*Article* **The Influence of IFRS Adoption on Banks' Cost of Equity: Evidence from European Banks**

#### **Sang-Giun Yim**

School of Finance and Accounting, Kookmin University, Kookmin University, 77, Jeongneung-ro, Seongbuk-gu, Seoul 02707, Korea; yimsg@kookmin.ac.kr; Tel.: +82-2-910-5464

Received: 18 February 2020; Accepted: 23 April 2020; Published: 26 April 2020

**Abstract:** This study examines how mandatory adoption of International Financial Reporting Standards (IFRS) in European countries affects banks' cost of equity. Supporters of IFRS argue that its adoption improves the quality of accounting information, which in turn decreases the cost of equity. However, banking regulators could intervene in the implementation of new accounting standards to protect the stability of the banking system, which would deteriorate banks' information environment and thereby increase the cost of equity. Using a regression analysis of European listed bank data, I find that banks' cost of equity increases after the adoption of IFRS in countries with strong bank supervisory offices. I also find that strong legal enforcement and additional disclosure requirements jointly reduce banks' cost of equity, but pre-IFRS inconsistencies between local accounting standards and regulatory standards jointly increase banks' cost of equity. This study contributes to the literature on market discipline in banking and has policy implications: The findings suggest that, when implementing new accounting standards, potential conflicts between financial reporting and banking regulations should be considered.

**Keywords:** cost of equity; IFRS adoption; European banks; corporate governance; banking regulation

#### **1. Introduction**

The 2007 US subprime mortgage crisis shows the importance of the banking system for sustainable economic growth. The adverse effects of this crisis not only impacted the banks and debtors as parties to the mortgage loan contracts, but it also spread across the entire financial system and the real economy. As a result, despite the US government's efforts to stabilize the financial system, real domestic production per capita in the United States decreased by more than 5% from the fourth quarter of 2007 to the second quarter of 2009. This shows how the soundness of the banking system is critical to sustainable economic growth.

While several government regulations have been adopted to maintain the stability of the banking industry, innovations in financial instruments have been developing quickly, and regulatory bodies are playing catch up with the financial market. Consequently, the role of market discipline is crucial because market mechanisms can adapt more flexibly and promptly to change.

Unlike government regulators, market participants are not authorized to access banks' private information. Therefore, the public information environment is critical for the market discipline of banks. Financial statements are a reliable and comprehensive source of public information. Hence, this study investigates the influence of changes in accounting standards on European banks' financial statements post-International Financial Reporting Standards (IFRS) adoption.

Researchers argue that IFRS adoption improves accounting quality because it requires more disclosure than most local European accounting standards pre-IFRS. They suggest that IFRS adoption improves both earnings quality and the information environment. Consequently, post-IFRS, security trading by foreign investors increased, and equity values increased. These studies mainly focus on the impact of IFRS adoption on non-financial firms and equity market characteristics, however, and pay little attention to the banking industry or to the use of accounting information in contracts [1].

IFRS adoption impacts banks differently from non-financial firms because banks possess financial assets. IFRS requires financial assets to be recorded at fair market value, which is a noisy measure of future cash flow. Hence, increased use of this measure post-IFRS could increase the noise in the prediction of cash flow from bank assets, which could increase banks' information risks. Furthermore, unlike the cost of equity for non-financial firms, that for banks could increase post-IFRS.

Furthermore, IFRS as a principle-based accounting system is more flexible than most of the pre-IFRS local accounting standards. In contrast to a rule-based accounting system, a principle-based accounting system allows managers more accounting choices. Thus, accounting information can vary depending on choices made during the preparation of the information. This could enhance decision-making because information selection could be tailored. However, the verifiability of the accounting information could suffer post-IFRS, as the same accounting information can be presented in different ways. Verifiability is critical in contracts [2] because low verifiability provides room for moral hazard regarding debt contracts using accounting information in the debt covenants. Thus, IFRS adoption could reduce the contractibility of accounting information [1]. In sum, although IFRS adoption could improve the information environment for equity markets, it could also have a negative impact on debt markets.

In most countries, the banking industry is regulated by a governmental or a non-governmental organization to protect the stability of the financial system. Should IFRS adoption increase the instability of debt markets, bank supervisors can intervene. When bank supervisors have especially strong power, they have great influence on banks' financial reporting. The bank supervisors' main concern is the stability of financial markets; therefore, if necessary, they could intervene in the financial reporting by managing the law or the implementation of accounting standards, as Skinner [3] reported using a Japanese case. Although the supervisors' intervention stabilizes the lending system of the country, the distortion in the adoption of new accounting standards damages the transparency of the accounting information. Consequently, banks' information risks increase, which increases banks' cost of equity.

Based on the argument above, I hypothesize that IFRS adoption increases banks' cost of equity in countries with strong banking regulations. I also conjecture that IFRS adoption decreases banks' cost of equity in countries with strong investor protection.

