Corporate Default Modelling Forecasting defaults and analysing the

Corporate Default Modelling Forecasting defaults and analysing the interaction between defaults and the real economy David Tysk Central Bank of Iceland June 16, 2010

Questions to be answered today • What is probability of default (PD)? • Are corporate defaults relevant for financial stability? • Does defaults interact with the real economy? • What data is available to model PD? • How good is the PD model? • Is it possible to make long term forecasts? • What does the crystal ball say?

What is probability of default? • Probability of default (PD) is a quantitative assessment of the likelihood that an obligor (e. g. , a corporation) will default within a specified period of time • Default rate (DR) is the ratio of defaulted corporations over the total number of corporations in a specific period of time • The average PD is an estimate of the default rate

PD – Here and there • PD period – There: The length of the period is often one year; e. g. , in Basel II – Here: Set to one quarter to enable analysis of quarterly variations (results are however sometimes annualised) • Default definition: – There: The Basel II definition of default is – simplified – equal to >90 days past due – Here: A corporation is defined as defaulted if it has filed for bankruptcy

Are corporate defaults relevant for financial stability? • Default rate: Annual corporate default rate • Loan loss ratio: Annual loan losses over loans and receivables to customers for the three main banks

Arguments for the corporate default rate as a measure of the risk of financial instability • The Icelandic corporate sector represents the largest credit risk in the Icelandic banking system • Neither loan losses nor defaults are leading or lagging the other variable • Loan losses are more complex to forecast due to operational risks and changes in accounting rules • Macro prudential – it captures the systematic risk in the banking system

Does the default rate interact with the real economy? • The Icelandic economy is modelled as a small, open economy with a vector autoregressive (VAR) model – Estimated on 1999/Q 1 to 2009/Q 4 data • Variables – Endogenous: lag 1 -2 quarters, output gap, inflation, real exchange rate, CBI monetary policy interest rate – Exogenous: lag 0 -2 quarters, foreign: output gap, inflation, short term interest rate • Test statistics – Stationary (largest |unit root| is 0. 89) – Lag order selection criteria suggest more lags – Residuals are normal and without auto-correlation

Default rate causes GAP, RS, (INF) – Include the default rate as endogenous in the VAR-model to analyse interaction • Granger causality test – Granger causality test indicates that DR causes • output gap (GAP_SA) • policy interest rate (RS) • inflation (INF) p-value=0. 1 • Impulse response – Default rate shock

Default rate is the preferred measure of the financial stance of the economy • Block-exogeneity test – Evaluate the predictive power of some commonly used measures of the financial stance of the economy – Default rate and loan losses shows highest predictive power –. . . but loan losses does not “Granger cause” any of the other variables

THE PD MODEL

What data is available to model PD? • Default data – From 1985 • Annual accounts – 1997 to 2008 accounts • Macro data – QMM database • Exclusions – Corporations that have not reported their accounts during the previous year are excluded, e. g. a company is excluded in 2005 if it has not by then reported the 2003 accounts

More than half a million quarterly observations of individual corporations • Dependent – Default indicator: Default or not? • Independent – 28 micro variables • Age variable • Ratios derived from balance sheets and income statements • Lagged 2 years – 12 macro (only domestic) • Lagged 2 quarters – 3 dummies to model quarterly variations and one trend variable were defined • 1999/Q 1 to 2009/Q 4 used to estimate the PD-model

PD – The definition • Probability of default (PD) – Let Dit be the default indicator of corporation i in period t. – Dit = 1 if i has defaulted in t, and zero otherwise – Probability of default, PDit, in period t is given by i. e. , Dit is a binary variable with parameter PDit – The default rate, rt, in period t is given by where nt is the number of corporations in period t.

