends.

40

– Node U. Optimist: E. Borrow. Binding.Pessimist: H. Lends.

– Node D.

Optimist: E, H. Borrows. Borrowing Constraint Binding.Pessimist:–. Lends.

• Regime 2.

– Node 1.

Optimist: E, H. Borrows. Borrowing Constraint Binding.Pessimist:–. Lends.

– Node U.

Optimist: E, H. Borrows. Binding.Pessimist: H. Lends.

– Node D.

Optimist: E, H. Borrows. Borrowing Constraint Binding.Pessimist:–. Lends.

• Regime 3.

– Node 1.

Optimist: E, H. Borrows. Borrowing Constraint Binding.Pessimist:–. Lends.

– Node U.

Optimist: E. Borrows. Not Binding.Pessimist: H. Lends.

– Node D.

Optimist: E, H. Borrows. Borrowing Constraint Binding.Pessimist:–. Lends.

• Regime 4.

– Node 1.

Optimist: E, H. Borrows. Not Binding.Pessimist:–. Lends.

41

– Node U.

Optimist: E, H. Borrows. Binding.Pessimist: H. Lends.

– Node D.

Optimist: E, H. Borrows. Borrowing Constraint Binding.Pessimist:–. Lends.

• Regime 5.

– Node 1.

Optimist: E,H. Borrows. Not Binding.Pessimist: -. Lends.

– Node U.

Optimist: E,H. No borrowing.Pessimist: H.

– Node D.

Optimist: E, H. Borrows. Binding.Pessimist: -. Lends.

• Regime 6.

– Node 1.

Optimist: E,H. Borrows. Binding.Pessimist: -. Lends.

– Node U.

Optimist: E,H. No borrowing.Pessimist: H.

– Node D.

Optimist: E, H. Borrows. Binding.Pessimist: -. Lends.

• Regime 7.

– Node 1.

Optimist: E,H. Borrows. Binding.Pessimist: -. Lends.

42

– Node U.

Optimist: E. Borrows. Binding.Pessimist: H. Lends.

– Node D.

Optimist: E, H. Borrows. Binding.Pessimist: H. Lends.

• Regime 8.

– Node 1.

Optimist: E,H. Borrows. Binding.Pessimist: -. Lends.

– Node U.

Optimist: E. No Borrowing.Pessimist: H.

– Node D.

Optimist: E, H. Borrows. Binding.Pessimist: H. Lends.

• Regime 9.

– Node 1.

Optimist: E,H. Borrows. Binding.Pessimist: -. Lends.

– Node U.

Optimist: E,H. No Borrowing.Pessimist: H.

– Node D.

Optimist: E, H. Borrows. Binding.Pessimist: H. Lends.

• Regime 10.

– Node 1.

Optimist: E,H. Borrows. Binding.Pessimist: H. Lends.

43

– Node U.

Optimist: E. Borrows. Binding.Pessimist: H. Lends.

– Node D.

Optimist: E, H. Borrows. Binding.Pessimist: H. Lends.

• Regime 11.

– Node 1.

Optimist: E,H. Borrows. Binding.Pessimist: H. Lends.

– Node U.

Optimist: E. No borrowing.Pessimist: H.

– Node D.

Optimist: E, H. Borrows. Binding.Pessimist: H. Lends.

• Regime 12.

– Node 1.

Optimist: E,H. Borrows. Binding.Pessimist: H. Lends.

– Node U.

Optimist: E, H. No borrowing.Pessimist: H.

– Node D.

Optimist: E, H. Borrows. Binding.Pessimist: H. Lends.

• No Contagion.

– Node 1.

Optimist: E,H.Pessimist: E, H. There is not borrowing.

44

– Node U.

Optimist: E, H.Pessimist: E,H. No Borrowing.

– Node D.

Optimist: E, H. Lends.Pessimist: E, H. Borrows. Not Binding until w = 40. Bindingafter that.

11.2 Lemmata

Consider a model with states U and D such that B(U) = B(D) = B. Supposethat rU = rD. Suppose that for some agent i∗, qi∗

Uσ = qi∗Dσfor all σ ∈ B, and

that xi∗U > xi∗

D and xi∗Uσ ≤ xi∗

Dσ for all σ ∈ B.

Lemma 1:Consider two assets j and k such that in equilibrium pUσj + DUσj ≥ pDσk +DDσk for all σ ∈ B, and such that yi∗

Dk > 0. Suppose j /∈ J c and k /∈ J c. ThenpUj > pDk.

Proof: By the first order conditions for equilibrium,

pUj ≥∑

σ∈B qi∗Uσ[pUσj + DUσj]dui∗(xi∗

Uσ)/dx

dui∗(xi∗U )/dx

≥∑

σ∈B qi∗Uσ[pDσk + DDσk]dui∗(xi∗

Uσ)/dx

dui∗(xi∗U )/dx

>

∑σ∈B qi∗

Dσ[pDσk + DDσk]dui∗(xi∗Dσ)/dx

dui∗(xi∗D)/dx

= pDk

Lemma 2:Consider two assets j and k such that in equilibrium pUσj + DUσj ≥ pDσk +DDσk for all σ ∈ B, and such that yi∗

Dk > 0. Suppose j ∈ J c. Then pUj > pDk.

Proof: for each s ∈ S, and each asset j′ ∈ J, recall that φi∗sj′ = 0

if j′ /∈ J c or if the aggregate collateral constraint is not binding, φi∗s <∑

j∈Jc yi∗sj minσ∈B(s)[psσj +Dsσj], and φi∗

sj′ = minσ∈B(s)[psσj′ +Dsσj′ ] otherwise.

