Come calcolare lo Z-Score di Altman: modello statistico previsione bancarotta aziendale per analisi finanziaria credito. Formula classica 1968: Z = 1.2×A + 1.4×B + 3.3×C + 0.6×D + 1.0×E, dove A = Working Capital / Total Assets (capitale circolante / attivo totale), B = Retained Earnings / Total Assets (utili portati a nuovo / attivo totale), C = EBIT / Total Assets (utile operativo / attivo totale), D = Market Value Equity / Total Liabilities (capitalizzazione / passivo totale), E = Sales / Total Assets (vendite / attivo totale rotation). Threshold: Z > 2.99 Safe Zone bankruptcy improbabile <0.5% probability 1 anno; 1.81 < Z < 2.99 Grey Zone monitoring richiesto 5-15% probability; Z 25% probability. Storia: Edward Ira Altman (USA 1941-) NYU Stern School Business Professor Finance 1968 PhD paper "Financial Ratios, Discriminant Analysis and the Prediction of Corporate Bankruptcy" Journal of Finance 23:589 multiple discriminant analysis MDA su 66 aziende USA pubbliche manifacturing dataset 1946-1965 33 bankrupt 33 non-bankrupt matched-pair sample 80% accuracy 1 anno predittiva 70% 2 anni. Versioni successive: Z-Score 1983 private companies Z = 0.717A + 0.847B + 3.107C + 0.420D + 0.998E (book value equity instead market) threshold 2.9/1.23;

Z-Score 1995 emerging markets non-manufacturing Z" = 6.56A + 3.26B + 6.72C + 1.05D (no E sales/TA) threshold 2.6/1.1. Strumento essenziale per: credit rating analysis Italia Cerved Group Milano 1988 fondata 1500 employees largest Italian credit rating agency, Crif Bologna 1988 fondata 5000 employees credit information Europe, Standard & Poor's S&P Italia Milano subsidiary, Moody's Italia Milano, Fitch Ratings Milano; bankruptcy prediction Italia Tribunali Concorsuali Roma Milano Napoli Torino procedure concorsuali fallimento concordato preventivo amministrazione straordinaria; Italia normativa Codice della Crisi d Impresa e dell Insolvenza CCII Decreto Legislativo 14/2019 entrato vigore luglio 2022; investor analysis Italia Borsa Italiana Milano Piazza Affari FTSE MIB 40 stocks; auditing Italia ODCEC Ordine Dottori Commercialisti Esperti Contabili Roma; ricerca finance: Bocconi Milano Statistica Decisioni Big Data, Sapienza Roma DIET Probabilità applicata, Bologna alma mater 1088 prima Europa Statistica DEMS, Politecnico Milano DEIB, Cattolica Milano CESPLA Centro Studi Programmazione Logistica.

Formula Z-Score Altman

Equazione classica 1968 public manufacturing: Z = 1.2A + 1.4B + 3.3C + 0.6D + 1.0E. A = Working Capital / Total Assets misura liquidità short-term. B = Retained Earnings / Total Assets misura cumulative profitability historical. C = EBIT / Total Assets misura operating profitability current. D = Market Value Equity / Total Liabilities misura solvency leverage relativa investor confidence. E = Sales / Total Assets asset turnover ratio efficienza operativa. Range tipico: A 0-0.5, B -0.5 to 0.5, C -0.2 to 0.3, D 0.1-3, E 0.5-3.

Threshold zones: Z > 2.99 Safe Zone (bankruptcy probability <0.5% within 1 year, 80% companies safe historical Altman 1968 sample); 1.81 ≤ Z ≤ 2.99 Grey Zone uncertainty area monitoring required (5-15% probability mixed risk); Z 25% probability default historically). Discrimination accuracy 80% Altman 1968 1-year prediction, 70% 2-year prediction Type I error (false positive distress) ~6%, Type II (false negative miss real distress) ~5%.

Z' Score 1983 private companies: Z' = 0.717A + 0.847B + 3.107C + 0.420D + 0.998E. Modificato per private companies senza market price: D = Book Value Equity / Total Liabilities (no market cap available). Coefficients refit smaller D weight 0.420 vs 0.6 reflecting illiquidity book value reliability. Threshold: Z' > 2.9 safe, 1.23 < Z' < 2.9 grey, Z' < 1.23 distress. Industrial manufacturing private firms accuracy 91% 1-year prediction.

