佳作分享|新冠肺炎疫情后政府支持中小企业的理论模型: 王氏变换的应用
Government support for SMEs in response to COVID-19: theoretical model using Wang transform
新冠肺炎疫情后政府支持中小企业的理论模型: 王氏变换的应用
Authors
Shaun Shuxun Wang
Southern University of Science and Technology, Shenzhen, China,and,
Jing Rong Goh
Risk Lighthouse International Pte Ltd, Singapore, Singapore,and,
Didier Sornette
ETH-Zurich, Zurich, Switzerland,and,
He Wang
Southern University of Science and Technology, Shenzhen, China,and,
Esther Ying Yang
Risk Lighthouse LLC, New York, New York, USA
Citation
Wang, S.S., Goh, J.R., Sornette, D., Wang, H. and Yang, E.Y. (2021), "Government support for SMEs in response to COVID-19: theoretical model using Wang transform", China Finance Review International, Vol. 11 No. 3, pp. 406-433. https://doi.org/10.1108/CFRI-05-2021-0088
摘要
新冠肺炎（COVID-19）的突发，使得中小企业的正常营运在相当一段时期内受到影响。我们的量化模型可以显示，政府提供的过桥贷款能够让中小企业的“内涵市场价值”得以存续，且适当的过桥贷款期限能够减少社会总福利的损失。
在金融市场中，风险定价的一个普遍原则是投资者要求“高回报要和高风险相匹配”。因为市场对承担风险所要求“公允”的回报。市场定价对某个特定风险的“风险中性概率测度”不同于该风险的“真实概率测度”。本文用王氏变换来计算银行给中小企业贷款的 “公允”贷款利率， 为政府调节利率补贴水平提供依据。为了激励银行发放更多的贷款，政府可以在正常的市场定价基础上给予每笔银行贷款一个利息补贴，银行能够从中获取利润，自然有动机发放更多贷款。
由于信息不对称的存在，银行并不总能准确识别出某一个企业是“好企业”还是“差企业”。错将贷款发放给“差企业”最后会造成银行的坏账损失，以及高额的社会机会成本。为了避免这些损失与成本，提升银行的风险筛选能力就显得尤为重要。本文用王氏变换来来描述银行的风险筛选能力，可以建立“分辨指数”，对银行的风险筛选能力进行评价。
Abstract
Purpose
Many governments are taking measures in support of small and medium-sized enterprises (SMEs) to mitigate the economic impact of the COVID-19 outbreak. This paper presents a theoretical model for evaluating various government measures, including insurance for bank loans, interest rate subsidy, bridge loans and relief of tax burdens.
Design/methodology/approach
This paper distinguishes a firm's intrinsic value and book value, where a firm can lose its intrinsic value when it encounters cash-flow crunch. Wang transform is applied to (1) calculating the appropriate level of interest rate subsidy payable to incentivize banks to issue more loans to SMEs and to extend the loan maturity of current debt to the SMEs, (2) describing the frailty distribution for SMEs and (3) defining banks' underwriting capability and overlap index in risk selection.
Findings
Government support for SMEs can be in the form of an appropriate level of interest rate subsidy payable to incentivize banks to issue more loans to SMEs and to extend the loan maturity of current debt to the SMEs.
Research limitations/implications
More available data on bank loans would have helped strengthen the empirical studies.
Practical implications
This paper makes policy recommendations of establishing policy-oriented banks or investment funds dedicated to supporting SMEs, developing risk indices for SMEs to facilitate refined risk underwriting, providing SMEs with long-term tax relief and early-stage equity-type investments.
Social implications
The model highlights the importance of providing bridge loans to SMEs during the COVID-19 disruption to prevent massive business closures.
Originality/value
This paper provides an analytical framework using Wang transform for analyzing the most effective form of government support for SMEs.
