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The Link Between Default and Recovery Rates

Ed Altman, Brooks BradyAndrea Resti, Andrea Sironi(based on an ISDA-sponsored research)

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Outline of this talk

Default and recovery rates in previous research worksAn empirical test of DR/RR correlationTwo simulation exercises: how the DR/RR correlation affects

Credit risk modelsProcyclicality issues

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Previous research works/1:credit pricing models

Main contributions

Relationship betweenPD and RR

RR is treated as:

2nd generationstructural

formmodels

1st generationstructural

formmodels

Reduced formmodels

Exogenous (constant or stochastic)

Litterman-Iben ’91, Madan-Unal ’95, JT ’95, JLT ’97, Duffie-

Singleton ’99

PD and RR areindependent

Endogenous: depends on structural

characteristics of the defaulted firm

Merton ’74, Black-Cox ’76, Geske ’77, Vasicek’84, Crouhy-Galai ’94, Mason Rosenfeld ‘84

PD and RR are inversely related

Exogenous and independent of the firm’s asset

value

Kim et al. ’93, Nielsen et al., Santa Clara ’93,

Hull-White ’95, Longstaff-Schwarz ‘95


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Previous research works/2:credit VaR models and beyond

Main contributions

Relationship betweenPD and RR

RR is treated as:

CreditVaR

models

Some latest contributions

Stochastic, depending on

some macro or supply factor

Frye ’00 and ’01,Jarrow ’01, Carey-Gordy ’01, Altman-

Brady ’01, Jokivoulle-Peura ’01, Hu and

Perraudin, ‘02

PD and RR are correlated, usually in a negative way

Constant (CSFP) or stochastic

Gupton et al. ’97, Wilson ’97, CSFP

’97, McQuown ’97, Crosbie ‘99


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Structure of the sample

About 1000 bonds (NYU Salomon Center database) defaulted between 1978 and 2001Define BRR as weighted average price of defaulted bonds as close to default date as possible

0%

10%

20%

30%

40%

50%

60%

70%

1978 1983 1988 1993 19980%

2%

4%

6%

8%

10%

12%

BRR DR (rhs)

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The univariate pictureRecovery Rate/Default Rate Association

Altman Defaulted Bonds Data Set (1982-2000)Dollar Weighted Average Recovery Rates to Dollar Weighted Average Default Rates

1997

1984

1996

19931983

1987

1994

1998

1985

1995

1988

1982

1992

1986

1989

19992000

1990

1991

y = -2.617x + 50.9R2 = 0.4498

y = -11.181Ln(x) + 52.332R2 = 0.5815

y = 0.5609x2 - 8.7564x + 60.61R2 = 0.6091

y = 52.739x-0.2834

R2 = 0.6004

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25

30

35

40

45

50

55

60

65

0 2 4 6 8 10 12

Default Rate (%)

Rec

over

y R

ate

(%)

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Mac

ro fa

ctor

sD

eman

d an

d su

pply

Multivariate models:explanatory variables

BRRBRR

BDRCBDRDefault rate on yigh-yieldbonds: level or 1-year change

BOA BDAOutstanding amount of high-yield bonds (or defaulted bonds)

BIR NYU Performance index (price change) of defaulted bonds

GDPC GDPIGDPGDP: level, chg,dummy (1 whenchg. < 1,55)

SRCSR S&P 500 index:level and change.

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Some multivariate results

Supply and demand variables explain

about 90% of BRR total variance

Macro factors are less significant:

GDP is “crowded out” by BDR

because of a strong (-67%) univariate

correlation

Model I Model II Model IIIConstant -1.55 -1.29 -1.02

(-9.27) (-4.51) (-6.36)BDR (log) -0.22 -0.13

(-5.18) (-1.96)BDRC -3.51 -3.45 -4.85

(-2.82) (-2.45) (-2.55)BOA -0.59 -0.85

(-2.60) (-2.18)BDA -10.60

(-1.84)BIR 0.20 0.33 0.43

(1.28) (2.14) (1.63)GDP 0.33

(2.14)R-square 91% 89% 68%

Dependent var.: BRR (log)

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A Montecarlo simulation based on a sample portfolio

250 loansbelonging to 7 different rating classes, total exposure 28,2 mln. €.Exposure at riskand long-term PDs of the loansare shown in the chart

0%

1%

2%

3%

4%

5%

6%

0 5 10 15

EXPOSURE (thousand euros)

PR

OB

AB

ILIT

Y O

F D

EFA

ULT

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Weightse.g., ½ + ½

Weightse.g., ½ + ½

Idiosyncraticrisk-factor

Idiosyncraticrisk-factor

Mr. Smith’slong-term PD

(known)

Mr. Smith’slong-term PD

(known)

Systemicrisk-factorSystemicrisk-factor

How short-term PDs are derived:(Credit Suisse Financial Products, 1997)