Z'' Score 1995 emerging markets non-manufacturing: Z'' = 6.56A + 3.26B + 6.72C + 1.05D (rimosso E asset turnover). Sviluppato Altman 1995 paper for emerging markets Latin America corporations service industries non-manufacturing. Coefficient large rebalanced. Threshold: Z'' > 2.6 safe, 1.1 < Z'' < 2.6 grey, Z'' < 1.1 distress. Service industries retail technology pharma benchmark.

Bond rating equivalent: Z > 8.15 = AAA highest rating; 7.6-8.15 = AA+; 7.3-7.6 = AA; 7-7.3 = AA-; 6.8-7 = A+; 6.5-6.8 = A; 6.3-6.5 = A-; 6.2-6.3 = BBB+; 6-6.2 = BBB; 5.9-6 = BBB-; 5.7-5.9 = BB+; 5.5-5.7 = BB; 5.4-5.5 = BB-; 5.3-5.4 = B+; 5.2-5.3 = B; 5-5.2 = B-; 4.9-5 = CCC+; 4.6-4.9 = CCC; 4-4.6 = CCC-; 3.7-4 = D distress imminent. Standard & Poor S&P Moody's Fitch credit ratings industry benchmark.

Storia e contesto

Edward Ira Altman (USA 1941-) New York University Stern School Business Max L. Heine Professor Finance 1967 PhD City University NY 1969 thesis "The Prediction of Corporate Bankruptcy: A Discriminant Analysis" applied Multiple Discriminant Analysis MDA Fisher 1936 statistical technique to financial ratios company classification bankrupt/non-bankrupt. 1968 famous paper "Financial Ratios, Discriminant Analysis and the Prediction of Corporate Bankruptcy" Journal of Finance 23(4):589-609 PhD thesis publication. Dataset: 66 USA public manufacturing corporations 1946-1965, 33 bankrupt 33 non-bankrupt matched-pair sample by industry size year, 22 financial ratios initially evaluated, final 5 ratios discriminant analysis selection. Altman further publications: 1977 "ZETA Analysis: A New Model to Identify Bankruptcy Risk of Corporations" Journal Banking Finance 1:29 ZETA model 7 variables better accuracy 90%; 1983 "Corporate Financial Distress: A Complete Guide to Predicting, Avoiding, and Dealing with Bankruptcy" Wiley book Z' private companies Z'' non-manufacturing variants; 2000 'Predicting Financial Distress of Companies' updated empirical study large dataset; 2017 'Distressed Debt Analysis: Strategies for Speculative Investors' Beard Books professional book. NYU Stern Salomon Center Financial Institutions founded 1972 director Altman 1990-2008. NYU Stern Business School founded 1900 located Greenwich Village Manhattan NYC.

Ronald Fisher (UK 1890-1962) statistician 1936 paper "The Use of Multiple Measurements in Taxonomic Problems" Annals of Eugenics 7:179 introduced linear discriminant analysis LDA later applied Altman financial ratios. William H. Beaver (USA 1940-) Stanford 1966 paper "Financial Ratios as Predictors of Failure" Journal Accounting Research 4:71 univariate analysis precursor Altman multivariate. Italia ricerca finance: Bocconi Milano Università Commerciale Luigi Bocconi 1902 fondata 14000 students top business school Italy, Department Finance prof Stefano Caselli decano; Sapienza Roma DIET Mathematica Statistica; Bologna alma mater 1088 prima Europa CdL Economia DEMS; LUISS Guido Carli Roma 1974 fondata 9000 students; CUOA Vicenza Business School; SDA Bocconi MBA. Italia industria credit analysis: Cerved Group Milano 1988 fondata Banca Intesa Mediobanca initially listed Borsa Italiana 2014, 1500 employees largest Italian credit rating agency, ION Group Andrea Pignataro 2024 acquisition $1.7 billion; Crif Bologna 1988 fondata 5000 employees Europe credit information network 50+ countries; Standard & Poor's S&P Global Ratings Italy Milano subsidiary; Moody's Italia Milano subsidiary; Fitch Ratings Milano subsidiary; Banca d'Italia Roma supervisione vigilanza credito; CONSOB Commissione Nazionale Società Borsa Roma supervisione mercati finanziari, Borsa Italiana Milano Piazza Affari FTSE MIB 40 stocks.