Keywords
COVID-19, SME, Bank loan, Government subsidy, Wang transform
文章结构
Introduction
Literature review
Wang Transform for pricing loan default risk
Firm’s intrinsic value versus book value
4.1 Double process
Structural model of bank loan default risk in relation to the SME’s intrinsic value
Economic disruption of COVID-19 and bridge loans for SMEs
6.1 Government emergency support by providing bridge loans to SMEs
Insurance pool for bank loans to SMEs
Interest rate subsidy for bank loans
Tax relief for SMEs
9.1 Optimal effective tax rate
Confidence intervals in estimating the drift term
Bank’s underwriting risk selection capability
11.1 Illustrative example
11.2 Some empirical evidence
Conclusion and discussion
研究成果
Expected loss of a bank loan equal the area underneath the loan default loss curve.
An illustration of Wang transform from loss curve S to price curve S*, where the plot is loss exceedance probability against the loss as%of loan value. The red-shaded region represents the risk premium.
Illustration of the distance to default model for one firm with different drift terms.
Net value creation vs bridge loan (with different shape parameters), and with M =2:5 (left panel) and M=3:5 (right panel).
The optimal bridge loan and exceedance threshold for different values of shape parameter and multiplier.
Illustration of the probability of exceedance against the loss as%of loan value, under a 50% coinsurance of a bank loan to SME.
An illustration of Wang transform from loss curve S to price curve S*, where the plot is loss exceedance probability against the loss as%of loan value, assuming that in the event of default, the recovery rate is zero.
Illustration of the loan default probability and the associated real interest rate and riskneutral interest rate, calculated using the Wang transform.
Some tabular values of the Wang transform frailty distribution, with median q0 = 10% and variation ofδ = 0:5.
Graphic illustration of the Wang transform frailty distribution, median q0 = 10% and variation of δ =0:5, with cumulative proportion of firms (left panel) and density of default probability bands (right panel) plotted against the default probability.
Bank with weak underwriting capability.
Bank with strong underwriting capability, where δstrong bank = 0:25.
Overlapping regions in loans to good firms and bad firms by banks with different underwriting capability. Left panel: bank with weak underwriting capability; right panel: bank with strong underwriting capability.
Reported bank loan default rates for the 1st Quarter 2020.
Bank loans made to SMEs as compared to bank asset for the 1st Quarter 2020.
Reported bank loan default rates for the 1st Quarter 2020 and the risk-neutral interest rate calculated using Wang transform.
主要结论
The economic impacts of COVID-19 are far reaching in terms of both national boundaries and time span. Many countries have rolled out measures to support SMEs which are struggling to survive amidst the economic downturns due to COVID-19.
Generally speaking, the effectiveness of government support for SMEs can be evaluated by how such measures help increase SMEs’ current cash liquidity and franchise value.
Government supported bridge loans are effective emergency measures in helping SMEs to cope with the impact of COVID-19. It is essential for governments to support SMEs and ensure their survivability as that would affect the economic stability in the country. Taking into account the opportunity cost of financial support (as they could have been deployed for other purposes), there is an optimal amount of bridge loan to be granted to SMEs depending on the duration of economic disruption of COVID-19.
Government-funded insurance pool for bank loans provide some but weak incentives for banks to issue loans to SMEs as such insurance does not reduce the probability of loan default in the first place.
As a more effective measure, governments can provide an interest rate subsidy to banks to incentivize them to issue more bank loans to SMEs and to have them extend the loan maturity of current debt to the SMEs. As common practice, government interest subsidy is used to help SMEs to pay a portion of the interest cost; however, banks do not have the flexibility to charge market risk-based interest rates for loans to SMEs. Thus, we propose that government can provide interest subsidy payable to banks to bring the total interest rate to a risk-based level. This would adequately compensate the banks for the increased risks when the banks issue more bank loans to SMEs or extend the loan maturity of current debt to SMEs. The paper applies the Wang transform to calculate the appropriate level of interest rate for SMEs with a given level of default risk, and thus quantifies the level of interest rate subsidy needed to incentivize banks to lend to SMEs.
Werecognize the limitation of existing banking channel in lending to SMEs, which require a different underwriting approach due to the relatively small size of loan amounts and large number of SMEs (where some SMEs have viable business and many others do not have a viable business). To enhance the underwriting efficiency for issuing loans to a large number of SMEs, a case is made for establishing policy-oriented banks or investment funds dedicated to supporting SMEs.
