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PPT – MFIN 7011: Credit Risk Management Summer, 2007 Dragon Tang PowerPoint presentation | free to download - id: 4b49a6-OTFmZ

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MFIN 7011 Credit Risk ManagementSummer,

2007Dragon Tang

- Lecture 18
- Consumer Credit Risk
- Thursday, August 2, 2007
- Readings
- Niu (2004) Agarwal, Chomsisengphet, Liu, and

Souleles (2006)

Consumer Credit Risk

- Objectives
- Credit scoring approach for consumer credit risk
- Practice, challenge, and opportunity

Consumer Credit

Low

High

Default Risk (low in general)

Consumer 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

Consumer 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?

- 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,especially about the

future. Casey Stengel

The credit DecisionScoring 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 applicant

Credit Scoring

- Project
- Input x feature vector
- Label y, default or not
- Data (xi , yi)
- Target yf(x)
- Objective
- Given new x, predict y so that probability of

error is minimal

Typical 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 Score

Not in the score demographic data

Characteristics of Data

- X
- Continuous
- Discrete
- Normal distribution?
- Y
- Binary data 0 or 1 (default)

Scoring Models

- Statistical Methods
- DA (Discriminant Analysis)
- Linear regression
- Logistic regression
- Probit analysis
- Non-parametric models
- Nearest-neighbor approach

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 Scoring

Cut-off Score

Good Credit

Bad Credit

Customers

Credit Score

Statistical 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

- The regression model is like
- For the true model, u can take only two values as

Y thus u cant be normally distributed. - u has heteroskedastic variances, which makes the

OLS inefficient - The estimated probability may well lie outside

0,1.

Statistical MethodsNearest-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 Models

- Non-statistical Methods
- Mathematical programming
- Recursive partitioning
- Expert systems
- Machine Learning
- Neural Networks
- Support Vector Machine (SVM)

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 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 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 Setup

- Directly models the default probability as a

function of the input variables X (a vector) - Define
- Assume

Logistic Regression Setup

- Assume the observations are independent, the

probability (likelihood) of the observed sample

is given by

Logistic Regression and ML

- ML estimator (of the coefficients as) for

Logistic Regression can be found by applying

non-linear optimization on the above likelihood

function. - The simplified version is given by

Logistic 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 (0,8), logits

take on values between (-8,8). 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.

Logistic Function and Distribution

Normal Distribution

The tails are much thinner than Logistic

RiskCalc Moodys Default Model

- Probit Regression
- Where x is the vector of the ratios

Neural 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 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)

- 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

w11

w12

H1

w1

O

w21

w2

H2

w22

X2

w02

w0

w01

1

1

Input Layer

Hidden Layer

Output Layer

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.

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, 201-25,1995 - Development, from 1995 to now

SVM 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 Classifier

- There are infinitely many lines that have zero

training error. - Which line should we choose?

Linear Classifier

- Choose the line with the largest margin.
- The optimal separating hyperplane (OSH)
- The large margin classifier

margin

Performance of SVM

- SP CreditModel White Paper
- Fan and Palaniswami (2000)
- SVM 70.3570.90
- NN 66.1168.33
- MDA 59.7963.68

Credit 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 Management

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

segment - Credit scoring
- Adaptive algorithms using credit bureau data and

firms 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 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, dont be judgmental,

integrating behavioral element and cash flow

profitability analysis (underwriting) - Collection strategies behavioral models are

useful

Credit 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?

- Agarwal, Chomsisengphet, Liu, and Souleles

(2006) - Some dont, 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

Chinas Consumer Spending

Chg

1997 1998 1999 2000 2001 2002 2003 97-03

Food 2684 2756 2845 3029 3326 3487 3789 41

MedicineHealthcare 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

TransportCommunication 290 337 385 437 498 554 614 112

EducationEntertainment 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

Chinas 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!

6

Summary

- Introduction to Consumer Credit Risk
- Credit scoring methods
- Practical issues
- Exam Saturday, August 4, 2PM

Review for Exam

- Topics
- Credit risk modeling structural/reduced-form/inco

mplete information - Recovery rate default correlation
- Credit derivatives
- Credit VaR/Basel II/consumer credit risk
- Question Types (tentative!)
- True or False (20)
- Multiple Choice (20)
- Short Answers (20)
- Problems (40)
- 60 conceptual 40 analytical
- Formulas will be provided if needed.

SVM Approach Details

Computing the Margin

- The plane separating and is defined by
- The dashed planes are given by

w

margin

Computing the Margin

- Divide by b
- Define new w w/b and a a/b

w

margin

We have defined a scalefor w and a

Computing the Margin

- We have
- which gives

x l(w)

l(w)

x

margin

Quadratic Programming Problem

- Maximizing the margin is equivalent to

minimizing w2. - Minimize w2 subject to the constraints

Where we have defined y(n) 1 for all y(n)

1 for all This enables us to write the

constraints as

Quadratic Programming Problem

Minimize the cost function (Lagrangian)

Here we have introduced non-negative Lagrange

multipliers ln ? 0 that express the constraints

Quadratic Programming Problem

- The first order conditions evaluated at the

optimal solution are - The solution can be derived (together with the

constraint)

Quadratic Programming Problem

- The original minimizing problem is equivalent to

the following maximizing problem (dual) - For non-support vectors, ? will be zero, as the

original constraint is not binding only a few

?s would be nonzero.

Quadratic Programming Problem

- Having solved for the optimal ?s (denoted as

), we can derive others - To classify a new data point x, simply solve