Credit risk assessment of high yield bonds: expected loss rate model

Credit risk assessment of high yield bonds: expected loss rate model2015-12-07 Zhihuihui RMB Trading and research

Zhihuihui, the author, worked in the fixed income Department of Security Securities.

Summary

Since March this year, the credit risk has been widely concerned, many bonds have been downgraded and credit spreads have fluctuated sharply. This paper establishes the expected loss rate model, then carries on the empirical analysis to the exchange high yield Bond's credit risk, the result shows that this model uses the asset market value information, compared with the traditional financial analysis method, carries on the certain leadership to the high yield bond credit risk appraisal.

Keywords: High yield bond credit risk expected loss rate model

1High Yield Bond overview

High-yield bonds originated in the United States, refers to the credit rating is lower than investment grade bonds, also known as junk bonds, mainly in the 1980 's as a leveraged financing tool developed. The US high-yield bond reached $336.1 billion in 13, with a balance of more than $1.3 trillion, accounting for 13% of the total corporate bond. The issuer is in a very diversified industry, with relatively large consumer, telecommunications and financial sectors, a wide range of investors and an active market turnover.

According to the attribute, there are two kinds of independent high-yield bond market in China, namely, low-level corporate debt and SME private debt. The small and medium enterprises private debt since the birth of June 2012, the development of relatively slow, low circulation. Investors mainly include bank management, brokerage, etc., trading poor, mainly holding due. In addition, small and medium-sized enterprises private debt generally have a variety of forms of security, the enterprise itself credit risk is diluted, the market level of pricing is not high, and information is very asymmetric, complete. Therefore, this paper focuses on the lower-level corporate debt of the exchange.

The lower-level corporate bonds of the exchange mainly refer to bonds with a credit rating of aa-and below, with a maturity yield of over 8%. Due to the existence of rigid payment, credit risk has been in a state of repression, leading to the late start of China's high-yield bonds.

2013, the economic downward pressure, accompanied by financial constraints, listed companies, profit deterioration, credit rating downward expansion, high-yield bonds appear widely. From the perspective of industry distribution, mainly concentrated in the steel, coal, chemical and other overcapacity industries, the traditional cyclical industry is poor; from the view of enterprise attribute, because of the weak of the private enterprise, the capital supply is limited, the high yield debt accounted for more than 60% in the exchange. The scope of investors is broader, brokers, funds are the main institutional investors of the transaction, also including individual investors. Since April 2014, exchange high-yield debt turnover significantly enlarged, the market is actively engaged in trading. Exchange bonds have formed an independent bond sector, and prices have fluctuated significantly.

In March 2014, the super-day debt announcement failed to pay interest and became the first single substantive default of the domestic coupon market, after the "Black Swan" frequency, the exchange high-yield debt market is increasingly concerned. Since then, market turnover has been magnified, liquidity has improved, and institutional investors have been significantly more enthusiastic about the high-yield debt of the exchange.

2Research Status

The research on credit risk assessment of high yield bonds is divided into two categories, that is, only considering the book value of the issuer, and comprehensively evaluating the credit risk based on the debtor's financial situation, management status and credit status, and taking into account the issuer's future income change and the book value of the assets, The credit risk is analyzed based on the fluctuation of the future income of the assets and the market value of the information.

Based on the author's book value analysis, the paper mainly focuses on the qualitative analyses, focusing on several key elements. In addition, the general need to consider the capital cost, economic cycle and other non-enterprise internal factors, such as book value, such as enterprise level and economic cycle and other external economic aspects of the analysis.

Then gradually study the practical quantitative model method of the debtor's solvency and willingness to carry out quantitative analysis, the main idea is to affect the debtor's management and development capacity and credit status of a number of book value variable indicators selected, and then give weight, through a specific model to obtain a credit comprehensive score or default probability value, To assess the level of credit risk of the debtor. There are three kinds of models: multivariate discriminant model, logit and probit regression model.

