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The Z-score formula for predicting bankruptcy was published in 1968 by Edward I. Altman, who was, at the time, an Assistant Professor of Finance at New York University. The formula may be used to determine the probability that a firm will go into bankruptcy within two years. Z-scores are used to predict corporate defaults and an easy-to-calculate control measure for the financial distress status of companies in academic studies. The Z-score uses multiple corporate income and balance sheet values to measure the financial health of a company.
The Z-score is a linear combination of four or five common business ratios, weighted by coefficients. The coefficients were estimated by identifying a set of firms which had declared bankruptcy and then collecting a matched sample of firms which had survived, with matching by industry and approximate size (assets).
Altman applied the statistical method of discriminant analysis to a dataset of publicly held manufacturers. The estimation was originally based on data from publicly held manufacturers, but has since been re-estimated based on other datasets for private manufacturing, non-manufacturing and service companies.
The original data sample consisted of 66 firms, half of which had filed for bankruptcy under Chapter 7. All businesses in the database were manufacturers, and small firms with assets of < $1 million were eliminated.
The original Z-score formula was as follows: [1]
Altman found that the ratio profile for the bankrupt group fell at −0.25 avg, and for the non-bankrupt group at +4.48 avg.
Altman's work built upon research by accounting researcher William Beaver and others. In the 1930s and on, Mervyn[ who? ] and others[ who? ] had collected matched samples and assessed that various accounting ratios appeared to be valuable in predicting bankruptcy.[ citation needed ] Altman Z-score is a customized version of the discriminant analysis technique of R. A. Fisher (1936).
William Beaver's work, published in 1966 and 1968, was the first to apply a statistical method, t-tests to predict bankruptcy for a pair-matched sample of firms. Beaver applied this method to evaluate the importance of each of several accounting ratios based on univariate analysis, using each accounting ratio one at a time. Altman's primary improvement was to apply a statistical method, discriminant analysis, which could take into account multiple variables simultaneously.
In its initial test, the Altman Z-score was found to be 72% accurate in predicting bankruptcy two years before the event, with a Type II error (false negatives) of 6% (Altman, 1968). In a series of subsequent tests covering three periods over the next 31 years (up until 1999), the model was found to be approximately 80–90% accurate in predicting bankruptcy one year before the event, with a Type II error (classifying the firm as bankrupt when it does not go bankrupt) of approximately 15–20% (Altman, 2000). [2]
This overstates the predictive ability of the Altman Z-score, however. Scholars have long criticized the Altman Z-score for being “largely descriptive statements devoid of predictive content ... Altman demonstrates that failed and non-failed firms have dissimilar ratios, not that ratios have predictive power. But the crucial problem is to make an inference in the reverse direction, i.e., from ratios to failures.” [3] From about 1985 onwards, the Z-scores gained wide acceptance by auditors, management accountants, courts, and database systems used for loan evaluation (Eidleman). The formula's approach has been used in a variety of contexts and countries, although it was designed originally for publicly held manufacturing companies with assets of more than $1 million. Later variations by Altman were designed to be applicable to privately held companies (the Altman Z'-score) and non-manufacturing companies (the Altman Z"-score).
Neither the Altman models nor other balance sheet-based models are recommended for use with financial companies. This is because of the opacity of financial companies' balance sheets and their frequent use of off-balance sheet items.
Modern academic default and bankruptcy prediction models rely heavily on market-based data rather than the accounting ratios predominant in the Altman Z-score. [4]
Z-score bankruptcy model:
Zones of discrimination:
Z-score bankruptcy model (non-manufacturers):
Z-score bankruptcy model (emerging markets):
Zones of discrimination:
Altman's Z-score for International Credit Rating Agencies | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Defaulter | Amount of Liabilities | Date of Default | Z-Score | Rating at the time of default | The Consequences | ||||||
(in $ billion) | In year of default | 1 year prior | 2 years prior | 3 years prior | 4 years prior | S&P | Moody's | Fitch | |||
Bear Stearns | 387 | 31-July-2007 | 0.29 | −0.79 | 0.45 | 0.4 | 0.36 | AA a A | A1 a A2 | Acquired by JP Morgan Chase | |
AIG | 807 | 16-Sep-2008 | −1.03 | −0.07 | −0.02 | 0.42 | 0.23 | AA− a A− | A1 a A2 | AA− a A− | Bailed out by US Government |
Lehman Brothers | 392 | 23-Sep-2008 | 0.06 | 0.09 | 0.03 | -0.03 | 0.29 | AA, A1 | P1 & A1 | AA− & F1+ | Bankrupt |
Washington Mutual Bank | 303 | 25-Sep-2008 | −0.35 | −0.3 | −0.07 | −0.13 | -0.3 | A− & A2 | Baa1 & P2 | A− & F2 | Acquired by JP Morgan Chase |
Ford Motors | 132 | 6-Apr-2009 | 1.32 | 1.03 | 1.23 | 1 | 1.29 | CC | Caa1, B3 | CCC, BB | Revived |
MF Global | 51 | 31-Oct-2011 | 0.23 | 0.47 | 0.37 | 0.41 | 0.46 | Baa2 a Caa | BBB a BB+ | Bankrupt | |