45

Suppose j ∈ J c and the collateral constraint is binding at U. Then φi∗Uj ≥

φi∗Dk. Then by the first order conditions for equilibrium,

pUj ≥∑

σ∈B qi∗Uσ[pUσj + DUσj − φi∗

Uj]dui∗(xi∗Uσ)/dx

dui∗(xi∗U )/dx

+1

1 + rU

φi∗

Uj

≥∑

σ∈B qi∗Uσ[pUσj + DUσj − φi∗

Dk]dui∗(xi∗Uσ)/dx

dui∗(xi∗U )/dx

+1

1 + rU

φi∗

Dk

≥∑

σ∈B qi∗Uσ[pDσk + DDσk − φi∗

Dk]dui∗(xi∗Uσ)/dx

dui∗(xi∗U )/dx

+1

1 + rU

φi∗

Dk

>

∑σ∈B qi∗

Dσ[pDσk + DDσk − φi∗Dk]dui∗(xi∗

Dσ)/dx

dui∗(xi∗D)/dx

+1

1 + rU

φi∗

Dk

=

∑σ∈B qi∗

Dσ[pDσk + DDσk − φi∗Dk]dui∗(xi∗

Dσ)/dx

dui∗(xi∗D)/dx

+1

1 + rD

φi∗

Dk

= pDk

Corollary:Suppose that in equilibrium pUσj + DUσj ≥ pDσj + DDσj for all σ ∈ B, andsuch that yi∗

Dj > 0. Then pUj > pDj.

Lemma 3:Consider two assets j and k such that in equilibrium pUσj + DUσj ≥ pDσk +DDσk for all σ ∈ B, and such that yi∗

Dk > 0. Suppose the collateral constraintis not binding for i∗at U, φi∗

U <∑

j∈Jc yi∗Uj minσ∈B(U)[pUσj +DUσj]. Then pUj >

pDk.

Proof:

pUj ≥∑

σ∈B qi∗Uσ[pUσj + DUσj]dui∗(xi∗

Uσ)/dx

dui∗(xi∗U )/dx

=

∑σ∈B qi∗

Uσ[pUσj + DUσj − φi∗Dk]dui∗(xi∗

Uσ)/dx

dui∗(xi∗U )/dx

+1

1 + rU

φi∗

Dk

≥∑

σ∈B qi∗Uσ[pDσk + DDσk − φi∗

Dk]dui∗(xi∗Uσ)/dx

dui∗(xi∗U )/dx

+1

1 + rU

φi∗

Dk

>

∑σ∈B qi∗

Dσ[pDσk + DDσk − φi∗Dk]dui∗(xi∗

Dσ)/dx

dui∗(xi∗D)/dx

+1

1 + rU

φi∗

Dk

=

∑σ∈B qi∗

Dσ[pDσk + DDσk − φi∗Dk]dui∗(xi∗

Dσ)/dx

dui∗(xi∗D)/dx

+1

1 + rD

φi∗

Dk

= pDk

46

Lemma 4:Suppose that in equilibrium there is an asset j with pUσj+DUσj ≥ pDσj+DDσj

for all σ ∈ B, and such that yi∗Dj > 0. Furthermore, suppose U and D are

the only immediate successors of some s, for example s = 1. Suppose rs = 0.Then psj > pDj.

Proof: There must be some agent i0 for whom the collateral constraintis not binding at s, while maintaining a positive consumption. For every i,including i0,

psj ≥qi0

U [pUj + DUj]dui0(xi0

U )/dx + qi0

D [pDj + DDj]dui0(xi0

D)/dx

dui0(xi0s )/dx

But for i0,qi0

U dui0(xi0

U )/dx + qi0

Ddui0(xi0

D)/dx

dui0(xi0s )/dx

= 1

showing that psj > [pDj + DDj] ≥ pDj giving our conclusion.

Lemma 5:Suppose for each of two assets ` = j, k, pUσ` + DUσ`j = pDσ` + DDσ` for allσ ∈ B, Furthermore, suppose the aggregate collateral constraint is bindingfor some agent i∗ at both U and D, or else at neither U nor D. Suppose i∗ isbuying asset j at both nodes U and D, and buying asset k at node D. Thenk falls further in price from U to D than j does, provided that its drop inunencumbered payoff is greater [pUσk +DUσk]−φi∗

Uk = [pDσk +DDσk]−φi∗Dk ≥

[pUσj + DUσj]− φi∗Uj = [pDσj + DDσj]− φi∗

Dj.

Proof: This follows immediately from the last computation.(Then φi∗Uj =

φi∗Dj for all assets j ∈ J.)

Lemma 6:Suppose U and D are the only immediate successors of some s, for examples = 1. Suppose rs = 0. Suppose j, k ∈ J c. Suppose under the conditions ofLemma 5, there is some agent i0 whose collateral constraint is binding at s,and i0 is buying j at s. Then k also falls further in price from s to D thanj, assuming no dividends are paid at D.

Proof: We can take φi∗sj = pDj and similarly φi∗

sk = pDk. Then

psj −pDj

1 + rs

=qi0

U [pUj − pDj]dui0(xi0

U )/dx + qi0

D [pDj − pDj]dui0(xi0

D)/dx

dui0(xi0s )/dx

47

=qi0

U [pUj − pDj]dui0(xi0

U )/dx

dui0(xi0s )/dx

A similar formula for psk− pDk

1+rsholds, except with an inequality. Noting that

rs = 0, the fall in the price of an asset from s to D is proportional to the gapin price between U and D.

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