Myths & Pitfalls in PIT versus TTC Credit Risk Management The impact of subtleties

A real-life example What is ***the*** PD?» Real-life example shows default rate and estimated Probability of Default (PD) for ships.» Can this be right?» Why does the regularly recalibrated rating system not adapt to reflect the increased default rates?» What is the correct PD in 2012? PD / Default rate Default rate PD 20% 10% Time 2007 2008 2009 2010 2011 2012 * d-fine All rights reserved 2

Proper Definition of PD depends on purpose» Without a precise question, there is no right answer What is the probability that the obligor defaults within the next 12 months given the current macroeconomic environment? What is the probability that the obligor defaults within a 12 month period given an average macroeconomic environment? Point-In-Time PD (PIT-PD) Through-The-Cycle PD (TTC-PD)» The right question to ask, depends on the intended purpose Accounting (IFRS 9): Evaluation of current fair value is intended. PIT-PD Risk Management: Focus on changing (worsening) economic environment. TTC-PD (+ Asset-Correlation R²) Credit institutes need to compute both, the PIT-PD and the TTC-PD. d-fine All rights reserved 3

Common Market Practice: Often no distinction between PIT and TTC» Mathematical Background: Merton model Obligor defaults, if asset value A falls below default threshold γ A = R X + 1 R 2 ε < γ TTC-PD is directly linked to default threshold γ PD TTC = Φ(γ) PIT-PD is the conditional default probability given the economic environment X PD PIT = Φ γ R X 1 R²» Common Market Practice Rating System» Credit institute typically operates rating systems that compute one PD-value PD RATING for each obligor.» This PD-value is typically neither purely TTC nor purely PIT but a hybrid, i.e. PD RATING = κ PD PIT + 1 κ PD TTC» The degree of pitness κ is typically unknown to the credit institute. PD RATING = κ PD PIT + 1 κ PD TTC Credit institutes typically compute hybrid PD without clear distinction between PIT and TTC perspective. d-fine All rights reserved 4

In an ideal world a single rating system provides PIT- and TTC-PD» Ideal world: Introduction of dual-channel rating system Dual-Channel Rating System» Ideally, a credit institute would operate a dual-channel rating system that computes for each obligor both, the PIT-PD and the TTC-PD.» Sometimes effective approaches are implemented in practice that intend to convert PIT-PDs into TTC-PDs, and vice versa, with effective factors.» However, a genuine dual-channel rating system is more than just a rescaling approach (see below). PD PIT PD TTC» Conceptual remarks on design of dual-cannel rating systems The difference between PIT and TTC rating systems is often ascribed to different temporal extensions of the calibration period. This is only partly true. The main difference is the dependence/independence on/of the macroeconomic environment. PIT-channel Built on risk drivers that adjust quickly on economic environment (earnings, behavioral data, ). TTC-channel Built on risk drivers that are rather independent of economic environment (sector, company size, ). d-fine All rights reserved 5

PIT and TTC rating systems behave quite oppositely» PIT rating system» TTC rating system» Rating class population depends on macroeconomic environment leading to strong systematic migrations.» Rating class population is independent of economic environment leading to only idiosyncratic migrations.» On the other hand, the observed default rates per rating class are (ideally) independent of economy.» On the other hand, the observed default rates per rating class fluctuate strongly depending on economy. Default rates per rating class PIT-RC1 PIT-RC2 PIT-RC3 Master-scale PD of RC1 Master-scale PD of RC2 Master-scale PD of RC3 Default rates per rating class TTC-RC1 TTC-RC2 TTC PD of RC1 TTC PD of RC2 TTC PD of RC3 t 0 t 1 t 2 t 3 Time t TTC-RC3 Re-Rating Re-Rating Re-Rating Re-Rating t 0 t 1 t 2 t 3 Time t Ideal PIT rating systems exhibit strong systematic migrations but rather constant default rates per rating class. TTC rating systems exhibit exactly the opposite behavior. d-fine All rights reserved 6