With the rapid development of financial derivatives, financial innovation, credit risk assessment methods have been improved, the future income of the debtor's assets and reflect the market value of information began to be taken into account, such as the Creditmetrics Model (1997), creditrisk+ (1996). In addition, after taking into account the factors that reflect the value of asset market, the paper develops a series of credit evaluation methods based on option pricing theory, and the structure method is more popular. Merton (1974) the option pricing formula is applied to the formula debt pricing, and the company's equity and debt can be regarded as the option based on the company's assets, and the debt is priced by option method.

Because the domestic bond market has not defaulted before, so the analysis of its credit risk has not aroused enough attention, but in the Commercial bank credit analysis carried out more theoretical and empirical research. Several large domestic credit rating companies, such as the grand Public international, the credibility of the credit rating more still rely on the company's book value based on the financial analysis, and combined with economic fundamentals of credit rating, has a large defect.

3expected loss rate model

1 objective function

The new Basel Accord, which was introduced in 2004, defines credit risk as the risk of loss due to debtor default, the core index stipulated in the internal rating law on credit risk is the expected loss rate (expected Loss Ratio), and the expected loss rate is a comprehensive index reflecting credit risk, and the expected loss rate (expected loss ratio) can also be divided into two parts: default rate (probability of default) and post-default loss rate (loss Give default). The default rate is the likelihood that a particular debt will default for a certain period of time, and the loss rate after default is the percentage of the investor's risk of loss relative to the principal and interest of the debt after the default. The impact of the two factors is not the same, the default rate is mainly related to the financial soundness, liquidity and other factors, and the loss rate after default is related to the priority of debt, mortgage guarantee and so on.

This article establishes the following objective function:

Among them, ELR is the expected loss rate, PD is the default probability, LGD is the default loss rate, the constraint is the nature of the debt, mainly the priority and the guarantee situation.

2 Hypothetical premise

Based on the assumptions made by Black,scholes (1973), we first make the following assumptions:

1, the market without friction, that is, there is no tax and transaction costs;

2, the short selling mechanism exists;

3, the transaction of assets is continuous;

4, enterprise value and capital structure independent (that is, MM theorem established);

5, the change of enterprise value V can be described by the following stochastic differential equation:

6. When the market value of the enterprise is greater than the debt to be repaid (default point), it will not default; That

3 Asset market value and volatility

This is an example of a listed company for analysis. The value of the corporate equity view as a call option based on the value of the company's assets is:

The solution of the model needs the relation function of the company's asset value fluctuation rate and the stock value fluctuation rate, and the general structured model is based on Merton (1974) on the asset volatility equation, that is, but a large number of documentary evidence shows that this relationship function is less applicable in China's capital market, Lu Wei, Chang, Liu Jianyun (2003) using a two-parameter Weibull distribution, the derived relationship function is:
, and using the data of 26 listed companies in Shanghai and Shenzhen to estimate parameters, and then carry on the empirical analysis, found that the model is more consistent with China's capital market practice than Merton model. Therefore, based on the data of 100 listed companies in Shanghai and Shenzhen, this paper uses the least squares estimation to derive the parameter value, that is to get the relation function:

The joint vertical (6) and the (7) iteration can get the value of the company asset market and its volatility.

4 default Probability

According to the results of Crouhy and Galai (1997), that is, the probability of default for risk neutrality, so we can get the probability of default in the credit risk factor is:

Among them, the company asset market value volatility is the United Vertical (6) and the formula (7), for the normal distribution.

5 default loss rate

6 Consideration of the nature of high-yield debt

If the nature of the high-yield debt is subordinated debt, that is, the order of repayment after other obligations, then its credit risk will be greater than the ordinary debt, if the nature of the debt is secured debt, then because the existence of the guarantor of the relative ordinary debt is less credit risk, if the issuer of high-yield bonds for other debtors to guarantee the debt, Then the secured debt will form its implicit debt, thereby increasing its credit risk. Regardless of the nature of the debt, the reason for the change of credit risk is to change the debtor's default probability and the creditor's default loss rate, the fundamental way is to change the debtor's default point. Therefore, the evaluation of credit risk after considering the nature of high-yield debt is attributed to the determination of the debtor's default point, so long as the default point is analyzed, then the default probability and the default loss rate are obtained by substituting the formula (8) and formula (10).

