Microsoft Word - 14168-51531-1-SM-writer2-new Asian Journal of Finance & Accounting ISSN 1946-052X 2019, Vol. 11, No. 1 ajfa.macrothink.org/ 141 Application of Credit Risk Management Model in Chinese Banks Chen Haojie (Corresponding Author) School of Economics & Management, Xiamen University Malaysia Campus Jalan Sunsuria, Bandar Sunsuria, 43900 Selangor D.E., Malaysia Tel: 60-1-0899-1663 E-mail: chj6869@icloud.com Ng Sin Huei School of Economics & Management, Xiamen University Malaysia Campus Jalan Sunsuria, Bandar Sunsuria, 43900 Selangor D.E., Malaysia Tel: 60-3-8705-5037 E-mail: shng@xmu.edu.my Lew Shian Loong School of Economics & Management, Xiamen University Malaysia Campus Jalan Sunsuria, Bandar Sunsuria, 43900 Selangor D.E., Malaysia Tel: 60-3-8705-5126 E-mail: shianloong.lew@xmu.edu.my Received: Nov. 29, 2018 Accepted: Jan. 24, 2019 Published: June 1, 2019 doi:10.5296/ajfa.v11i1.14168 URL: https://doi.org/10.5296/ajfa.v11i1.14168 Abstract The main objective of this paper is to perform empirical analysis and research on the KMV and Zeta models, discussing whether banks in China could adopt both models in their credit risk management practices. In order to measure credit risk, the KMV model focuses on “Expected Default Probability” (EDP) that is calculated using Black-Scholes Option Pricing Formula. On the other hand, the Zeta Model focuses on determining the probability of a company going bankrupt two years prior to the event. Previous research on risk management has shown that the primary risk the banks generally face is credit risk as an increasingly greater number of banks suffer losses because of credit issues. This paper therefore aims to add to the existing literature a strong case for the relevance of both the KMV and Zeta models to be considered in the topic of banks’ credit risk management. Keywords: KMV model, Zeta model, Expected default probability (EDP), Credit risk assessment Asian Journal of Finance & Accounting ISSN 1946-052X 2019, Vol. 11, No. 1 ajfa.macrothink.org/ 142 1. Introduction 1.1 Background Since the 1990s the global economic, political and technological landscapes have experienced a wide range of dramatic transformations, which have subsequently fueled an exponential growth in credit risk. And with the inception of a floating exchange rate regime, financial markets throughout the world have since witnessed an ongoing process of deregulation. While greater financial liquidity worldwide is creating opportunities for new capital sources to thrive, the increasing complexity of credit risk is posing a host of challenges. In China, due to the current financial system in place, credit risk has inevitably become the main factor of financial risk—which is also influenced by:  indirect financing that dominates the financial structure,  precarious relationship between banks and enterprises,  vague business distinction between bank policy and commerce,  inadequate financial management,  weak sense of risk,  lack of effective internal mechanisms and risk prevention measures, and  information asymmetry between borrowers and lenders, which could potentially lead to moral hazard. On the evidence of the above, the financial risk situation in China reflects the more obvious characteristics of the traditional form of financial risk—as opposed to what is usually seen in other developed countries. The credit risk faced by the commercial banks in China is largely affected by bad credit assets, tendency towards concentration of credit risk and insufficient credit risk management. So, measuring credit risk has become imperative to banks. The credit risk exposure featured in the New Basel Accord mainly involves five essential aspects, namely corporate risk, bank risk, retail risk, sovereign risk and equity risk— fully affirming the important role of IRB in risk management and capital regulation. The New Basel Accord proposes an IRB method for calculating credit risk, where the data analysis time period required for parameter estimation is long, and the source and content requirements are very high. Using the PD (probability of default ), LGD (loss given default, which is amount of money a bank or other financial institution losses when a borrower defaults on a loan ), EAD (exposure at default, which is the total value a bank is exposed to when a loan defaults ) and M (maturity is the date on which the life of a transaction or financial instrument ends, after which it must either be reviewed.), we could ascertain the risk weight of different asset situations and then determine the risk assets. As the credit risk management model gradually develops from being qualitative to being quantitative, both the KMV model and the Zeta model will be used to discuss the feasibility of applying a credit risk management model in China. Asian Journal of Finance & Accounting ISSN 1946-052X 2019, Vol. 11, No. 1 ajfa.macrothink.org/ 143 2. Literature Review 2.1 Literature Review There are a number of research papers that revolve around credit risk management models, but for the purposes of our study, we shall focus our attention on those that discuss the KMV model and the Zeta model. Generally, the most common credit default model is the KMV model whereas the most accurate bankrupt probability model is the Zeta model. Some scholars in China have researched the adaptability of KMV Model in China. Zhang Lin and Zhang Jialin (2000) as well as Wang Qiong and Chen Jinxian (2002) presented a theoretical comparison between the KMV model and the other models—pointing out that the KMV model might be more appropriate for the credit risk assessment of a public company. Xue Feng, Lu Wei, Zhao Heng Jie and Liu Jiyun (2003) used the data of China's stock market to determine the relationship function between the 𝜎 and 𝜎 in the actual equity market as they performed an empirical analysis based on a particular stock. Qiao Zhuo et al (2003) discussed the basic characteristics of the KMV model without any empirical evidence. On the other hand, Yi Danhui and Wu Jianmin (2004) calculated and compared the distance to default and default probability. With 30 companies in China randomly selected from the Shenzhen and Shanghai stock markets, the researchers verified the feasibility of measuring the listed company’s credit risk by using distance to default. According to Peter Crosbie (2003) the credit risk model can be summarized as follows. Credit risk can be divided into two components: single risk and portfolio risk. While single risk consists of PD, LGD and migration risk (Migration risk is a change in value caused by a deviation of the actual probability of a future default by an