Logistic regression is used to model PD • Generalised linear model for binomial regression • Dit. . . dependent variable, default/non-default • Sjit. . . independent variables, micro and macro • PD given the information S is modelled with the logistic function • Fitting: Maximum likelihood using an iteratively reweighted least squares algorithm

Some financial variables behave badly 1. Calculate default rate 2. Estimate PD = f(v) 3. Calculate the score S 4. Derive value-to-score 5. Estimate PD = f(s)

. . . but macro variables are fairly nice

Automated factor selection process to reduce the risk of over-fitting • Single factor analysis – exclusions – Factors with incorrect sign are excluded; e. g. , GDP growth – Factors with “complex” behaviour are excluded; e. g. , size • Regression – exclusions – Factors with coefficients with incorrect sign; e. g. , EBITDA/revenues – Factors with insignificant coefficients; e. g. , inflation • K-fold cross validation – exclusions – Factors with high variance in the coefficient; e. g. , dividend • Marginal contribution – exclusion – Factors with negative marginal contribution

Increased output gap, a stronger króna, and a lower interest rate reduce the PD • 43 variables are reduced to 15 – 9 micro: Age, unpaid taxes and liquidity most important – 3 macro: Real exchange rate most important – 3 dummies for quarterly variations

Validation of the calibration is more difficult than of the discriminatory power • Micro level – Discriminatory power: accuracy ratio (AR) • Takes on value 1 if the model is perfect and 0 if the model has no discriminatory power – Calibration: Binomial test • Defaults are assumed to be independent • Aggregate level – Calibration: Binomial test • Defaults are assumed to be independent – Time-varying changes : R-square • α-value = 5% and two-sided confidence intervals

Discriminatory power is stable over time

The model is well calibrated

Time variations are well modelled

Quarterly variations are well modelled

TTC intends to minimise pro-cyclicality • Two canonical approaches to PD-model design • “Point-in-time” (PIT) – PIT will tend to adjust the PD quickly to macro changes – Gives time varying capital requirements – PD is calibrated to the default rate at each point in time • “Through-the-cycle” (TTC) – More-or-less constant even as macro changes over time – Gives less time varying capital requirements – At any time, PD is calibrated to the long-term default rate • Validation of either design requires a long time series of data

Macro gives PIT characteristics • Base model • “Point-in-time” • Re-estimated model excluding macro • “Through-the-cycle”

The micro-macro approach is superior to other approaches • The value-to-score transformation increases discriminatory power significantly • Macro increases the aggregate performance • PD model has as high or higher R-square than other models

Is it possible to make long term forecasts of the default rate? • Independent variables need to be forecasted • Two options to forecast macro – The SOE VAR-model with/without DR as exogenous – The Central-Bank of Iceland's (CBI) baseline forecast • Forecasting micro is much more challenging – No obvious method – Is the portfolio mix stable? Corporations are born, grow older (and die? ) • Age variable kept constant – Account variables are modelled using a VAR-model • Endogenous: lag 1 -(2) quarters, micro variables • Exogenous: lag 0 quarters, macro variables

Forecast validation – model selection • Forecasts – 3 -year forecasts – Total 39 forecasts • Forecast validation – Focus on aggregate performance, i. e. , the default rate – Average R 2 Macro • Selection of forecast – Macro forecast – Account forecast PD model Micro forecast Default rate forecast

The macro model generates accurate forecasts • Macro forecast: CBI’s baseline forecast is preferred – The small, open economy VAR-model gives as accurate default rate forecasts as actual macro data – Including DR in the VAR-model doesn’t improve forecasts • Micro forecast: VAR(1, 0)-model is preferred – A VAR-model with few lags is preferred over static accounts and a VAR-model with more lags

What does the crystal ball say? • Given CBI’s baseline forecast the default rate is expected to be slightly higher in 2010 than 2009 • . . . and reach average levels first in 2012

Main conclusions • Corporate defaults are relevant for financial stability • The default rate shows highly significant predictive power for the real economy • Predictive power increases with the micro-macro approach and the value-to-score transformation • Macro dramatically increase the aggregate performance of the PD model • An increased output gap, a stronger króna, and a lower policy interest rate reduce the PD • The PD model performs well under extraordinary conditions

This is not the end, just the beginning. . . • Applications – Model and stress-test regulatory capital requirements and credit losses – Simulation of the banking sector’s capital position and profitability, especially from a macroprudential perspective – Industry and large exposure analysis • Research – Does the predictive power vary across industries? – Does un-lagged forecasted variables improve the performance? – Further link the default rate and financial stability – Further link monetary policy and financial stability