Codice della Crisi d Impresa e dell Insolvenza CCII Decreto Legislativo 14/2019 entrato vigore luglio 2022 Italian bankruptcy reform updating Legge Fallimentare R.D. 267/1942 outdated procedures. ODCEC Ordine Dottori Commercialisti Esperti Contabili Roma 117000 commercialisti Italia statutory auditing professional. AIA Associazione Italiana Internal Auditors Milano 1972. Italia famous bankruptcy cases: Parmalat 2003 Calisto Tanzi Collecchio Parma food multinational $14 billion accounting fraud bankruptcy retrospective Z-score deviation; Banca Popolare Vicenza 2017 Veneto financial collapse; Banca Etruria 2015; Monte dei Paschi di Siena MPS Italian oldest bank 1472 fondata bailout 2017 government; Alitalia 2008-2017 bankruptcy multiple commissario straordinario 2008-2021. USA bankruptcy cases retrospective Altman Z-score: Enron 2001 Houston Texas accounting fraud Z-score 0.5 distress 6 months prior; Lehman Brothers 2008 NY 158-year history $613B liabilities Z-score 1.2 distress 1 year prior; WorldCom 2002 telecom $11B fraud Z-score 0.7 distress; Bethlehem Steel 2001 Z-score 0.6 distress 2 years prior. USA universities finance: NYU Stern Greenwich Village Manhattan founded 1900 Altman professor; Wharton Penn Philadelphia PA founded 1881 oldest US business school; Harvard Business School Boston MA 1908; Booth Chicago IL 1898; Columbia Graduate Business NY 1916; MIT Sloan Cambridge MA 1914; Stanford Graduate School Business GSB Palo Alto CA 1925;

Kellogg Northwestern Evanston IL 1908; Tuck Dartmouth Hanover NH 1900 oldest graduate business; Yale School Management New Haven CT 1976; UC Berkeley Haas Berkeley CA; UCLA Anderson LA; UMich Ross Ann Arbor; Duke Fuqua Durham NC; Cornell Johnson Ithaca NY; UNC Kenan-Flagler Chapel Hill NC. Software financial analysis: Bloomberg Terminal NYC subscription $24000/year financial data; Reuters Refinitiv Thomson; FactSet; Capital IQ S&P; Moody's Risk Calc default prediction model commercial; SAS Statistical Analysis System Cary NC; Stata College Station TX; R deSolve Bayesian; Python pandas numpy scipy matplotlib. Bankruptcy law: USA Bankruptcy Code 1978 Title 11 USC Chapter 7 liquidation, Chapter 11 reorganization, Chapter 13 individual debt; UNCITRAL Model Law Cross-Border Insolvency 1997 international harmonization.

Tabella Z-Score zones esempi

• Z > 2.99 Safe Zone: bankruptcy probability <0.5% 1 year
• 1.81 < Z < 2.99 Grey Zone: 5-15% probability monitoring required
• Z < 1.81 Distress Zone: >25% probability bankruptcy 1-2 years
• Z' > 2.9 private safe: 1983 private companies model
• Z' < 1.23 private distress: 1983 private companies model
• Z'' > 2.6 non-manufacturing safe: 1995 emerging markets
• Z'' < 1.1 non-manufacturing distress: 1995 emerging
• Bond AAA equivalent: Z > 8.15
• Bond BBB equivalent: Z = 6.0
• Bond BB equivalent: Z = 5.5
• Bond B equivalent: Z = 5.2
• Bond CCC equivalent: Z = 4.6
• Bond D equivalent: Z < 4.0
• Working Capital ratio A: 0.1-0.5 healthy
• Retained Earnings ratio B: -0.2 to 0.5
• EBIT/Total Assets C: -0.1 to 0.2 ROA
• Market/Book Equity D: 0.5-3
• Sales/Total Assets E: 0.5-3 asset turnover
• Altman 1968 paper: Journal Finance 23:589 66 companies sample
• Altman 1968 accuracy: 80% 1-year, 70% 2-year
• ZETA 1977: 7 variables 90% accuracy improvement
• USA Enron 2001: Z=0.5 6 months prior bankruptcy
• USA Lehman Brothers 2008: Z=1.2 1 year prior $613B
• USA WorldCom 2002: Z=0.7 distress accounting fraud
• Italia Parmalat 2003: bankruptcy $14B fraud Tanzi Collecchio
• Italia MPS Monte Paschi 2017: bailout 1472 oldest bank
• Italia Banca Popolare Vicenza 2017: financial collapse
• USA Bankruptcy Code 1978: Chapter 7 11 13
• Italia CCII 2019: Codice Crisi Impresa Insolvenza
• Italia ODCEC: 117000 commercialisti Roma

