商业银行信用风险管理

1. 商业银行信用风险管理 Credit Risk Management in Banking: A Modern Perspective 石晓军

2. Chapter 3 信用风险的关键维度、PD估计与银行内部评级

3. 一、Summary • Dimensions of credit risk • PD estimation and validation • Rating practices in USA banking

4. 二、Dimensions of Credit Risk • Mark Carey （2000） Fed • Key dimensions may include: • A rating that reflects the Expected Default Frequency (EDF), or Default Probability (PD) of the borrower, estimated over one year, • A separate consideration of the facility’s risk; the Loss Given Default (LGD), • A measure of exposure (EAD), • A maturity adjustment （M）, • A granularity adjustment（G）. • Expected losses (EL); Unexpected losses (UL)

5. Confidence interval Risk Capital EL Covered by reserve (allowance+provision) Frequency of loss  Expected loss  Stress loss  Unexpected loss 0 Amount of loss

6. Data: Moody’s database of bond ratings and defaults during 1970-98). • 方法：resampling to examine which dimensions are important • Rationale: • EL and UL as credit risk indicator • Control other dimensions, construct contrasting groups to see whether a typical dimension influences EL and UL significantly • Examine PD LGD Granularity

7. Parameters of Base Case

8. Average and Bad-Tail Loss Rates for Base Case • Loss Rates for Portfolios With Loans in a Single Grade

9. Loss Rates as the Fraction of Subordinated Loans Varies, Variable LGDs • LGDs are permitted to vary randomly across individual credit events • Mean LGDs for senior and subordinated defaults are 44 and 63 percent respectively • for senior and subordinated restructurings are 22 and 24 percent

10. Loss Rates as the Fraction of Subordinated Loans Varies, Fixed LGDs • LGDs are held fixed for each type of credit event and priority. LGD values for senior and subordinated defaults are 10 and 50 percent, respectively • for senior and subordinated restructurings are 5 and 20 percent, respectively.

11. Loss Rates For Different Degrees of Portfolio Granularity

12. Loss Rates For Different Loan-to-One-Borrower Limits

13. Tail Loss Rates Based on All Years, Good Years, and Bad Years

14. P. Jackson; W. Perraudin 1999/10 Bank of England • (i) What is the relative riskiness of credit exposures across different maturities? • (ii) Does the nature of credit risk vary across different countries? • (iii) Do credit exposures with the same rating behave differently depending on the type of borrower(sovereign versus non-sovereign, bank versus industrial or utility)? • (iv) Do credit risk models successfully track risks associated with credit portfolios? • (v) Are ratings by agencies such as Moody’s or Standard & Poor’s reliable? • (vi) Does the credit risk of loans differ from that of bonds

15. maturity • whether there is a significant maturity structure to credit risk

16. VaR depend markedly on the average duration of the exposures included in a portfolio. This maturity effect is greater for high credit quality portfolios. • For average-quality portfolios VaRs for exposures of 2 and 10-year maturity are 5.4 and 10.0 • For high credit quality portfolios, the corresponding VaRs are 2.7 and 7.6.

17. Countries • major ratings agencies delivers a comparable measure of the riskiness of obligors across countries. • to expect some difference in ratings transitions because the history of financial stability varies across countries • examine whether the ratings of obligors domiciled in the United States behave differently from those domiciled in Japan and the United Kingdom • Moody’s senior unsecured bond ratings (excluding municipals) from December 1970 to December 1997.

19. ratings transitions for UK and US obligors are similar • ratings transitions for Japanese obligors are different. • In particular, ratings for prime (AAA) Japanese companies were more volatile • Bonds issued by AA-rated Japanese and European obligors are priced at a 10 basis point discount and a 4 basis point premium respectively compared with those of AA-rated US obligors. • AAA-rated European bonds are priced at a 4 basis point premium compared with US AAA’s while Japanese AAA-rated bonds are rated at a 4 basis point discount

20. type of obligor • sovereigns, banks and industrials • (i) exposures to sovereigns less risky than those to non-sovereigns with the same rating, and (ii) are exposures to banks less risky than those to industrials? • spreads for US dollar denominated sovereign debt over US corporate debt of a similar rating

21. This may mean that recovery rates on sovereign exposures are typically lower and less timely than those on corporates. • For bank and industrial, ratings transitions for types of obligor over ten year horizons

23. banks in all ratings categories down to B are significantly less likely to default than non-banks. • the volatility of ratings changes is higher for banks than for industrials but large movements in ratings are just as likely if not more likely for industrials.