According to the definition of the default point, if the high-yield debt is subordinated, the total amount of the debt is, then the default point is:

If a high-yield bond is a secured bond, the general case is "unconditional joint liability guarantee" and, in accordance with the legal definition of "unconditional joint and several liability guarantee", the breach of the debt can only be confirmed if the two companies default at the same time. At this point, the credit risk brought by this guarantee can be reduced to the debtor's default point. If the guarantor defaults, then the default point of the debt remains unchanged, if the guarantor does not default, then the default will be 0. The default probability of setting a guarantor is that the default point can be obtained according to the full probability formula:

If the debtor has a debt guarantee against the issuer of the other debt, according to the legal definition of the secured obligation, the implied debt will have an effect on the credit risk of the secured obligation only if the debt is actually defaulted, at which time the guarantor will repay the guarantor's debt and obtain the value of the guarantor's assets, Thus the equivalent of the guarantor's breach of contract increases the value of the guarantor company less than its outstanding debt. The total amount of the secured debt is the probability of default of the secured company, the value of the asset in the event of default, which may be a breach of the nature of the obligation:

7 expected loss rate

1, ordinary debt (priority no guarantee)

The formula (9) and the formula (10) substituting (1) are available:

2. Subordinated debt and secured debt

If a high-yielding debt is subordinated, a secured bond, or a debtor has secured a debt to other debtors, the solution to its expected loss rate requires that the default point in the response be put into the model, i.e. (11), (12), (13) respectively, into simultaneous equations (6) and (7), Get new asset value and new asset value volatility, then substituting (9) and formula (10) to get the new, and then substituting (14) is the final.

4Empirical Analysis

1 parameter Setting

According to the whole derivation process of the model, we can estimate the following parameters, such as equity market value, equity market value volatility, debt default point db, risk-free interest rate and maturity T.

A. Equity market value

China's securities market situation is very special, the stock is considered to be divided into circulating stocks and non-tradable shares. Since non-tradable shares have no market price, how to determine the market value of non-tradable shares is a difficult problem, reference to the full circulation of listed companies in the study of non-tradable shares pricing, the net assets per share to calculate the price of illiquid shares.

Market value of circulating stock = average closing price of December week X number of shares

Market value of non-tradable shares = net assets per share × non-tradable shares

Equity market value of listed companies = market value of tradable shares + market value of non-tradable shares

B. Volatility of equity market value

This paper uses the historical volatility method to estimate the volatility of equity market value of listed companies in the next year. Assuming the stock price of a listed company satisfies a logarithmic normal distribution, the stock weekly yield is:

where n is the number of trading weeks for one year.

c. Point of default

Due to the fact that the substantive breach of the bond market occurred this year, it is difficult to rely on historical default information to determine the best default point, this paper uses Jeffrey R.bohn (1999) to carry on the empirical analysis to a large number of corporate default events, The most frequent tipping point is that the company's asset value is approximately equal to the short-term liabilities plus 1/2 long-term liabilities, namely:

If the debt is of a subordinated debt, a secured obligation or the debtor has secured a debt to other debtors, the breach is available in the following order (11), (12) and (13):

D. Risk-free rates

In this paper, the risk-free rate adopts the maturity yield of one-year national debt and carries on the moving average processing.

2 Sample Selection

This paper selects the company debt which has not expired on July 31, 2014, the yield of maturity is above 9%, the debt rating is aa-and below, evaluates its current credit status, and the historical fluctuation of credit risk of the representative coupon.

The data of the sample debtor is from wind information, which is programmed by MATLAB, and the output result is PD of default probability, LGD of default loss rate and ELR of expected loss rate.

