15442_SovereignRisk

7/30/2019 15442_SovereignRisk

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Sovereign Risk

Adrien Verdelhan

MIT Sloan

April 2013


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Road Map for Today

1 Optimal Sovereign Debt and DefaultWorkhorse ModelBenchmark Empirical Spreads

2 Sovereign Risk PremiaPortfolios of EMBI Excess ReturnsCross-sectional Asset PricingModel


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Literature

Empirical studies of sovereign bonds and CDS: Acharya, Drechsler, andSchnabl (2012), Ang and Longstaff (2011), Broner, Lorenzoni, and Schmukler (2011),Longstaff, Pan, Pedersen and Singleton (2011), Pan and Singleton (2008), Fostel andGeanakoplos (2008), Gonzales-Rozada and Yeyati (2008), Hilscher and Nosbusch (2008),Bekaert, Harvey and Lundblad (2007), Weigle and Gemmill (2006), Benczur and Ilut

(2006), Bernoth, von Hagen and Schuknecht (2004), Adler and Qi (2003), McGuire andSchrijvers (2003), Ferrucci (2003), Arora and Cerisola (2001), Westphalen (2001), Kaminand von Kleist (1999), Edwards (1984), Eichengreen and Mody (1998).

Models of sovereign borrowing: Arellano and Ramanarayanan (2012), Acharyaand Rajan (2011), Jeanneret (2010), Broner and Ventura (2010), Andrade (2009),Hatchondo and Martinez (2009), Pouzo (2009), Arellano (2008), Amador (2008),

Guerrieri and Kondor (2008), Bolton and Jeanne (2008), Mendoza and Yue (2008),Lizarazo (2008), Broner (2008), Pan and Singleton (2008), Aguiar and Gopinath (2006),Yue (2005), Duffie, Pedersen, and Singleton (2003), Amador (2003), Alvarez andJermann (2000), Cole and Kehoe (2000), Kocherlakota (1996), Zame (1993), Kehoe andLevine (1993), Atkeson (1991), Bulow and Rogoff (1989), Eaton and Gersovitz (1981).


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The Workhorse Model: Eaton and Gersovitz (1981)

Recent version in, for example, Arellano (2008), Aguiar and Gopinath(2006), Arellano and Ramanarayanan (2012)

Timing of events in period t:

1 household receives stochastic endowment YBt ,

2 government repays outstanding debt Btt1 or defaults,

3 if government repays:

it borrows Bt+1t at the price Qt,it makes a lump-sum good transfer to the household.

4 if government defaults:

it is excluded from international capital markets for a stochasticnumber of periods,faces a direct output cost YB,deft .


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Endowment: borrowers

Arellano (2008): Yit = ezit

Aguiar and Gopinath (2007): Two components: Yit = ezitit

a transitory component zit,

a time-varying mean (or permanent component) it.

zit = z(1 z) + zzit1 +

z,it

it = Git

it1,

git = log(Git) = g(1 g) + ggit1 + g,it .

g,i and z,i are i.i.d normal, E(g,iz,i) = 0.


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Investors

Lenders are:

risk neutral,

behave competitively,

supply any quantity of funds demanded at a price Qt,

Lenders maximize expected profits QB + 11+rB, where denotesthe expected default probability (zero recovery in case of default).

Thus bond prices satisfy:

Q =1

1 + r.


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Recursive Equilibrium

State variables:

x = [yi, s], Markovian with conditional density f(x, x).

B is the quantity of debt coming to maturity.

Value of the option to default or stay in the contract is:

vo(B, x) = max{vc(B, B, x), vd(x)}

Value of default is:

vd(x) = u(ydef) + x

[vo(0, x) + (1 )vd(x)]f(x, x)dx

Value of staying in the contract is:

vc(B, x) = MaxB{u(c) +

xvo(B, x)f(x, x)dx}


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Equilibrium Interest Rate in Arellano (2008)


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EMBI Global Market Value

1992 1994 1996 1998 2000 2002 2004 2006 20080

50

100

150

200

250

300

EMBI Global Market Value

EM

BIGM

arketValue(inbillionsUSD)

Source: Datastream


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EMBI Spreads and Standard & Poors Credit Ratings

A BBB BB B CCC CC0

500

1000

1500

2000

2500

3000

3500EMBI G and S&P Ratings as of May 2009

S&P Ratings

EMBIGS

pread(basispo

ints)

ARG

BEL

BRA

BUL

CHILCHI

COL

DOM

ECU

EGY

EL

HUN

IND

KAZ

LEB

MALMEX

PAK

PANPER PHI

POL

RUS

SER

SOU TUN

UKR

URU

VEN

VIE


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Is It All About Default Probabilities?

