edward i. altman, brooks brady, andrea resti, and andrea sironi 羅德謙　詹燿華

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 requirements proposed by Basel Committee.

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)

AV

“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 RR decreases

“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

→ no “sudden surprises”

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 models is rather limited

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 the supply and the demand of defaulted securities

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

default risk

The Effects of the PD, LGD correlation on

Credit Risk Measures: Simulation Results

PDshort=PDlong*SHOCK*

Main Results of the LGD simulation

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 BDA(-) Bond default amount

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 500 stock index from the previous year

Default Rate and Losses

Univariate Models

Univariate Model

Recovery Rate/Default Rate Association

Multivariate Models (1987~2000)

Multivariate Models (1987~2000)

Multivariate Models (1987~2000)

Multivariate Models (1987~2000)

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