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标准普尔和穆迪违约损失率衡量方法研究资信论坛-上海新世纪资信

标准普尔和穆迪违约损失率衡量方法研究资信论坛-上海新世纪资信
标准普尔和穆迪违约损失率衡量方法研究资信论坛-上海新世纪资信

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标准普尔和穆迪违约损失率衡量方法研究

郑宇 黄德民/文

违约损失率(Loss Given Default)与债权人的自身利益息息相关,主要指债务人发生违约后给债权人造成损失的程度。违约损失率一般与宏观经济、偿债法律顺序、企业自身素质等因素存在相关关系。在违约损失率较大时,即使违约率较小,债权人仍需要客观评估当债务违约后面对巨大损失时自身的风险承受能力,因此违约损失率的衡量是信用评级不可或缺的考虑因素。

一、标准普尔公司违约损失率衡量方法

标准普尔公司(以下简称“标准普尔”)对违约损失率(Loss Given Default)的研究涉及非常广泛的范围,包括大中型企业、金融机构、保险公司、项目融资(Project Finance)、资产融资(Asset Finance)、房地产、贸易融资(Trade Finance)、地方政府及主权等方面。标准普尔的违约损失率衡量方法涉及基于挽回风险(Recovery Risk)的分析工具,可以对配对分析(Peer Analysis)、情景分析(Scenario Analysis)和主动资产组合管理(Active Portfolio Management)提供支持。

图1 从劣质贷款中分辨优质贷款1

1两个信用风险维度(违约风险和挽回风险)的分离可以在不同方面分析和管理风险。银行在授信方面能够通过有效的结构化措施使预期损失达到最小。

1.打分卡模型(SCORECARDS)

在较低违约风险的环境中,标准普尔的打分体系通过已测试的以内部评级为基础的方法体系进行违约损失率的估计。

标准普尔的打分体系包括以下特征:①包括广泛的子行业和资产分类(A s s e t Class);②可以在一个连续的范围(Scale)内上进行违约损失率的点估计,可以映射于任何离散的挽回比例;③当挽回率数据不完备时,通过专家分析在一致的方法和统计框架下增加要素(Inputs);④可以使用EXCEL工作表进行整合和表示。

图2 企业违约损失率打分卡样本

资料来源:标准普尔《Loss Given Default》

2.决策树模型(DECISION-TREE MODELS)

决策树模型是对违约损失率和违约风险敞口进行计算和信息整合的一种银行授信(Facilities)风险评级方法体系,其特征包括:①通过历史违约率与深入(In-deepth)分析相结合的方式进行预测,内部数据可以通过外部资源来证实所选的风险要素水平;②在风险要素的选择、数量、复杂性方面结合不同行业、项目的特征进行选择;③违约损失率的判定以实证经验为基础,但也会对风险要素进行适当调整,以得到更好的违约损失率;

④在压力测试等情景中与监管框架(例如巴塞尔协议)相一致。

图3 决策树样本

资料来源:标准普尔《Loss Given Default》

3.LOSSSTATS模型

此模型主要采用统计方法对违约损失率进行估计,其数据来源为LossStats数据库。此模型可以对最终挽回率和违约后30天的挽回率(通过变卖资产)进行估计。

4.模型验证(VALIDATION)

模型验证包括银行授信损失评估和使用内部挽回评级或违约损失率估计的检验,其内容包括模型验证分析、框架和流程设计、效果检验(与基准对比和后验测试)和内部验证程序检验。

5.确定基准点(BECHMARKING)

标准普尔在其现有的方法体系下通过设置观察目标(结构化框架)确定基准点,其确认并不以分布较低的历史数据奇异点为基础。标准普尔的基准点不但可以应用于已经过标准普尔公开评级的主体,也可以应用于没有公开评级的单一独立的主体。一旦基准点确认之后,标准普尔会采用多种的统计测试进行检验。

图4 债务缓冲(Debt Cushion)和担保关系直方图样本

资料来源:标准普尔《Loss Given Default》

二、穆迪公司违约损失率衡量方法

穆迪公司(以下简称“穆迪”)基于金融工具、公司、行业、宏观经济的相关数据推出LOSSCALC模型,该模型主要对违约损失率进行预测。LOSSCALC模型的预测精度远远大于历史移动平均法等一般预测方法,这主要归功于穆迪积累了超过1800个美国违约的贷款、债券和优先股的挽回数据,时间跨度超过20年,这大大提高了穆迪违约损失率模型的预测准确性。

1.重要模型变量

LOSSCALC模型运用9个解释变量(Explanatory factors)来预测违约损失率,涵盖债务类型、资本结构、行业和宏观经济四个方面,其中债务类型包括债务品种(贷款、债券和优先股)和保障类型(担保、优先无担保和次级等);资本结构主要指杠杆水平和偿债顺序;行业主要采用行业移动平均挽回水平和银行使用的其他观察指标;宏观经济包括

一年期RiskCalc 违约概率中值、穆迪违约债券指数(Moody's Bankrupt Bond Index )、未来12月投机级违约率(Trailing 12-month Speculative Grade Default Rate )和各类经济领先指标。这些指标基本不存在相关关系。由于模型中各个指标统计显著性较高,整个模型在各个指标共同作用下会提供更加准确的预测。

