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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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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
4
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
PD and RR areindependent
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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
PD and RR areindependent
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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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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
20
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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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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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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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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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.