Limited participation and local currency sovereign debt

Limited Participation and Local Currency Sovereign Debt
Nicola Borri, LUISS, Rome
Kirill Shakhnov, EIEF, Rome
ADEMU Conference – Toulouse, 4 April 2018

Motivation
Large increase in the stock of EM sovereign bonds denominated in local currency
over last 15 years graph graph yields
Local currency ≈ US$4.2 trillions (2016)
Foreign currency ≈ US$900 billions (2016)
Large increase in foreign holdings of local currency EM debt graph graph table
The average share in local currency from ≈ 5% in 2004 to approximately 15% in
2016 (≈ US$600 billions)
Large diﬀerences across countries, and over time graph
The average share in foreign currency ≈ 45%
Extremely low government bond rates in developed countries after Great Recession graph

Questions
What explains the large increase in foreign holdings of local currency EM
sovereign bonds?
What are the implications of the change in currency composition of EM
government debt and in the shares held by foreign investors?
for EM: better and less risky funding costs?
for foreign investors: better portfolio diversiﬁcation?

This Paper
We lay down a model with limited market participation and diﬀerent investors
foreign investors are specialized in foreign currency denominated EM debt
local investors are specialized in local currency denominated EM debt
some foreign investors access both markets after paying entry cost
risk-aversion of foreign investors is time-varying and counter-cyclical

Main Findings
When risk-aversion is suﬃciently low, beneﬁts of investing in foreign markets are
greater than entry costs
The larger the share of foreign investors in the market for local currency bonds,
the higher their sensitivity to global shocks and correlation with foreign currency
bonds
Feeding actual U.S. interest rate data after the Great Recession to the model
results in strong increase in fraction of local currency debt held by foreigners

Literature
Segmented markets and limits to arbitrage: Gromb and Vayanos (2002);
Lamont and Thaler (2003); Gromb and Vayanos (2010); Gabaix and Maggiori
(2015); Greenwood et al. (2016)
Entry of foreign investors into local currency debt markets: Bekaert and
Harvey (2000), Eichengreen et al. (2007), Burger and Warnock (2006, 2007),
Alfaro et al. (2008), Hale et al. (2016), Du and Schreger (2016)
Sovereign bond prices and local&global shocks: Borri and Verdelhan (2011),
Longstaﬀ et al. (2011), Ang and Longstaﬀ (2013), Borri and Shakhnov (2017),
Borri (2017)

Outline
Motivation
Model: one risky asset
Model: two risky assets
Endogenous entry & time-varying risk aversion
Simulation
Conclusions

Model: a simpliﬁed framework
(1 asset, 1 investor, exchange rate & default risk)
Single risky asset and a single set of ”specialized” investors
Risky asset is a defaultable long-term bond denominated in local currency (LC)
Investors are foreigners with an objective function in foreign currency (FC) (e.g.,
U.S. hedge funds)
Investors have also access to short-term risk-free asset denominated in FC (e.g., a
U.S. T-bill)

The risky asset is a portfolio of perpetual bonds with per-period coupon C
denominated in LC
Every period, a share ht of the bonds defaults and investors recover, in this case,
a fraction Lt
The return on the bond portfolio is
Rt+1 =
(1 − Zt+1)(Pt+1 + C)
Pt
,
where P is the bond price, and Zt+1 = ht+1Lt+1 the default realization at t + 1.

Denote with St the exchange rate in units of LC per unit of FC (i.e., S ↑ is a LC
depreciation vis-`a-vis FC)
The return on the bond portfolio in FC is
Rt+1 =
(1 − Zt+1)(Pt+1 + C)
Pt
St
St+1
, (1)
where denotes variables in FC
Apply Campbell and Shiller (1988) log-linear approximation to (1)
rt+1 ≈ k + θpt+1 + (1 − θ)c − pt − zt+1 − ∆st+1, (2)
where θ = 1/(1 + exp (c − ¯p)), zt+1 = log(1 − Zt+1) and k is a constant of
approximation.

