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Department of Economics
MARKET MODELS VS. ACCOUNTING MODELS
– DEFAULT PREDICTION DURING THE FINANCIAL TURMOIL
Author: Daniel Demirel
Tutor: Anders Vilhelmsson
TABLE OF CONTENT
PART I. INTRODUCTION
1.2 PROBLEM SPECIFICATION
PART II. THEORY
2.1 PREVIOUS RESEARCH
2.3 Z‐SCORE MODEL
2.4 MERTON 1974
2.5 MODIFIED MERTON
PART III. EMPERICAL STUDY
PART IV. TEST RESULTS
4.1 TYPE I AND TYPE II ERRORS
4.2 MODIFIED MERTON
PART V. COMPARING THE MODELS
5.1 CUMULATIVE ACCURACY PROFILE (CAP)
5.2 ACCURACY RATIO (AR)
5.3 COMPUTING THE CAP AND AR (EMPIRICALLY)
PART VI. CONCLUSION
During the past few years we have experienced an extraordinary turbulence in the financial markets. Stock markets in freefall, countless of bankruptcies and government interventions to save huge financial institutions have been regular events. During these times the focal point has been risk management. Poor risk management has been one of the main reasons for the experienced crisis. Credit risk in particular has been a widely discussed topic, which has divided both academics and professionals. Credit rating agencies’ assessments have been subject to immense criticism and many are questioning their methods and the accuracy of credit risk models in general. Credit risk is the risk you are exposed to when lending money to someone, that the counterparty fails to meet its obligation with agreed terms. When the borrower cannot payback the loan, he defaults on the loan. The lender looses out on the money and is required to write off the claim from its balance sheet. This may in some cases lead to the lender experiencing financial distress and a bankruptcy threat. The reason for managing credit risk correctly is the lender’s wish to maximise the return by maintaining a sound exposure to credit risk1.
1.2 Problem specification To be able to manage the credit risk, the lender need to have a good idea on how likely the borrower is to default. There are a number of different models available to estimate the likelihood of a borrower defaulting. We have examined two models using different sort of input when predicting default: the famous z-score by Altman’s from 1968 uses date collected from companies’ financial statements and a modified Merton model, where the input are obtained from the financial markets. The modified Merton, created by Byström (2005) model is built on Merton’s (1974) model.
1 PRINCIPLES FOR THE MANAGEMENT OF CREDIT RISK, Consultative paper issued by the Basel Committee on Banking Supervision (1999).
1.4 Disposition The first part of the paper is available to give the reader an adequate background to the reason for this study, while Part II provides a comprehensive description of the theory behind the models used in the analysis. The focus on the analysis procedure can be found in Part III, where an explanation on how the study has been conducted is included. Part IV runs through the result and an interpretation of the models’ test score is given. Part V stresses the importance of using appropriate comparison methods and briefly focus on the theory behind the particular process carried out in this study. Results from the comparison are also presented in this section followed by an analysis of the two models’ default predicting ability. The final part, Part VI is a concluding section, where the study and its findings are summed up and an ultimate statement is made.
PART II. THEORY
Altman’s z-score model and the Merton model are widely used among professionals handling credit risk and have therefore been chosen to represent the two different model categories that are the cause of this paper. However, the modified Merton is a modification of the original Merton (1974) and contains a few new critical assumptions in order to simplify the model. The result of the comparison will be interpreted as an indication to which model category is the most accurate. Will the modified Merton model, due to the fact that it uses market information, give a better forecast of companies in distress or will the accounting based z-score model be more accurate when predicting bankruptcies.
5 The important and also the appealing matter of this paper is that it examines the accuracy of the models during recent year. During years when the markets have been extremely volatile and many companies have experienced financial distress due to tremendous uncertainty and turbulence in the markets. We should therefore expect a market-based model, such as the modified Merton, to perform better than the z-score model. The market based model should be quicker to react to the changes of the firm’s financial position. Whereas the accounting based model only presents information of the past, which may not be sufficient in predicting the future. The modified Merton model however, also uses historical share/asset prices to compute the volatility but is more forward looking in its approach to predicting bankruptcies, according to Saunders and Allen (2002). Since the price of the stock is representative for the future prospects of the firm. In an efficient market, the share prices should reflect the books of the company.
Other information (not found in the accounting statement of the company, e.g. future cash flows) might have an impact on the likelihood of default and is also reflected in the valuation of the company. Another weakness of the z-score is the possibility that the firm’s accounting people have manipulated the input data and the financial reports does not represent the actual state of the firm. This would obviously take away the truthfulness of the model. The accuracy of the default predicting models should (theoretically) not be depended on time or sample used in the model. Mensah (1984) found sample dependence to occur in accounting based models. Mensah (1984) suggested the models to be redeveloped and variables changed to fit the specific sample.
