Revisiting Credit Scoring Models in a Basel 2

Revisiting Credit Scoring Models in a Basel 2 Environment Edward I. Altman 鄭硯霆 鄭開明 林雨賢

Introduction • 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.

Introduction • 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 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 Analysis • There are some attacks on ratio analysis from scholarly world. • Beaver(1967. 1968) found some indicators could 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 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 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 Analysis • MDA derives a linear combination of these characteristics that best discriminates between the groups. Z=V 1 X 1+V 2 X 2+…+Vn. Xn 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 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 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 Model 1 • SAMPLE SELECTION Bankrupt Group 33 manufacturers who have filed a bankruptcy petition under Chapter X of the National Bankruptcy Act (1946~1965) Non-Bankrupt Group 33 regular manufacturers

Development of the Z-Score Model 2 • 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 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

Development of the Z-Score Model 4 • VARIABLE SELECTION • 22 potentially helpful variables were compiled for evaluation • 5 were eventually selected as being the best predictors of corporate bankruptcy 4) Final decision by analyst 2) Evaluate intercorrelations among variables 1) Observe statistical significance 3) Observe predictive accuracy

Development of the Z-Score Model 5 • THE Z-Score Model Z = 1. 2 X 1 + 1. 4 X 2 + 3. 3 X 3 + 0. 6 X 4 + 1. 0 X 5 where • X 1 is working capital / total assets • X 2 is retained earnings / total assets • X 3 is earnings before interest and taxes / total assets • X 4 is market value of equity / book value of liabilities • X 5 is sales / total assets • Model is NOT standardized – Cutoff score is NOT zero

Development of the Z-Score Model 6 • X 1, 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

Development of the Z-Score Model 7 • X 2, 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

Development of the Z-Score Model 8 • X 3, 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

Development of the Z-Score Model 9 • X 4, 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

Development of the Z-Score Model 10 • X 5, 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

Development of the Z-Score Model 11 • All variables other than X 5 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

Development of the Z-Score Model 12 • Testing model on other sets of data • OS, HS = Original and Holdout Sample Classification & Prediction Accuracy Z-Score 1968 Credit Scoring Model Data Used Cutoff OS Score (33) HS (25) 1969 - 1976 - 19971975 1999 (86) (110) (120) 1 yr pr. 2. 675 94% 1 yr pr. 1. 81 88% 96% 92% 82% 75% 85% 78% 94% 84% 2 yr pr. 2. 675 72% 80% 68% 75% 74%

Adaptation for Private Firms • Z-Score model is for publicly traded firms – X 4 requires stock price data – Ad hoc adjustments are not allowed • A REVISED Z-SCORE MODEL Z’ = 0. 72 X 1 + 0. 85 X 2 + 3. 11 X 3 + 0. 42 X 4 + 1. 00 X 5 • Book value is used for X 4 in the revised model

Bond 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. Manufacturers and Emerging Markets • Eliminate X 5 to minimize industry effects • Again, the book value is used for X 4 • Yet another revised Z-Scoring model Z = 6. 56 X 1 + 3. 26 X 2 + 6. 72 X 3 + 1. 05 X 4 • A constant of 3. 25 is added for emerging markets to standardize the scores

ZETA Credit Risk Model • Improvement on Z-Scoring Model • Focuses explicitly on recent developments in the financial market • Works well up to 5 years of financial data before bankruptcy • Includes non-linear (e. g. quadratic) and linear discriminant models

Macro Economic Impact and Loss Estimation • 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 and Model Efficiency • Include explicit estimates for the prior PD and the possible costs of the model’s errors. The optimal cutoff score (Zc): where q 1, q 2=prior probability of bankrupt (q 1) or nonbankrupt (q 2) , and C 1, C 11=costs of Type I and Type II errors

Group Prior Probabilities, Error Costs and Model Efficiency • The efficiency of the ZETA bankruptcy classification model with alternative strategies. The expected cost of ZETA (ECZETA): ECZETA=q 1(M 12/N 1)C 1+q 2(M 21/N 2)C 11 where M 12, M 21 = observed type I and type II errors (misses) respectively, and N 1, N 2 =number of observations in the bankrupt (N 1) and non-bankrupt (N 2) groups.

ECZETA=q 1(M 12/N 1)C 1+q 2(M 21/N 2)C 11

Cost 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 Actual bankrupt Actual nonbankrupt Predicted nonbankrupt True bankrupt Type I error Type II error True nonbankrupt

PD 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 (EDF) Model • It is based conceptually on Merton’s option-theoretic, zero coupon, corporate bond valuation approach. • Steps:

Estimate Va , σa 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 KMV Approach Call Option Value = Market Value of Equity Strike Price = Book Liabilities Implied Underlying Asset Value Implies Market Value of Assets

Estimate Va, σa Option value (market value of equity) Stock price Strike price (market value of (Book liability) asset)

Estimate V a , σa the result 2. Estimateσa -KMV and others in the literature have resolved this problem. In terms:

Calculate distance to default 1. KMV assumes default point=short term liability+0. 5*long term liability 2. Distance to default= 3. It is a normalized measure and thus may be used for comparing one company with another.

Figure from KMV Distribution of asset value at horizon Value Asset Volatility (1 Std Dev) Asset Value Distance-to-Default = 3 Standard deviations Default Point EDF Today 1 Yr Time

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

From 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 EDF Case from KMV Form a “bucket of similar DD companies 1/1/1978 4. 8 1 year later, how many have defaulted? 4. 8 2 years later. . . 4. 8 4. 95 5. 0 4. 95 5. 0 5. 1 5. 2 5. 1 5. 2 • 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

Scaling DD to EDF Credit Measures Expected Default Frequency EDF 43 bp DD 4 s Distance to Default

KMV strength and weakness (Altman) • Strength 1. Responsive to changing conditions , (EDF updated quarterly) 2. Based on stock market data which is timely and contains a forward looking view 3. Strong theoretical underpinnings 4. Can be applied to any publicly-traded company

KMV strength and weakness • Weakness 1. 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 companies 3. 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 Rating

Conclusion • 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. ”

Comments • 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