Abstract: The significant role of micro and small enterprises (MSE) in China’s economy has been recognized. They contribute substantially to the Gross Domestic Production (GDP), export earnings and employment opportunities. However, the poor availability of financing, especially accessing credit, is a major constraint on the development and growth of MSE. Because many small enterprises are unable to provide financial data for credit rating, commercial banks would not assess their true financial position so that they would reject credit applications. Though MSE borrow from banks on a small scale, the high default rate of MSE has led to huge losses, which also makes banks reluctant to make loan commitments to MSE. Thus, banks are faced with the challenge of controlling the credit risk of MSE loan portfolio in order to protect the interests of shareholders. At the same time, they also need to serve the task of inclusive finance for the development of MSE.
This paper studies an optimal micro-credit loans allocation problem from three perspectives: bank shareholders, regulators and MSE. We build a 0-1 mixed-integer nonlinear optimization model for banks to provide loans for MSE. In this model, decision variables are defined as whether to issue loans and the amount of loans; the objective function is set to maximize the expected return of the loan portfolio; and the constraints are established to ensure that the bank’s capital adequacy ratio (CAR) is not less than the regulatory requirement of 8% and the number of enterprises receiving loans is not lower than the target set by the bank. The innovations of this paper are as follows: firstly, while the objective of maximizing loan revenue to satisfy the needs of shareholders is considered, CAR constraint is introduced to control the overall credit risk; secondly, the need for inclusive finance is combined with the asset allocation problem of banks to ensure more small enterprises’ access to loans and alleviation of their financing difficulties to a certain extent; thirdly, the method incorporating with invoice data for computing a small company’s default probability is proposed. Invoice data can be used to analyze the relationship transaction information among enterprises, and thus can reflect the impact of changes in the credit quality of enterprises in the supply chain on default risk of enterprises applying for loans. For those small enterprises that may not provide balance-sheet data for banks to evaluate their financial position, with the help of the default probability method developed in this study they may get a credit rating, and thus the chance of obtaining loans would increase.
In numerical experiments, credit data of 6460 enterprises from ABC, a commercial bank in China, is used to construct an asset allocation scheme. Among them, 3752 enterprises provide financial and non-financial data, and invoice data; 1278 enterprises only provide financial and non-financial data. The remaining 1430 enterprises only have invoice data. Sensitivity tests are applied to examine the influence of target CAR, the number of enterprises receiving loans and other factors on the optimal asset allocation. The results show that: (1)524 enterprises that only provide the invoice data receive loan approvals; (2)our asset allocation is sensitive to key factors. With the increase in capital adequacy ratio, funds flow from enterprises with lower credit-rating to enterprises with higher credit-rated, but the return rate of loan portfolio decreases. As the number of enterprises receiving loans increases, some of the loans originally allocated to higher credit-rated enterprises flow to lower-rated enterprises, but the bank’s capital adequacy ratio meets regulatory requirement. Finally, a comparison with an existing widely used bank asset allocation model shows that our model outperforms the existing one in terms of capital adequacy level and the number of enterprises getting loans, and provides an effective way to deal with the trade-off between credit risk control and promotion of inclusive finance.
In addition to invoice data, MSE tax data, water, gas and electricity charges data may also be valuable. The role of these data in pre-loan default risk assessment, asset allocation decisions, and post-loan financial situation monitoring of MSE is worth studying in the future.

Key words: small business loans, default risk, asset allocation, capital adequacy ratio, inclusiveness

摘要： 文章以是否为企业发放贷款和贷出额度为决策变量,以贷款组合的期望收益最大为目标函数,以满足银行资本充足率不低于监管要求的8%、以及贷款惠及企业数量不小于银行既定目标为约束条件,构建了面向小微企业贷款决策的0-1混合整数非线性优化模型。本文的创新和特色:一是考虑贷款收益最大化目标的同时,引入监管要求的资本充足率约束,满足银行股东权益要求,控制整体信贷风险;二是将普惠需求与资产配置问题结合起来,保证银行收益以及信用风险可控的前提下、实现更多小企业获贷,在一定程度上缓解小微企业融资难问题。在数值实验部分,本文运用我国某商业银行ABC的6460家小微企业信贷数据,构建了资产配置方案,并进行了一系列重要参数敏感性检验。结果显示,银行目标资本充足率以及贷出企业数量的限制都会影响小微企业资产配置情况。随着目标资本充足率增加,资金会从信用等级较低的贷款企业流向信用等级较高的公司,但贷款组合收益率会降低;随着获贷企业数量增加,原本配置在较高信用等级的贷款会部分流向较低等级贷款企业,但资本充足率达标,仍保证整体信贷风险可控。

关键词: 小企业贷款, 违约风险, 资产配置, 资本充足率, 普惠