From (2) derive expression for pt and solve forward
pt =
1
1 − θ
k + c −
∞
∑
i=0
θi
Et [rt+1+i + zt+1+i + ∆st+1+i ] (3)
Apply (3) to promised cash ﬂows (i.e., zt+1+i = 0 ∀i) to get
pt =
1
1 − θ
k + c −
1
1 − θ
yt (4)
where yt is the yield-to-maturity in LC.
Use (4) in (2) and get
rt+1 ≈
1
1 − θ
yt −
θ
1 − θ
yt+1 − zt+1 − ∆st+1 (5)

Exogenous risk-factors
1. short-term risk-free rate: rf
2. default realization: z
3. risky asset supply: q
4. exchange rate: ∆s
Let x = rf − ¯rf zt+1 − ¯z qt+1 − ¯q ∆st+1 − ∆¯s and
= rf z q ∆s
Assume xt+1 = xt Γ + t+1, where Σ is the variance-covariance matrix of the
vector of innovations t+1

A mass 1 of specialized foreign investors with risk tolerance τ purchases the risky
long-term bonds in LC and the short-term risk-free asset in FC.
Investors are concerned with interim wealth at t + 1 and have mean-variance
preferences
max
bt
btEt (rxt+1) − (2τ)−1
b2
t Vart (rxt+1) ,
where rxt+1 = rt+1 − rf ,t
FOC
Et (rxt+1) = (1/τ)btV (1)
(6)
where V (1) = Vart (rxt+1) is the equilibrium variance.

We conjecture that equilibrium yield takes a linear form in the vector of states
yt = α0 + α xt (7)
and pick α0 and α so that market-clearing holds equilibrium selection
The excess return
Et [rxt+1] = (α0 − ¯r − ¯z − ∆¯s) +
1
1 − θ
α − er xt −
θ
1 − θ
α + ez + e∆s Γxt.
where ei is a vector of all zeros and 1 in position i
Conditional variance
V (1)
=
θ
1 − θ
α + ez,∆s Σ
θ
1 − θ
α + ez,∆s
Market clearing: bt = qt

Combining (6)–(7) we get a closed-form expression for the equilibrium yield when Γ and
Σ are diagonal diagonal Γ and Σ
yt =
interest rate risk premium
¯r +
1 − θ
1 − ρr θ
(rt − ¯r ) +
default rate risk premium
¯z +
1 − θ
1 − ρz θ
ρz (zt − ¯z) +
exchange rate risk premium
∆¯s +
1 − θ
1 − ρ∆s θ
(∆st − ∆¯s)
+
V (1)
τ
( ¯q)
unconditional term premium
+
V (1)
τ
1 − θ
1 − ρqθ
(qt − ¯q)
conditional term premium
Note that
the yield is more sensitive to the risk factors the higher their persistence
the risk-tolerance parameter τ shows up only in the last two terms (i.e, term
premium)

A Model with Partially Segmented Markets
(2 risky assets, 3 investors, exchange rate & default risk)
Build on Greenwood et al. (2016) and Gromb and Vayanos (2002) diﬀerences wrt GHL
Three assets
1. risky long-term local currency bond (A)
2. risky long-term foreign currency denominated bond (B)
3. short-term risk free in foreign currency
Three types of investors
1. nA specialists in A debt
2. nB specialists in B debt
3. 1 − nB − nA generalists in both A and B debt
All investors have same mean-variance preferences with risk tolerance τ

(2 assets, 3 investors, exchange rate & default risk)
Returns on the perpetual bonds
RA,t+1 =
(1 − ZA
t+1)(PA,t+1 + CA)
PA,t
RB,t+1 =
(1 − ZB
t+1)(PB,t+1 + CB )
PB,t
denotes variables in foreign currency (i.e., U.S. dollar).