Think about a one-period zero-coupon sovereign bond.

Let rf denote the real risk-free rate, r the return on the sovereignbond, p the default probability and rec the recovery rate in case ofdefaults.

Invest one dollar in a risk-free asset or in a sovereign bond.

If investors are risk-neutral, expected returns are the same:

1 + rf = (1 p) (1 + r) + p rec

NB: We observe rf and r. If we assume a value for rec, then we cancompute p:

p =r rf

1 + r rec

Then expected excess returns should be zero: Not true in the data!


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Back to the Euler Equation

Pt = Et[Mt+1Xt+1]

Pt: price 1-period zero-coupon bond (face value = 1),

Mt+1: investors stochastic discount factor (SDF),

Xt+1: indicator function (1 if repayment, 0 if default).

We can express the bond price as:

Pt =Et(Xt+1)

Rft+ covt(Mt+1, Xt+1),

where Rft = 1/Et(Mt+1) is the risk-free rate.

Pt depends on:

discounted payoff,

risk adjustment component.

Example: CDX, cf Coval, Jurek, and Stafford (2009)


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No, Risk Matters!

Heres the intuition:

Emerging countries tend to default when they are in trouble (i.e inbad times for them).

Take two countries: Mexico and Thailand.

Assume that they have the same default probability.

Bad times in Mexico are likely to correspond to bad times in the US,

Less so for Thailand.

For a given identical default probability, Mexican sovereign bonds aremore risky than Thai bonds for the US investor.


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Sovereign Risk Premia: Borri and Verdelhan (2012)

Study:

sovereign debt

issued by emerging and developing countries

in US dollars.

Focus on benchmark JP Morgan EMBI indices.

Take the perspective of a US investor.


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Findings

Large cross section of average holding period excess returns

between countries with low and high probability of default and lowand high connection to the US:

Use Standard and Poors credit ratings to measure default probability;

Use bond market betas to measure connection to the US.

These excess returns are risk premia.

One single risk factor, the BBB US corporate bond return, explains thecross sectional variation in average excess returns.

A model with optimal sovereign borrowing and default andexternal habit preferences replicates qualitatively these results.

Pure Peso explanations of excess returns unlikely in simulated data;

Risk premia link countries: countries default more frequently wheninvestors risk aversion is high.


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Key Mechanism

Investors risk aversion affects debt quantities and prices:

Take the example of countries with business cycles positively correlatedto the US

These countries are riskier (i.e tend to default in bad times) higherexcess returns

They are more likely to default when investors risk aversion is high

Every period, tradeoff between paying back debt and borrowing againvs default

If investors risk aversion is high, risk premia are high, and so areborrowing costs

Borrowing again is less attractive, and thus defaults are more likely.

Opening up capital markets exposes emerging countries to USbusiness cycle risk.


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Data: EMBI Returns

Data from JP Morgan EMBI Global.

EMBI Global is the most liquid US-dollar emerging market index

Start from daily return price data in US dollars.

Build end-of-month series from December 1993 to May 2011.

Sample of 41 emerging countries:

Argentina, Belize, Brazil, Bulgaria, Chile, China, Colombia, Cote DIvoire, Croatia,Dominican Republic, Ecuador, Egypt, El Salvador, Gabon, Ghana, Hungary, Indonesia,Iraq, Kazakhstan, Lebanon, Malaysia, Mexico, Morocco, Pakistan, Panama, Peru,Philippines, Poland, Russia, Serbia, South Africa, South Korea, Sri Lanka, Thailand,Trinidad and Tobago, Tunisia, Turkey, Ukraine, Uruguay, Venezuela, Vietnam.


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EMBI Excess Returns and Market Betas

Log excess return on buying country is EMBI bond at date t andselling it at date t+ 1:

re,it+1 = pit+1 p

it r

ft .

pi: Country i log bond price in US dollars.

rf: US risk free rate in US dollars.