4 Empirical results and analysis

A. Credit status at the end of the two quarter

Table 1 2014 Two quarter-end credit status (according to expected loss rate)

As shown in table 1, based on the expected loss rate model, the credit risk level of the exchange high yield bond is basically the same as the expected loss rate and the probability of default. The same external rating of the bond, the qualification is actually very different, for example, although all for the aa-rating, 900 million city debt credit risk is significantly higher than the other bonds, the probability of default is 12.76%, while the default loss rate is also high, mainly related to the rapid decline in the real estate industry.

Figure 1 Credit risk and credit premium comparison

Credit Premium is the root of credit risk, so the same credit quality of credit debt, theoretically investors demand the credit premium should be very similar, while observing the statistics of the exchange high-yield bond credit level and the market credit premium (relative to the same term national debt), the credit premium does not reflect the credit level better, Certainly should consider the market capital, supply and demand parties and other elements, but 12 Molong 01, 11 in the credit risk of the central, and the credit premium is significantly higher than the other coupons, 12 construction peak debt, 11 steel 02 of the credit premium may be underestimated, the two or three bond has a more obvious valuation bias.

B. History of credit risk changes

Figure 2 900 million city debt since the end of 2010, credit risk to the net has a certain degree of leadership

2011 two ago, the industry upstream cycle, the business performance is better, the credit risk is low, and small improvement; After the three quarter of 2011, the real estate market was in a phase of adjustment; 2012 year of Four seasons began, the industry boom quickly rebounded, credit risk fell; After 2014 years of frequent credit events, coupled with declining industry , credit risk rises. Generally speaking, the credit risk of the expected loss rate represents a certain lead in the net trend of the exchange high yield bond, but the significance is still not strong.

In terms of pricing composition, the credit premium mainly includes tax premium, risk premium and liquidity premium, in addition to the relative stability of the tax premium, the credit premium mainly reflects credit risk and liquidity premium. Until 2014, the rigid payment of credit debt had always existed, the credit premium embodied liquidity risk, the debt default in March this year, the public offering bonds just broke down, and the importance of credit risk to the exchange high-yield bond prices continued to rebound. It is expected that credit risk will be more prominent in the trend of the net price of high-yield debt thereafter.

5Conclusion

Since 2013, the exchange of high-yield bonds into an independent plate, the level of the two-tier market volatility increased, credit risk is increasingly valued, while the volatility of credit premiums also provides investors with trading opportunities. In this paper, we establish the expected loss rate model, combine the enterprise financial data with market data such as asset market value, and quantify the credit risk of the exchange high yield bonds.

Introducing the new Basel Accord and combining the characteristics of high yield bond with the traditional credit debt, the expected loss rate as a comprehensive reflection of its credit risk, then based on the structured analysis method of credit risk assessment, using Merton (1974) structured way of thinking, the equity and debt as the option based on the company's assets, Combining the option pricing formula and Liu Jianyun (2003) to study the relationship function which is more suitable to the characteristics of China's capital market, the value of the assets and its volatility are solved, and the probability of default and the rate of default loss are analyzed using Crouhy and Galai (1997) and Merton (1974). And finally obtains the expected loss rate, then considers the debt priority, the guarantee condition and so on the nature condition the expected loss rate, considers the debt nature to its credit risk influence the fundamental way lies in changes the default point, thus developed the complete expected loss rate model, as the full text theory Foundation and the core analysis method.

On the basis of establishing the expected loss rate model, this chapter has carried on the empirical research to the credit level analysis of the exchange high yield debt. Compared with the real credit risk implied by the market, the results show that the expected loss rate model is better, and it can help to find the market error and construct the risk-free arbitrage combination. In addition, the expected loss rate for high-yield bonds in the net trend of a certain lead, and with the rigidity of the payment is broken, credit risk will be more sufficient to reflect credit risks, therefore, the model will gradually improve the effectiveness.

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Credit risk assessment of high yield bonds: expected loss rate model