Apply Campbell and Shiller (1988) log-linear approximation
rxA,t+1 ≈
1
1 − θA
yA,t −
θA
1 − θA
yA,t+1 − zA
t+1 − rt,
rxA,t+1 ≈
1
1 − θA
yA,t −
θA
1 − θA
yA,t+1 − zA
t+1 − rt − ∆st+1,
rxB,t+1 ≈
1
1 − θB
yB,t −
θB
1 − θB
yB,t+1 − zB
t+1 − rt ,
Note that investors diﬀer with respect to their source of funding

Exogenous Risk Factors
1. global and local risk r and r
2. default risk zi i = {A, B}
3. supply shocks qi i = {A, B}
4. exchange rate risk ∆s

Specialists maximize a quadratic utility function
max
bt
btEt [rxt+1] − (2τ)−1
b2
t Vart [rxt+1] ,
and their optimality conditions are
bA,t = τA
Et [rxA,t+1]
Vart [rxA,t+1]
, bB,t = τB
Et rxB,t+1
Vart rxB,t+1

Generalists maximize the same quadratic utility function
max
dA,t ,dB,t
Et [rxdt ,t+1] − (2τB )−1
Vart [rxdt ,t+1] ,
where rxdt ,t+1 = dA,trxA,t+1 + dB,trxB,t+1
The optimality condition for generalists is
dA,t
dB,t
=
τB
1 − R2
A,B



Et [rxA,t+1]
Vart [rxA,t+1]
− βB|A
Et [rxB,t+1]
Vart [rxB,t+1]
Et [rxB,t+1]
Vart [rxB,t+1]
− βA|B
Et [rxA,t+1]
Vart [rxA,t+1]



where βA|B, βB|A are OLS slope coeﬃcients in regressions of rxA,t+1 on rxB,t+1,
and vice-versa, and R2
A,B the corresponding R-square

Market clearing
nAbA,t + (1 − nA − nB )dA,t = qA,t
nBbB,t + (1 − nA − nB )dB,t = qB,t

Endogenous Entry
We now introduce endogenous entry of foreign investors in the market for LC
bonds and time-varying risk tolerance
when generalists invest in the LC asset, they must pay a per period ﬁx cost ψ
specialists in asset B every period can decide whether to become generalists, pay the
fee ψt and invest also in asset A
the entry condition for specialists in B is
∆u ≡ ug
t − us,B
t = ψt (8)
where ug
t is utility for generalists and us,B
t of specialists in B in t
The entry cost is a proxy for transaction costs in order to operate in the local
market and/or development of local ﬁnancial market

Endogenous Entry
The utility of specialists is
us,B
t =
τB,t+1
2
x2
B (9)
where xB =
Et [rxB,t+1]
Vart [rxB,t+1]
denotes the risk-adjusted return on asset B
The utility of generalists is
ug
t =
τB,t+1
2 (1 + corAB,t )
x2
A − xAxBcorAB,t
(1 − corAB,t )
+
x2
B − xAxBcorAB,t
(1 − corAB,t )
where xA are the risk-adjusted return on A and corAB,t the correlation coeﬃcient
between the conditional excess returns on the two assets

Time-Varying Risk Aversion
We introduce time-varying risk aversion in a reduce form
we assume that local investors risk-tolerance is constant and equal to ¯τA
the risk-tolerance of foreign investors is instead a function of state variables
τB,t+1 = ¯τB + κ xt (10)
where κ is a vector of loadings on the states
note that τB,t+1 is pre-determined at t and is taken as given by investors in their
portfolio decisions
in empirical estimation we simply assume the only non-zero coefficient of κ is for the
risk-free rate in foreign currency (i.e., τB,t+1 high when interest rate is low)
this could be endogeneized in model with habit preferences when the intertemporal
substitution effect dominates the precautionary saving effect

Simulation (I/II)
Collect all bond issuance with initial maturity of more than 1 year since 1988 for
Brazil from Bloomberg (in LC and FC) and aggregate data at monthly frequency
(price, quantity, and rating at issuance)
Estimate Γ and Σ using data for Brazil
rt return on the US t-bills, rt return on money market Brazilian rate
zt = ∑
Nt
k=1
Rk,t Ik,t
∑
Nt
k=1 Ik,t
the weighted average of ratings at the issuance (in LC and FC
respectively)
qt =
∑T
i=0 ∑
Nt−i
k=1 Ik,t−i −Mk,t−i
GDPt
the cumulative net issuance of bonds over GDP (in LC
and FC respectively)
∆st Brazilian Real to U.S. dollar spot rate