24. Bonds vs. loans • So far, little is known about differences between the credit risk of relatively liquid exposures (bonds) and illiquid exposures (loans). • default rates are lower for private debt placements than for publicly issued debt especially in the sub-investment grade categories.

25. 维度 研究文献 主要方法 表征维度的指标 信用风险度量 影响程度 Basel II是否考虑 PD Carey （2000） 重复抽样 不同的等级 EL UL(VaR) 大 是 LGD Carey （2000） 重复抽样 债务的级别 EL UL(VaR) 大 是 粒度 Carey （2000） 重复抽样 不同的组合构成 EL UL(VaR) 显著 是 期限结构 Kiesel, Perraudin, Taylor (1999) 模拟分析 到期期限 VaR 大 是 宏观经济状况 Carey （2000） 重复抽样 不同的周期阶段 EL UL(VaR) 大 不明显 国别 Nickell, Perraudin ,Varotto (1999) 信用等级转移矩阵 不同国家 等级迁移特征的相似性 有差异 未 Perraudin, Taylor (1999) 信用利差 不同国家 信用利差 有差异 未 借款人类型 Jackson; Perraudin 1999 信用利差 主权、银行、或工业贷款 信用利差 有差异 未 Nickell, Perraudin, Varotto (1998) 信用等级转移矩阵 主权、银行、或工业贷款 违约率与波动性 有差异 未

26. 三、PD estimation • 违约率估计方法分类 • 基于统计的方法 • DA • Logistic • 基于神经网络、数据挖掘的方法 • ANN • SVM • 基于期权的方法 • KMV • 基于利率期限结构的方法

27. 评论 • 基于统计的方法 • 直接方法，容易理解，但是“缺乏坚实的理论基础”，线性问题也是经常受到攻击的问题 • 基于神经网络、数据挖掘的方法 • 非线性的，但是“黑匣子”，Altman等（1994）的著名评论，“无本质改善”，同样无理论基础 • 基于期权、利率期限结构的方法 • 坚实的理论基础，精巧漂亮的数学表达 • 实施要求高、假设条件多，在新兴市场常常失败 • 布丁做得好不好关键要看可口不可口

28. DA类方法的几个问题 • 正态性 • 线性性 • 指标选择 • Logistic方法的几个问题 • 最优样本配比是什么？ • 最优分界点是什么？ • 原始假设是否成立？ • 统计方法的关键问题 • 样本选择 • 指标选择 • 效果检验

29. 正态性检验 • 线性判别分析模型必须要满足变量间独立、无共线性、数据维数不宜太高、服从正态分布、各组的协方差矩阵是相等的苛刻的条件才能够获得较高的判别效率 • Kolmogorov-Smirnov和Shapiro-Wilk正态性检验 • 24个变量中只有两个变量，流动资本比率和规模，可以认为服从正态分布，它们的Kolmogorov-Smirnov检验、Shapiro-Wilk检验的显著性水平分别为0.2，0.2；0.197331，0.582305。其余变量的显著性水平大多数在E-5到E-18次方的数量级上，因此，我们有充分的把握拒绝正态分布假设。

30. Tests of Normality 变量 Kolmogorov-Smirnov Shapiro-Wilk Statistic Sig. Statistic Sig. 流动资本比率 0.053657 0.2 0.974764 0.197331 债务与有形净值比率 0.415429 2.2E-32 0.195276 3.27E-17 存货周转率 0.45763 1.2E-39 0.254109 1.3E-16 财务杠杆 0.448136 6E-38 0.13511 8.6E-18 资产负债率 0.109678 0.047184 0.947631 0.007477 长期负债比率 0.269735 4.79E-13 0.663319 5.02E-11 速动比率 0.240895 2.84E-10 0.741511 1.89E-09 总资产报酬率 0.165687 0.000112 0.880803 1.24E-05 权益盈利率 0.248037 6.3E-11 0.606155 5E-12 销售利润率 0.362907 2.18E-24 0.29522 3.59E-16 每股收益 0.153071 0.000567 0.941112 0.003597 经营活动现金流量与债务总额比率 0.099829 0.099942 0.947055 0.007002 经营活动现金流净额与销售收入比率 0.22254 1.09E-08 0.686731 1.39E-10 和 0.400306 5.79E-30 0.476133 5.65E-14 营运资本比率 0.309612 1.87E-17 0.317434 6.31E-16 权益市场值/总债务的账面值 0.253375 1.98E-11 0.629958 1.27E-11 销售收入/总资产 0.18032 1.4E-05 0.838171 5.34E-07 税息前收益/总资产 0.361058 3.97E-24 0.236462 8.53E-17 标准偏差 0.478738 1.47E-43 0.122618 6.58E-18 利息保障倍数 0.28568 9.93E-15 0.713025 4.67E-10 留存收益/总资产 0.387836 4.86E-28 0.21817 5.55E-17 流动比率 0.220477 1.61E-08 0.778771 1.38E-08 资本化率 0.367459 4.91E-25 0.257493 1.41E-16 规模（总资产的自然对数） 0.067792 0.2 0.984519 0.582305

