Credit scoring models — Altman Z-score, Merton, scorecards.
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Credit scoring models — Altman Z-score, Merton, scorecards.
Edward Altman's discriminant analysis model predicts corporate bankruptcy using five financial ratios. Originally developed for publicly traded manufacturers (1968).
Original Z-Score (public manufacturing):
Z = 1.2 * X1 + 1.4 * X2 + 3.3 * X3 + 0.6 * X4 + 1.0 * X5
X1 = Working Capital / Total Assets (liquidity)
X2 = Retained Earnings / Total Assets (cumulative profitability)
X3 = EBIT / Total Assets (operating efficiency)
X4 = Market Value Equity / Book Value Debt (solvency)
X5 = Sales / Total Assets (asset turnover)
Z'-Score (private firms): Replaces market value of equity with book value. Revised coefficients and cutoffs (Z' < 1.23 = distress).
Z''-Score (non-manufacturing / emerging markets): Drops X5 (Sales/Total Assets) to remove industry bias from asset turnover. Suitable for service firms and emerging market companies.
Based on the Black-Scholes option pricing framework. Equity is modeled as a call option on the firm's assets with a strike price equal to the face value of debt.
DD = (ln(V/D) + (mu - 0.5 * sigma_V^2) * T) / (sigma_V * sqrt(T))
Strengths: Market-based, forward-looking, continuous updating. Weaknesses: Requires liquid equity market, assumes single debt maturity, sensitive to equity volatility estimation.
Statistical models (typically logistic regression) that assign points to borrower characteristics to produce a credit score.
Development process:
Transition matrices show the probability of moving from one rating grade to another over a defined horizon (typically one year).
From \ To AAA AA A BBB BB B CCC/D
AAA 90.0 8.5 1.0 0.3 0.1 0.0 0.1
AA 1.0 88.0 8.5 1.5 0.5 0.3 0.2
A 0.1 2.0 87.0 7.5 2.0 0.8 0.6
BBB 0.0 0.3 4.0 84.0 7.0 3.0 1.7
BB 0.0 0.1 0.5 5.0 78.0 10.0 6.4
Company: [Name] Year: [Year]
Value Ratio
Working Capital $12.5M
Total Assets $85.0M X1 = 0.147
Retained Earnings $28.0M X2 = 0.329
EBIT $10.2M X3 = 0.120
Market Value of Equity $45.0M
Book Value of Total Debt $35.0M X4 = 1.286
Sales $92.0M X5 = 1.082
Z-Score = 1.2(0.147) + 1.4(0.329) + 3.3(0.120) + 0.6(1.286) + 1.0(1.082)
= 0.176 + 0.461 + 0.396 + 0.772 + 1.082
= 2.887
Assessment: Grey zone — monitor closely. Declining from 3.15 prior year.
Key concern: Working capital deterioration (X1 dropped from 0.210 to 0.147)
Borrower: [Name] Application Date: [Date]
Attribute Value WoE Bin Points
Debt/EBITDA 3.2x 2.5-4.0x +35
Interest Coverage 4.5x 3.0-5.0x +28
Current Ratio 1.4x 1.2-1.6x +22
Revenue Growth (3yr) 8% 5-10% +18
Years in Business 12 10-20 +15
Industry Risk Medium B +10
Management Quality Strong A +20
Total Score: 148 + Base Score (200) = 348
Mapped PD: 0.85%
Internal Rating: BB+
Metric Current Period Prior Period Threshold Status
AUROC 0.82 0.84 > 0.70 Pass
Gini Coefficient 0.64 0.68 > 0.40 Pass
KS Statistic 0.52 0.55 > 0.30 Pass
PSI (score distribution) 0.12 0.08 < 0.25 Pass
Hosmer-Lemeshow (p-value) 0.35 0.42 > 0.05 Pass
Predicted vs Actual DR 1.2% vs 1.4% 1.1% vs 1.0% Within 20% Pass