关键词: 信用风险, 评价体系, 似然函数, 0-1规划, 小企业贷款

Abstract: Small enterprises play an important role in alleviating employment and improving the vitality of national economic development, but the current situation of difficult and expensive financing for small enterprises hasalways existed. At present, a large number of studies have been conducted on the credit risk of small enterprises, and significant results have been achieved in the risk control of small enterprises. For example, at the end of 2021, the non-performing loan ratio of Chinese commercial banks was only 1.73%, however the balance of non-performing loans of Chinese commercial banks was as high as 2.8 trillion yuan, and although the risk judgment in this field has a certain effect, it has a lot of room for improvement. A reasonable credit risk evaluation of small enterprises is conducive to improving the current situation of financing difficulties, promoting financial development and increasing employment. The premise of evaluating the credit risk of small enterprises is to establish a set of reasonable credit risk evaluation index system. This involves two scientific issues: One is how to select the indicators that can be used for credit evaluation, that is, the indicators with default judgment ability. Second, different combinations of indicators can form different indicator systems. n indicators can form 2ⁿ-1 indicator systems. How to select an optimal credit risk evaluation indicator system? This paper puts forward a new standard of measuring the index and the default discrimination ability of the index system by the value of the log likelihood function. Taking the maximum value of the log likelihood function as the objective function, a 0-1 integer programming is constructed, and the credit risk evaluation index system of small enterprises with the maximum default discrimination ability is solved by the genetic algorithm. The data of small business loans of a regional commercial bank in China in 28 regions including Beijing, Tianjin, Dalian and Chengdu are selected as the empirical data of this paper, and these data are all loans that have been settled by banks, because the outstanding business could not determine whether a default occurred. Based on the loan data of small enterprises distributed in 28 cities of a commercial bank in China, a set of credit evaluation index system covering 17 indices such as “operating profit margin”, “credit situation of small enterprises”, “Engel coefficient”, “Cash recovery rate of all assets”, “Cash content of net profit”, “Ratio of net assets to loan balance at the end of the year” and “iquidity of collateral” is established. The index system constructed in this paper is compared with the index system constructed by forward search algorithm, backward search algorithm and single index screening method. Through the overall discrimination accuracy and the second type of error determined by confusion matrix, it is determined that the index system constructed by this model has higher discrimination accuracy of default risk. Research prospect: By deleting invalid indicators that are not significantly related to the default of small enterprises, this paper selects an index combination with the greatest default identification ability among the different combinations of remaining indicators to form the optimal evaluation system for credit risk of small enterprises. In this process, it is not considered that a single indicator is invalid, but the combination of multiple invalid indicators is not necessarily invalid, so the next step of research will consider not deleting a single invalid indicator, but selecting the optimal indicator system among different combinations of all indicators. This research has improved the rating theory and method of credit risk management, established a small enterprise credit evaluation system, and made up for the deficiency of the existing bank credit rating system.

Key words: credit risk, evaluation system, likelihood function, 0-1 programming, small business loans