revisiting credit scoring models in a basel 2 environment edward i. altman 鄭硯霆鄭開明...

Revisiting Credit Scoring Models in a Basel 2

Environment

Edward I. Altman

鄭硯霆鄭開明林雨賢鄭硯霆鄭開明林雨賢

IntroductionIntroduction• Credit scoring models have been remotivated

and given significance by the pronouncements of the Basel 2. Coincidentally, defaults and bankruptcies reached unprecedented levels in US in 2001 and 2002.

• This paper primarily discusses Z-Score model and its recent developments.

• Also discussing the KMV approach and comparing it with Z-Score in the Enron case.

IntroductionIntroduction• To assign appropriate default probabilities on

firms involve three steps process. 1.credit scoring models 2.capital market risk equivalents (usually bond

ratings) 3.assignment of PD and LGDs

Credit Scoring ModelsCredit Scoring Models• Credit scoring models involve the

combinations of a set of quantifiable financial indicators of firm performance with few additional qualitative variables.

• This paper will concentrate on the quantitative measures, but one should not underestimate the importance of qualitative measures.

Traditional Ratio AnalysisTraditional Ratio Analysis• There are some attacks on ratio analysis from

scholarly world.• Beaver(1967.1968) found some indicators coul

d discriminate between failed and nonfailed firms with univariate analysis.

• Ratios measuring profitability, liquidity, and solvency seemed to be the most significant indicators. But the order of their importance is not clear.

Traditional Ratio AnalysisTraditional Ratio Analysis• There are three questions about ratio

analysis. 1.Which ratios are most important? 2.What weights should be attached to

those selected ratios? 3.How should the weights be objectively

established?

Multiple Discriminant AnalysisMultiple Discriminant Analysis• MDA is a statistical technique used to

classify an observation into one of several groups dependent upon the observation’s individual characteristics.

• It is primarily used to classify or make predictions in problems where the dependent variables in qualitative form.

Multiple Discriminant AnalysisMultiple Discriminant Analysis• MDA derives a linear combination of these cha

racteristics that best discriminates between the groups.

Z=V1X1+V2X2+…+VnXn

Vi=discriminant coefficients Xi=independent variables maxλ=SSB/SSW

SSB=sum of squares between groups SSW=sum of squares within groups solve Vi

Multiple Discriminant AnalysisMultiple Discriminant Analysis• The advantage of MDA 1.the potential of analyzing the entire

profile of the object simultaneously rather than sequentially examining its individual characteristics.

2.the reduction of the analyst’s space dimensionally.

3.potentially yielding a model with a relatively small number of selected measurements that convey a great deal of information.

Multiple Discriminant AnalysisMultiple Discriminant Analysis• The criticism of MDA 1.MDA has the same assumptions with

multiple regression. But in the real world, financial data violates these requirements.

2.MDA has the problem of over-sampling.

Development of the Z-Score Development of the Z-Score Model 1Model 1

• SAMPLE SELECTION

Bankrupt Group Non-Bankrupt Group

33 manufacturers who have filed a bankruptcy petition under Chapter X of the National Bankruptcy Act (1946~1965)

33 regular manufacturers


• 20-year old sample is NOT optimal– Average ratios shift over time

• To make up for this, a careful choice of the non-bankruptcy group is done– Stratified, random sample by industry and

size

• Data used are those dated 1 annual reporting period prior to bankruptcy– these are the most relevant, accurate data

Development of the Z-Score Development of the Z-Score Model 3 Model 3

• Most firms selected have assets between $1 million and $25 million– Firms outside this range do not go bankrupt

as often (at least prior to 1966)– Since financial ratios are used in this model,

they by nature deflate statistics by size

• The model has proven to be robust enough to accommodate both large and small firms alike


• VARIABLE SELECTION• 22 potentially helpful variables were

compiled for evaluation• 5 were eventually selected as being the

best predictors of corporate bankruptcy

1) Observe statistical significance

2) Evaluate inter-correlations among variables

3) Observe predictive accuracy

4) Final decision by analyst


• THE Z-Score ModelZ = 1.2XZ = 1.2X11 + 1.4X + 1.4X22 + 3.3X + 3.3X33 + 0.6X + 0.6X44 + 1.0X + 1.0X55

where• X1 is working capital / total assets• X2 is retained earnings / total assets• X3 is earnings before interest and taxes /

total assets• X4 is market value of equity / book value of

liabilities• X5 is sales / total assets• Model is NOT standardized

– Cutoff score is NOT zero


• X1, Working Capital / Total Asset

(WC / TA)• Consistent operating losses will

result in shrinking current assets to total assets

• Current ratio and quick ratio are NOT as helpful as this one

• Only tangible assets are used


• X2, Retained Earnings / Total Assets

(RE / TA)• Measures cumulative profitability over

time– Age of firm and its use of leverage are

implicitly considered in this ratio

• Younger firms are discriminated– But younger firms also tend to fail more

• Higher leverage also means less debt


• X3, Earnings before Interest and Taxes / Total Assets

(EBIT / TA)• A firm’s ultimate existence is based

on the earning power of its assets• Earning power also help determine

the fair value of assets, which can then be used to detect insolvency


• X4, Market Value of Equity / Book Value of Total Liabilities

(MVE / TL)• Equity = combined market value of all

shares of stock• Liabilities = long term + short term• Shows how much value the firm’s asset

can lose before becoming insolvent• An aspect often overlooked in other

studies


• X5, Sales / Total Assets(S / TA)