Altman's Z-scores of largest Indian Defaulters during April 2005 to March 2013 | |||||||||
---|---|---|---|---|---|---|---|---|---|
Defaulter | Amount of Liabilities (in Rs cr) | Date of default | Z-Score | Rating at the time of default | The Consequences | ||||
in Crore | In the Year of default | 1 yr prior to default | 2 yr prior to default | 3 yr prior to default | 4 yr prior to default | ||||
Arvind Products | 251.8 | 10-Feb-2009 | 1.58 | 1.93 | 2.14 | 1.61 | 1.73 | CRSIL BBB | Restructured |
Ansal Properties & Infraestructure | 1359 | 5-Oct-2009 | 2.3 | 3.21 | 4.22 | 4.85 | 3.06 | Fitch BBB | Restructured |
Kingfisher Airlines Limited | 4105.88 | 1-Dec-2011 | −2.36 | 1.85 | 0.61 | 0.79 | 1.93 | CRISIL D | Non Operational |
Royal Orchid Hotel Limited | 220 | 31-Mar-2012 | 0.77 | 1.06 | 1.17 | 1.62 | 2.17 | ICRA BBB+ | Restructured |
Deccan Chronicle Holdings | 3902 | 2-Jul-2012 | −0.12 | 2.74 | 3.01 | 2.54 | 2.77 | Care A1 | Assets sold by banks |
Suzlon Energy Limited | 10948 | 17-Jun-2012 | −0.11 | 1.23 | 1.28 | 1.19 | 1.24 | ICRA BBB− a D | Restructured |
Fundamental analysis, in accounting and finance, is the analysis of a business's financial statements ; health; competitors and markets. It also considers the overall state of the economy and factors including interest rates, production, earnings, employment, GDP, housing, manufacturing and management. There are two basic approaches that can be used: bottom up analysis and top down analysis. These terms are used to distinguish such analysis from other types of investment analysis, such as quantitative and technical.
In finance, default is failure to meet the legal obligations of a loan, for example when a home buyer fails to make a mortgage payment, or when a corporation or government fails to pay a bond which has reached maturity. A national or sovereign default is the failure or refusal of a government to repay its national debt.
Credit risk is the possibility of losing a lender holds due to a risk of default on a debt that may arise from a borrower failing to make required payments. In the first resort, the risk is that of the lender and includes lost principal and interest, disruption to cash flows, and increased collection costs. The loss may be complete or partial. In an efficient market, higher levels of credit risk will be associated with higher borrowing costs. Because of this, measures of borrowing costs such as yield spreads can be used to infer credit risk levels based on assessments by market participants.
Stock valuation is the method of calculating theoretical values of companies and their stocks. The main use of these methods is to predict future market prices, or more generally, potential market prices, and thus to profit from price movement – stocks that are judged undervalued are bought, while stocks that are judged overvalued are sold, in the expectation that undervalued stocks will overall rise in value, while overvalued stocks will generally decrease in value. A target price is a price at which an analyst believes a stock to be fairly valued relative to its projected and historical earnings.
A financial analyst is a professional, undertaking financial analysis for external or internal clients as a core feature of the job. The role may specifically be titled securities analyst, research analyst, equity analyst, investment analyst, or ratings analyst. The job title is a broad one: in banking, and industry more generally, various other analyst-roles cover financial management and (credit) risk management, as opposed to focusing on investments and valuation; these are also discussed in this article.
In corporate finance, capital structure refers to the mix of various forms of external funds, known as capital, used to finance a business. It consists of shareholders' equity, debt, and preferred stock, and is detailed in the company's balance sheet. The larger the debt component is in relation to the other sources of capital, the greater financial leverage the firm is said to have. Too much debt can increase the risk of the company and reduce its financial flexibility, which at some point creates concern among investors and results in a greater cost of capital. Company management is responsible for establishing a capital structure for the corporation that makes optimal use of financial leverage and holds the cost of capital as low as possible.
Distressed securities are securities over companies or government entities that are experiencing financial or operational distress, default, or are under bankruptcy. As far as debt securities, this is called distressed debt. Purchasing or holding such distressed-debt creates significant risk due to the possibility that bankruptcy may render such securities worthless.
Linear discriminant analysis (LDA), normal discriminant analysis (NDA), or discriminant function analysis is a generalization of Fisher's linear discriminant, a method used in statistics and other fields, to find a linear combination of features that characterizes or separates two or more classes of objects or events. The resulting combination may be used as a linear classifier, or, more commonly, for dimensionality reduction before later classification.
Financial distress is a term in corporate finance used to indicate a condition when promises to creditors of a company are broken or honored with difficulty. If financial distress cannot be relieved, it can lead to bankruptcy. Financial distress is usually associated with some costs to the company; these are known as costs of financial distress.