表1 LOSSCALC 模型的解释变量

资料来源:穆迪《Model For Predicting Loss Given Default Modeling Methodology 》

图5 各个基本因素对预测LGD 的相对影响

资料来源:穆迪《Model For Predicting Loss Given Default Modeling Methodology 》

2.分析框架

穆迪LossCalc 违约损失率模型的框架与穆迪RiskCalc 违约率模型分析的分析框架基本一致,包括因子转换(Transformation )、建模(Modeling )和映射(Mapping )。因子转换指通过把相关影响因子转换成模型变量,例如,穆迪认为在选择宏观经济变量中使用复合指数的预测效果会比采用单独宏观经济指标的效果好;在债务类型和偿债顺序方面使用平均历史违约损失率会获得更好的预测效果。在建模方面,LossCalc 模型主要使用回归方法。在映射方面,穆迪会比较LossCalc 模型输出和历史违约率的统计结果。

LossCalc模型使用的违约债务价格(Defaulted Debt Prices)在统计意义上并不符合正态分布(Normal Distribution),因此为了取得更好的预测效果穆迪公司使用贝塔分布(Beta-Distribution)代替正态分布假设。贝塔分布区间为0至1,且不受对称性假设限制。贝塔分布可以大致通过“中心”(Center)和“形状”(Shape)两个要素来表达,因此在描述数据分布方面更强的灵活性,例如贝塔分布可以更好地描述具有在1或者0的边界区域具有更高的概率分布特征的数据,而这些统计学特征在描述某些价值比率(如挽回率)时较为有用。在实际操作方面,由于债务类型的平均挽回分布的差异较大,LossCalc 模型首先根据不同的债务(例如贷款、债券和优先股)进行分组,然后把这些变量从贝塔分布转换为正态分布。相应地,这只需要观察挽回率的平均值μ、标准差σ和临界值(Bounding Values)。正态转换后变量的概率值与贝塔分布对应的概率值相一致。

此前的分析主要基于单变量(Univariate)情况的考虑。在建立多变量的最终模型("Overall" Model)之前,为了使每个解释变量显著程度(Significance)更高,LossCalc模型需要对部分解释变量进行进一步转换。这一转换的最终结果称为“子模型”(Mini-model)。其中,债务优先等级(Seniority Class)变量和行业LGD变量即为“子模型”,具有较强的解释性和显著性。其他一些子模型显著性较低,例如杠杆率(Leverage)、取对数(Logs)或时间序列中变化量比实际水平值等。

在确定解释变量的正态分布和显著性等特征后,L o s s C a l c模型通过计量回归(Regression)的线性加权(Linear Weighted)方式来解释自变量和子模型对因变量(违约挽回值)的影响。模型的数学表达式如下:

r^ =α+β1χ1+β2χ2+β3χ3+...+βkχk

其中χ

i 是自变量和子模型,β

i

为权重,标准化的r为违约挽回值,注意上述公式的r是

通过正态分布的方式表达的,需要通过逆矩阵变换(Inverse)转化为原贝塔分布的形式。

L o s s C a l c模型在违约挽回方面进行置信区间的预测(C o n f i d e n c e I n t e r v a l Estimation)。置信区间提供了实际值在假定概率(类似多次试验中特定结果出现的次数)下落入某一预测区间的估计范围。置信区间的宽度提供了预测精度(Precision of the Estimate)的相关信息。例如,80%的置信区间代表着我们可以相信80%的试验结果或实际值(True Value)会落在预测区间之内,另外只有20%的真实值会落在置信区间之外。

虽然回归模型可以进行置信区间的预测,但其预测的置信区间范围较大,不利于挽回率的估计。因此,穆迪通过建立、估计、检验条件置信区间(Conditional CI)预测方法来实现范围更小的置信区间估计。实际上,穆迪已经建立在较小的置信区间下多维度结果查询表(Multi-dimensional Lookup Table),可以通过不同资产类型和偿债优先度、宏观经济因素等标识进行查找,并提供了误差预测分布(类似标准差)、实证角度下(Empricial)的置信区间的范围等信息。

3.有效性检验

在检验L o s s C a l c模型的有效性方面,穆迪采用移动验证法(Wa l k F o r w a r d Validation),主要方式为采用一段时期的数据进行模型拟合,然后把拟合后的模型与之后的一段时期数据进行对比和检验,再不断地重复这一过程直到测试至当前时点为止。因此,LossCalc模型不会出现以某类样本数据为基础的拟合模型检验同源数据的现象,从而不会出现过度拟合(Over-fitting)的结果。在时期选取长度方面,穆迪会跨越多个经济周期进行模型的检验。

穆迪认为,模型检验是建立模型可信度的一个必要步骤,因此必须通过严格和严谨的方式进行检验,同时也需要对计划外的错误进行修正。例如,在不同模型对比检验中,采用同样的数据源至关重要,但实际操作中往往会出现统一模型在不同样本测试下出现预测效果的差异。为了减少这种差异,避免误导性的结果出现,穆迪在LossCalc模型和其他基准模型(如历史平均挽回率估计法)的对比中会采用完全一致的数据源和测试范围。

三、结论

从两家公司披露的违约损失率模型来看,标准普尔更希望通过多角度对违约损失率的实际形成过程和主要影响因素进行更好地描述,而穆迪更侧重于从数理分析的角度来提高违约损失率的预测精度。从实际的可借鉴性来看,由于穆迪的模型推导和操作步骤的披露更为充分,因此穆迪LossCalc模型可参考性更强,但也应借鉴学习标准普尔对违约损失率的主要观点和预测方式。

我国债券市场形成较晚,目前在历史、市场规模、规范化程度、技术研究等方面与美欧相比仍存在一定的差距。基于我国债券市场违约损失率历史数据匮乏的实际情况,我们应对债务违约损失预测的难度和重要性有着更为清醒的认识,通过借鉴外国先进经验与符合中国国情的自主创新相结合的方式对违约损失率进行更深入地研究和预测。

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