Market beta iEMBI: slope coefficient in the regression:

re,it+1 = i + iEMBIre,mt+1 + t+1.

re,m log total excess return on MSCI US equity index

Betas are computed on 200-day rolling windows iEMBI,t.


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Data: Default Probability

Data from Standard and Poors.

Start from S&Ps credit ratings for foreign currency denominatedlong-term debt.

Convert letter grade credit ratings into numerical index (1 to 23, ahigher number means a higher probability of default).


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EMBI Portfolios

Countries are ranked on two dimensions:their default probabilities,

their bond market betas.

At the end of each month t, sort all countries into 2 groups on thebasis of their iEMBI,t (information up to date t).

Within each group, sort countries into 3 portfolios on the basis oftheir default probabilities at the end of each month t.

Compute the log excess return re,jt+1 for each portfolio j = 1, 2, ..., 6by averaging:

re,jt+1 =

1

Nj

iPj

re,it+1.


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Cross-section of Excess Returns

Portfolios 1 2 3 4 5 6

j

EMBI Low HighS&P Low Medium High Low Medium High

EMBI Bond Market Beta: jEMBIMean 0.09 0.13 0.10 0.39 0.47 0.64Std. Dev. 0.16 0.20 0.20 0.33 0.31 0.38

S&P Default Rating: dpj

Mean 7.15 9.60 13.10 10.05 12.25 15.22Std. Dev. 1.52 1.00 1.03 1.68 0.96 1.47

Excess Return: re,j

Mean 3.75 4.13 6.92 8.44 8.78 14.62s.e [1.75] [2.15] [2.76] [2.98] [3.90] [5.09]

Std. Dev. 7.34 9.08 11.42 11.80 15.25 20.72SR 0.51 0.45 0.61 0.71 0.58 0.71

Debt/GNPMean 0.11 0.16 0.33 0.27 0.30 0.33Std. Dev. 0.05 0.09 0.08 0.09 0.08 0.09

Annualized monthly excess returns. Monthly Data. Higher S&Ps credit ratings is higher default probability.Sample period is 1/1995 5/2011.


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Spreads in Sovereign Bond Returns

Spreads between high and low default probability countries: 470 bp

on average.

Spreads between high and low bond market beta countries: 570 bpon average.


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Cross-Sectional Asset Pricing

Re,jt+1 has a zero price:

E[Mt+1Re,jt+1] = 0.

where M is the stochastic discount factor of US investors.

M is linear in the pricing factors f:

Mt+1 = 1 b(ft+1 ),

where b is the vector of factor loadings.

Candidate risk factors:

returns on US stock market;

returns on US corporate bond market: USBBB.


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No Arbitrage Restrictions

The Euler equation E[MRe,j] = E[Re,j b(f )Re,j] = 0 impliesthat:

E[Re,j] = ffbE[(f )Re,j]

ff.

-pricing model:E[Re,j] = j.

where = ffb and ff = E(ft f)(ft f) is the variance-covariance matrix of the factors.

No arbitrage implies:

Risk Factor = E[ReRisk Factor]


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Model Fit: The Left Panel is Misleading...

5 10 152

4

6

8

10

12

14

16

Predicted Mean Excess Return (in %)

ActualMeanExcessReturn(in%)

1 2

3

4 5

6

5 10 152

4

6

8

10

12

14

16

Predicted Mean Excess Return (in %)

ActualMeanExcessReturn(in%)

1 2

3

4 5

6


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Risk Prices

USBBB bUSBBB R2 RMSE 2

FMB 7.22 1.64 84.38 1.31

[2.49] [0.56] 54.08(2.58) (0.59) 60.38

Mean 4.43[1.84]


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s? Significant s?

Portfolio j

0(%) j

USBBBR2(%) 2() p value

1 0.17 0.76 38.93[0.12] [0.09]

2 0.20 0.85 32.14[0.19] [0.12]

3 0.02 0.87 21.31[0.23] [0.13]

4 0.03 1.06 29.44[0.25] [0.16]

5 0.10 1.31 27.07[0.30] [0.20]

6 0.05 1.84 28.93[0.50] [0.38]

All 5.79 44.69


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Conditional Asset Pricing

Conditional Euler equation:

Et[Mt+1ztRe,jt+1] = 0,

to test this prediction.

ztRe,jt+1 is a managed portfolio.

zt is the CBOE volatility index VIX and summarizes all theinformation set of the investor.

