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Default Recovery Rates and Implied Default Probability Estimations: Evidence from the Argentinean Crisis, December 2001. Ramiro Sosa Navarro (University of Evry, EPEE)y January 2005 Abstract This paper estimates both the default recovery rates and the risk-neutral default probabilities of the Argentinean Sovereign Bonds during the crisis of December 2001. The model presented by J. Merrick Jr ...

1 Introduction

Over the last thirty years the theory of pricing credit risk has been put

forward in order to measure corporate debt Even if similar approaches

should be applied for the calculation of sovereign risk it becomes essen

tial to point out the di erences between risky corporate debt and risky

sovereign debt as well as their consequences in valuing assets For in

stance emerging country sovereign bonds are issued in countries such as

the United States of America and the United Kingdom under completely

di erent legal jurisdiction and capacity of enforcement if compared with

corporate bonds Emerging countries are more stable than corporations

they are fewer in number they have longer term economic planning

they do not default as frequently as corporations do and they do not

typically disappear Consequently there is considerably less empirical

evidence of default on sovereign debt than on corporate debt 1

As regards the theoretical background most of the models focus on

default risk adopting static assumptions treating default recovery rates

either as a constant parameter or as a stochastic variable independent of

the probability of default The connection between default recovery rates

and implied default rates has traditionally been disregarded by credit

risk models Accordingly the problem faced by analysts in 2001 was

how to settle default recovery rates and the implied default probability

of their portfolios only on the grounds of their bond prices Now if

the bond price is a function of two unknown determinants how could

analysts calculate both of them simultaneously and consistently

Thus the approaches applied by portfolio managers in Argentina

in 2001 were grounded on the analysis of domestic and foreign data

generated by earlier international crises such as those of Mexico 1995

Russia 1998 and Brazil 1999 One of the approaches consisted in the

analysis of the time series in relation to indicators such as peaks trends

and the volatility of domestic and foreign sovereign bond price levels

An alternative approach based on a sensitivity analysis considers the

bond market price or spreads in order to calculate the implied default

probability for di erent possible recovery rates This method entails

forming conjectures about the value of recovery and the size of spread

by resorting to evidence provided by earlier crises 2

For a survey of the literature concerning this topic see Altman Edward Andrea

Resti and Andrea Sironi 2004 Default Recovery Rate in Credit Risk Modeling A

Review of the Literature and Empirical Evidence Economic Notes by Banca dei

Monte dei Paschi di Siena Volume 33

For an example of this approach see Federico Sturzenegger 2000 Defaults

The disadvantage of this approach is that its outcomes result from

di erent bond temporal term structures and hence from di erent bond

durations when compared to those of the analysed bonds Consequently

the information provided is misleading Moreover the approach does not

include information concerning recently issued bonds nor the particular

macroeconomic conditions of the country subject to analysis There

fore these methods neglect highly relevant information which is later

incorporated ad hoc into the analysis

Knowledge of both bond price determinants the default recovery

rate and the implied default probability enables the analyst to antici

pate the value of their position in case of default and assume a long or

short position according to the benchmark among other strategic deci

sions As a result the motivation of this research was based on the lack

of methodology applied by Argentinean portfolio managers in valuing

their stressed portfolios of Sovereign Bonds in the period previous to the

economic collapse

In order to avoid these disadvantages we have applied a model origi

nally presented by Merrick 2001 to estimate the default recovery rates

and the implied default probabilities in Argentinean Sovereign Bond

1 1 Brief Summary of Events Preceding the Crisis

Before presenting the model it is worth looking at the most important

events which caused the Argentinean crisis in December 2001 In August

1998 Russia defaulted on their public debt depriving Argentina of access

to the international capital market Five months later Brazil devalued

their currency causing Argentina s competitiveness in foreign markets

to deteriorate The economy sank into recession with twin de cits

a trade balance gap and a scal budget gap which foreigners were

less and less willing to nance Argentinean economy needed to regain

competitiveness and since the exchange rate could not be permitted to

fall prices and wages had to drop In December 1999 after the general

election Mr De la R a was elected to o ce but the new political

structure was too weak to face the strong political change necessary to

overcome the crisis

As a consequence peso quotation edged downwards tax revenues

faltered and Argentina s debts in US dollars became harder to repay In

Episodes in 90 s Factbook Tool kit and Preliminary Lessons prepared for the

World Bank page 14

spite of this Argentina refused to fold and kept raising the stakes At the