obligor from the expected probability of future default, adversely affecting the present value of the contract with the obligor today), portfolio risk comprises risk exposure and default correlations. In order to determine a company’s credit risk default probability, we must calculate the company’s value of assets, asset risk and leverage. As for the three-step method to calculate the expected default frequency of the KMV model, we must first estimate the market value of the company’s assets and then calculate the volatility of those assets. And after we calculate the Distance to Default based on the volatility of the company’s assets, we must eventually convert the Distance to Default to the expected default frequency using empirical distribution. As pointed out by Peter Crosbie (2003) the measurement of EDF is an effective tool in managing the credit process of institutions and continuous monitoring is the only way for detecting deterioration in credit quality. Because the EDF value is a real probability, it is widely used by institutions to measure credit risk. Michel Crouhy, Dan Galai and Robert Mark (2000) performed a comprehensive analysis on the current credit risk models—comparing the CreditMetrics, KMV, CreditRisk+ and CreditProtfolioView models. CreditMetrics is a credit migration approach proposed by JP Morgan that accounts for the change of the company’s credit quality within a time period. Meanwhile, the option pricing method or structural approach is initiated by KMV based on the asset value model originally proposed by Merton. KMV is then used to further develop the option pricing theory. As the endogenous default process in the model is compatible with the capital structure of the company, the company will suffer default when the asset value of the company is below a certain level. On the other hand, CreditRisk+ is an actuarial approach Asian Journal of Finance & Accounting ISSN 1946-052X 2019, Vol. 11, No. 1 ajfa.macrothink.org/ 144 proposed by Credit Suisse Financial Products (CSFP) to calculate default probability. Focusing on default probability using joint conditional distribution, this approach assumes that individual bonds and loans follow an exogenous Poisson process. As for the last model, Credit Portfolio View—proposed by McKinsey—is a time model using discrete time periods. Unlike the other models, Credi tPortfolio View uses macroscopic variables—such as unemployment rate, government expenditure and GDP growth—that play a vital role in the credit cycle of the economy. According to Michel Crouhy, Dan Galai and Robert Mark (2000) both the Credit Portfolio View and KMV methods are based on the same empirical observation, with their default risk and migration probability changing over time. While the KMV method adopts microeconomic factors by using the market value of assets to measure the PD of the debtor, the Credit Portfolio View method links the PD to the probability of mitigation by using macroeconomic factors. But we still need to calibrate default data for every country and corresponding industries. And the ad-hoc procedure in adjusting the mitigation matrix is another obvious limitation. Being more practical than the simple Bayesian model though, the proposed models should perform better because the revision of transition probability depends on the accumulation of internal professional knowledge of the bank's credit department and the internal credit quality assessment of a bank's given credit portfolio. The KMV method is related to the Credit Portfolio View method since the company's market value is mostly dependent on the economic situation. Therefore, the transition matrices produced by the KMV and Credit Portfolio View methods are comparable. Edward I. Altman and Anthony Saunders (1998) summarized the development of credit risk models in the last two decades. First, the researchers discussed the evolution of individual loans and portfolio of the loans credit risk measurement put forward by the Journal of Banking & Finance and other well-known publications. Subsequently, the researchers presented a new mortality risk framework that could be used to measure the risk and return of loans and bonds. Offering us some hope for analyzing the risk-return structure of portfolio of debt instruments exposed to credit risk, the framework basically uses a variant Z-score model—called 𝑍 − 𝑆𝑐𝑜𝑟𝑒 model—to determine unexpected losses (the unexpected loss is the average total loss over and above the mean loss. It is calculated as a standard deviation from the mean at a certain confidence level. It is also referred to as Credit VaR.) and to assign a bond rating that is equivalent to the portfolio which each loan or bond may enter. As these scores and rating equivalents can consistently estimate expected losses, we should have a specific procedure for estimating unexpected losses if we have access to the standard deviation around the expected losses. Edward I. Altman and Anthony Saunders (1998) also discussed the portfolio risk. The unexpected loss measure of 𝑈𝐴𝐿 in the portfolio includes the correlation between the expected loss during the sample measurement period and the unexpected loss of personal assets. So, by comparing the bond rating equivalents, we can compute the expected value of the unexpected loss by using the standard deviation of the expected loss. It has also been highlighted that in order to gain the experience and confidence in applying this fixed income portfolio technology, we must spend more time in studying additional samples. Asian Journal of Finance & Accounting ISSN 1946-052X 2019, Vol. 11, No. 1 ajfa.macrothink.org/ 145 Stephen Kealhofer and Matthew Kurbat (2002) discussed the use of Merton's method to predict default based on debt ratings and accounting variables. Adding Moody's rating and accounting variables into Merton's method can significantly improve the viability of default prediction. It is important to note that both the Moody's ratings and the accounting variables contain default prediction information that is beyond the predictive information presented in Merton's method. However, it is still possible to show all default predictive information of Moody’s ratings and accounting variables in the KMV expected default frequencies. With less incorrect default identification that is observed in other models, the expected default frequencies of KMV are more uniform. It is also worth noting that Merton's approach generally performs better than Moody's credit rating or other accounting ratios in forecasting default conditions—due to the stronger connection that Merton’s approach has with accounting variables. To predict future share price, Merton's method uses historical share price information that includes information ratios such as return on asset and returns on equity. It has also been pointed out that the Merton’s approach is unfair, due to the various judgements made about non-defaulting companies. Every method faces the possibility of generating too many false rejections, but this is hardly surprising since ratings and accounting ratios cannot be fully projected in the share price. There are just too many factors affecting the share price. 