Consumer credit-risk3440

1Summer 08, MFIN7011, Tang Consumer Credit Risk

MFIN 7011: Credit Risk

Summer, 2008Dragon Tang

MFIN 7011: Credit Risk

Summer, 2008Dragon Tang

Lecture 15Consumer Credit Risk

Thursday, August 7, 2008

Readings: Niu (2004); Agarwal, Chomsisengphet,

Liu, and Souleles (2006)


Consumer Credit RiskConsumer Credit Risk

Objectives:

1. Credit scoring approach for consumer credit risk

2. Practice, challenge, and opportunity


Consumer CreditConsumer Credit

Credit Products

Fixed Term Revolving

Residential Mortgage Retail Finance Personal Loans Overdrafts Credit Cards

Default Risk(low in general)

Low High

4Consumer Credit Risk

Consumer LendingConsumer Lending

• Examples:

– Automobile loans

– Home equity loans

– Revolving credit

• There is an exponential growth in consumer credit outstanding in the US, from USD 9.8 billion in 1946 to USD 2411 billion in January 2007

– $878 billion revolving; $1526 billion non-revolving

– Currently interest rate is 13%; interest accessed is 15%

Summer 08, MFIN7011, Tang


Consumer vs. Corporate LendingConsumer vs. Corporate Lending

• Consumer lending is not as glamorous as corporate lending

• Consumer lending is a volume business, where low cost producers who can manage the credit losses are able to enjoy profitable margins

• Corporate lending is often unprofitable as every bank is chasing the same corporate customers, depressing margins



Consumer Credit Risk: Art or Science?Consumer Credit Risk: Art or Science?

Art: consumers care about reputation Value of reputation is hard to model Reduced form model may be useful

Science: creditworthiness can be predicted from financial health Using structural models of Merton type

The answer is probably both! Hybrid structural-reduced form model should be

most promising


Never make predictions,Never make predictions,especially about the future.especially about the future.

——Casey StengelCasey Stengel


The credit Decision

Scoring vs. JudgmentalThe credit Decision

Scoring vs. Judgmental• Both methods

– Assume that the future will resemble the past

– Compare applicants to past experience

– Aim to grant credit only to acceptable risks

• Added value of scoring

– Defines degree of credit risk for each applicant

– Ranks risk relative to other applicants

– Allows decisions based on degree of risk

– Enables tracking of performance over time

– Permits known and measurable adjustments

– Permits decision automation


Evaluating the credit applicantEvaluating the credit applicant

Time at present addressTime at present addressTime at present jobTime at present jobResidential statusResidential statusDebt ratioDebt ratioBank referenceBank referenceAgeAgeIncomeIncome # of Recent inquiries# of Recent inquiries% of Balance to avail. lines% of Balance to avail. lines# of Major derogs.# of Major derogs.OverallOverall

DecisionDecisionOdds of repaymentOdds of repayment

•••

CHARACTERISTICSCHARACTERISTICSCHARACTERISTICSCHARACTERISTICS

++++--++++

N / AN / A--

--++++++

AcceptAccept??

•••

JUDGMENTJUDGMENTJUDGMENTJUDGMENT

1212202055

21212828151555

-7-710103535

212212

AcceptAccept11:111:1

•••

CREDIT SCORINGCREDIT SCORINGCREDIT SCORINGCREDIT SCORING


Credit ScoringCredit Scoring

• Project

– Input x feature vector

– Label y, default or not

– Data (xi , yi)

– Target y=f(x)

• Objective

– Given new x, predict y so that probability of error is minimal



Typical Input DataTypical Input Data

Time at present address 0-1, 1-2, 3-4, 5+ years

Home status Owner, tenant, other

Telephone Yes, no

Applicant's annual income $(0-10000), $(11000-20000), $(21000+)

Credit card Yes, no

Type of bank account Cheque and/or savings, none

Age 18-25, 26-40, 41-55, 55+ years

Type of occupation Coded

Purpose of loan Coded

Marital status Married, divorced, single, widow

Time with bank Years

Time with employer Years


Input Data: FICO ScoreInput Data: FICO Score

Not in the score: demographic data


Characteristics of DataCharacteristics of Data

• X:

– Continuous

– Discrete

– Normal distribution?