The market prices of risk associated with the USBBB factorincrease in bad times, when the implied US stock market volatilityis high.


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Conditional Asset Pricing

USBBB USBBBVIX bUSBBB bUSBBBVIX R2 RMSE 2

FMB 5.00 20.68 0.20 0.39 90.48 3.39

[3.47] [8.62] [2.98] [0.69] 2.52(3.57) (8.79) (3.08) (0.72) 3.90

Mean 4.43 18.87[1.84] [6.26]

A P i i S


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Asset Pricing Summary

Risk is priced on sovereign bond markets:

Large cross-section of excess returns

No arbitrage condition not rejected:

Estimated market price of risk higher but not statistically different fromthe mean of the risk factor (NB: no transaction costs here.)

Higher risk premia in bad times

M I li i ?


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Macro Implications?

Cost of debt, borrowing and default choice are all endogenous.We need a model of optimal sovereign borrowing and default:

N-1 small open economies (borrowers),

1 large developed economy (US, lender),

Framework a la Eaton and Gersovitz (1981), Aguiar and Gopinath(2006) and Arellano (2008),

But:

Lenders are risk-averse: external habit preferences as in Campbell andCochrane (1999).

The borrowers endowment is composed of a transitory component anda time-varying mean.

One source of heterogeneity among borrowers: countries differ intheir correlation with respect to the US business cycle.

Wh E l H bi ?


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Why External Habits?

Models with power utility preferences do not produce large spreads inexcess returns.

Intuition:

Assume same probability of default, same yield volatility.

Spreads depend on covt(Mt+1, Re,it+1) covt(Mt+1, Re,jt+1).Maximum spreads between high and low-correlation countries:

2cre 2 2 1.5% 13% 80bp.

Matching the data with CRRA implies a very high risk-aversioncoefficient and implausible risk-free rates.

External habit implies that risk aversion is time-varying and higherin bad times.

E d t l d


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Endowment: lenders

US consumption growth is a random walk:

ct = g + t.

Emerging countries only differ according to their conditionalcorrelation to the developed economy:

E(zi

) = i.

I t


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Investors

Lenders are:

risk averse,

behave competitively,

supply any quantity of funds demanded at a price Qt,

have external habit preferences over their consumption endowmentdescribed by:

Et

t=0

()t(CtHt)1 1

1 .

Ht is the external habit level and corresponds to a time-varyingsubsistence level or social externality.

If lenders were risk neutral, there would be no role for covariancesin sovereign bond prices.

Model Parameters


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Model Parameters

Variable Notation Value

Lenders

Risk-aversion 2.00

Mean consumption growth (%) g 1.89

Standard deviation of consumption growth (%) 1.50

Persistence of the surplus consumption ratio 0.87

Mean risk-free rate (%) rf 1.00

Borrowers

Endowment

Permanent: Persistence g 0.20

Permanent: Standard deviation (%) g 4.00

Permanent: Mean (%) g 2.31

Temporary: Persistence z 0.90

Temporary: Standard deviation (%) z 2.00

Temporary: Mean (%) z Var(z)/2Preferences

Risk-aversion 2.00

Discount factor 0.80

Direct default cost (%) 4.00

Probability of re-entry (%) 10.00

Results


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Results

A model with both large sovereign debt levels and large spreads:

time-varying mean growth rates incentives to borrow (e.g., good

times ahead, but want to consume now) large debt

But, sometimes, ... unexpected bad news (e.g., negative temporaryshocks) defaults large spreads

Defaults and bond prices depend not only on the borrowers, but alsoon the lenders economic conditions

Key Mechanism Again


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Key Mechanism, Again

Investors risk aversion affect debt quantities and prices:

Take the example of countries with business cycles positively correlatedto the US

These countries are riskier (e.g tend to default in bad times) higherexcess returns

They are more likely to default when investors risk aversion is high

Every period, tradeoff between paying back debt and borrowing againvs default

If investors risk aversion is high, risk premia are high, and so areborrowing costs

Borrowing again is less attractive, and thus defaults are more likely.