3. Research Methodology 3.1 KMV Model Overview The original intention of KMV Corporation in creating the KMV model was to estimate the default probability of KMV company’s borrowers. The KMV model has two stages. The first stage of the KMV model is to test the precision of the model by comparing the predicted results with the actual results. It has been observed that in most cases the KMV model can truly reflect the size of credit risk, thanks to a high sensitivity to credit risk. The second stage of KMV model is to verify the validity of the model—a subject that many famous scholars have studied before. The pricing basis of the KMV model is modern option pricing theory, which has been a major innovation in the measurement of credit default. The KMV model has several advantages. Besides fully utilizing the information available in the capital market, the KMV model can be used to quantitatively analyze the credit risk of listed companies. Since the data used by the KMV model is derived from stock price information of listed companies rather than internal data that is generated within the company itself, the company's current credit situation can be accurately projected. In addition, the KMV model is based on a number of previous theories— such as corporate finance theory and option pricing theory—so there is a theoretical basis to support its viability. The KMV model is more suitable for credit quality evaluation of listed companies because listed companies are more transparent about their data whereas the data of non-listed companies is less accessible. When we apply the KMV model to non-listed companies, we need to adjust the parameters of the model. And because the expected default probability is the result of comparative analysis, the accuracy of the model may be somewhat compromised. Most importantly, the KMV model assumes that the value of company assets conforms to the Asian Journal of Finance & Accounting ISSN 1946-052X 2019, Vol. 11, No. 1 ajfa.macrothink.org/ 146 characteristics of lognormal distribution, but the value of company assets generally exhibits non-normal statistical characteristics in reality. In short, the KMV model offers certain practical significance in calculating the probability of default. 3.2 Zeta Model Overview Derived from quantitative and qualitative methods, the scoring model is a statistical method which uses a large amount of historical data to determine parameters and predict variables of default probability. LDA (Linear discriminant analysis: it is a generalization of Fisher’s linear discriminant, a method used in statistics, pattern recognition and machine learning to find a linear combination of features that characterizes or separates two or more classes of objects or events. ) is one of the most commonly used statistical methods in developing scoring models. Generally, due to the choice of exogenous variables, default composition and default definition, usage of the LDA-based model is reduced. An LDA produces a scoring function, which is a linear function of variables. These variables are chosen based on their estimated contribution to the likelihood of default, the large number of qualitative characteristics and the accounting ratios. Each accounting ratio could have a big or small impact on the overall score, as determined by Altman’s Z-score. Although there are many ways to calculate Z-score, the most commonly used method is the least squares method. Proposed by Edward I. Altman, an Assistant Professor of Finance at New York University in 1968, Z-score is a quantitative analysis method used to determine the condition of the balance sheet. The lower the Z-score, the greater the probability for the company to face a financial problem in the future under normal circumstances. LDA divides the companies into two groups: performing or solvent companies and defaulting or insolvent companies. One of the challenges of such classification is whether or not we can predict which companies will be solvent and which companies will be insolvent before default. Although the approach is flawed as both solvent and insolvent companies may have similar scores, the Z cut-off point is used to distinguish the two groups. Altman’s Z-score is also used to estimate the possibility of financial distress, which is denoted by a weighted average of five financial ratios. As sharp decline in the company's share price is mostly caused by balance sheet issues, financial statements have a strong influence on shareholders' judgement of the company. The importance of financial ratios is therefore self- evident. Altman’ s initial research was based on financial data from manufacturing companies. Focusing on 66 companies where half had applied for bankruptcy, Altman calculated various financial indicators for those 66 companies, obtained their corresponding weights through discrete methods and selected the most important weights to build the relevant model. To validate the model, Altman calculated the Z-score for groups of bankrupt and non-bankrupt but sick companies, i.e. ST companies. Altman’s goal was to ascertain how well the model could distinguish between sick companies and those that had gone bankrupt. Asian Journal of Finance & Accounting ISSN 1946-052X 2019, Vol. 11, No. 1 ajfa.macrothink.org/ 147 It was observed that Altman's model predicted with a 72% accuracy a company’s bankruptcy two years in advance. In the next 31 years of testing though, it was discovered that the accuracy of the model in predicting bankruptcy one year in advance had eventually increased to 80%– 90%. Using the Z-score to rank a group of European companies in 2009, Graham Secker—a Morgan Stanley strategy analyst—found that companies with weaker balance sheets underperformed in most cases as those with a Z score of less than 1 usually underperformed by more than 4%. If the company is not listed, the market value of the company cannot be obtained directly. The Zeta model therefore has different forms for listed companies and non-listed companies. When the company is listed, the Z-score is calculated as follows: 𝑍 = 1.2𝑋 + 1.4𝑋 + 3.3𝑋 + 0.6𝑋 + 1.0𝑋 where Z: the overall index of the Z-score model 𝑋 : working capital / total assets This suggests the company may experience shrinking liquidity when the company’s liquid assets double. 