Esempi numerici dettagliati

Esempio 1 - Safe Zone azienda sana. Working Capital=500M, Total Assets=1000M, Retained Earnings=400M, EBIT=150M, Market Value Equity=800M, Total Liabilities=300M, Sales=1500M. A=0.5 high liquidity; B=0.4 strong cumulative; C=0.15 strong ROA 15%; D=2.67 high market premium book; E=1.5 efficient asset turnover. Z = 1.2*0.5 + 1.4*0.4 + 3.3*0.15 + 0.6*2.67 + 1.0*1.5 = 0.6+0.56+0.495+1.602+1.5 = 4.757. Z > 2.99 Safe Zone, bankruptcy probability <0.5% 1 year. Italia: typical FTSE MIB top stock Borsa Italiana Milano blue chip.

Esempio 2 - Grey Zone monitoring. WC=100M, TA=1000M, RE=100M, EBIT=50M, MV equity=300M, TL=500M, Sales=800M. A=0.1 low liquidity; B=0.1 modest cumulative; C=0.05 weak ROA 5%; D=0.6 moderate; E=0.8 average. Z = 1.2*0.1 + 1.4*0.1 + 3.3*0.05 + 0.6*0.6 + 1.0*0.8 = 0.12+0.14+0.165+0.36+0.8 = 1.585. Z < 1.81 Distress Zone (close to grey 1.81-2.99 transition). Italia tipica PMI Italian medium-sized enterprise weak balance sheet need turnaround. Italia ODCEC commercialisti monitoring required.

Esempio 3 - Distress Zone bankruptcy probabile. WC=-50M (negative working capital crisis), TA=1000M, RE=-200M (cumulative losses), EBIT=-100M (operating loss), MV equity=100M (low market value), TL=800M (high leverage), Sales=500M. A=-0.05 negative liquidity crisis; B=-0.2 cumulative deficit; C=-0.1 negative ROA -10%; D=0.125 high leverage; E=0.5 weak turnover. Z = 1.2*(-0.05) + 1.4*(-0.2) + 3.3*(-0.1) + 0.6*0.125 + 1.0*0.5 = -0.06 -0.28 -0.33 +0.075 +0.5 = -0.095. Z << 1.81 Distress severe. Italia typical: pre-bankruptcy company Tribunale Concorsuale procedura concordato preventivo CCII 2019.

Esempio 4 - Z' Private Company variant. Stesso input ma company_type=private_manufacturing. Z' = 0.717*A + 0.847*B + 3.107*C + 0.420*D + 0.998*E. Per Esempio 1 healthy: Z' = 0.717*0.5 + 0.847*0.4 + 3.107*0.15 + 0.420*2.67 + 0.998*1.5 = 0.359+0.339+0.466+1.121+1.497 = 3.782. Z' > 2.9 Safe Zone private companies. Threshold private 1.23/2.9 differs public 1.81/2.99. Italia: private companies SRL SAS used Z' variant Cerved Crif credit assessment.

Esempio 5 - USA Lehman Brothers retrospective 2008. Pre-bankruptcy financial position 2007 Q4. Working Capital ~$50B, Total Assets $691B, Retained Earnings $20B, EBIT $4B (margin compressed pre-crisis), Market Equity $30B (down from $60B 2006), Total Liabilities $613B, Sales $59B. A=0.072, B=0.029, C=0.006, D=0.049, E=0.085. Z = 1.2*0.072 + 1.4*0.029 + 3.3*0.006 + 0.6*0.049 + 1.0*0.085 = 0.086+0.041+0.020+0.029+0.085 = 0.262. Z << 1.81 Distress Severe! Z=1.2 estimate Altman prior bankruptcy 158-year history Lehman $613B liabilities largest USA bankruptcy ever September 15 2008.

Limiti e considerazioni

1. Modello statistico empirico based 1968 sample 66 USA manufacturing companies pubbliche, generalization periodo dataset specific industry.
2. Service industries technology pharma healthcare finance assicurazioni banche non-manufacturing: usare Z'' variant 1995 emerging markets adatto.
3. Private companies senza market cap: usare Z' 1983 variant book value equity instead market.
4. Country-specific accounting standards: USA GAAP vs IFRS Europa Italian dual reporting, ratios differ slightly.
5. Cyclical industries: airlines automotive construction high beta business cycle, Z-score volatile accuracy lower.
6. Banking financial institutions: Altman Z-score not designed banks, alternative Texas Ratio NPL ratio better.
7. Off-balance sheet items: derivatives leases pre-IFRS 16 understated leverage, real Z-score lower.
8. Aggressive accounting: revenue recognition fraud Enron WorldCom inflated earnings real Z-score lower retrospective audit.
9. Modern equity markets: stock buybacks Apple $100B+ reduce market cap denominator D, distort ratio.
10. Cross-border IFRS GAAP differences: deferred taxes intangibles goodwill different treatment.