• Y:

– Binary data: 0 or 1 (=default)


Scoring ModelsScoring Models

• Statistical Methods

– DA (Discriminant Analysis)

– Linear regression

– Logistic regression

– Probit analysis

– Non-parametric models

» Nearest-neighbor approach


Statistical Methods: Discriminant Analysis

Statistical Methods: Discriminant Analysis

• Multivariate statistical analysis: several predictors (independent variables) and several groups (categorical dependent variable, e.g. 0 and 1)

• Predictive DA: for a new observation, calculate the discriminant score, then classify it according to the score

• The objective is to maximize the between group to within group sum of squares ratio that results in the best discrimination between the groups (within group variance is solely due to randomness; between group variability is due to the difference of the means)

• Normal distribution for the response variables (dependent variables) is assumed (but normality only becomes important if significance tests are to be taken for small samples)


Statistical Credit ScoringStatistical Credit Scoring

Credit Score

#C

ust

om

ers Good

CreditBad Credit

Cut-off Score


Statistical Credit ScoringStatistical Credit Scoring

Credit scoring systems:

• Altman Z-score model:

• Z = .012 X1+.014 X2+.033 X3 +.006 X4 +1.0 X5

– X1 = working capital/total assets ratio

– X2 = retained earnings/total assets ratio

– X3 = earnings before interest and taxes/total assets ratio

– X4 = market value of equity/book value of total liabilities ratio

– X5 = sales/total assets ratio


Statistical Methods: Linear Regression

Statistical Methods: Linear Regression

• The regression model is like:

• For the true model, u can take only two values as Y; thus u can’t be normally distributed.

• u has heteroskedastic variances, which makes the OLS inefficient

• The estimated probability may well lie outside [0,1].

0 'i i iY X u


Statistical Methods:Nearest-Neighbor Approach

Statistical Methods:Nearest-Neighbor Approach

• A historical database has been divided into two groups (good and bad)

• When a consumer comes, calculate the distance between the consumer and everyone in the database

• The consumer will be classified in the category which is the same as the nearest one(s)

• Problems:– The definition of distance and the number of the nearest

ones– Scoring speed: when a new x comes, we need calculate

the distance between the new x and all of the historical data; too much calculation!


Scoring ModelsScoring Models

• Non-statistical Methods

– Mathematical programming

– Recursive partitioning

– Expert systems

– Machine Learning

» Neural Networks

» Support Vector Machine (SVM)


Which Method is Best?Which Method is Best?• In general there is no overall best method. What is best will

depend on the details of the problem:

– The data structure

– The characteristics used

– The extent to which it is possible to separate the classes by using those characteristics

– The objective of the classification (overall misclassification rate, cost-weighted misclassification rate, bad risk rate among those accepted, some measure of profitability, etc.)

• In the following slides, we will introduce three models, Logistic, Neural Networks, and SVM in detail, which are used widely today


Logistic RegressionLogistic Regression

• Empirical studies show, logistic regression may perform better than linear models (Hence, better than Discriminant Analysis), when data is nonnormal (particularly for binary data), or when covariance matrices of the two groups are not identical.

• Therefore, logistic regression is the preferred method among the statistical methods

• Probit regression is similar to logistic regression


Performing Logistic RegressionPerforming Logistic Regression

• Logistic Regression can be performed using the Maximum Likelihood method

• In the maximum likelihood method, we are seeking parameter values that maximize the likelihood of the observations occurring


Logistic Regression: SetupLogistic Regression: Setup

• Directly models the default probability as a function of the input variables X (a vector)

• Define

• Assume

1: if obligor defaults

0: if obligor does notl

lY

l

Pr obligor defaults| l lP X l X

'1

1 exp

l lP X h a X

h xx


Logistic Regression: SetupLogistic Regression: Setup

• Assume the observations are independent, the probability (likelihood) of the observed sample is given by

1

1

1 1

0

( ) 1 ( )

( ) 1 ( )

1( )

1 exp

ll

nYY

l ll

m n

l ll l m

l

i lii

L P X P X

P X P X

P X

a a X


Logistic Regression and MLLogistic Regression and ML

• ML estimator (of the coefficients a’s) for Logistic Regression can be found by applying non-linear optimization on the above likelihood function.

• The simplified version is given by

n

l ilii

m

l ilii

Xaa

Xaa

L

10

10

exp1

exp

0 01 1

or log log 1 expm n

i li i lil i l i

L a a X a a X


Logistic Regression and MLLogistic Regression and ML

• It is easy to show that the log of the odds (= logit) are a linear function:

• Therefore, the odds per se are a multiplicative function.

• Since probability takes on values between (0,1), the odds take on values between (0,∞), logits take on values between (-∞,∞). So, it looks very much like linear regression, and it does not need to restrict the dependent variable to values of {0, 1}.