)~~(~2211 xwxwpp ii +=

Mr. Smith’sshort-term PD

(stochastic)

Mr. Smith’sshort-term PD

(stochastic)

Both are gamma-distributed with mean 1

Key:DeterminisicStochastic

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Gamma distributionfor idiosyncratic

noise

Gamma distributionfor background factor

1. Draw a backgroundfactor and some noise from 2

gamma distributions

x2

x1

5. Loop 100,000 times

$

3. Based on the adjusted PDs, draw the borrowers

defaulting in this scenario

)( 2211 xwxw + =x

1.0%2.0%0.5%2.0%1.0%1.0%1.0%2.0%…2.0%0.5%2.0%1.0%

1.3%2.6%0.7%2.6%1.3%1.3%1.3%2.6%…2.6%0.7%2.6%1.3%

2. Use macro factor and noise to adjust the 250 long term PDs to their

conditional values

4. Based on recovery ratescompute lossesand file them

The simulation engine: overview

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3approaches

3approaches

Detail: three approaches to recovery rates

1: Recovery rates are fixed

Basically, this amountsto the standard Creditrisk+ model

2: Recovery rates are stochastic,yet uncorrelated with PD

as in the CreditmetricsTM model

3: Recovery rates andPD are stochastic and

correlated*

3: Recovery rates andPD are stochastic and

correlated*

*High values for the macro factor (i.e., recession scenarios) bring in RRs close to 10%, while low values in the macro factor are associated with RRs of about 90%

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Simulation results

Delta1 2 3 (3-1)/1

Expected loss 46.26 45.81 59.85 +29.4%

Standard errors 98.17 97.84 127.16 +29.5%VaR 95 190 188 245 +28.9%

99 435 437 564 +29.6%99.5 549 546 710 +29.3%99.9 809 815 1,053 +30.1%

RR modeled according to approach:

…both unexpected and expected losses are severely underestimated

Moreover, cyclical swings may be stronger than expected

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The procyclicality issue

As the economic cycle worsens, so do ratings.This means that, under the new rating-based Basel rules, a bank would have to raise more capital or to reduce its loan bookThe latter would make economic slowdowns even worse…

In the “advanced” internal rating-based approach proposed by the BCBS, banks are allowed to use their own estimates of recovery rates

What if these estimates are reduced as the economy slows, when the supply of defaulted assets increases?

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The procyclicality issue:a simulation exercise

Suppose we set up a bank in 1980:Its loan mix (by rating) is set according to a sample of 26 US banks (Treacy and Carey, 2000) or to the average portfolio mix of Italian banks (Marullo, 2000)

Let the bank’s loans migrate across rating classes according to S&P’s transition matrices

Bad quality loansincrease in bad times

(e.g., in 1990)

1980 1990 2000AAA 3% 3% 2%AA 5% 7% 9%A 13% 20% 25%BBB 28% 25% 30%BB 39% 21% 19%B 10% 20% 14%CCC 2% 4% 2%

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The procyclicality issue:a simulation exercise

Suppose we set up a bank in 1980:Its loan mix (by rating) is set according to a sample of 26 US banks (Treacy and Carey, 2000) or to the average portfolio mix of Italian banks (Marullo, 2000)

Let the bank’s loans migrate across rating classes according to S&P’s transition matricesEvery year between 1980 and 2000 compute capital adjustments according to Basel II rulesSee by how much the loan book may grow, or must shrink, to comply with capital ratios

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Simulation results: base case

Change in loan portfolio size

-10%

-5%

0%

5%

10%

15%

20%

25%

1981 1984 1987 1990 1993 1996 1999

CP2, corporate

Nov01, corporate

The Nov 2001 curve reduces capital requirements in a static sense, but would not ease procyclicality, at least for good quality loan portfolios: the increase in capital when moving to an AAA- to a CCC-rated loan is

lower, but rating changes for top-quality loans can bring about a sharper change in capital

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Base case: procyclicality hits twice

Average credit spreads on new loans

1.0%1.2%1.4%1.6%1.8%2.0%2.2%2.4%

1981 1984 1987 1990 1993 1996 1999

CP2, corporate

Nov01, corporate

Banks raise rates as credit quality starts to deteriorate. This increases

financial charges for their customers and, in turn, prompts more defaults..

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Advanced IRB: effects of the PD/LGD correlation

Change in loan portfolio size

-40%-30%-20%-10%

0%10%20%30%40%50%

1981 1984 1987 1990 1993 1996 1999

CP2 corporate -base simulation

CP2, corporate

Nov01, corporate

Procyclical swings tend to be much wider than in base case

Bank spreads (not shown) also become more volatile

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Final remarks

The link between DR and RR has an important impact on some relevant issues

Expected losses and reservesUnexpected losses and credit VaR measuresProcyclicality and overall adequacy of the new Basel rules

Bond market data suggest that this link might be present across the cycleMore research on typical bank data is needed.

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