beginning of 2001 Argentina requested a USD 15 billion loan from the

IMF which was known as blindaje or armour In order to buy some

time in June 2001 the country completed the notorious megaswap in

which near dated securities were exchanged for longer dated securities

higher yielding bonds In August 2001 Argentina received a second 8

billion bail out Finally political turmoil and lack of further assistance

from multilateral institutions drove Argentina into default in December

2001 see Graph1

Graph 1 Argentinean Sovereign Debt Spread

Relevant Pre Default Events

JPM EMBI ARGENTINE STRIPPED SPREAD

Second IMF

Basic Points bp

Megaswap for Near dated

to Long dated Bonds

Brazil devalues First IMF Bail out

the Real the Blindaje

01 01 2002

01 01 1999

01 02 1999

01 03 1999

01 04 1999

01 05 1999

01 06 1999

01 07 1999

01 08 1999

01 09 1999

01 10 1999

01 11 1999

01 12 1999

01 01 2000

01 02 2000

01 03 2000

01 04 2000

01 05 2000

01 06 2000

01 07 2000

01 08 2000

01 09 2000

01 10 2000

01 11 2000

01 12 2000

01 01 2001

01 02 2001

01 03 2001

01 04 2001

01 05 2001

01 06 2001

01 07 2001

01 08 2001

01 09 2001

01 10 2001

01 11 2001

01 12 2001

01 02 2002

01 03 2002

This paper is divided in three sections Section II describes the Model

and the Data Section III analyses the estimations and results and Sec

tion IV presents the conclusions Finally the Appendix produces a de

tailed presentation of the estimated results and other complementary

macroeconomic data

2 The Model

This section presents the pricing framework for N period sovereign bonds

which is made up of four elements

The rst element is the bond structure which is made up of the

coupons and the principal showing the amount of the coupon paid in

period t as Ct and the amount of the principal paid on due date in

period N as FN

The second component is the default recovery rate which is repre

sented with letter R In this analysis R is the amount paid to the

bondholder immediately after default has been announced If the scal

authority defaults on the public debt the following scheme takes place

the coupons are not longer paid but the investors will receive a xed

fractional recovery of the face value immediately after defaulting 3

The third element is the adjusted risk neutral payment probability

distribution We will de ne Pt as the joint probability of no default be

tween the moment when the bond is issued and the moment t Moreover

denote the adjusted probability of default during the speci c date t 1

to date t period as pt Thus the risk free adjusted default probability is

indicated by means of pt and is de ned as 4

p t Pt Pt 1

The fourth and last element is the risk free present value discounted

factor for a time t cash ow denoted ft The discount rate used is the

risk free rate since the asset risk is captured by the probabilities of each

possible cash ow as it is shown below in equation 1

Having described the four elements we are in a better position to

state equation 1 which enables us to value a bond through the ex

pected present value of cash ows As it has already been suggested by

Jonkhart 1979 Fons 1987 and Hurley and Jonson 1996 we state

that the present value of a bond is the sum of its expected cash ows

coupons principal and the recovery rate multiplied or adjusted by

their probability As in Leland and Toft 1996 and Merrick 2001

the probability distribution used here is interpreted as the implied risk

neutral distribution Henceforward we are implicitly referring to risk

neutral probabilities

V0 fPt ft Ct g fPN fN FN g fpt ft Rg 1

The bond s current value is viewed as the probability weighted sum

of the coupon ows the principal and the recovery rate It should be

The recovery rate can also be de ned as the expected present value of cash

ows which have been or are to be reprogrammed For a detailed presentation see

Recovery Rates The Search of Meaning High Yield Merrill Lynch March 2000

Alternatively the probability

Pof receiving a promised date t coupon payment Pt

can be expressed as Pt 1 s 1 ps

noted that expressing the pricing equation in these terms implies that

the asset risk becomes captured by the implied default probability and

its complement the implied probability of payment As a consequence

all possible cash ows coupons principal and the recovery rate remain

discounted at the risk free rate Otherwise the asset risk is generally

enclosed in the discount rate factor

Let us now outline the model a little further Before stating the

joint probability of no default Pt we de ne the risk neutral default

probability rate noted as t Previous researches such as Fons 1987

and Bhanot 1998 consider a constant t Our proposal as much as

Merrick 2001 understands t as an increasing linear function with

respect to time t as it is shown in equation 2

The purpose of this function is to capture the default probability

temporal term structure throughout time in a parsimonious way This

formalisation registers the fact that in a critical period the probability

of default is greater as the deadline of the coupons and the amortisation

become closer in time 5

Thus the joint probability of no default Pt can be de ned as

In which parameters and are restricted so that Pt is always

less than or equal to one and greater or equal to zero Consequently

equation 4 explicitly states the three unknown elements R and

incorporated in the model

V0 1 t t ft Ct 4

1 N N fN FN

1 t t ft R

Otherwise during crisis long term default probabilities might be lower than the

short term conditional on the sovereign s ability to avoid the case to fall into default