Errori comuni

1. Confondere Working Capital con Cash: WC = Current Assets - Current Liabilities, NOT cash.
2. Confondere EBIT vs EBITDA vs Net Income: Altman uses EBIT operating earnings before interest tax.
3. Pretendere Z-score applicabile banks financial: alternative metrics needed Texas Ratio.
4. Usare book value invece market equity per public companies: incorretto, Z-score originale uses market cap.
5. Trascurare currency consistency: total assets $ vs sales €, conversion needed.
6. Z' Z'' variants confusion: Z' private (1983 book value), Z'' emerging non-manufacturing (1995 no E).
7. Pretendere Z>2.99 bankruptcy impossible: false negatives 5% historical, monitoring still useful.
8. Trascurare time-series trend: single Z-score snapshot, monitor declining trend critical.
9. JavaScript Math precision: ratios small numbers underflow potential, scaling.
10. Confondere total liabilities con total debt: liabilities include accounts payable + accrued expenses + LTD.

Applicazioni numerate

1. Italia credit rating industria: Cerved Group Milano 1988 fondata 1500 employees largest Italian credit rating agency, ION Group Andrea Pignataro 2024 acquisition $1.7B; Crif Bologna 1988 fondata 5000 employees Europe credit information 50+ countries.
2. Italia rating agencies: Standard & Poor's S&P Global Ratings Italy Milano subsidiary; Moody's Italia Milano; Fitch Ratings Milano; Banca d'Italia Roma supervisione credito.
3. Italia normativa CCII: Codice della Crisi d'Impresa e dell Insolvenza Decreto Legislativo 14/2019 entrato vigore luglio 2022 Italian bankruptcy reform.
4. Italia famous bankruptcy cases: Parmalat 2003 Calisto Tanzi Collecchio Parma food multinational $14B fraud; Banca Popolare Vicenza 2017 Veneto; MPS Monte dei Paschi di Siena 1472 oldest bank bailout 2017.
5. Italia universities finance: Bocconi Milano Università Commerciale Luigi Bocconi 1902 14000 students top business school Italy; Sapienza Roma DIET; Bologna alma mater 1088 DEMS; LUISS Guido Carli Roma 1974 9000 students; SDA Bocconi MBA.
6. Italia ODCEC commercialisti: Ordine Dottori Commercialisti Esperti Contabili Roma 117000 commercialisti Italia statutory auditing professional.
7. Italia Borsa CONSOB: Borsa Italiana Milano Piazza Affari FTSE MIB 40 stocks; CONSOB Commissione Nazionale Società Borsa Roma supervisione mercati financial regulator.
8. USA bankruptcy cases: Enron 2001 Houston Texas accounting fraud Z=0.5 6 months prior; Lehman Brothers 2008 $613B liabilities Z=1.2 1 year prior; WorldCom 2002 $11B fraud Z=0.7.
9. USA universities finance: NYU Stern Greenwich Village Manhattan 1900 Altman professor; Wharton Penn Philadelphia 1881 oldest; Harvard Business 1908; Booth Chicago 1898; Columbia GSB NY 1916.
10. Software analysis: Bloomberg Terminal NYC $24000/year; Reuters Refinitiv; FactSet; Capital IQ S&P; Moody's Risk Calc; SAS Cary NC; R Python.

Per supporto

Per domande tecniche: info@calcoi.com. Strumento didattico financial analysis. Per applicazioni Altman EI 1968 'Financial Ratios, Discriminant Analysis and the Prediction of Corporate Bankruptcy' Journal Finance 23:589, Altman EI 1977 ZETA Analysis Journal Banking Finance 1:29, Altman EI 1983 'Corporate Financial Distress' Wiley book Z' Z'' variants, Altman EI 2000 'Predicting Financial Distress', Beaver WH 1966 'Financial Ratios as Predictors of Failure' Journal Accounting Research 4:71.

Aggiornato a luglio 2026