1. DEFAULT AND THE MATURITY
STRUCTURE IN SOVEREIGN BONDS
Written by: Cristina Arellano and Ananth Ramanaraynan
Presented by: Daniela Vargas, Li Jiayao

2. WHAT IS THIS PAPER ABOUT?
 Maturity composition and the term structure of
interest rate spreads of government debt in
emerging markets
 As interest rate spread , debt maturity shortens–
spread on short bond rise more than long-term
spread.
 Analyzes the optimal maturity structure

3. OUTLINE
1. Introduction
2. Emerging market bond data
3. Difference between Default and Maturity
4. Quantitate analysis
5. Simultaneous results
6. Risk Premia in Sovereign bonds
7. Conclusion

4. INTRODUCTION
 Model of sovereign debt: borrowing country choose a time-
varying maturity structure of debt.
 Bond prices compensate lenders for the expected loss from default
and interest rate spreads.
 Interest rate spreads , maturity debt , short-term spread
more than long-term spreads.
 When high spreads, maturity .
 Estimate spread curves and duration of bonds issued of
emerging economies.
 1 year spread is below 50th percentile: average new debt 7.3
yrs. 1-year spreads are above 50th percentile, average new
debt 5.8 yrs.
 Slope of spread curves is 2 %.
 Bond Price= f(debt maturity, income): optimal debt maturity

5. INTRODUCTION
 debt+ income= spreads: long-term spreads
are higher than short-term spreads
 debt + income= spreads: long-term spreads
rises less than short-term spreads.
 P(low default, upward-sloping spread)
 P(high default, inverted spread): Portfolio shifts
 Brazil: 10th yr spread is on average 1.8% higher
than 1-year spread above 90th %

6. EMERGING MARKET BOND DATA
 Observe the behavior of interest rates spread over
default-free bonds across different maturities, and
the maturity of new debt issued covaries with
spreads.
 Yield is related to
 Spreads: March 1996-April 2011
 Zero-coupon bonds are estimated with secondary
market data of the price of coupon-bearing bonds.

7. TIME SERIES OF SHORT AND LONG SPREADS

8. SPREADS AND MATURITY COMPOSITION OF
DEBT
 Maturity of bond is measured:
 Number of years from the issue date until the maturity
date
 Bond’s duration: weighted average of the number of
years until each of the bond’s future payments
(Macaulay 1938).

9. AVERAGE SPREADS, MATURITY AND DURATION,
CONDITIONAL ON LEVEL OF 1-YEAR SPREAD
 Maturity yields on Emerging market bonds are high, principal
payment at maturity date is severely discounted. Bound’s value
comes from coupon payments made before maturity.
 Argentina, Brazil: average time-to-maturity of bonds issued during
periods of high spreads compared to low spreads. Brazil bonds
mature 5 years sooner when spreads are high.

10. MODEL
 Dynamic model: International borrowing with
endogenous default and multiple maturities of debt.
 Long-term debt: hedge against future fluctuations in
interest rate spreads
 Short-term: more effective at providing incentives to
repay.
 Trade-offs: quantitatively important for understanding
maturity structure in emerging markets
 Allow risk premia in sovereign bonds’ prices: changing
equilibrium bond price function, and borrowing/default
behavior.
 Time-varying risk in analyzed but tradeoff of risk-neutral
lenders is highlighted

11. MODEL

12. THE BENEFIT OF SHORT TERM DEBT
 Short debt allows larger borrowing because of an
incentive benefit relative to long-term debt.
 Two key assumption behind the incentive benefit of
short-term debt:
 Lack of commitment in debt policies inherent in the
Markov equilibria
 Punishment arises only in the event of an explicit
default.
 If lenders could instead impose a punishment
deviating from a given debt policy or could enrich
debt contracts with future debt limits then the
incentive benefit of short-term debt would be
diminished.

13. BENEFIT OF LONG-TERM DEBT
 Assume borrower has concave utility + Uncertainty
default risk varies
 Borrower’s utility
 Suppose endowments and the default punishment
satisfy
 Equilibrium the borrower defaults if income in
t2 is and repays in all other states

14. BORROWER’S BUDGET CONSTRAINTS
 This is an equilibrium because the allocation
maximizes expected utility subject to borrower’s
budget constraints:
 Write the FOC for borrower’s utility

 S.T.

15. CYCLICAL MATURITY STRUCTURE &
DISCUSSION
 When income reaches a certain level, long-term
debt becomes constrained, and the borrower shifts
to issuing short-term debt more heavily.
 In our model: short-term debt has an incentive
benefit relative to long-term debt that arises solely
from the borrower’s lack of commitment (to
repayment and to future debt decisions), and how it
affects price functions for short-term and long-term
debt.

16. QUANTITATIVE ANALYSIS
 Utility function of the borrower: =2
Income=

17. QUANTITATIVE ANALYSIS
 Average debt to GDP ratio is about half of that observed in the
data.

18. BONDS PRICES AND POLICY FUNCTIONS FOR
DEBT
 Trade off between the incentive benefit of short-term debt and the
hedging benefit of long-term debt with the bond price functions and
decision rules from the calibrated model
 Short term debt has more lenient borrowing limits—incentive to repay
is less sensitive to level of short-term debt than long-term debt.

19. BOND PRICES AND POLICY FUNCTIONS FOR
DEBT
 Debt decision rules as a f(short-term debt (
 Incentives effects of both types of debt as f(potential choices for debt
 Short-term debt is used
more heavily –incentives to
repay falls faster as a
function of long-term
loans than as a function of
short-term loans

20. SIMULATION RESULTS
 Simulate the model and report statistics on the
dynamic behavior of spreads and the maturity
composition of debt from limiting distribution of debt
holdings.
 The probability of default is mean-reverting and
persistent.
 The effect of mean-reverting and persistent default
probabilities on the spread curve are the same as in
the case of credit spreads for corporate debt.

21. SIMULATION RESULTS
 Maturity composition: Quantitative predictions for
the maturity composition of debt.
 The model the duration for short and long bonds
equal.
 Short-term debt always has an incentive benefit
because ratio is less than 1.

22. SIMULATION RESULTS
 Table below quantifies the incentives and hedging
benefits that determine the maturity composition.
 Maturity shortens
 Maturity of debt is determined by the shapes of the
bond prices function

23. RISK PREMIA IN SOVEREIGN BONDS
 Risk Premia – compensation for risk aversion
 We consider actuarially fair pricing for bonds to illustrate
the main mechanism driving the maturity structure.
 We define the pricing kernel as a function of only the
borrower’s income because it is a parsimonious way to
model risk premia that vary with the probability of
default.

24. RESULTS
 Risk premia:
 Model: + average spread curve of 0.6%
 Volatility short spread , short spread closer
 ≠ Tight connection between average spreads & default probabilities

25. RESULTS
 Actuarially fair yields:
 Risk premia for each maturity:
Short: (0.9/2.4)= 40% Long: (0.8/3.0)= 30%
 Risk premia= better fit
 However, it changes the equilibrium quantities of debt in a way that
worsen the fit to data on quantities.
 It lowers debt levels and shorten average maturity.

26. CONCLUSION
 In data for emerging markets, changes in the
maturity composition of debt commove with
changes in the term structure of spreads:
 When spreads on short-term debt are low, long-term
spreads are higher than short-term spreads, and the
maturity of debt issued is long.
 When short-term spreads , long-term spread (but
less)and the maturity of debt shortens.
 Highlight this trade-off between the benefits of
short-term and long-term debt in quantitative,
dynamic model with endogenous default and
multiple, long-term assets.

27. THANK YOU!