• It is not solvable using OLS.

i

liil

l XaaXP

XP0)(1

)(ln


Logistic Function and DistributionLogistic Function and Distribution

)(exp1

1

0 ii xaa


Normal DistributionNormal Distribution

The tails are much thinner than Logistic


RiskCalc: Moody’s Default Model

RiskCalc: Moody’s Default Model

• Probit Regression

– Where x is the vector of the ratios

–

–

2'

Prob( | ; )

( ' )

1exp( )

22

x

y default x

x

tdt

1( ) 'y x


Neural NetworksNeural Networks• Non-parametric method

• Non-linear model estimation technique: e.g.– Saturation effect: i.e. marginal effect of a financial ratio

may decline quickly

– Multiplicative factors: highly leveraged firms have a harder time borrowing money

• Neural networks decide how to combine and transform the raw characteristics in the data, as well as yielding estimates of the parameters of the decision surface

• Well suited to situations where we have a poor understanding of the data structure


Neural NetworksNeural Networks

• Use the logistic function as the activation function in all the nodes

• Works well with classification problems

• Drawbacks

– May take much longer to train

– In credit scoring, there is solid understanding of data


Multilayer Perceptron (MLP)Multilayer Perceptron (MLP)

• The input values X are sent along with 1 to the hidden layer neuron

• The hidden layer generates a weight and generates a nonlinear output that is sent to the next layer

• The output neuron takes 1 with input from the hidden layer and generates the output signal

• When learning occurs, the weights are adjusted so that the final OUTs produce the least error (The output of a single neuron is called OUT)

X1

X2

1

H1

H2

1

O

Input Layer

Hidden Layer

Output Layer

w01

w12

w21

w22

w11

w02

w1

w2

w0


Multilayer Perceptron (MLP)Multilayer Perceptron (MLP)

• Input nodes do not perform processing

• Each hidden and output node processes the signals by an activation function. The most frequently used is given on the right.

• The parameters, w, are obtained by “training” the Neural Net to historical data.

parameters ofVector :

signalsinput ofVector :

)(

)(exp1

1)(

01

w

x

wxwxg

xgxf

n

iii


Support Vector Machine (SVM)Support Vector Machine (SVM)

• A relatively new promising supervised learning method for

– Pattern recognition (Classification)

– Regression estimation

• This originates from the statistical learning theory developed by Vaqnik and Chervonenkis

– 1960s, Vapnik V. N., Support Vector

– 1995, Statistical Learning Theory

» Vapnik, V. N., “The Nature of Statistical Learning Theory”. New York: Springer-Verlag, 1995 2

» Cortes C. and Vapnik, V. N., “Support Vector Networks”, Machine Learning, 20:1-25,1995

– Development, from 1995 to now


SVM ExtensionSVM Extension

• Proximal Support Vector Machine (PSVM)

– Glenn Fung and Olvi L. Mangasariany 2001

• Incremental and Decremental Support Vector Machine Learning

• Least Squares Support Vector Machine (LS-SVM)

• Also, SVMs can be seen as a new training method for learning machines (such as NNs)


Linear ClassifierLinear Classifier

• There are infinitely many lines that have zero training error.

• Which line should we choose?


margin

• Choose the line with the largest margin.

– The optimal separating hyperplane (OSH)

• The “large margin classifier”

”Support Vectors”

Linear ClassifierLinear Classifier


Performance of SVMPerformance of SVM

• S&P CreditModel White Paper

• Fan and Palaniswami (2000):

– SVM 70.35%–70.90%

– NN 66.11%–68.33%

– MDA 59.79%–63.68%


Credit Scoring and BeyondCredit Scoring and Beyond• Data collected at application will become outdated

pretty fast

• The way a customer uses its credit account is an indicator for future performance (Behavior Scoring)

• This leads to an update path of PD and credit control tools

• The future is moving into profitability scoring.– Banks should not only care about getting its money back

– Banks want to extend credit to those it can make a positive NPV, risk-adjusted


Best Practice in Consumer Credit Risk ManagementBest Practice in Consumer Credit Risk Management

Credit decision-making Adopt to changes in economy or within customer

segment

Credit scoring Adaptive algorithms using credit bureau data and firm’s

own experience Loss forecasting Historical delinquency rates and charge-off trend analysis Delinquency flow and segmented vintage analysis

Portfolio management Risk adjusted return on capital (RAROC)


Analytical TechniquesAnalytical Techniques

Response analysis: avoid adverse selection consequences that result in increased concentrations of high-risk borrowers

Pricing strategies: avoid “follow the competition”, focus on segment profitability and cash flow

Loan amount determination: avoid to be judgmental, quantify probabilities of losses

Credit loss forecasting: decompositional roll rate modeling, trend and seasonal indexing, and vintage curve

Portfolio management strategies: important for repricing and retention, don’t be judgmental, integrating behavioral element and cash flow profitability analysis (underwriting)

Collection strategies: behavioral models are useful


Credit Scoring and Loss ForecastingCredit Scoring and Loss Forecasting

Two critical components of consumer credit risk analysis Corresponds to default probabilities and loss given

default

These two are linked Loss given default is higher when default probability is

greater Market and economic variables matter In bad economic states, there will be more default and

lower recovery Good modeling should achieve stability


Do Consumers Choose the Right Credit Contracts?Do Consumers Choose the Right Credit Contracts?