Simulation (I/II)
1. Simulate model for constant values of risk tolerance and grid of values for the
fraction of generalists
2. Impulse responses when fraction of generalists is small and equal to 30% (i.e.,
average value for Brazil) and large and equal to 70%
3. Estimation of utility diﬀerence ∆u between generalists and specialists in asset B
for diﬀerent values of the fraction of generalists and risk tolerance
4. Feed model actual U.S. short-term interest rate after Great Recession to estimate
time-varying risk tolerance of foreign investors and equilibrium fraction of
generalists

Fixed Number of Generalists (I/II)
0 0.2 0.4 0.6 0.8 1
2
2.5
3
3.5
4
4.5
mean yields (%)
yA
yB
0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
1.2
Var returns (%)
VarA
VarB
0 0.2 0.4 0.6 0.8 1
0.045
0.05
0.055
0.06
0.065
0.07
correlation of returns
0 0.2 0.4 0.6 0.8 1
0.38
0.4
0.42
0.44
0.46
entry
u

Fixed Number of Generalists (II/II)
LC bonds have larger yields and variance of returns regardless of fraction of
generalists
LC bonds yield declines a bit with fraction of generalists
When the fraction of generalists increases, the correlation between LC and FC
bond returns increases
Fraction of generalists ≈ 30%

IRFs (I/II)
0 5 10 15 20
2
4
6
8
10
12
%
shock to rf
us
0 5 10 15 20
-0.01
0
0.01
0.02
0.03
0.04
%
shock to s
yA
(low fract)
yA
(high fract)
yB
(low fract)
yB
(high fract)
0 5 10 15 20
1
2
3
4
5
6
%
shock to zB
0 5 10 15 20
0
5
10
15
20
%
shock to zA

IRFs (II/II)
shock to U.S. short term rate affects more FC bond yields, and LC bond yields
when fraction of generalists is large
shock to exchange rate affects only LC bonds, and the more so the larger the
shocks to the default realization of FC bonds affects also LC bonds when fraction
of generalists is large
shocks to the default realization of LC bonds affects mostly LC bonds, and the
more so the lower the fraction of generalists

Entry (I/II)
1.5
200
2
2.5
3
150 0.95
10
-4
3.5
0.9
4
u
0.85100
4.5
0.8
generalists (%)
5
0.75
50 0.7
0.65
0 0.6

Entry (II/II)
For a given level of risk tolerance, the beneﬁts of becoming generalists decline
with the share of generalists
For a given level of the share of generalists, the beneﬁts of becoming generalists
increase with the risk tolerance

Entry after the Great Recession

Conclusion
We build a model of partially segmented markets where foreign investors are
specialized in EM bonds in FC and local investors in LC, and foreign investors can
also invest in LC bonds after paying a fee
- for a given fee level, benefits to foreign investors from entering the LC bond market
are larger the lower their risk aversion
- the sensitivity to global shocks of LC bonds is higher the larger the share of foreign
investors in the market for LC bonds
- when foreign investors’ risk aversion is positively correlated to U.S. short-term
interest rates, the model predicts the significant increase in the share of LC bonds
held by foreign investors that we observe in the data after the Great Recession
The model can be used to study counterfactual scenarios, like the effect of the
exit of the Fed from the low interest rate environment

Aggregate EM Debt
(in USD)
2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
AssetsinUSDbillions
local currency
foreign currency
back to motivation

Aggregate Foreign EM Debt Holdings Shares
(as % of local and foreign currency debt)
2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016
0
10
20
30
40
50
60
70
Assetsas%ofEMdebtinlocalandforeigncurrency
local currency
foreign currency
back to motivation

Aggregate Foreign EM Debt Holdings
(as % of EM GDP)
2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016
0.5
1
1.5
2
2.5
3
3.5
Assetsas%ofEMGDP
local currency
foreign currency
back to motivation

Foreign Holdings of EM Government Debt Securities in Local Currency (%
of total)
back to motivation