𝑋 : retained earnings / total assets This ratio measures profitability, which reflects the company's age and earning power. 𝑋 : earnings before interest and tax / total assets This ratio shows the efficiency of the company in generating earnings under the same asset size. 𝑋 : market value of equity / book value of total liabilities This ratio provides a quick test of how much the company’s assets can fall before the company becomes technically insolvent, i.e. when its liabilities exceed its assets. 𝑋 : sales / total assets This ratio represents asset turnover, which measures how effectively the company uses its assets to generates sales. A great deal of factual research has shown that investors must do some serious due diligence before considering whether to invest in a company with an Altman Z-score of close to or less than 3. Companies can be classified according to their Z-score as follows:  When the company’s Z-score is more than 2.99, based on the financial figures only, the company is placed in the “Safe” zone.  When the company's Z-score ranges from 1.80 to 2.99, based on the financial figures only, the company is placed in the “Grey” zone. The company may or may not go bankrupt in the next two years. Asian Journal of Finance & Accounting ISSN 1946-052X 2019, Vol. 11, No. 1 ajfa.macrothink.org/ 148  When the company's Z-score is less than 1.80, based on the financial figures only, the company is placed in the “Distress” zone. There is a high probability that the company will face distress in the next two years. When the company is not listed, the Z-score is calculated as follows: 𝑍 = 0.717𝑋 + 0.847𝑋 + 3.107𝑋 + 0.42𝑋 + 0.998𝑋 where Z: the overall index of the Z-score model for private manufacturing companies 𝑋 : working capital / total assets This suggests the company may experience shrinking liquidity when the company’s liquid assets double. 𝑋 : retained earnings / total assets This ratio measures profitability that reflects the company's age and earning power. 𝑋 : earnings before interest and tax / total assets This ratio shows the efficiency of the company in generating earnings under the same asset size. 𝑋 : book value of equity / total liabilities This formula uses the book value of equity, not the market value of equity. 𝑋 : sales / total assets This ratio represents asset turnover, which measures how effectively the company uses its assets to generates sales. Non-listed companies can be classified according to their Z-score as follows:  When the company’s Z-score is more than 2.9, based on the financial figures only, the company is placed in the “Safe” zone.  When the company's Z-score ranges from 1.23 to 2.9, based on the financial figures only, the company is placed in the “Grey” zone. The company may or may not go bankrupt in the next two years.  When the company's Z-score is less than 1.23, based on the financial figures only, the company is placed in the “Distress” zone. There is a high probability that the company will face distress in the next two years. Asset turnover changes according to the industry the company is in. Since the above formula is mainly used for companies in the manufacturing industry, we need to consider the following Altman models that provide corresponding formulas for non-manufacturing companies. For non-manufacturing companies, the Z-score is calculated as follows: Asian Journal of Finance & Accounting ISSN 1946-052X 2019, Vol. 11, No. 1 ajfa.macrothink.org/ 149 𝑍 = 6.56𝑋 + 3.26𝑋 + 6.72𝑋 + 1.05𝑋 where Z: the overall index of the Z-score model for private manufacturing companies 𝑋 : working capital / total assets This suggests the company may experience shrinking liquidity when the company’s liquid assets double. 𝑋 : retained earnings / total assets This ratio measures profitability that reflects the company's age and earning power. 𝑋 : earnings before interest and tax / total assets This ratio shows the efficiency of the company in generating earnings under the same asset size. 𝑋 : book value of equity / total liabilities This formula uses the book value of equity, not the market value of equity. Non-manufacturing companies can be classified according to their Z-score as follows:  When the company’s Z-score is more than 2.6, based on the financial figures only, the company is placed in the “Safe” zone.  When the company's Z-score ranges from 1.1 to 2.6, based on the financial figures only, the company is placed in the “Grey” zone. The company may or may not go bankrupt in the next two years.  When the company's Z-score is less than 1.1, based on the financial figures only, the company is placed in the “Distress” zone. There is a high probability that the company will face distress in the next two years. 3.3 Data Acquisition Since information on the bad credit records of listed companies is not disclosed publicly, we must use other means to ascertain the default probability of these companies. One way of computing the default probability is to calculate the stock yield using information on the stock price of the listed companies and then determine the default distance. 30 listed companies have been randomly selected from China’s Shanghai and Shenzhen stock markets. The financial data of these companies from 1 January 2017 to 31 December 2017 is shown in Table 1. There are 10 listed companies with good performance, 10 listed companies with mediocre performance and 10 listed companies with poor performance. Through the following analysis, the feasibility of the KMV and Zeta models in reality can be ascertained. According to the empirical analysis of a large number of default events, it has been highlighted by the KMV model that: Asian Journal of Finance & Accounting ISSN 1946-052X 2019, Vol. 11, No. 1 ajfa.macrothink.org/ 150  when the long-term debt value is less than 1.5 times the short-term debt value, the most frequent default critical point is located near the company's short-term debt value plus 0.5 times the long-term debt value, but  when the long-term debt value is more than 1.5 times the short-term debt value, the most frequent default critical point is located near the company's 0.7 times total of short-term debt value and long-term debt value. There are some basic assumptions in this paper.  The default distance formula that defines the company's market value is larger than its debt value in a year, assuming that the growth rate of the company's asset value is zero.  