ICAAP: PIT-PDs lead to cyclically oscillating Capital Requirements» Determination of ICAAP Credit Risk Capital Requirements» Credit institute typically operates credit portfolio model to compute ICAAP credit risk capital requirements on basis of PD, asset correlation R², LGD, EAD, and many other parameters.» PDs used in credit portfolio model are typically taken directly from rating system, i.e. hybrid PDs with certain degree of pitness κ. PD R² LGD EAD Credit Portfolio Model» As a consequence the interpretation and properties of the resulting capital requirements depend on the pitness κ of the underlying rating system. Credit risk capital requirement» Rather PIT-PDs (small κ)» Rather TTC-PDs (large κ)» Property: Resulting capital requirement depends cyclically on macroeconomic environment, i.e. more increasing capital requirements in crisis.» Interpretation: Resulting capital requirements guarantee survival of upcoming 12-month period given the current macroeconomic environment with given certainty (e.g 99.95%).» Property: Resulting capital requirement independent of macroeconomic environment, i.e. constant capital requirements also in crisis.» Interpretation: Resulting capital requirements guarantee survival (statistically) of 1999 out of the 2000 upcoming years (for 99.95% certainty level) independent of current macroeconomic environment. PIT-type rating systems induce cyclically oscillating capital requirements. TTC-PDs should better be used. d-fine All rights reserved 8

PD Term Structure modelling: Standard approach invalid for PIT-PD» Determination of PD-Term-Structure» In particular, IFRS-9 Lifetime Expected Loss requires PIT-PD-Term Structure due to LEL = Maturity t EAD t PD PIT t LGD(t)» Term Structure PD(t) caused by migration processes.» Typically insufficient data render direct determination infeasible.» Indirect approach for computing PD(t) based on exponentiation of migration matrix M typically pursued. PD t n = m 1,1 m 1,2 m 1,3 m 2,1 m 2,2 m 2,3 m 3,1 m 3,2 m 3,3 n PD(t 0 )» Prerequisite for validity is Markov property of migrations.» Idiosyncratic (TTC-) migrations are a Markov process.» Systematic (PIT-) migrations are not a Markov process.» Standard exponentiation approach conceptually invalid for desired PIT-PD-Term-Structure.» Dramatic overestimation of convergence velocity of PIT-PD. d-fine All rights reserved 9

PD Term Structure modelling: Consistent approach possible» Constructing a conceptually consistent PIT-PD Term Structure» First Step: Construct TTC-PD-Term-Structure by standard migration matrix exponentiation approach.» Rationale: TTC migration is a Markov process. PD TTC t n = M TTC n PD TTC (t 0 )» Second Step: Construct PD PIT (t) on basis of TTC curve:» For current date t 0 determine PD PIT (t 0 ) and PD TTC (t 0 ) (e.g. by means of dual-channel rating system).» With given asset-correlation R² compute current X(t 0 ).» For future time t: Mitigate economic downturn by computing future expectation of factor X(t) given current factor X(t 0 ) assuming auto-correlation α according to E X t X t 0 ~ න X t e X t 2 +2αX t X t 0 dxt» Auto-Correlation α = cor X t, X t+1 given by historic observations.» Use X(t) to translate PD TTC (t) into PD PIT (t). d-fine All rights reserved 10

EBA stress testing: Simple rescaling of PDs insufficient» Conceptual considerations» For stress testing stressed macroeconomic risk drivers X(t) typically given (e.g. GDP growth -2% for first year, -1.5% for second ).» GDP decline needs to be translated into stressed PDs.» This is typically done by regression analysis yielding factor f stress PD stress = f stress PD» Factor f stress must match pitness degree κ of rating PD.» Problems with this approach:» Method cannot provide stressed migration matrices.» Method cannot provide genuine stressed PD term structure. Conceptually consistent standard approach to stress testing not yet established. d-fine All rights reserved 11

EBA stress testing: Genuine stressed PD term structure can be constructed» Constructing genuine stressed migration matrices and PD term structure» For stress testing stressed macroeconomic risk drivers X(t) typically given (e.g. GDP growth -2% for first year, -1.5% for second ).» Given the asset correlation R 2 the macroeconomic X(t) can be used to translated PIT- and TTC-PDs.» TTC term structure obtained from PD TTC t n = M TTC n PD TTC (t 0 )» Stressed PIT-PD term structure given by PD PIT (t) resulting from given (stressed) X(t).» Corresponding stressed migration matrices obtained by clustering the resulting stressed PD PIT (t) into rating classes.» Result: The stressed PIT-PD term structure is strongly affected by assumed stress at short time scales but converges to the same equilibrium limit as in the unstressed scenario. d-fine All rights reserved 12

Conclusion A consistent credit risk management requires a clean distinction between Point-In-Time (PIT) and Through-The-Cycle (TTC) PD. In practice, these subtleties often need to be respected more carefully. Unawareness in this subject affects various fields in risk management and may lead to - pro-cyclical oscillations of ICAAP Capital Requirements. - unrealistic PD Term Structure models. - conceptually inconsistent stress testing methodologies. d-fine All rights reserved 13

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