DEFAULT AND THE MATURITY STRUCTURE IN SOVEREIGN BONDS

Written by: Cristina Arellano and Ananth Ramanaraynan

Presented by: Daniela Vargas, Li Jiayao

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

OUTLINE

1. Introduction2. Emerging market bond data3. Difference between Default and Maturity4. Quantitate analysis 5. Simultaneous results 6. Risk Premia in Sovereign bonds7. Conclusion

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

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 %

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.

TIME SERIES OF SHORT AND LONG SPREADS

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).

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.

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

MODEL

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.

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

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.

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.

QUANTITATIVE ANALYSIS Utility function of the borrower: =2

Income=

QUANTITATIVE ANALYSIS Average debt to GDP ratio is about half of that

observed in the data.

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.

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

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.

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.

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

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.

RESULTS Risk premia:

Model: + average spread curve of 0.6% Volatility short spread , short spread closer ≠ Tight connection between average spreads & default

probabilities

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.

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.

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