Oldman Z-factor

The Z-factor model published by Altman in 1968 (original English Altman’s Z-Score or Z-Score for short ) is the first multivariate insolvency forecasting procedure for companies. For private individuals, however, multivariate analysis methods were already being used at this time. In the financial literature it is still used today as a benchmark for assessing the forecast quality of rating systems and forms the basis of commercial rating procedures. There are currently three versions of the Z-factor method, which are referred to as the Z, Z 'and Z "models. Recent empirical studies consistently show that none of the model versions of the Z-factor method are well suited for forecasting corporate insolvencies More suitable metrics are publicly available.

The different model versions of the Z-factor method

The Z-factor method

The Altman Z-factor method was parameterized by means of the multivariate linear discriminant analysis and classifies the companies to be assessed into two groups ("probably solvent" vs. "probably insolvent "). In practice, the z-factor value is also interpreted ordinally . On the basis of a sample of 33 insolvent and 33 solvent companies, Altman (1968) succeeded in correctly classifying 31 of the insolvent and 32 of the non-insolvent companies with a forecast horizon of one year. The assignment was based on the discriminant function:

{\ displaystyle Z = 1 {,} 2X_ {1} +1 {,} 4X_ {2} +3 {,} 3X_ {3} +0 {,} 6X_ {4} +0 {,} 999X_ {5}}

Legend:

${\ displaystyle X_ {1}}$ = (Current assets - short-term liabilities) / total assets,
${\ displaystyle X_ {2}}$ = retained earnings / total assets,
${\ displaystyle X_ {3}}$ = Earnings before interest and taxes (EBIT) / total assets,
${\ displaystyle X_ {4}}$ = Market value of equity / total liabilities,
${\ displaystyle X_ {5}}$ = Sales / total assets

According to this procedure, companies with a Z-factor value of less than 1.81 are considered to be at high risk of insolvency over a one-year perspective, while companies with a Z-score value greater than 2.99 are considered safe.

The Z 'factor method

In order to also be able to apply the Z-factor method to unlisted companies , in a later model revision the definition of the key figure for the market value of equity was replaced by its book value and all coefficients were re-estimated: ${\ displaystyle X_ {4}}$

{\ displaystyle Z '= 0 {,} 717X_ {1} +0 {,} 847X_ {2} +3 {,} 107X_ {3} +0 {,} 420X_ {4}' + 0 {,} 998X_ {5th }}

Legend:

${\ displaystyle X_ {4} '}$ = Book value of equity / total liabilities

for the other variables see above

With Z 'over 2.9 there is no risk of insolvency, companies with Z' less than 1.23 are at risk of insolvency.

The Z "factor method

Since the key figure was viewed as too industry-dependent, it was removed as part of a third version of the model, the aim of which was to apply the model to companies outside the manufacturing sector. The coefficients of the remaining variables were re-estimated: ${\ displaystyle X_ {5}}$

{\ displaystyle Z '' = 6 {,} 56X_ {1} +3 {,} 26X_ {2} +6 {,} 72X_ {3} +1 {,} 05X_ {4} '}

Legend: see Z'-factor method

According to this model, companies with a Z "value less than 1.10 are considered to be at risk of bankruptcy.

Results of current empirical studies

In a meta-study of ten empirical studies, each of which included several thousand companies, the forecasting performance of the various Z-factor methods was measured. Even if the Z-factor model was originally adapted to US stock corporations with data from (from today's perspective) 40 to 60-year-old annual financial statements , the univariate forecast performance of the key figures used (with the exception of the key figure X5, which starts with the Z " Factor method was no longer used) in the current annual financial statements of international, German or Austrian medium-sized companies. However, the calibration of the coefficients is worse . With the exception of the original Altmans study (1968) and its later studies, the empirical results consistently show below-average forecasting performance of the three Z-factor method. This applies not only in comparison to the models developed by the respective authors themselves - but also in comparison to the (univariate) forecast performance of individual key figures, such as the return on investment (annual surplus / balance sheet total) or the equity ratio (E equity / total assets).

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↑ see Sobehart et al. (2000, p. 6), Falkenstein, Boral, Carty (2000, p. 9), Frerichs, Wahrenburg (2003, p. 4), Balcaen, Ooghe (2004, p. 11)
↑ see Altman (1968, p. 591)
↑ Falkenstein, Boral, Carty (2003, p. 74): "The most well-known quantitative model for private firms in the US is Altman's Z-score. Virtually every accounting or financial analysis book uses Z-score to demonstrate how financial statement data can be translated into an equation that helps predict default. [...] "
↑ The Z-Score procedure is based on the ratings of the agencies CONFIRM GmbH and IKU, which offer their services for 1,200 euros or 312 euros per rating, see Romeike, Wehrspon (2004, p. 18, p. 27 and p . 29).
↑ See the studies examined in Bemmann (2005, pp. 75ff.), Which report all the key figures and aggregation rules used.
↑ See Altman, Saunders (1998, p. 1737) for a method of assigning Z-scores to S&P ratings on the basis of 750 rated US companies.
↑ In Altman (1968, p 594) is given the following formula . In this formula, however, the variables to must be entered as absolute percentage values (for example 33 instead of 33% ). See Altman (2000, p. 12f.) On this and the above formula. ${\ displaystyle Z = 0 {,} 012X_ {1} +0 {,} 014X_ {2} +0 {,} 033X_ {3} +0 {,} 006X_ {4} +0 {,} 999X_ {5}}$ ${\ displaystyle X_ {1}}$ ${\ displaystyle X_ {4}}$

↑ see Altman (1968, p. 606)

↑ see Altman (2000, p. 25)

↑ ^a ^b see Altman (2002, p. 22)

↑ see Bemmann (2005, p. 69ff.)