Default Frontiers


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Default Frontiers

0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1

0.06

0.04

0.02

0

0.02

0.04

0.06

Debt level B today

Endowmentshockz

Default Policy Sets (Defaults occur in the area below the frontier)

Low mean growth rate (g), high riskaversion (low s)

Low mean growth rate (g), low riskaversion (high s)

High mean growth rate (g), high riskaversion (low s)

High mean growth rate (g), low riskaversion (high s)

Sovereign Bond Prices


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Sovereign Bond Prices

0.4 0.3 0.2 0.10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Debt level B tomorrow

BondpriceQ

Impact of growth rates

low z, low g

low z, high g

high z, low g

high z, high g

0.4 0.3 0.2 0.10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Debt level B tomorrow

BondpriceQ

Impact of riskaversion

low z

low z, no r.p.

high z

high z, no r.p.

Simulated Data


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Simulated Data

Generate simulated data for 36 small open economies.

The only source of heterogeneity across countries is the correlation oftheir endowment process with the US endowment.

Correlations range from -0.5 to 0.5.

Sort bonds only on one dimension.

In the model, precise measures of expected default probabilities andconsumption correlations.

But this is a one-factor model: one source of risk is priced(correlation between US endowment shocks and bond returns).

Similar results when using simulated stock market betas.

Additional potential source of heterogeneity: endowment volatility.

Portfolios - Simulated Data


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Portfolios Simulated Data


Stock market beta: Mkt (Pre-Formation)Mean 0.25 0.12 0.05 0.00 0.05 0.13Std 0.20 0.15 0.11 0.10 0.10 0.13

Default probabilityMean 5.85 5.41 4.89 4.50 4.17 3.84

Std 1.33 1.21 1.09 1.02 0.96 0.91Excess return: re

Mean 1.24 0.66 0.14 0.29 0.52 0.65Std 21.06 19.73 18.64 17.88 17.28 16.68Std* 1.02 1.01 1.01 1.02 1.03 1.04

Debt/OutputMean 30.14 29.71 29.29 29.01 28.67 28.52Std 7.09 6.92 6.78 6.73 6.73 6.67

Stock market beta: Mkt (Post-Formation)Mean 0.14 0.08 0.04 0.00 0.03 0.05

Std 0.01 0.01 0.01 0.01 0.01 0.01

Simulation Results


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Simulation Results

Reasonable consumption and output dynamics, and large debt/GDPratios

A cross-section of sovereign bond excess returns...

smaller than in the data (180 bp vs 500 bp)

reminder: only one-quarter bonds, no term premium

as in the data, high excess returns

do not correspond to higher debt levels,

but correspond to higher stock market betas

... that corresponds to risk premia.

Risk-Neutral Investors and Peso Explanation?


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Risk Neutral Investors and Peso Explanation?


Panel I: Low-Default-Probability Sample

Stock market beta: MktMean 0.36 0.05 0.01 0.00 0.03 0.27


Excess return: re

Mean 2.44 2.47 2.51 2.53 2.50 2.50Std 6.80 6.73 6.69 6.64 6.68 5.57

Panel II: Full Sample

Stock market beta: MktMean 0.01 0.01 0.01 0.01 0.01 0.01


Excess return: re

Mean 0.00 0.00 0.00 0.00 0.00 0.00Std 22.91 22.91 22.91 22.91 22.91 22.91

Implications


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Implications

Interest rate elasticity of debt:

No monotonic increase in interest rates when debt levels increase.

Output-interest rate correlations:

Depends on the cross-country correlation of business cycles.

Monetary unions:

More synchronized business cycles higher sovereign risk premia.

Conclusion


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Empirically, countries with higher bond betas offer higherreturns.

Timing of expected sovereign payoffs matters.

Low payoffs in bad times = risky sovereign bonds.

Models of optimal borrowing and defaults with risk neutral investors

cannot account for our empirical findings.Investors risk aversion affect optimal debt quantities andprices.

Habit preferences lead to a cross-section of sovereign bond excess

returns.Riskier countries are more likely to default when investors risk aversionis high.

Opening up capital markets exposes emerging countries to USbusiness cycle risk.

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