The Merton model’s major weakness is the set of assumptions that may not represent reality. For example is the assumption that stock returns are normally distributed, something that is not always reflected in the real world. (Assumptions explained in detail below). Previous comparing research has had contradicting result and a final decision on which model is superior has not been able to have been taken. For example did Campbell et al (2006) find that the Merton model was not accurate enough to predict default, but Kealhofer and Kurbat (2001) found that the Merton approach outperforms various accounting ratios and argues that the Merton model already contain all the information in accounting ratios, and more.
2.1 Previous Research Many studies highlighting the accuracy of default prediction models have been carried out before, for both academics and professionals have relied on the models. The marketbased Merton model has been under scrutiny from a vast number of academics and many modifications in attempts to improve the model have been conducted. However, there are few published studies where accounting based models and market based models have been compared on the basis of their power. Reisz and Perlich (2004) found that the accounting based z-score outperform the structural models on a one year time horizon, but looses its power when the time horizon is further away from failure.
Agarwal and Taffler (2008) tests a UK adapted z-score model and two versions of the Merton model. The two versions of Merton models came from Hillegeis et al (2004) and Bharath and Shumway (2004), where slightly different methods of computing the asset value and volatility are used. Agarwal and Taffler (2008) set of data is taken from before the financial crisis. Agarwal and Taffler (2008) find little difference between the accounting based and the market based model. Hillegeis et al (2004) reaches the same conclusion when they test the models. They argue that due to the model’s assumptions, it is not surprising that the market based models do not perform better. The need to back out asset value and volatility is another reason for the inaccuracy according to Hillegeis et al (2004).
2.2 Models Two models have been chosen to represent one of the model categories each. The zscore model was created by Edward I. Altman in the 1960’s and uses accounting data as it’s main components. The market based category is represented by a modified Merton model. The z-score model and the Merton model has been around for decades and have been used by many credit risk managers and analysed in many studies. They are two of the most frequently used models. The models will be explained in detail below, first the z-score model and then the original Merton model followed by the modified version.
The test in this study is made on a random sample of companies. Some of them manufacturing firms and some of them non-manufacturing firms. They are/were all
The reason for using the modified Merton model in the paper is its simplicity’s moderate impact on the result Byström could extract from his study. It would be interesting to see by representing the market based models, if this simplified model could outperform a classic model like z-score model.
2.3 Z-score model Altman builds his work on Beaver’s (1966) article on financial ratios as a tool for predicting failures.2 Beaver conducted a univariate analysis and found that a number of ratios could distinguish between failed companies and non-failed companies up to five years prior to failure. His work implied that by using more than only one ratio at the time (a multivariate approach) the analysis could be more successful. Altman (1968) assesses the analytical quality of ratio analysis by combing a set of financial ratios in a multi discriminant analysis approach on corporate bankruptcy prediction. A multi discriminant analysis is a method used to separate the observations into defined groups. In Altman’s case he referrers to the two classes as bankrupt and non-bankrupt. The discriminant function is Z = V1X1 + V2X2 +…..VnXn
V1X1,….Vn = discriminant coefficient and V2X2,….Xn = independent variables.
2 Beaves defined failure as the inability of a firm to pay its financial obligations as they mature. A firm is said to have failed when any of the following events have occured: bankruptcy, bond default, an overdrawn bank account, or nonpayment of a prefered stock dividends.
Table 1. Altman defines the z‐scores in to three classes. A score up to 1.80 describes a firm that will go bankrupt. If the company score 3 or above, it should have no problems with bankruptcy. 1.81 – 2.99 is a zone of ignorance, where the future of the firm is unclear. A z-value below 1.81 indicates a distressed company likely to file for bankruptcy, while a z-value above 2.99 show financial strength and are unlikely to go bankrupt. Altman defines a zone of ignorance, a grey area, when the model produces a z-value 1.81 – 2.99, where the model is unable to distinguish a bankrupt from a non-bankrupt firm.
Altman produced five appropriate ratio categories for the model. He tested a total of 22, variables and found that five variables were doing a better job predicting failure than the others. He tested the variables’ statistical significance and for inter-correlation between them. To test the individual discriminant ability of the variables, Altman conducted a Ftest. The test stressed the difference between the average values of the ratios to the values of the ratios within each group. He found X1 – X4 to be significant at the 0.001 level, while X5 did not show a significant difference between the classes. Altman still chose to include all five of the variables since on a strictly univariate level, they all (including X5) produced a lower value for bankrupt firms then for non-bankrupt firms.
His sample contained of 66 observations, which half of them were bankrupt companies and the other half non-bankrupt companies. The firms in his sample all had total assets between $1 - $25 million. In his study, Altman finds his approach to be accurate in 95% of the cases. He finds that his model can predict bankruptcies accurately up to two years prior to the companies were actually failing. The model’s accuracy is declining quickly the further away from the two years prior to bankruptcy the model is predicting.
Z = 0.012 X1 + 0.014 X2 + 0.033 X3 + 0.006 X4 + 0.999 X5 Where X1 = Working capital/Total asset Working capital is the difference between current assets and current liabilities. Altman considered two other liquidity ratios but found working capital/total assets to be the most suitable. It is a measure that compares the size of the net liquidity to the total capitalisation.
X2 = Retained Earnings/Total assets