The stock price of a company is consistent with logarithmic normal distribution and the stock price volatility is derived from stock price logarithmically.  The annual volatility of equity is computed using the stock closing price of the 252 trading days in 2017.  The annual risk-free interest rate is fixed. The standard one-year maturity yield of China’s treasury bond in 2017 and 𝑟 = 2.7484% are used.  Equity is a call option on the firm value with a strike price that is equal to the face value of debt. Asian Journal of Finance & Accounting ISSN 1946-052X 2019, Vol. 11, No. 1 ajfa.macrothink.org/ 151 Table 1. 30 Listed Companies from Shanghai and Shenzhen Stock Markets Blue-chip Companies (Note 1) Ordinary Companies (Note 2) Code Industry Code Industry 600519 Wine & Beverage 600000 Banking 002302 Metal & Nonmetal 000905 Transportation 300176 Machinery & Equipment & Instrument 600549 Metal & Nonmetal 002307 Construction Business 603377 Transportation 002081 Decoration 600479 Pharmaceuticals 600808 Metal & Nonmetal 002403 Metal & Nonmetal 000709 Metal & Nonmetal 600826 Business Brokerage & Agency 601919 Marine Traffic 300220 Electronics 601899 Nonferrous Metal Mining 300104 Information Dissemination Service 600340 Real Estate Development 600363 Electronics ST Companies (Note 3) ST Companies Code Industry Code Industry 600860 Machinery & Equipment & Instrument 600608 Metal & Nonmetal 002490 Machinery & Equipment & Instrument 600403 Coal Mining 000526 Real Estate Development 601005 Metal & Nonmetal 600696 Real Estate Development 000932 Metal & Nonmetal 000595 Machinery & Equipment & Instrument 000982 Textile & Clothing &Fur Note 1. Blue-ship Companies: They are the mature companies in the stock market that represent the stalwarts of industry-safe, stable, profitable, and long-lasting companies that represent relatively safe, low volatility investments. Note 2. Ordinary Companies: The companies with mediocre performance. Note 3. ST Companies: ST stand for special treatment. Under regulation of Shenzhen Stock Exchange and Shanghai Stock Exchange, in the event of financial issues or other abnormal conditions of listed companies that make investors unable to judge the future of the companies and may endanger the interest of investors, the Stock Exchange shall take special treatment on these stocks. Asian Journal of Finance & Accounting ISSN 1946-052X 2019, Vol. 11, No. 1 ajfa.macrothink.org/ 152 4. Calculation and Results 4.1 The Calculation and Results Equity Value Volatility (𝜎 ) In this paper, the volatility of equity value is derived from historical stock price data. Assuming that the stock price of listed companies conforms with logarithmic normal distribution, the volatility of equity value is expressed as: 𝛿 = 𝑙𝑛 𝑆 𝑆 𝜎 = ∑ 𝛿 − ( ) ∑ where 𝑆 , 𝑆 : the stock closing price on day 𝑖 and 𝑖 − 1 𝑛: the trading day, where 252 days have been selected as the benchmark 𝛿 : the log return at time 𝑖 𝜎 : the annual volatility of equity value The results, including the volatility of equity value computed using Microsoft Excel, are shown in Table 2. Asian Journal of Finance & Accounting ISSN 1946-052X 2019, Vol. 11, No. 1 ajfa.macrothink.org/ 153 Table 2. Average Return and Annual Equity Volatility of Selected Companies Blue-chip Stock Common Stock Code Average Return* Annual Equity Volatility Code Average Return* Annual Equity Volatility 600519 0.3010% 0.2026 600000 -0.1063% 0.2302 002302 0.3453% 0.6604 000905 0.0059% 0.4636 300176 0.5908% 0.5288 600549 0.0639% 0.4549 002307 0.1180% 0.6060 603377 0.0006% 0.2424 002081 0.1805% 0.2988 600479 -0.0466% 0.2272 600808 0.1512% 0.3902 002403 -0.0738% 0.2005 000709 0.0650% 0.4288 600826 -0.3042% 0.3112 601919 0.1023% 0.3495 300220 -0.1605% 0.4474 601899 0.1284% 0.2531 300104 -0.3490% 0.7298 600340 0.1124% 0.3755 600363 -0.1158% 0.3480 ST Stock ST Stock Code Average Return (Note 1) Annual Equity Volatility Code Average Return* Annual Equity Volatility 600860 -0.2184% 0.3106 600608 -0.2975% 0.3795 002490 -0.2840% 0.3850 600403 -0.0819% 0.1850 000526 -0.0336% 0.2347 601005 -0.0653% 0.1994 600696 -0.2577% 0.3426 000932 0.1206% 0.4118 000595 -0.2903% 0.4744 000982 -0.3955% 0.3613 Note 1. Average Return: It means daily average return. DPT (Default point is the level of the market value of a company’s assets, below which the firm would fail to make scheduled debt payments. The default point is firm specific and is a function of the firm’s liability structure.) According to the 2017 annual report of the selected listed companies, DPT can be derived from year-end short-term liabilities and long-term liabilities. Existing companies use a variety of debt instruments (with different maturities, coupons and so forth) so there is no unique DPT. Asian Journal of Finance & Accounting ISSN 1946-052X 2019, Vol. 11, No. 1 ajfa.macrothink.org/ 154 “Purely empirical” rule of thumb (De Servigny/ Renault [2004] and KMV [2002]) where STD is short term debt and LTD is long term debt: De𝑓𝑎𝑢𝑙𝑡 𝑃𝑜𝑖𝑛𝑡 = 𝑆𝑇𝐷 + 0.5𝐿𝑇𝐷 𝑖𝑓 𝐿𝑇𝐷/𝑆𝑇𝐷 < 1.5 𝑆𝑇𝐷 + 0.7 − 0.3𝑆𝑇𝐷 𝐿𝑇𝐷 ∗ 𝐿𝑇𝐷 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 The results are shown in Table 3. Table 3. DPT of Selected Companies Blue-chip Stock Code Short-term Debt (Million) Long-term Debt (Million) DPT (Million) 600519 38,574.92 15.57 38,582.70 002302 9,489.41 2,023.70 10,501.26 300176 1,349.78 191.77 1,445.67 002307 10,844.23 5,439.59 13,564.02 002081 16,022.89 411.32 16,228.55 600808 28,093.36 10,324.06 33,255.39 000709 113,240.57 29,248.25 127,864.70 601919 43,491.99 45,987.43 66,485.71 601899 28,793.59 22,878.83 40,233.01 600340 228,063.69 76,768.47 266,447.92 Common Stock Code Short-term Debt (Million) Long-term Debt (Million) DPT (Million) 000905 2,974.20 1,578.95 3,763.68 600549 8,200.72 1,902.12 9,151.78 603377 709.74 256.82 838.15 600479 934.39 111.33 990.05 Asian Journal of Finance & Accounting ISSN 1946-052X 2019, Vol. 11, No. 1 ajfa.macrothink.org/ 155 002403 1,530.95 562.85 1,812.38 600826 958.60 332.15 1,124.68 300220 99.56 1.31 100.21 300104 14,494.25 4,069.89 16,529.19 600363 1,682.18 66.09 1,715.23 ST Stock Code Short-term Debt (Million) Long-term Debt (Million) DPT (Million) 002490 3,531.93 759.54 3,911.70 000526 3,501.99 17.64 3,510.81 600696 501.90 16.58 510.19 000595 883.89 225.15 996.47 600608 121.21 4.75 123.59 600403 8,595.46 846.06 9,018.49 601005 4,810.95 3,397.55 6,509.72 000932 47,920.36 12,428.63 54,134.67 000982 8,469.57 1,773.63 9,356.39 Asset Value Volatility (𝜎 ) The KMV model assumes that when the asset value of a company is less than the value of its liabilities, the company will default. We can get the market value and volatility of assets through the Black-Scholes-Merton (BSM) options pricing