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MFIN 7011: Credit Risk Management Summer, 2007 Dragon Tang

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Title: MFIN 7011: Credit Risk Management Summer, 2007 Dragon Tang


1
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)

2
Consumer Credit Risk
  • Objectives
  • Credit scoring approach for consumer credit risk
  • Practice, challenge, and opportunity

3
Consumer Credit
Low
High
Default Risk (low in general)
4
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

5
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

6
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

7
Never make predictions,especially about the
future. Casey Stengel
8
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

9
Evaluating the credit applicant
10
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

11
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

12
Input Data FICO Score
Not in the score demographic data
13
Characteristics of Data
  • X
  • Continuous
  • Discrete
  • Normal distribution?
  • Y
  • Binary data 0 or 1 (default)

14
Scoring Models
  • Statistical Methods
  • DA (Discriminant Analysis)
  • Linear regression
  • Logistic regression
  • Probit analysis
  • Non-parametric models
  • Nearest-neighbor approach

15
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)

16
Statistical Credit Scoring
Cut-off Score
Good Credit
Bad Credit
Customers
Credit Score
17
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

18
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.

19
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!

20
Scoring Models
  • Non-statistical Methods
  • Mathematical programming
  • Recursive partitioning
  • Expert systems
  • Machine Learning
  • Neural Networks
  • Support Vector Machine (SVM)

21
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

22
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

23
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

24
Logistic Regression Setup
  • Directly models the default probability as a
    function of the input variables X (a vector)
  • Define
  • Assume

25
Logistic Regression Setup
  • Assume the observations are independent, the
    probability (likelihood) of the observed sample
    is given by

26
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

27
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.

28
Logistic Function and Distribution
29
Normal Distribution
The tails are much thinner than Logistic
30
RiskCalc Moodys Default Model
  • Probit Regression
  • Where x is the vector of the ratios

31
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

32
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

33
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
34
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.

35
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

36
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)

37
Linear Classifier
  • There are infinitely many lines that have zero
    training error.
  • Which line should we choose?

38
Linear Classifier
  • Choose the line with the largest margin.
  • The optimal separating hyperplane (OSH)
  • The large margin classifier

margin
39
Performance of SVM
  • SP CreditModel White Paper
  • Fan and Palaniswami (2000)
  • SVM 70.3570.90
  • NN 66.1168.33
  • MDA 59.7963.68

40
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

41
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)

42
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

43
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

44
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

45
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
46
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!

47
6
48
Summary
  • Introduction to Consumer Credit Risk
  • Credit scoring methods
  • Practical issues
  • Exam Saturday, August 4, 2PM

49
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.

50
SVM Approach Details
51
Computing the Margin
  • The plane separating and is defined by
  • The dashed planes are given by


w
margin
52
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
53
Computing the Margin
  • We have
  • which gives

x l(w)
l(w)
x
margin
54
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
55
Quadratic Programming Problem
Minimize the cost function (Lagrangian)
Here we have introduced non-negative Lagrange
multipliers ln ? 0 that express the constraints
56
Quadratic Programming Problem
  • The first order conditions evaluated at the
    optimal solution are
  • The solution can be derived (together with the
    constraint)

57
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.

58
Quadratic Programming Problem
  • Having solved for the optimal ?s (denoted as
    ), we can derive others
  • To classify a new data point x, simply solve
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