Other measures of government support can come in the form of tax relief. A key concept used in our theoretical model is a firm’s franchise value in equation (10) as the sum of discounted future after-tax earnings. Based on equation (10), when the effective tax rate τðθiÞ for SMEs is reduced, this would increase the firm’s franchise value. Currently, a common type of government support measure is to provide temporary tax reliefs (i.e. three months, 6 months tax relief). This can indeed serve as a type of incentive for companies and increase the amount of available working capital for the companies. However, we note that a key issue faced by companies is a lack of demand for their products and services. Therefore, stimulating confidence in the economy for the consumers is also essential in boosting consumption and aggregate demand. Therefore, reducing tax burdens should be done in conjunction with providing a more predictable business environment. We propose that by providing support from both the demand- and supply side, this would have a more profound effect in creating tangible value for the SMEs. Having many new short-term initiatives do not necessarily help to instill confidence within the market participants.
Government support for bank loans should be steered toward SMEs with higher intrinsic value. As the government is not in the business of risk underwriting or serving the loans, it is essential for government support to leverage on the underwriting capabilities of financial institutions, capital markets or Internet-based risk exchange platforms. Our paper showed how the bank’s underwriting capability affects the proportion of bank loans issued to good firms versus bad firms. The Wang transform method is applied to describe the underwriting capability of banks. This led to the concept of the overlap index which is a novel proxy of the bank’s underwriting capability in selecting risks.
It is advisable for the government to support the development of the risk management industry equipped with strong underwriting capability. Government can provide support for innovative risk information services for SMEs and online risk exchange platforms for the SME community to facilitate better information about the business prospects of SMEs. One specific suggestion is for government to support the development of risk indices for SMEs, including both downside risk and upside potential; such risk indices for SMEs would need to incorporate macro-level, sector-level and firm-level economic and business information, thus quite an enormous undertaking and may require collaboration between universities and various industry participants.
Government can achieve greater leverage effect by helping SMEs with high franchise value to tap into the private funds through securitization and early-stage angel investing. Collateralizing commercial loans and bank financing by granting a security interest in IP is a growing practice in Internet-based SMEs and in technology sectors. Currently, the markets for intellectual property asset-based securities are still in an infant stage as the universe of knowledgeable buyers and sellers is limited; however, it is growing with more interests from a variety of investors. For firmswith high IP content, government support for SMEs can be in the form of early-stage start-up loan facilitated by private sector angel investors or asset management firms, where government support can be turned into equity stake in later stage We hope that our paper can lay the groundwork for other researchers to conduct additional research on government support for SMEs, especially within the context of the COVID-19 situation. series-A funding.
作者简介
王树勋自 2019 年 12 月起任南方科技大学金融系讲席教授和系主任。王树勋于 1986 年毕业于北京大学数学系，1993 年毕业于加拿大滑铁卢大学统计和精算系，获理学博士学位。1994 年至 1997 年在加拿大滑铁卢大学任教；1997-2004 年在法国再保险公司工作；2004 年至 2013 年在美国乔治亚州立大学鲁滨逊商学院任教并于 2008 年晋升为终身讲席教授；2013 年至 2015年在瑞士日内瓦协会任常务副秘书长；2015 年至 2019 年在新加坡南洋理工大学任保险与金融研究中心主任、银行与金融系教授。
王树勋在国际权威杂志发表过近四十篇学术论文，包括《科学》杂志、《电气电子工程师学会杂志》、《环太平洋金融杂志》、《国际精算杂志》、《风险和保险杂志》、《保险数学和经济杂志》。他的学术论文曾获得 2018 年美国肯塔基大学“金融风险管理优秀论文奖“、北美保险学会“最有影响力的论文奖”、先后 8 次获得国际精算协会最佳论文奖。他拥有 2 项美国专利、1 项临时专利。他曾担任《国际精算杂志》的主编。以他的姓氏命名的“王氏变换”数学公式被广泛应用于巨灾险、信用风险和天气衍生类产品的定价模型。王树勋有着北美财产险高级精算师资格。
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