• Measures sales-generating ability– Capacity for dealing with competition

• Insignificant on a univariate level– But very significant in this model

• Wide variations among industries and across countries


• All variables other than X5 show significant difference among groups

• All ratios indicate higher values for non-bankrupt firms

• All the coefficients have positive values

• The greater the firm’s distress potential, the lower the Z-score


Classification & Prediction Accuracy Z-Score 1968 Credit Scoring Model

Data Used

CutoffScore

OS

(33)

HS

(25)

1969-1975(86)

1976-1995(110)

1997-1999(120)

1yr pr.

2.675 94% 96% 82% 85% 94%

1yr pr.

1.81 88% 92% 75% 78% 84%

2yr pr.

2.675 72% 80% 68% 75% 74%

• Testing model on other sets of data• OS, HS = Original and Holdout Sample

Adaptation for Private FirmsAdaptation for Private Firms• Z-Score model is for publicly traded firms

– X4 requires stock price data

– Ad hoc adjustments are not allowed

• A REVISED Z-SCORE MODEL

Z’ = 0.72XZ’ = 0.72X11 + 0.85X + 0.85X22 + 3.11X + 3.11X33 + 0.42X + 0.42X44 + + 1.00X1.00X55

• Book value is used for X4 in the revised model

Bond Rating EquivalentsBond Rating Equivalents• Once again, a credit scoring model is

to estimate PD and LGD• The Z-Score can be linked to a Bond

Rating, and a Bond Rating can be linked to a PD and an LGD

Adaptation for Non-Adaptation for Non-Manufacturers and Emerging Manufacturers and Emerging

MarketsMarkets• Eliminate X5 to minimize industry effects

• Again, the book value is used for X4

• Yet another revised Z-Scoring model

Z = 6.56 XZ = 6.56 X11 + 3.26 X + 3.26 X22 + 6.72 X + 6.72 X33 + 1.05 X + 1.05 X44

• A constant of 3.25 is added for emerging markets to standardize the scores

ZETA Credit Risk ModelZETA Credit Risk Model• Improvement on Z-Scoring Model• Focuses explicitly on recent developmen

ts in the financial market• Works well up to 5 years of financial dat

a before bankruptcy• Includes non-linear (e.g. quadratic) and l

inear discriminant models

Macro Economic Impact and Loss Macro Economic Impact and Loss EstimationEstimation

• All of the aforementioned models are regardless of the performance of the economy and the economy’s impact on PDs and LGDs.

• Some recent attempts have experimented with including variables which can capture these exogenous factors – like GDP growth.

• One idea is to add an aggregate default measure for each year to capture a high or low risk environment. Such attempts have only achieved modest to date.

Group Prior Probabilities, Error Costs Group Prior Probabilities, Error Costs and Model Efficiencyand Model Efficiency

• Include explicit estimates for the prior PD and the possible costs of the model’s errors. The optimal cutoff score (Zc):

where q1,q2=prior probability of bankrupt (q1) or nonbankrupt (q2)

,and C1,C11=costs of Type I and Type II errors

1 1

2 11c

q cZ n

q c

Group Prior Probabilities, Error Costs Group Prior Probabilities, Error Costs and Model Efficiencyand Model Efficiency

• The efficiency of the ZETA bankruptcy classification model with alternative strategies. The expected cost of ZETA (ECZETA):

ECZETA=q1(M12/N1)C1+q2(M21/N2)C11

where M12, M21 = observed type I and type II errors (misses) respectively, and N1, N 2 =number of observations in the bankrupt (N1) and non-bankrupt (N2)

groups.

Bankrupt group(N1)

Non-bankrupt group(N2)

Predicted nonbankrupt(M12)

Predicted bankrupt

Predicted bankrupt(M21)

Predict nonbankrupt

All firm

q1

q2

M12/N1

M12/N2

- C 1

- C 1 1

Type I error

Type II error

ECECZETAZETA=q=q11(M(M1212/N/N11)C)C11+q+q22(M(M2121/N/N22)C)C1111

Cost of Classification ErrorsCost of Classification Errors

1.Type I error bankruptcy classification: an accepted loan that defaults.=>LGD

2. Type II error bankruptcy classification: a rejected loan that would have paid-off successfully.=>a type of opportunity cost

Predictedbankrupt

Predictednonbankrupt

Actual bankrupt True bankrupt Type I error

Actualnonbankrupt

Type II errorTrue nonbankrupt

PD and Recovery ratePD and Recovery rate

• Most modern credit risk model assume independent between PD and RR.(p.152)

• Altman, Brady, Resti, and Sironi[2002]show there is significant negative correlation between PD and RR.