Agarwal, Chomsisengphet, Liu, and Souleles (2006):

Some don’t, especially when the stake is small But consumers with high balance do!

Other issues: Personal bankruptcy in the U.S. soared! Avoid/fight predatory lending! (e.g., subprime lending) China is starting to have a consumer credit market


China’s Consumer Spending

China’s Consumer Spending

%Chg

1997 1998 1999 2000 2001 2002 200397-03

Food 2684 2756 2845 3029 3326 3487 3789 41%

Medicine&Healthcare

213 255 300 356 401 455 506 138

%

Clothing 785 750 728 791 866 885 958 22%

Household Durables

414 485 569 595 657 727 790 91%

Transport&Communication

290 337 385 437 498 554 614 112

%

Education&Entertainment

550 643 739 837 945 1057 1170 113

%

Housing 424 507 599 663 752 842 931 120

%

Services 244 268 296 330 367 400 441 80%

TOTAL 5603 6001 6462 7037 7811 8407 9198 64%



China’s Consumer Credit Market

China’s Consumer Credit Market

• 1999-2004: Growth rate 52%– Automobile loans: 110%

» Only 15% of auto sales, compared to 80% in U.S.– Bankcard: 36%

» Mostly debit cards– Mortgage: 1000%

» Still a long way to go! Only 8% of GDP, compared to 45% in developed economies

• Other markets– Student loan– Credit cards!

• More opportunities are waiting!


47Summer 08, MFIN7011, Tang Consumer Credit Risk 6

Consumer loans vs GDP per Capita

0

5,000

10,000

15,000

20,000

25,000

30,000

35,000constant 2000 US$

0

5

10

15

20

25

30

35% of GDP

GDP per capita Consumer loans to GDP

Sources: World Bank, Fitch, Central Banks and Banks Superintendencies.


SummarySummary

Introduction to Consumer Credit Risk: Credit scoring methods Practical issues

Next: Credit VaR and Basel II


SVM Approach DetailsSVM Approach Details


• The plane separating and is defined by

• The dashed planes are given by

margin

Computing the MarginComputing the Margin

aT xw

w

ba

baT

T

xw

xw


• Divide by b

• Define new w = w/b and α = a/b

margin


1//

1//

bab

babT

T

xw

xw

w

1

1

xw

xwT

T

We have defined a scalefor w and a


• We have

• which givesmargin


1

( ( )) 1

( ) margin

T

T

w x

w x w

ww)

x

x + w)

w

2margin


Quadratic Programming ProblemQuadratic Programming Problem

( ) 1 ( ) 1( ) 1 ( ) 1

T

T

n y nn y n

w xw x

Maximizing the margin is equivalent to minimizing ||w||2. Minimize ||w||2 subject to the constraints:

Where we have definedy(n) = +1 for all y(n) = –1 for all

This enables us to write the constraints as

01])()[( nny T xw



2

1

1( ) ( ) 1

2with , ,

NT

p nn

p p

L y n n

L L

w w x

w

Minimize the cost function (Lagrangian)

Here we have introduced non-negative Lagrange multipliers ln 0 that express the constraints

01)()(

nnyL T

n

p xw



• The first order conditions evaluated at the optimal solution are

• The solution can be derived (together with the constraint)

1

1

0

( ) 0

( ) ( ) 1 0

Np

nn

N

w p nn

Tn

Ly n

L y n n

y n n n

w x

w x



• The original minimizing problem is equivalent to the following maximizing problem (dual)

• For non-support vectors, λ will be zero, as the original constraint is not binding; only a few λ’s would be nonzero.

1 1 1

1

1( ) ( ) ( )

2

. . 0 and 0

N N NT

D n m nn n m

N

n nn

L y m y n m n

s t y n

x x



• Having solved for the optimal λ’s (denoted as ), we can derive others

• To classify a new data point x, simply solve

1

( )

( ) ( ) 1 0

N

nn

Tn

y n n

y n n n

w x

w x

sgn T w x

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