关键词: 小企业贷款, 违约风险, 资产配置, 资本充足率, 普惠

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