This e ect is not captured by this assumption

Having established the equations it is possible to present the model

that allows for a consistent estimation of the three unknown parameters

which will in turn enable us to know the default recovery rate and the

default probability temporal term structure

2 1 Estimation Strategy

In order to estimate the unknown parameters we de ne the bond s

model value Vi 0 by substituting in equation 4 the three unknown

parameters by its estimations R Then consider at date t 0 a

cross section of I outstanding bonds indexed by the subscript i Now

we are able to de ne the sum square of residuals SSR at date 0 as

SSR0 Vi 0 Vi 0 5

where Vi 0 denote the market value of the ith bond at the date 0

recalling that Vi 0 is the estimated ith bond price

The each day estimation parameters can be achieved by getting the

value for R and that minimise equation 5 subject to the average

cross sectional bond pricing residual equalised to zero expressed as

Vi 0 Vi 0 0 6

As a consequence the model as a whole is formalised through the

statement of ve equations it means i 1 5 Then for each day in

the sample it was constructed the cash ow event tree for each of the ith

bonds according to equation 4 Next initial guesses were used for the

unknowns to estimate the parameters Finally a Solver was employed to

minimise square residuals equation 5 on condition that the average

sum of errors is equalised to zero equation 6 Subsequently this exer

cise is repeated for each day of the analysed period The Solver applies

the Generalised Gradients Method to estimate the unknown elements 6

For the model to be consistent it is assumed that the bonds have

a cross default clause which is a realistic assumption in the case of

Argentina This assumption implies that there is a representative default

recovery rate for the economy as a whole

In this paper we have used the Solver included in Microsoft O ce Package

Notice that the estimations were computed using an algorithm of

non linear optimisation subject to non linear constraints So it does

not guarantee that the results are the global solution However experi

mentations with alternative initial guesses conduct to the same results

The Appendix includes an example that shows the estimated results

based on the market price structure of October 1st 2001 The data and

results concerning the fourth quarter 2001 are shown in a Table

It have been selected the ve most representative bonds of the econ

omy i e the bonds which have been most actively traded in the short

medium and long term From these ve bonds we obtain the default re

covery rate and the default probability temporal term structure which

are the most representative determinants of the economy for a given

market price structure at each moment in time

2 2 The Data

For the period subject to analysis October 2001 December 2001 we

have considered 5 Global Bonds denominated Eurobonds at a xed

rate with semestrial coupons and amortisation at nish These charac

teristics are speci ed below

Table 1 Sample of US Dollar denominated Eurobonds

Name Issue Date Maturity Date Coupons

Arg 03 20 Dec 1993 20 Dec 2003 8 375

Arg 06 09 Oct 1996 09 Oct 2006 11 000

Arg 10 15 Mar 2000 15 Mar 2010 11 375

Arg 17 30 Jan 1997 30 Oct 2017 11 375

Arg 27 19 Sep 1997 19 Sep 2027 9 758

These bonds are not guaranteed They have a cross default clause

and they were issued under the jurisdiction of English Courts in London

This analysis was carried out considering the daily prices supplied by

the Secretary of Finances of the National Ministry of Economy from the

Argentine Republic

Figure 1a shows the average daily prices for the bonds which have

been described as representative of the economy for the period we are

analysing Figure 1b in turn speci es the same series considering each

of the bonds individually

Figure 1a Average Bond Prices

Average Price

Bond Price for each USD 100 Face Value

October November December

Figure 1b Individual Bond Prices

RA 03 RA 06 RA 10 RA 17 RA 27

Bond Price for each USD 100 Face Value

October November December

3 Estimation Results

This section deals with the model estimations concerning the aforemen

tioned Eurobonds for the case of the Argentinean domestic crisis It will

be focu on the fourth quarter 2001

It is worth noticing that the Base Default Probability is denoted in

the model by means of parameter Alfa and it de nes the current de

fault probability The estimations regarding parameter Beta which

is employed to calculate the default probability temporal term struc

