基于逐步判别分析的小企业债信评级模型及实证

Debt rating model of small businesses and empirical analysis based on stepwise discriminant

债信评级就是衡量债务违约风险的大小,以便于投资者掌握债务回收的可能性。本文通过逐步判别分析和共线性检验的方法构建债信评级模型,并以中国某区域性商业银行1231个小企业贷款客户为实证样本进行债信评级体系构建。本文的创新与特色一是通过逐步判别分析将所有客户的第j个指标数据分为违约和非违约两组样本,根据违约、非违约样本组内的数据差异越小、而违约与非违约样本组间的数据差异越大,则第j个指标越能区分违约和非违约两种状态的思路,筛选出F检验值显著、即对违约与否鉴别能力显著的指标,改变了现有研究遴选指标的标准不能反映指标违约鉴别能力的弊端。二是通过共线性检验方法,以一个指标为因变量、其余指标为自变量建立线性回归方程,根据线性回归方程的方差膨胀因子VIFj越大、这个指标越可以被其它指标线性表示的思路删除因变量这个冗余指标,避免了现有研究的债信评级指标用于评价小企业时存在冗余的弊端。三是根据违约样本和非违约样本的组内差异越小、组间差异越大、这个指标对违约状态的鉴别能力越强、权重越大的思路对指标进行赋权,改变了现有研究对评级指标进行赋权不能反映指标违约判别能力的弊端。实证结果表明:小企业非财务因素比财务因素更能判别小企业贷款的违约风险,并且外部宏观环境、企业法人代表基本情况对小企业的还款能力的影响更为重要。

Debt rating is aimed at measuring the possibility of debt default. Thus, indicators in debt rating system must be able to identify default risk significantly. Establishing a debt rating system will help investors measure the possibility of debt recovery and help enterprises issue bonds and get loans. Thus, the establishment of a debt rating system is very important. For small businesses, establishing a debt rating system is rather difficult because small businesses’ information is relatively unreal and incomplete. This research applies stepwise discriminant and collinearity tests to establish a debt rating indicators system of small businesses including 26 indicators, such as, quick ratio, industry sentiment index, and pledge guarantee. This research builds a debt rating model of small businesses by weighting indicators based on discriminant ability. This paper does empirical analysis about building the debt rating model for 1231 loan customers in a regional commercial bank of China. Firstly, we use the stepwise discriminant to screen indicators which can distinguish between default and non-default significantly. The data of index Xj can be divided into the default group and non-default group. Because of smaller differences in two groups and the greater differences between the two groups, the index Xj will be more able to distinguish between default and non-default. By this way, we can screen the indicators which can distinguish between default and non-default. It changes the shortcoming of screening indicators in the existing research which cannot reflect the discriminant ability. Secondly, we apply the collinearity test to delete indicators which reflect repetitive information. When the variance inflation factor VIFj is great, this indicator can be linearly expressed by other indicators. We deleted the indicators which can be linearly expressed by other indicators. It avoids the indicator system that has repetitive information. Through those mentioned above the “stepwise discriminant- collinearity test,”, we can construct a debt rating indicators system. Thirdly, we compute the weight of indicators based on U statistic. When the difference in two groups of default and non-default is the smaller, difference between two groups of default and non-default is the greater, the discriminant ability of the indicator is greater, and the weight is bigger. The weight cannot reflect the discriminant ability of indicators in the existing research. We compute the customer's credit score based on the linear weighted method. Last, according to the principle that the higher credit rating, and the lower LGD (Loss Given Default), we finally divide customers into nine credit grade and calculate LGD of every rating customer. It can measure the default risk of customers at different credit ratings, and it will help banks to decide which customers banks should offer loans. In this paper, empirical analysis is about constructing a debt rating system for 1231 small businesses. We screen the credit risk evaluation indicators system and establish a credit risk evaluation model for small businesses. The empirical result shows that firstly the indicator system including liquidity ratio, industry climate index and guarantee can distinguish between default and non-default signally and deletes the indicators using repetitive information. Secondly, non-financial factors can affect more the default risk of the small business than financial factors. The external macro environment factor and the basic situation of the enterprise's legal person are more important. Finally, the correct rate to discriminant default of the debt rating model in this research is 88%. It shows that the accuracy of this model is relatively high.