The risk free rate
2002 2004 2006 2008 2010 2012 2014 2016 2018
0
1
2
3
4
5
6
back to motivation Notes: Yield on 3-Month Treasury Bill

Differences in default risk?
mean absolute differences in credit ratings
Brazil
C
hile
C
hinaC
olom
biaH
ungary
IndiaIndonesiaM
alaysia
M
exico
Peru
Philippines
PolandR
om
ania
R
ussia
South
Africa
Turkey
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
Figure: This figure plots the mean absolute difference in credit ratings on debt denominated in foreign and
local currency. Credit ratings are from S&P for the period 2002:3–2016:12 and are converted in a numerical
ordering with AAA=1 and SD=16 simple differences in ratings .

Local currency market negligible?
local currency debt: share of total governmebt debt (2016:Q3, %)
Brazil
C
hile
C
hinaC
olom
biaH
ungary
IndiaIndonesiaM
alaysia
M
exico
Peru
Philippines
PolandR
om
ania
R
ussia
South
Africa
Turkey
0
10
20
30
40
50
60
70
80
90
100
Figure: Local currency debt as a share of total government debt at 2016:Q3. Data are from a sample of 16
emerging countries from Arslanalp and Tsuda (2014).

Market integration?
local currency debt: share held by foreign investors (2016:Q3,%)
Brazil
C
hile
C
hinaC
olom
biaH
ungary
IndiaIndonesiaM
alaysia
M
exico
Peru
Philippines
PolandR
om
ania
R
ussia
South
Africa
Turkey
0
5
10
15
20
25
30
35
Figure: Share of local currency debt held by foreign investors in 2016:Q3. Data are from a sample of 16
emerging countries from Arslanalp and Tsuda (2014).

Simple differences in credit ratings
mean differences in credit ratings
Brazil
C
hile
C
hinaC
olom
biaH
ungary
IndiaIndonesiaM
alaysia
M
exico
Peru
Philippines
PolandR
om
ania
R
ussia
South
Africa
Turkey
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
Figure: This figure plots the mean difference in credit ratings on debt denominated in foreign and local
currency. Credit ratings are from S&P for the period 2002:3–2016:12 and are converted in a numerical ordering
with AAA=1 and SD=16 back .

Data
Figure: Yields on local and foreign currency denominated government debt. Yields on local currency debt are
from the J.P. Morgan GBI-Broad indices. Yields on foreign currency denominated debt are from J.P. Morgan
EMBI Plus indices. Data are at monthly frequency for the period 2002:3–2016:12.

Asset Pricing (Standard Model)
If the LOP holds, and investors can form portfolios freely, there exists a SDF Mt+1 that
prices any excess return Re,i
t+1:
Et Mt+1Re,i
t+1 = 0
Assuming that returns and SDF are lognormal, the Euler equation implies
Et (re,i
t+1) = −
covt (mt+1, re,i
t+1)
vart (mt+1)
βi
t
vart (mt+1)
λt
where lower cases denote logs.
If M is an excess return, its market price of risk λ should be equal to its mean as beta is
equal to 1 (no-arbitrage condition).
back

Special case: Γ and Σ diagonal (single asset model)
In order to get simple closed-form solutions, it is convenient to take Γ and Σ as
diagonal matrices
Γ =




ρr 0 0 0
0 ρz 0 0
0 0 ρq 0
0 0 0 ρ∆s



 , Σ =




σ2
r 0 0 0
0 σ2
z 0 0
0 0 σ2
q 0
0 0 0 σ2
∆s




back

Combining (6)–(??) we get expression for the excess holding period return for the
foreign investor is
Et [rxt+1] =
interest rate risk premium
τ−1 θ
1 − ρr θ
σ r
2
qt +
credit risk premium
τ−1 1
1 − ρr θ
σ z
2
qt +
+
1
1 − ρr θ
σ ∆s
2
qt
exchange rate risk premium
+ τ−1 θ
1 − ρr θ
σ q
2
V (1)
2
qt
supply risk premium
(11)
back