method. The model also assumes that the company's capital structure contains only equity and short-term debt, which are recognized as cash or cash equivalents. Long-term debt is considered permanent and can be converted into preferred stock. Having made the above basic assumptions, we can use recursion based on the following formula to find out the asset value volatility: 𝐸 = 𝑉 ∗ 𝑁(𝑑 ) − 𝐷 ∗ 𝑒 ( ) ∗ 𝑁(𝑑 ) 𝑑 = 𝑙𝑛 ∗ ( ) 𝜎 ∗ √𝑇 − 𝑡 + 1 2 𝜎 ∗ √𝑇 − 𝑡 𝑑 = 𝑑 − 𝜎 ∗ √𝑇 − 𝑡 Asian Journal of Finance & Accounting ISSN 1946-052X 2019, Vol. 11, No. 1 ajfa.macrothink.org/ 156 𝑁(𝑑) = 1 √2𝜋 𝑒 𝑑 The relationship between volatility of the underlying asset value (𝜎 ) and the volatility of the equity market value (𝜎 ) is as follows: 𝜎 = 𝑁(𝑑 ) ∗ 𝑉 𝐸 ∗ 𝜎 𝐷𝑒𝑓𝑎𝑢𝑙𝑡𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 = 1 − 𝑁(𝑑 ) = 𝑁(−𝑑 ) where V: market value of the asset D: face value of the company’s zero-coupon debt maturing at T (only liability) 𝜎 : the standard deviation of the assets value 𝜎 : the standard deviation of the equity value 𝑟: the risk-free interest rate 𝑁(𝑑): cumulative normal distribution function evaluated at d 𝑇 − 𝑡: the time interval (maturity) Using Microsoft Excel, the equations are solved via the iterative method. The asset value volatility has been calculated and the results are shown in Table 4. Table 4. Default Probability of Selected Companies Blue-chip Stock Code Market Value Assets (Million) Asset Volatility 𝑑 𝑑 Default Probability 600519 914,768.11 0.1941 16.5527 16.3586 1.888E-60 002302 32,617.70 0.4478 2.8161 2.3683 0.0089344 300176 15,402.80 0.4792 5.2347 4.7556 9.894E-07 002307 19,913.22 0.1932 2.2260 2.0328 0.0210386 002081 56,724.04 0.2133 6.1026 5.8893 1.939E-09 600808 65,059.21 0.1908 3.7574 3.5667 0.0001808 000709 169,277.27 0.1049 2.9891 2.8842 0.0019622 601919 135,649.89 0.1782 4.2445 4.0663 2.388E-05 601899 50,804.34 0.0527 4.9771 4.9244 4.231E-07 Asian Journal of Finance & Accounting ISSN 1946-052X 2019, Vol. 11, No. 1 ajfa.macrothink.org/ 157 600340 359,203.70 0.0970 3.4128 3.3158 0.0004569 Common Stock Code Market Value Assets (Million) Asset Volatility 𝑑 𝑑 Default Probability 600000 5,258,054.19 0.0162 6.2116 6.1955 2.906E-10 000905 9,360.42 0.2772 3.5249 3.2478 0.0005816 600549 37,121.61 0.3427 4.3370 3.9943 3.244E-05 603377 17,629.75 0.2309 13.4270 13.1961 4.618E-40 600479 5,879.61 0.1890 9.6679 9.4790 1.284E-21 002403 6,145.85 0.1414 8.9007 8.7593 9.824E-19 600826 6,664.54 0.2587 7.1146 6.8560 3.542E-12 300220 2,639.11 0.4305 7.8778 7.4473 4.762E-14 300104 77,687.31 0.5745 3.0287 2.4542 0.0070603 600363 7,285.30 0.2661 5.6716 5.4055 3.231E-08 ST Stock Code Market Value Assets (Million) Asset Volatility 𝑑 𝑑 Default Probability 600860 3,725.82 0.2416 6.465176 6.223527 2.431E-10 002490 7,829.14 0.1926 3.841322 3.648702 0.0001318 000526 7,039.24 0.1176 6.206955 6.089336 5.669E-10 600696 2,505.90 0.2728 6.071256 5.798442 3.347E-09 000595 4,978.31 0.3794 4.50202 4.122615 1.873E-05 600608 2,728.17 0.3624 8.796849 8.434495 1.663E-17 600403 20,207.49 0.1025 8.194313 8.091863 2.938E-16 601005 25,684.72 0.1488 9.481618 9.332787 5.156E-21 000932 78,591.60 0.1281 3.187562 3.059412 0.0011089 000982 15,674.04 0.1456 3.80494 3.659331 0.0001264 Recovery Rate (𝜌 ), Expected Loss Given Default (LGD) According to Merton´s model, at the default point of the face value of the debt, the distance to default can be calculated using the volatility of the company’s assets. When the computed "Distance to Default" is high, the company is less likely to default. Since the asset value Asian Journal of Finance & Accounting ISSN 1946-052X 2019, Vol. 11, No. 1 ajfa.macrothink.org/ 158 volatility has already been computed, the aim here is to calculate the Distance to Default in order to determine the probability of default. The following formula is used: 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒𝐷𝑒𝑓𝑎𝑢𝑙𝑡(𝐷𝐷) = 𝑉 − 𝐷𝑃𝑇 𝜎 𝑉 where 𝑉 : the market value of the company’s assets 𝜎 : the standard deviation of the asset value The Merton model for LGD assumes that the company’s value is lognormal distributed with a constant volatility and the company only has one liability, which is zero-coupon debt issue. The formula is as follows: 𝑅𝑒𝑐𝑜𝑣𝑒𝑟𝑦 𝐺𝑖𝑣𝑒𝑛 𝐷𝑒𝑓𝑎𝑢𝑙𝑡 (𝑅𝐺𝐷 ) = 𝑉 ∗ 𝑁(−𝑑 )/𝑁(−𝑑 ) Recovery Rate (𝜌 ) = 𝑅𝐺𝐷 /𝐷 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝐿𝑜𝑠𝑠 𝐺𝑖𝑣𝑒𝑛 𝐷𝑒𝑓𝑎𝑢𝑙𝑡 (𝐿𝐺𝐷 ) = 𝑒 ∗ 𝐷 − 𝑅𝐺𝐷 where 𝑉 : the market value of the company’s assets at time t 𝐷: the face value of the company’s zero-coupon debt maturing at T (only liability) 𝑟: the expected return on the value of the company, which uses risk-free interest rates Using Microsoft Excel, the recovery rate, recovery given default and expected loss given default are computed. The results are shown in Table 5. Table 5. Distance to Default and Expected Loss Given Default of Selected Companies Blue-chip Stock Code Distance to Default Recovery Given Default (Million) Recovery Rate Expected Loss Given Default (Million) 600519 4.9358 37,099.84 96.1567% 37,536.74 002302 1.5141 8,872.21 84.4871% 10,216.57 300176 1.8911 1,286.08 88.9608% 1,406.48 002307 1.6501 12,311.94 90.7691% 13,196.30 002081 3.3470 15,263.45 94.0531% 15,788.60 600808 2.5626 30,891.31 92.8911% 32,353.85 000709 2.3322 120,700.76 94.3973% 124,398.32 Asian Journal of Finance & Accounting ISSN 1946-052X 2019, Vol. 11, No. 1 ajfa.macrothink.org/ 159 601919 2.8609 62,211.96 93.5719% 64,683.30 601899 3.9503 38,756.33 96.3297% 39,142.30 600340 2.6633 252,787.43 94.8731% 259,224.59 Common Stock Code Distance to Default Recovery Given Default (Million) Recovery Rate Expected Loss Given Default (Million) 600000 4.3444 4,744,171.22 97.0474% 4,755,985.17 000905 2.1573 3,408.85 90.5725% 3,661.64 600549 2.1984 8,262.13 90.2789% 8,903.68 603377 4.1250 801.56 95.6342% 815.43 600479 4.4011 944.77 95.4266% 963.21 002403 4.9864 1,735.90 95.7804% 1,763.24 600826 3.2137 1,055.87 93.8818% 1,094.19 300220 2.2349 92.33 92.1360% 97.50 300104 1.3702 13,512.09 81.7468% 16,081.09 600363 2.8733 1,594.77 92.9770% 1,668.73 ST Stock Code Distance to Default Recovery Given Default (Million) Recovery Rate Expected Loss Given Default (Million) 600860 3.2200 775.52 93.8114% 804.27 002490 2.5977 3,635.02 92.9270% 3,805.65 000526 4.2617 3,353.92 95.5313% 3,415.63 600696 2.9192 475.15 93.1316% 496.36 000595 2.1081 894.55 89.7720% 969.45 600608 2.6347 115.41 93.3809% 120.24 600403 5.4046 8,667.37 96.1066% 8,774.00 601005 5.0161 6,235.95 95.7944% 6,333.24 000932 2.4283 50,845.72 93.9245% 52,667.10 000982 2.7681 8,791.66 93.9643% 9,102.74 Asian Journal of Finance & Accounting ISSN 1946-052X 2019, Vol. 11, No. 1 ajfa.macrothink.org/ 160 4.2 Zeta Model Empirical Analysis The