ture shows an increasing linear trend with respect to time as it was

de ned However we will not analyse the estimations of the Betas and

the changes in the steepness of the temporal term structure In what

follows both the default recovery rates and base default probabilities

estimations are presented in Figure 2a 7

Figure 2a Estimated Default Recovery Rates and Base Default

Probabilities

Alpha Recovery Rates

US Dollar and Percentage

It is depicted that between October 1st and December 28th 2001 the

average bond market value re ected a downward trend falling from USD

59 5 to USD 27 6 for each USD 100 face value Similarly default recovery

rates descended from USD 28 5 to USD 20 1 reaching its maximum level

USD 40 9 on October 19th and its minimum USD 14 6 on November

13th Conversely the base default probability registered an increase

from 14 8 to 40 4 reaching its maximum level 45 5 December 21st

and its minimum 13 3 on October 19th

Notice that on October 19th the estimations show it the maximum re

covery rate USD 40 9 and its minimum base default probability 13 3

On the other hand on December 21st the base default probability reg

istered maximum level 45 5 while the default recovery rate is one of

the lowest in the sample USD 20 8 Thus both embedded determinants

become relevant in explaining bond price volatility while they seem to

follow a negative correlation but long periods have to be considered for

instance one and half month equivalent to 30 observations Figure 2b

shows the estimation results depicting linear trend lines

Regarding the shape of the default probability temporal term structure another

approach is presented in more detailed way by Andritzky J R 2004

Figure 2b Estimated Recovery Rates and Default Probabilities with

linear trendlines

Alpha Recovery Rates

US Dollar and Percentage

Regarding the standard deviation of the estimations they are due to

the fact that for some estimation the square residuals are low one digit

whereas for others estimations the square residuals range from 15 to 30

See in the Appendix the table of input data and estimation results

The cases in which residuals are close to zero and so the estimations

are very accurately the Solver has found a combination of estimated

parameters and so estimated bond prices which exactly reproduce

the yield duration market curve See in the Appendix the example for

October 1st

The information provided by the model enables the individualisation

of the parameters ruling over market prices But in order to improve

the quality of the information supplied it has been plotted the series

considering a two period and four period moving average to obtain a

more stable series which can average out the statistic errors See Figure

Figure 3 Default Recovery Rate and Base Default Probability with

Figure 3a Two moving average Figure 3b Four moving average

Alpha Recovery Rates Alpha Recovery Rates

Price for each USD 100 Face Value

Price for each USD 100 Face Value

Dates Dates

As it can be seen in Figures 2 the period October 1st October 10th

shows that both curves are stable and that the default recovery rate

registers a downward trend whereas the Default Probability reveals an

upward trend both being coherent with a drop in bond prices It must

be observed that both determinants show a moderate gradient which cor

responds to the trend intensity registered by market prices see Figures

1 Subsequently the opposite phenomenon is registered from October

11th to October 19th Thus the Model presented is capable of assessing

slight oscillations in market prices However for some short periods two

weeks which equal 10 observations the estimations register a positive

correlation between recovery rates and base default probabilities

A negative relationship is accomplished if we take a longer period

so that statistic errors can be compensated for Considering the period

extending from October 19th to December 21st along which bond prices

registered a downward trend it is possible to observe that default re

covery rates start at USD 40 9 for each USD 100 face value and reach

USD 20 8 whereas base default probability starts at 13 3 and reaches

45 5 See below Figures 4

Figure 4 Default Recovery Rate and Base Default Probability with

From October 19th to December 21st

Figure 4a Logarithmic Trendline

Alpha Recovery Rates

US Dollar and Percentage

Figure 4b Linear Trendline

Alpha Recovery Rates

US Dollar and Percentage

To sum up the increase in prices was accompanied by an increase in

default recovery rates and a fall of implied default probabilities Con