Solution: general case
Formally, we conjecture that the long-term yields in market A and B are
yA,t = αA0 + αA1xt,
yB,t = αB0 + αB1xt,
the demands of generalists are
dA,t = δA0 + δA1xt,
dB,t = δB0 + δB1xt,

Solution: general case
3 Variances and covariance
VI = ∑
J
θI
1 − θI
αI,J
2
σ2
J , I = {A, B, C}, J = {r , z, ∆s, qA, qB }
CA,B = ∑
J
θAθB
(1 − θA)(1 − θB )
αC,J αB,J
2
σ2
J , J = {r , z, qA, qB }
Generalists demand δA1 as a function of αA1
δA0 = τ
VB (αC0 − ¯r − ¯z − ∆¯s) − CA,B (αB0 − ¯r − ¯z)
VAVB − (CA,B )2
,
δA1 = τ




VB
1
1−θA
αC1 − er − θA
1−θA
αC1 + ez + e∆s Γ
−CA,B
1
1−θB
αB1 − er −
θB
1−θB
αB1 + ez Γ




VAVB − (CA,B )2
back

Equilibrium Selection
In a similar framework, GHL show that a linear equilibrium exists only if investors
are sufficiently risk-tolerant (i.e., if τ is large enough)
When investors are sufficiently risk tolerant, there two types of solutions
1. yields are highly sensitive to supply shocks and bonds very risky so that investors
want to be compensated with large returns (i.e., large changes in yields)
2. yields are less sensitive to supply shocks and bonds less risky, so that investors
require smaller returns
Following GHL, we focus on the solution that implies that yields are less sensitive
to changes in their own supply
it is possible to show that the first root is explosive when σ q→∞
back

Diﬀerences with respect to GHL
1. We assume that both assets are defaultable long-term bonds
2. We introduce exchange rate risk
3. We assume that foreign investors are specialized in FC bonds, and local investors
in LC bonds
4. We assume that generalist investors invest in both markets
5. We introduce endogenous entry in the pool of generalists
6. We assume that foreign investors have time-varying risk aversion tied to the
risk-less U.S. short-term interest rate
back

Table: Foreign holdings shares
Min Max Mean Min Max Mean
foreign currency (%) local currency (%)
Brazil 5.36 30.75 16.80 0.99 20.27 8.36
Chile 85.50 100.00 99.32 3.14 8.86 5.75
China 0.09 2.09 0.90 0.00 3.18 0.57
Colombia 46.02 65.47 51.04 4.46 22.27 8.37
Hungary 38.95 72.70 53.55 21.04 43.65 30.08
India 0.00 0.01 0.00 0.12 4.03 1.23
Indonesia 1.16 40.79 13.52 1.63 39.63 19.96
Malaysia 0.00 41.24 21.31 12.37 37.34 24.49
Mexico 57.99 100.00 100.00 4.36 37.99 18.50
Peru 16.39 60.71 28.99 0.00 56.61 27.61
Philippines 40.22 100.00 61.14 0.00 14.63 5.16
Poland 32.65 64.11 51.48 13.33 41.89 25.38
Romania 11.94 40.41 27.52 5.40 22.38 15.89
Russia 10.49 38.00 24.11 0.12 23.12 6.42
South Africa 23.14 40.72 30.97 6.54 38.01 18.97
Turkey 17.79 58.91 34.44 5.08 24.48 13.34
back

Formally, we say that markets are integrated if a conditional CAPM model prices
both assets
Et [rxt+1] = τ−1
B Vart [rxt+1]st = βt [rxt+1, rxM,t+1]Et [rxM,t+1],
where rxM,t+1 = strxt+1 is the market portfolio.
In our framework, for each asset
rxi,t+1 − Et [rxi,t+1] = φ t+1
where φ = φA φB contains the factor loadings of each asset on the factor
innovations.
If 1 − nA − nB = 1, then
Et [rxt+1] = τ−1
Vart [rxt+1]st = φ τ−1
Σφ st
λt

References I
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——— (2007): “Foreign participation in local currency bond markets,” Review of Financial
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References II
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References III
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Longstaff, F. A., J. Pan, L. H. Pedersen, and K. J. Singleton (2011): “How sovereign is
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