5 Lyn Thomas Risk Stream Ccri2011

7/31/2019 5 Lyn Thomas Risk Stream Ccri2011

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Lyn C Thomas

Quantitative Financial Risk Management Centre,

School of Management

University of Southampton, UK

ICCR London Oct 4 2011

Modelling credit risk in portfolios of consumer loans:

how to uncrunch credit

Why and how to put economicfactors into risk management

systems


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Outline

Scoring as a way of modelling retail credit risk

Problems with scoring because no economics involved

Incorporating macro economic impacts into scorecards

Case study from invoice discounting


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Scoring as a way of modellingretail credit risk

Retail credit risk models traditionally based on scorecards Application scorecards and behavioural scorecards

Use sample from 2-3 years ago to relate borrowercharacteristics (application, performance, bureau) to

default status 1 year later. Objective is to get ranking accurate

Measured using KS, Gini Cut-off chosen using business measures not default probability

Assumption is relative ranking of credit worthinessconstant over time

No need to include economic variables


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reas where lack ofeconomic factors affected scorecards

Problems with bureau scores in US subprime mortgage crisis

Other issue- fraud, disconnect between time periods of model and originator risk SEC highlighted scores inability to respond to changes in economy

Problems with credit rating agency PD estimates for portfolios of mortgages ( RMBS) Models did not integrate application scores and economics correctly so ratings were

downgraded ll

Basel required score to translate to long run average probability of default (PD)

Score to PD does vary over time because of economic changes Without economics in scorecards how to estimate score to long run average PD How to build models for stress testing

Vantage ScoreDetails of Real estate scores2003-2008


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Decomposition of log odds score

Log odds score ( logistic regression gives log odds scores; linear

regression gives transformed log odds )

Use Bayes theorem to split into population odds plus weights ofevidence ( adjustment due to individual characteristics)

If pG pB proportion of Goods ( Bads in population)n

( | )( | ) ( | )( ) ln ln ln ln ln ln ( ) ( )

( | | ( | ) ( | )

G G

pop Pop

B B

p p G pp G p Gs o I s woe

p B p p B p p B

xx x

x x x

x x x

( )

( ) ( )

( | )( ) ln ( | ) ( | ) 1

( | )

1( | )

1 1

s

s s

p Gs p G p B

p B

ep G

e e

x

x x

x

x x x x

x

x-

+ =

= =+ +

X

x

@


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hy introduce economic andmarket variables into score?

Normally scores thought of as static but they are really dynamic : want score

at time t to be

What scorecard gives iswhere to is when scorecard built

Solution: put economic conditions, e(t), into scorecard

Obviously spop(e) depends on e

spop(e) is transformation of population default rate; must change over time

Does woe(x,e) depend on e: if so need interaction terms between economicvariables and borrower characteristics

( , ) ( , ( )) ( ( )) ( , ( ))Pop

s t s t s t woe t x x e e x e

( , ) ( ) ( , )Pops t s t woe t x x

0 0 0( , ) ( ) ( , )

Pops t s t woe t x x

1 1( ( )) ( ) ( )pop m ms e t c e t c e t

1 1

( , ) ( ( ) ( ))m n

ij j i

i j

woe t c IndicatorFunction x e t

x


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Which economic variables?

Little published literature on this

Some work on which variables impact on corporate defaults Some work on impact of economic conditions on mortgage defaults Really nothing on unsecured consumer credit

Possible variables

General economy:

GDP Libor interest rates Production index FTSE

Impact of economy on households Unemployment rate

Price indices Consumer confidence House price index

Lending environment Net lending Mortgage lending


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Case Study:Invoice Discounting Example

Scorecard built to estimate default risk of small firms, wherebank is invoice discounter (like factoring)

Give loan using firms invoices to customers as collateral

Scorecard built circa 2005/6 continued to discriminate wellthrough 2009

But estimate of number of firms defaulting grossly

underestimated in 2008/9.


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Scorecard without Economic Variables

Training In time Test Out of time Test

Gini 62 63 60

KS 46.46 48.83 46.34

HLtest (Chi

square)43.16 26.93 1470.94

Actual defaults 4666 2247 1409Expected defaults 4666 2201 605


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Scorecard with Confidence Index andFTSE as economics estimate s pop(e)

Version 1 Training In time Test Out of timeTest

Gini 63 63 59

KS 47.12 49.00 48.80

HLtest (Chi

square)32.51 29.95 63.81

Actual defaults 4666 2247 1409Expected defaults 4666 2202 1306


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Model with interactions(Confidence and FTSE):economics estimate of spop(e) and woe (e)

Training In time Test Out of timeTest

Gini 63 63 57

KS 47.03 49.27 44.17

HL(Chi square) 31.75 21.49 81.69

Actual defaults 4666 2247 1409

Expected

defaults4666 2204 1383


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Conclusions Economic variables can be added to scorecards

Need longer time periods in samples to get varying economic conditions

Adding straight variables estimates spop

No improvement in discrimination Impressive improvement in probability of default prediction

Adding interaction variables estimates woe(x,e)

Not clear what improvement this gives Which variables are affected by economics Will segmentation work better ?

Need to ensure not all time dependent changes have to be explainedby economics

Alternative approach is to keep scorecard fixed and to use economics inscore to PD transformation

Reinterpret hazard function approach in this way Roll rates/markov chains can be functions of economics

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5 Lyn Thomas Risk Stream Ccri2011