31. Box’s M F Sig 2605.638 6.373075(Approx.) 7.4E-180 • 协方差矩阵是否相等的检验 • Box’s M检验 • 拒绝协方差矩阵相等假设

32. 指标选择 • 尽可能多地考虑所有财务比率提供的信息的前提下,实现对企业经营状况的准确判别和预测成为典型判别分析法面临的首要问题。 • Altman选取的这5个（Z-Score模型）最优变量组合对中国的企业而言并不一定是最优的，关键问题就变成：如何寻找到能够反映我国的特定情况的“最优变量组合”呢？引入主成分分析法 • 利用标准样本首先确定出主成分，采用的是逐步增加变量，通过最终的主成份含义来确定

33. 主成分 表达式 F1 还债能力主成分 债务与有形净值比率×(-0.817)+财务杠杆×(-0.591)+资产负债率×(-0.886)+流动比率×0.774+速动比率×0.822 F2 盈利能力主成分 权益盈利率×0.872+每股收益×0.923 F3 还款意愿主成分 长期负债比率×(-0.749)+资产报酬率×0.755+经营活动现金流量与债务总额比率×0.79+和×(-0.596) F4 资本结构主成分 营运资本比率×0.881+流动资本比率×0.958 F5 营运能力主成分 存货周转率×0.85+销售利润率×0.758+经营活动现金流净额与销售收入比率×0.586

34. 利润增长情况 债务增长情况 还款意愿等级 正 负 好 正 正 最差 负 负 最好 负 正 一般 特色变量：还款意愿 设定：如果一个企业利润增长是负的，也就是企业钱少了，而同时它的债务增长也是负的，亦即没钱了还要还钱，那么说明它的还款意愿很好；反之如果它的利润增长为正，而债务增长为正，则说明它有了钱却还不还钱，它的还款意愿是差的。利润增长速度和债务增长速度的和作为刻画企业还款意愿的指标，两者速度和的值越小则还款意愿越好。

35. Logistic: 最优配比与最优分界点 • 一是在我国建立Logit模型时，样本违约公司与健康公司的配比是否会对模型的效率产生影响？二是最优分界点应该如何确定？ • 基本理论（适用性）：以任意比率来配比财务危机公司和健全公司，都能够保证抽样分布满足Logit分布，从而保证了Logit分析方法的适用性。 • 最优性问题是存在的，可以解的 • 解决的策略：实证比较方法 • 基本策略是：首先设计出最可能出现的几种样本配比比率，并同时设计出常用的分界点，然后比较不同配比比率与不同分界点条件下Logit模型的后续样本预测效率，以此为主要依据判断适用于我国的最优样本配比与分界点。

36. 实证结论： • 1、样本配比比率与分界点对Logistic违约模型的估计与效率有明显的影响。 • 2、健康公司的配比不应太大。

37. 3、1:1的配比比率可能并不适合我国的情况 • 以1:3为配比比率、0.647为分界点比较适合我国的情况。

38. 违约率是否服从Logistic分布 • Cramer（2004）的研究表明，一般的Logistic模型可能并不适用于贷款违约率的建模，关键的原因是，出现呆帐这个事件本身并不服从Logistic分布。他利用荷兰的商业银行经营的627笔呆帐与20189笔正常贷款构成的样本进行了实证研究，给出的重要证据是，一般的Logistic违约率模型难以通过Hosmer-Lemeshow拟合优度检验；在Hosmer-Lemeshow检验中容易出现高估低端组的违约概率而低估高端组的违约概率的情况（本文称之为Cramer问题）。为此，Cramer提出了边界Logistic方法。