The following outline is provided as an overview of and topical guide to finance:
Credit analysis is the method by which one calculates the creditworthiness of a business or organization. In other words, It is the evaluation of the ability of a company to honor its financial obligations. The audited financial statements of a large company might be analyzed when it issues or has issued bonds. Or, a bank may analyze the financial statements of a small business before making or renewing a commercial loan. The term refers to either case, whether the business is large or small. A credit analyst is the finance professional undertaking this role.
Edward I. Altman is a Professor of Finance, Emeritus, at New York University's Stern School of Business. He is best known for the development of the Altman Z-score for predicting bankruptcy which he published in 1968. Professor Altman is a leading academic on the High-Yield and Distressed Debt markets and is the pioneer in the building of models for credit risk management and bankruptcy prediction.
Forensic accountants are experienced auditors, accountants, and investigators of legal and financial documents that are hired to look into possible suspicions of fraudulent activity within a company; or are hired by a company who may just want to prevent fraudulent activities from occurring. They also provide services in areas such as accounting, antitrust, damages, analysis, valuation, and general consulting. Forensic accountants have also been used in divorces, bankruptcy, insurance claims, personal injury claims, fraudulent claims, construction, royalty audits, and tracking terrorism by investigating financial records. Many forensic accountants work closely with law enforcement personnel and lawyers during investigations and often appear as expert witnesses during trials.
Bankruptcy prediction is the art of predicting bankruptcy and various measures of financial distress of public firms. It is a vast area of finance and accounting research. The importance of the area is due in part to the relevance for creditors and investors in evaluating the likelihood that a firm may go bankrupt.
A period of financial distress occurs when the price of a company or an asset or an index of a set of assets in a market is declining with the danger of a sudden crash of value occurring, either because the company is experiencing increasing problems of cash flow or a deteriorating credit balance or because the price had become too high as a result of a speculative bubble that has now peaked.
A financial ratio or accounting ratio states the relative magnitude of two selected numerical values taken from an enterprise's financial statements. Often used in accounting, there are many standard ratios used to try to evaluate the overall financial condition of a corporation or other organization. Financial ratios may be used by managers within a firm, by current and potential shareholders (owners) of a firm, and by a firm's creditors. Financial analysts use financial ratios to compare the strengths and weaknesses in various companies. If shares in a company are traded in a financial market, the market price of the shares is used in certain financial ratios.
The Ohlson O-score for predicting bankruptcy is a multi-factor financial formula postulated in 1980 by Dr. James Ohlson of the New York University Stern Accounting Department as an alternative to the Altman Z-score for predicting financial distress.
The Beneish model is a statistical model that uses financial ratios calculated with accounting data of a specific company in order to check if it is likely that the reported earnings of the company have been manipulated.
Financial stability is the absence of system-wide episodes in which a financial crisis occurs and is characterised as an economy with low volatility. It also involves financial systems' stress-resilience being able to cope with both good and bad times. Financial stability is the aim of most governments and central banks. The aim is not to prevent crisis or stop bad financial decisions. It is there to hold the economy together and keep the system running smoothly while such events are happening.
"Cindy" Yoshiko Shirata is a Japanese accounting scholar who specialized in corporate bankruptcy prediction. She is best known for her SAF2002 bankruptcy prediction model. Her bankruptcy prediction model has been used by major banks and rating companies in Japan. She is considered one of the most well-known experts to develop bankruptcy prediction models in Japan.
Altman, Edward I. (July 2000). "Predicting Financial Distress of Companies" (PDF). Stern.nyu.edu: 15–22.
Altman, Edward I. (September 1968). "Financial Ratios, Discriminant Analysis and the Prediction of Corporate Bankruptcy". Journal of Finance. 23 (4): 189–209. doi:10.1111/j.1540-6261.1968.tb00843.x. S2CID 154437292.
Altman, Edward I. (May 2002). "Revisiting Credit Scoring Models in a Basel II Environment" (PDF). Prepared for "Credit Rating: Methodologies, Rationale, and Default Risk", London Risk Books 2002. Archived from the original (PDF) on 2006-09-18. Retrieved 2007-08-08.
Eidleman, Gregory J. (1995-02-01). "Z-Scores – A Guide to Failure Prediction". The CPA Journal Online.
Fisher, Ronald Aylmer (1936). "The Use of Multiple Measurements in Taxonomic Problems". Annals of Eugenics. 7 (2): 179. doi:10.1111/j.1469-1809.1936.tb02137.x. hdl: 2440/15227 .
The Use of Credit Scoring Modules and the Importance of a Credit Culture by Dr. Edward I Altman, Stern School of Business, New York University.
On the other hand all the defaults in case of Indian rated companies were in non-structured financial products. Defaulters like Arvind Products, Suzlon, Royal Orchid Hotel, Deccan Chronicle Holding & Ansal Properties had investment grade ratings either at the time of default or just a few days before the default. Altman's Z score predicted default in case of Royal Orchid, Arvind Products & Suzlon Energy, which was not reflected in the ratings. This showed that simple model like Altman's Z score was more informative than the ratings given by Credit Rating Agencies. Thus the findings of the case studies support the findings of overall accuracy of Indian Credit Rating Agencies based on default rates. So Indian Credit Rating Agencies have to improve the accuracy & timeliness of the ratings of normal non structured products.