Edward I. Altman, Brooks Brady, Andrea Resti, and Andrea Sironi 羅德謙 詹燿華

1. 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

2. 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.

3. 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

4. “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)

5. “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

6. “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

7. “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”

8. 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

9. 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

10. 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.

12. 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

13. Montecarlo Simulation • Assumptions of recovery rate: • deterministic • stochastic, yet uncorrelated with the probabilities of default. • stochastic, and partially correlated with default risk

14. The Effects of the PD, LGD correlation on Credit Risk Measures: Simulation Results PDshort=PDlong*SHOCK*

15. Main Results of the LGD simulation

16. 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

17. 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

18. 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

19. Default Rate and Losses DR RR Default loss rate

20. Univariate Models

21. Univariate Model

22. Recovery Rate/Default Rate Association

23. Multivariate Models (1987~2000)

24. Multivariate Models (1987~2000)

25. Multivariate Models (1987~2000)

26. Multivariate Models (1987~2000)

28. 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

29. The LGD/PD link and the Procyclicality Effect

30. 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