• Higher default rate lower recovery rate and greater losses

• The bottom-line is that Basel 2 has made a real contribution to build credit models that involve scoring techniques, default and loss estimates, and portfolio approaches to the credit risk problem.

The Expected Default Frequency The Expected Default Frequency (EDF) Model(EDF) Model

• It is based conceptually on Merton’s option-theoretic, zero coupon, corporate bond valuation approach.

• Steps:

Estimate Va , σ a

Calculate DD

Scale DD to EDF

Estimate Estimate VVaa , σ , σaa

1.estimate Va Equity is viewed as a call option on the firm’s

assets: the right, but not the obligation, to “buy” the firm’s assets from the lender by re-paying the debt.

Standard Options Terms

Call Option Value

Strike Price

Implied Underlying Asset Value

KMV Approach

= Market Value of Equity

= Book Liabilities

Implies Market Value of Assets

Estimate VEstimate Vaa, σ, σaa

Option value(market value of equity)

Stock price(market value of asset)

Strike price(Book liability)

Estimate Estimate VVaa , σ , σaa

the result

2.Estimateσa

-KMV and others in the literature have resolved this problem. In terms:

T

21

ln

12

2

121

a

a

aT

dd

T

TrDV

dwheredNDedVNE

1 e a e ag E N d V

Calculate distance to defaultCalculate distance to default

1.KMV assumes default point=short term liability+0.5*long term

liability2.Distance to default=

3.It is a normalized measure and thus may be used for comparing one company with another.

expected market value of asset V default point

volitility of assets a

1 Yr

Distribution of asset value at horizon

AssetValue

Today

EDFTime

Value

Default PointDistance-to-Default =3 Standard deviations

Asset Volatility(1 Std Dev)

Figure from KMVFigure from KMV

The question is :The question is :distance to default is also an distance to default is also an ordinal measure akin to a bond ordinal measure akin to a bond rating, but it still does not tell rating, but it still does not tell you what the you what the default default probabilityprobability is. is.

From DD to EDFFrom DD to EDF

• KMV didn’t use the probability from normal distribution because credit risk is not normal!

• Statistics books don’t go beyond 3.49—we see firms that are 4-6 standard deviations from default subsequently defaulting.

• KMV uses historical default experience to determine an expected default frequency as a function of distance to default.

Scaling DD to EDFScaling DD to EDF

Form a “bucket of similar DD companies 1/1/1978

4.8 4.8

4.9 4.95 5.0

5.1 5.1 5.2

4.8 4.8 4.8

4.9 4.95 5.0

5.1 5.1 5.2

4.8 4.8 4.8

4.9 4.95 5.0

5.1 5.1 5.2

4.8

1 year later, how many have defaulted? 2 years later...

• Repeat the exercise for all ranges of DD•Measure forward default observations for periods from 1 year to 5 years•Form new buckets every year through the present and repeat steps

Case from KMV

Scaling DD to EDF Credit Scaling DD to EDF Credit MeasuresMeasures

Distanceto Default

ExpectedDefaultFrequency

EDF 43 bp

DD 4s

KMV strength and weakness (Altman)KMV strength and weakness (Altman)

• Strength1.Responsive to changing conditions ,(EDF

updated quarterly)2. Based on stock market data which is

timely and contains a forward looking view3. Strong theoretical underpinnings4. Can be applied to any publicly-traded

company

KMV strength and weaknessKMV strength and weakness

• Weakness1. Difficult to diagnose a theoretical EDF (what is

the distribution of asset return outcomes)2. Problems in applying model to private companies

and thinly-traded companies3. Results sensitive to stock market movements

(does the stock-market over-react to news?)• 4. Ad-hoc definition of anticipated liabilities (i.e..

50% of long-term debt)

The Enron Example: Model Versus The Enron Example: Model Versus Rating Rating

ConclusionConclusion

• Although tools like Z-score and EDF were available, losses were still incurred by even the most sophisticated investors and financial institutions.

• What a needed is a “credit-culture.”

CommentsComments• Do KMV and Z-score model work in

Taiwan?• For Z-Score

– There may be faulty accounting practices

• For KMV– There may be extraneous forces trying to

maintain stocks at a certain price

• Conclusion – more researches needed

revisiting credit scoring models in a basel 2 environment edward i. altman 鄭硯霆 鄭開明...

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revisiting credit scoring models in a basel 2 environment edward i. altman 鄭硯霆鄭開明...