The Link between Default and Recovery Rates:
Implications for Credit Risk Models and Procyclicality Edward I. Altman, Brooks Brady,
Andrea Resti, and Andrea Sironi 羅德謙 詹燿華
Introduction
This paper analyzes the impacts of credit models’
assumptions
The association between probability of default (PD) and the
loss given default(LGD) on banks loans and corporate bonds
The effects of this relationship on credit VaR models
The Effects of the PD-LGD Correlation on Credit Risk
Measure: Simulation Results
The Procyclicality effects of the new capital
The Relationship between PD and RR
Credit risk Model
Credit pricing models
• “First generation” structural-form models
• “Second generation” structural-form models
• Reduced-form models
Portfolio credit value-at-risk (VaR) model
Finally, the relationship between probability of
default (PD) and recovery rates (RR) are briefly analyzed
“First generation” structural-form models:
the Merton approach
Using the principles of option pricing
(Balck and Scholes, 1973)
Default occurs when the value of a firm’s assets
(the market value of the firm) is lower than that of its liabilities
The payment to the debtholders
=Min( market value of the firm, face value of the debt ) = face value of the debt – put option (S= ,K=D)
A
“First generation” structural-form models:
the Merton approach
Using the principles of option pricing (Cont’)
(Balck and Scholes, 1973)
PD and RR are a function of the structural characteristic
of the firm: asset volatility (business risk) and leverage (financial risk)
PD and RR is inversely related
If the firm’s value increases → PD decreases and
RR increases
If firm’s asset volatility increases → PD increases and
“Second generation” structural-form models:
It’s assumed default may occur at any time
between the issuance and maturity of the debt
RR is exogenous and independent from the
firm’s asset value
RR is generally defined as a fixed ratio of the
outstanding debt value and is therefore independent from PD
“Second generation” structural-form models:
Three drawbacks
They still require estimates for the parameters of
the firm’s asset value, which is nonobservable
They cannot incorporate credit-rating changes
Most structural-form models assume that the value
of the firm is continuous in time. Therefore, the time of default can be predicted just before it happens
Reduced-form models
Reduced-form models assume an exogenous
RR that is either a constant or a stochastic variable independent from PD
Reduced-form models introduce separate
assumptions on the dynamic of PD and RR, which are modeled independently from the structural features of the firm
Empirical evidence concerning reduced-form
Latest contributions on the PD-RR
relationship
Frye (2000a and 2000b), Jarrow (2001), … ,
Altman and Brady (2002)
Both PD and RR are stochastic variables
which depend on a common systematic risk factor( the state of the economy).
PD and RR are negatively correlated.
In the “macroeconomic approach” it derives from
the common dependence on one single systematic factor.
In the “microeconomic approach” it derives from
Credit Value at Risk Models
Credit VaR models assume an exogenous RR that is
either a constant or a stochastic variable independent from PD
It is important to highlight that all credit VaR models
treat PD and RR as two independent variables.
CreditMetrics JP Morgan 1997 independent CreditPortfolioView McKinsey 1997 independent KMV
CreditManager KMV 1997 independent CreditRisk CSFP 1997 constant
Concluding Remarks
Merton(1974) derives an inverse relationship
between PD and RR
The credit models developed in 1990’s treat
PD and RR as independent, which is strongly
contrasts with the empirical evidence
In the next section we relax the assumption
of independence between PD and RR and simulate the impact on VaR models
Montecarlo Simulation
Assumptions of recovery rate:
deterministic
stochastic, yet uncorrelated with the
probabilities of default.
stochastic, and partially correlated with
The Effects of the PD, LGD correlation on Credit Risk Measures: Simulation Results
Empirical Results for RR
Rating agencies: Moody’s, S&P, and Fitch
Two dependent variable:
BRR: aggregate annual bond recovery rate BLRR: the logarithm of BRR
Two least squares regression models
Univariate → 60% explanation power Multivariate → 90% explanation power
Explanatory Variables( Supply Side )
BDR(-) The weighted average default rate on
bonds in the high yield bond market
BDRC(-) One year change in BDR
BOA(-) Total amount of high yield bonds
outstanding for a particular year
Explanatory Variables( Demand Side )
GDP(+) Annual GDP growth rate
GDPC(+) Change in the annual GDP growth rate
from the previous year
GDPI(+) Takes the value of 1 when GDP growth
was less than 1.5% and 0 when GDP
growth was greater than 1.5%
SR(+) Annual return on S&P 500 stock index SRC(+) Change in the annual return on S&P
The LGD/PD Link and the
Procyclicality Effect
The Procyclicality Effect
when economy is slowing
→ PD↑
→ Bank’s regulatory capital ↑ → Corporate loan size ↓
vice versa
Due to the new internal ratings-based (IRB)
approach to regulatory capital, the banks’ portfolio (Loan size) has the procyclicality effect with PD
The LGD/PD link and
the Procyclicality Effect
Concluding Remark
The link between PD and RR
Some credit models treat them as independent r.v.
This assumption may be unrealistic through simulation results or empirical evidence
The simulation result: The significant difference between RR assumptions is about 30%
The empirical evidence: the statistic models show that PD is substantial inversed correlated with RR
The link between PD and RR will bring about a sharp
increase in the “procyclicality” effect of the new Basel Accord