companies we choose are listed companies, so the Z-score is calculated as follows: 𝑍 = 1.2𝑋 + 1.4𝑋 + 3.3𝑋 + 0.6𝑋 + 1.0𝑋 We use this formula to calculate the results, which are shown in Table 6. Table 6. Zeta Value of Selected Companies Blue-chip Companies Code T1 T2 T3 T4 T5 Zeta 600519 0.5473 0.6554 0.2893 32.4543 0.4536 22.4552 002302 0.3020 0.1224 0.0113 1.9210 0.8187 2.5422 300176 0.0740 0.2570 0.2456 9.0539 1.1087 7.8001 002307 0.0386 0.0222 0.0065 0.3899 0.5024 0.8350 002081 0.2895 0.3077 0.0829 2.4641 0.7450 3.2750 600808 -0.0557 0.1073 0.0783 0.7075 1.0144 1.7804 000709 -0.3208 0.0626 0.0163 0.2906 0.5731 0.5040 601919 -0.0304 -0.1180 0.0372 0.7730 0.6792 1.0641 601899 -0.0013 0.2409 0.0563 0.2046 1.0586 1.7027 600340 0.3204 0.0577 0.0343 0.3043 0.1587 0.9196 Ordinary Companies Code T1 T2 T3 T4 T5 Zeta 600000 -0.0092 0.0349 0.0115 0.0648 0.0275 0.1418 000905 -0.0666 0.2626 0.0289 1.2292 1.6965 2.8172 600549 0.0818 0.1282 0.0641 2.7685 0.7527 2.9028 603377 0.0848 0.1782 0.1043 17.3725 0.3713 11.4903 600479 0.4548 0.2660 0.0902 4.6758 0.9683 4.9895 002403 0.1849 0.1414 0.0418 2.0697 0.7085 2.5082 600826 0.3751 0.3929 0.0766 4.2920 0.6934 4.5214 300220 0.2985 0.0910 -0.1467 25.1713 0.5266 15.6310 300104 -0.3677 -0.6672 -0.9727 3.2944 0.3965 -2.2120 600363 0.1573 0.2709 0.0554 3.1860 0.7050 3.3673 ST Companies Asian Journal of Finance & Accounting ISSN 1946-052X 2019, Vol. 11, No. 1 ajfa.macrothink.org/ 161 Code T1 T2 T3 T4 T5 Zeta 600860 0.1126 -0.2712 0.0016 3.2187 0.6252 2.3170 002490 -0.1457 0.0342 0.0073 0.9128 0.4765 0.9214 000526 -0.5585 -0.0239 0.0220 1.0025 0.7842 0.7547 600696 0.1339 -0.1299 0.0239 3.8492 0.2153 2.5827 000595 0.0128 -0.2673 -0.0090 3.5903 0.2319 1.9975 600608 0.3596 -3.7899 0.2883 20.6771 2.4788 10.9623 600403 -0.1046 0.2574 0.0269 1.1851 0.4157 1.4503 601005 -0.0021 -0.4586 -0.2710 2.3360 0.5292 0.3920 000932 -0.2410 0.0038 0.0715 0.4053 1.0230 1.2181 000982 -0.2457 -0.1577 -0.0013 0.6168 0.2301 0.0803 5. Discussion 5.1 Discussion In order to determine the applicability of the KMV and Zeta models in China, the default probability of listed companies should be compared with the credit rating that credit rating agencies have issued them. Credit rating is an evaluation of the borrower’s creditworthiness performed by credit rating agencies. Since China’s economic system is now a market economy, credit rating is more important than ever. To investors credit rating is a good indicator of the company’s ability to fulfil its financial obligations, so the credit ratings given by these credit rating agencies have a strong influence on investors’ decision of whether to invest or not. Good credit ratings could therefore help China attract greater foreign direct investment. In China, there are five main credit rating agencies licensed by the government, which are respectively Dagong Global Credit Rating, China Cheng Xin International Credit Rating, China Lianhe Credit Rating, Golden Credit Rating International, and Shanghai Brilliance Credit Rating & Investors Service. According to the Credit Rating and Certification Centre of the People’s Republic of China Department of Commerce Research Institute, the credit ratings of the selected listed companies can be divided into several categories. The companies’ creditworthiness is mainly assessed according to the company's financial data and financial indicators, which include the company's operating turnover changes, financial debt sales ratio, financial debt degree, physical asset turnover, efficiency of investment assets, efficiency of intangible assets, current account benefit cost ratio, anomaly coefficient, residual force coefficient of payment, cost system and various asset coefficients. The corresponding credit rating is then ascertained using a proper weighting ratio. The comparison between the default probability, Z-score and credit rating of the 30 selected listed companies is shown in Table 9. Asian Journal of Finance & Accounting ISSN 1946-052X 2019, Vol. 11, No. 1 ajfa.macrothink.org/ 162 Table 9. Comparison Between Default Probability, Z-score and Credit Rating Blue-chip Companies Ordinary Companies Code Default Probability Z-score Credit Rating Code Default Probability Z-score Credit Rating 600519 1.888E-60 22.4552 BBB 600000 2.9056E-10 0.1418 BBB 002302 0.0089344 2.5422 BBB 000905 0.00058159 2.8172 A 300176 9.894E-07 7.8001 BBB 600549 3.2441E-05 2.9028 A 002307 0.0210386 0.8350 CCC 603377 4.6181E-40 11.4903 BB 002081 1.939E-09 3.2750 BB 600479 1.2839E-21 4.9895 AA 600808 0.0001808 1.7804 BB 002403 9.8236E-19 2.5082 AA 000709 0.0019622 0.5040 CCC 600826 3.5418E-12 4.5214 A 601919 2.388E-05 1.0641 BB 300220 4.762E-14 15.6310 BB 601899 4.231E-07 1.7027 BBB 300104 0.00706027 -2.2120 CC 600340 0.0004569 0.9196 CCC 600363 3.2305E-08 3.3673 A ST Companies ST Companies Code Default Probability Z-score Credit Rating Code Default Probability Z-score Credit Rating 600860 2.431E-10 2.3170 CCC 600608 1.6632E-17 10.9623 C 002490 0.0001318 0.9214 D 600403 2.938E-16 1.4503 CC 000526 5.669E-10 0.7547 D 601005 5.1561E-21 0.3920 D 600696 3.347E-09 2.5827 D 000932 0.00110886 1.2181 BB 000595 1.873E-05 1.9975 C 000982 0.00012644 0.0803 B Asian Journal of Finance & Accounting ISSN 1946-052X 2019, Vol. 11, No. 1 ajfa.macrothink.org/ 163 5.2 Advantages and Disadvantages It is self-evident that KMV is of great importance to contemporary credit risk research. The KMV model is a default probability prediction model based on the modern option pricing theory, which is an important innovation of traditional credit risk measurement. The KMV model can take into account information in the capital market as well as quantification and analysis of credit risk for all listed companies. Since the data required by the model comes from the stock market, market information is fully utilized—leading to a better reflection of the current credit standing of listed companies. In addition, the KMV model is based on contemporary corporate finance theory and option pricing theory, so there is a strong theoretical foundation to rely on. The KMV model has become the most important credit risk rating model in the world thanks to the strong theoretical basis and low hypothetical condition. Application of the KMV model can improve the validity of credit risk analysis of commercial banks in China, offering a useful reference to credit risk managers. However, every model is flawed; the KMV model is no exception. First of all, the scope of application of the KMV model has certain limitations. Generally, the KMV model is more practical for listed companies than non-listed companies. Since information on listed companies is more