versely the reduction in prices was accompanied by a drop in default

recovery rates and an increase in implied default probabilities The re

sults obtained show that for long periods e g a two month period the

model produces results which are consistent in time

3 1 Interpretation of Results

Market information produced between December 10th and December

28th before and after default was o cially announced is presented in

the following Table

Table 2 Estimated Parameters

Before and after Default December 24th

Average Recovery

Date RA 03 RA 06 RA 10 RA 17 RA 27

Price Rate

10 Dec 36 8 32 8 29 0 29 0 29 0 31 32 20 73

11 Dec 36 0 34 0 29 0 30 0 29 0 31 60 22 04

12 Dec 35 9 34 4 30 1 30 0 31 0 32 28 24 16

14 Dec 37 0 33 1 30 0 27 1 32 0 31 84 22 15

17 Dec 37 0 33 6 29 4 30 0 31 5 32 20 23 30

18 Dec 35 5 34 0 30 5 27 5 32 0 31 90 24 21

19 Dec 36 1 33 4 29 5 25 8 30 0 30 96 20 77

20 Dec 28 5 34 5 29 5 26 3 32 0 30 16 16 08

21 Dec 28 9 28 5 26 0 23 9 25 3 26 52 20 79

26 Dec 28 0 28 0 23 3 23 9 26 0 25 84 20 01

27 Dec 29 8 25 5 24 0 26 0 23 0 25 66 17 50

28 Dec 31 0 28 0 26 0 28 0 25 0 27 60 20 15

These data show that the market adjusted the bond prices falling

from USD 30 02 for each USD 100 face value to USD 26 5 on December

21st after the resignation of the Minister of Economy and the President

instead of producing the adjustment on December 26th after default

was o cially announced Thus we understand that Argentina really

defaulted on December 21st 8

As regards the default recovery rates evidenced between December

10th and December 28th these estimations make for a good approxima

tion to the market value as they present quite small square residuals

except for those registered on December 20th It should be obseved that

estimations recorded on December 20th registered square residuals of

three digits Consequently in order to obtain a better approximation to

this value we will take the average value of default recovery rates in the

pre default period i e between December 10th and December 19th

This average value amounts to USD 22 48 9

Brief chronicle of the events leading to the crisis On December 20th the Minister

of Economy Dr Domingo F Cavallo and the President Dr Fernando De La R a

submit their resignation On December 21st the president of the Senate Dr Ram n

Puerta takes over provisionally for a 48 hour period On December 23rd Dr Adolfo

Rodr guez Saa is appointed as President On December 24th he announces the

country s insolvency before the National Congress

Given that the market price on December 20th registers USD 30 2 less than the

prices registered between December 10th and December 19th USD 31 0 USD 32 3

the Default Recovery Rate implicit in that price should be marginally smaller but in

no case close to USD 16 08

To sum up the results before and after market adjustment were as

Period 10 20 12 2001

Data Interval Average

Average Price USD 30 2 USD 32 3 USD 31 5

Recovery Rate 1 USD 20 7 USD 24 2 USD 22 5

Period 21 28 12 2001

Data Interval Average

Average Price 2 USD 25 8 USD 27 6 USD 26 4

Recovery Rate USD 20 8 USD 17 5 USD 19 6

Market average prices registered as of December 21st the date the

market considers Argentina defaulted are considered as the default

recovery rates validated by the market As a result this paper compares

market prices registered on December 21st and the default recovery rate

evidenced on December 20th In other words if the economic system

unexpectedly defaults in a period t the market price in the period t 1

should be equal to the recovery rate implicit in the last market price

Thus we have that

Data Interval Average

The difference

USD 5 1 USD 3 4 USD 3 9

It follows that bonds were overvalued at USD 3 9 on average in a

range of USD 5 1 and USD 3 4 that is by 12 9 We interpret that

it would have been correct to adopt a short position and buy when the

market evidenced the model estimations that is when the assets were

quoted at average values of USD 22 5 in a range of USD 20 7 and USD

24 2 10 as it happened as of May 2002

However for a proper interpretation of the data it is crucial to sit

uate the model in the market conditions registered at the time With

this respect two elements should be highlighted Firstly the Stage 1

of the debt swap started on October 30th the public debt held by do

mestic investors was forcibly swapped in this stage replacing the bonds

which accrued an annual 10 4 interest on average with bonds quoted

at a 6 annual interest rate This explains why Argentinean Bonds were

These values are correspondent with the Recovery Rates previous to the market

adjustment