↑ see Hayden (2003, pp. 14, 18)

Web links

literature

Altman, EI (1968): Financial Ratios, Discriminant Analysis and the Prediction of Corporate Bankruptcy (PDF; 1.2 MB), in Journal of Finance, Vol. 23 (4), pp. 589-610, 1968
Altman, EI, Saunders, A. (1998): Credit Risk Measurement: Developments over the last 20 years (PDF; 1.4 MB), in Journal of Banking and Finance, Vol. 21, pp. 1721–1742, 1998
Altman, EI (2000): Predicting financial distress of companies: revisiting the Z-score and Zeta ® models (PDF; 135 kB), Working Paper, New York University, 2000
Altman, EI (2002): Revisiting Credit Scoring Models in a Basel 2 Environment , Working Paper, Stern School of Business, New York University, 05/2002
Altman / Iwanicz-Drozdowska / Laitinen: Distressed Firm and Bankruptcy prediction in an international context: a review and empirical analysis of Altman's Z-Score Model , Working Paper, Stern School of Business, New York University, 07/2014
Balcaen, S., Ooghe, H. (2004): 35 Years of Studies on Business Failure: An Overview of the Classic Statistical Methodologies and their Related Problems , Vlerick Leuven Gent Working Paper Series 2004/15, 2004, also published in British Accounting Review, Vol. 38 (1), pp. 63-93, 2006
Bemmann, M. (2005): Improvement of the comparability of estimation quality results of insolvency prognosis studies , in Dresden Discussion Paper Series in Economics 08/2005
Falkenstein, E., Boral, A., Carty, L. (2000): RiskCalc ™ For Private Companies , Moody's KMV, 2000
Frerichs, H., Wahrenburg, M. (2003): Evaluating internal credit rating systems depending on bank size , Working Paper Series: Finance and Accounting, Johann Wolfgang Goethe-Universität Frankfurt Am Main, No. 115, 09/2003
Hayden, E. (2003): Are Credit Scoring Models Sensitive With Respect to Default Definitions? Evidence from the Austrian Market , Working Paper, University of Vienna, 2003
Romeike, F., Wehrspohn, U. (2004): Market study of rating software for companies (PDF; 1.3 MB), 2004, excerpts published in RATINGaktuell 06/2004, pp. 10–19, 2004
Sobehart, JR, Stein, RM, Mikityanska, V., Li, L. (2000): Moody's Public Firm Risk Model: A Hybrid Approach to Modeling Short Term Default Risk , Moody's Investors Service , Rating Methodology, Report # 53853, 03 / 2000

[1] see Sobehart et al. (2000, p. 6), Falkenstein, Boral, Carty (2000, p. 9), Frerichs, Wahrenburg (2003, p. 4), Balcaen, Ooghe (2004, p. 11)

[2] see Altman (1968, p. 591)

[3] Falkenstein, Boral, Carty (2003, p. 74): "The most well-known quantitative model for private firms in the US is Altman's Z-score. Virtually every accounting or financial analysis book uses Z-score to demonstrate how financial statement data can be translated into an equation that helps predict default. [...] "

[4] The Z-Score procedure is based on the ratings of the agencies CONFIRM GmbH and IKU, which offer their services for 1,200 euros or 312 euros per rating, see Romeike, Wehrspon (2004, p. 18, p. 27 and p . 29).

[5] See the studies examined in Bemmann (2005, pp. 75ff.), Which report all the key figures and aggregation rules used.

[6] See Altman, Saunders (1998, p. 1737) for a method of assigning Z-scores to S&P ratings on the basis of 750 rated US companies.

[7] In Altman (1968, p 594) is given the following formula . In this formula, however, the variables to must be entered as absolute percentage values (for example 33 instead of 33% ). See Altman (2000, p. 12f.) On this and the above formula. ${\ displaystyle Z = 0 {,} 012X_ {1} +0 {,} 014X_ {2} +0 {,} 033X_ {3} +0 {,} 006X_ {4} +0 {,} 999X_ {5}}$ ${\ displaystyle X_ {1}}$ ${\ displaystyle X_ {4}}$

[8] see Altman (1968, p. 606)

[9] see Altman (2000, p. 25)

[alt22-10] see Altman (2002, p. 22)

[11] see Bemmann (2005, p. 69ff.)

[12] see Hayden (2003, pp. 14, 18)