accessible, the market value of listed companies is easier to determine. On the other hand, information on non-listed companies is not publicly disclosed. As accounting indicators are pivotal to the KMV model, it is therefore a challenge to use the model for non- listed companies. So, we need to make some adjustments to the important variables of the KMV model when we are dealing with non-listed companies. And the expected default probability of the companies is obtained through comparative analysis, which may reduce the accuracy of calculation to a certain extent. The KMV model also assumes that the asset value of a company is subordinated to lognormal distribution, but in actual fact the asset value of a company does not necessarily conform to this characteristic. The KMV model cannot measure portfolio risk too due to the complexity and uncertainty of the market. Consequently, we cannot get the actual default correlation between two different companies. But the combination of Copula function theory and KMV model may help us overcome this problem for now. In short, with the gradual development and perfection of China's securities market, it will be a feasible choice for banks to use stock market data to evaluate the credit standing of listed companies. 6. Conclusion and Recommendations 6.1 Conclusion The main purposes of this paper are as follows:  By using the share price and financial reporting information of these listed companies, we compute the distance to default and credit default probability based on the KMV model. Asian Journal of Finance & Accounting ISSN 1946-052X 2019, Vol. 11, No. 1 ajfa.macrothink.org/ 164  By using financial statements of these listed companies, we compute the Z-score based on the Zeta Model to determine the probability of the company going bankrupt within the next two years.  By comparing the default probability of the KMV model and the Z-score of the Zeta model with the credit rating of these listed companies, we ascertain whether application of credit risk management model in China’s banks is feasible. Having met the above objectives of the paper, the following conclusion can be made. Blue- chip companies generally have a relatively larger Z-score and a relatively smaller default probability. The Z-score of ST companies is generally less than 1.80. For companies with a high Z-score value, the default probability of the KMV model is relatively lower in general and their credit rating is generally better, i.e. class A and B. In general, for companies with a low Z-score value, the default probability of the KMV model is relatively larger in general and their credit rating is generally poorer. But in class C and D, a few companies’ default probability under KMV model is very low and their Z-score is very high, i.e. 600608 and 600696. This situation may be due to insufficient sample size and list companies’ wrong financial statements though they have been audited. It is obvious that credit rating is affected by many factors, which include the credit default risk of the subject of evaluation, the ability and willingness of the economic entity to fulfil the debt and other financial obligations on time in accordance with the contract, and the technical and professional experience of the third-party credit rating agency. The process of issuing credit ratings involves a complex and structured risk assessment of credit products. The increasing complexity of investment products has only made the relationship between rating and product risk more important than ever. But the consequences of default on these complex products may be minimal since the risk of default can be dispersed. So, the default probability derived from the KMV model and the Zeta model cannot completely correspond to the entity’s credit rating as these indicators are only some reference bases to help investors make an informed decision. 6.2 Recommendations In the previous study, we found that the company's credit rating, Z-score and default probability do not correspond one by one. We can try to amend the specific subjects of the financial statements. By modifying these figures, we can get effective financial results. If there are opportunities in the future, I will re-analysis credit risk and consider more comprehensive factors. It is self-evident that the measurement of credit risk is of great importance to banks. The risk management team of banks should establish the right model where benefit is balanced against risk. Banks have the responsibility to do the following actions to minimize the size of credit risk:  Establish appropriate risk control models that are based on the actual situation, and quantitatively and qualitatively analyze its credit risk. Asian Journal of Finance & Accounting ISSN 1946-052X 2019, Vol. 11, No. 1 ajfa.macrothink.org/ 165  Promote the reliability of data sources in order to provide a reasonable basis for the evaluation of enterprises’ credit risk.  Maintain the independence of internal control to enhance impartiality of the evaluation results.  Train employees regularly to strengthen their ability to review credit and to promote their awareness of the adequacy and necessity of the credit process. References Altman, E. I., Zhang, L., & Yen, J. (2007, November). Corporate Financial Distress Diagnosis in Chinese. 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Moody’s Public firm Risk Model: a Hybrid Asian Journal of Finance & Accounting ISSN 1946-052X 2019, Vol. 11, No. 1 ajfa.macrothink.org/ 166 Approach to Modeling Short Term Default Risk, Moody’s Investors Services Shen Z, Zhang, & Dan W. (2010). Global Financial Crisis's Impact on the Credit Risk of Logistics Companies: Comparative Analysis between China and US with KMV Model. 2010 International Conference on Management of e-Commerce and e- Government, 116-121 https://ieeexplore.ieee.org/document/5628642 Tudela, M., & Young, G. (2005). A Merton-model approach to assessing the default risk of UK public companies. International Journal of Theoretical and Applied Finance, 8(06), 737-761. https://doi.org/10.1142/S0219024905003256 Vasicek, Oldrich. (2000). Comments on ‘Equity Market Value and its Importance for Credit Analysis: Facts and Fiction’,” KMV Corporation. Appendices The solution procedure of multivariate equation for Blue-chip Companies. The solution procedure of multivariate equation for Ordinary Companies. Asian Journal of Finance & Accounting ISSN 1946-052X 2019, Vol. 11, No. 1 ajfa.macrothink.org/ 167 The solution procedure of multivariate equation for ST Companies. Asian Journal of Finance & Accounting ISSN 1946-052X 2019, Vol. 11, No. 1 ajfa.macrothink.org/ 168