Using European listed bank data, I test my hypotheses through a multivariate regression analysis. The results show that IFRS adoption increases banks' cost of equity in countries with strong banking supervision, supporting my conjecture. In examining the effect of additional disclosure requirements, I find that strong legal enforcement and additional IFRS disclosure requirements jointly reduce banks' cost of equity. However, banks' cost of equity is increased by the joint effect of the improvement of comparability by IFRS adoption and banking regulatory power.

This study contributes to the literature in several ways. First, this is one of the few studies that examines how IFRS adoption affects the valuation of the banking sector. Armstrong et al. [4] report that the market reaction of banks' stock prices to IFRS adoption is stronger than that of other industries. Meanwhile, Daske et al. [5] and Li [6] examine the effect of IFRS adoption on market reaction, but they do not examine the banking industry.

Second, this study has policy implications. The importance of market discipline in banking increases as financial instruments become more complex [7]. As seen in the 2007 Mortgage Crisis in the United States, financial instruments have recently been innovated at a rapid pace, and government regulations are not keeping up with the pace of innovation in financial instruments. However, market participants can respond quickly to market innovation, unlike government regulations. Thus, market discipline can supplement government regulation. Since investors rely on public information, high-quality accounting information is important in the market discipline of banks [8]. As this research suggests, in addition to high-quality accounting information, country-level banking governance is necessary for the efficient market discipline of banks.

Third, this study shows the interaction between the institutional environment of banks and changes in accounting standards. Researchers have pointed out that the institutional environment influences financial reporting [9–11]. Supporting this argument, studies on mandatory IFRS adoption suggest that investor protection facilitates IFRS adoption [6,12]. However, few studies have examined the role of bank regulation in adopting new accounting standards.

The remainder of this paper proceeds as follows. Section 2 summarizes prior studies regarding the effect of IFRS adoption on the cost of equity, institutional environments of the banking industry, and the economic consequences of IFRS adoption. Section 3 documents hypothesis development. Section 4 presents the research design, sample selection, and descriptive statistics. Section 5 documents the results of regression analyses. Section 6 concludes the paper.

#### **2. Literature Review and Background**

#### *2.1. The E*ff*ect of IFRS Adoption*

Prior studies argue that IFRS adoption improves several aspects of financial reporting, the information environment, and capital markets. Empirical studies find that earnings quality [13,14] and the information environment [12,15,16] are improved following IFRS adoption. Consequently, security trading [5,17,18] and equity valuation [5,6] improve post-IFRS.

Theory expects that the quality of disclosure is negatively related to the cost of equity [19–21], which is backed by empirical evidence [22,23]. Since IFRS adoption improves the transparency of accounting information and the information environment, researchers expect that IFRS adoption decreases the cost of equity. Li [6] finds evidence supporting this using European non-financial firm data.

However, IFRS adoption also has a negative consequence because it increases a manager's choice of accounting policy, which reduces the contractibility of the accounting information. Supporting this argument, Ball et al. [1] report that IFRS adoption reduces accounting-based debt covenants. This study implies that IFRS adoption is not welcomed by bank regulators because it reduces the contractibility of debt contracts, which results in instability in the financial markets. In addition, the findings of Ball et al. [1] also suggest that banks' risks increase post-IFRS because banks' lending contracts that utilize accounting information in debt covenants become inefficient.

#### *2.2. The Institutional Environment of Listed Banks*

This study focuses on the equity capital in European listed banks, which are exposed to two different types of institutional environments: Bank supervision and disclosure regulation. Listed banks are regulated by banking supervisory offices. Although the detailed structures of bank supervisory systems vary by country [24], the ultimate goal of supervisory offices is the same, namely, to safeguard the stability of the financing system because the stability of financial markets plays a critical role in the economic growth of the country. As a publicly listed firm, listed banks are also bound to the disclosure requirements of investors, whose main concern is not in protecting the stability of the markets, but in protecting investors' private interests.

The difference in policy objectives between bank regulation and corporate disclosure creates conflicts between accounting policy and bank regulation. Skinner [3] investigates the adoption of deferred tax accounting in Japan in 1998, during which Japanese banks' regulatory capital was insufficient. Thus, to maintain banks' solvency, the Japanese government and bank regulators decided to use a deferred tax asset as regulatory capital. Because maintaining the solvency of banks is more important for the country's economy, the quality of accounting information was sacrificed during the adoption of deferred tax asset accounting. Skinner [1] implies that banking regulations limit or distort the adoption of new accounting standards if the standards negatively affect the solvency of banks. IFRS adoption could necessitate regulatory intervention, as in the case investigated by Skinner [3]. Bischof [25] also pointed out that there are incentives to prevent European bank regulators from introducing new accounting standards

that affect banks' financial statements, which means that the intervention of bank supervisory offices in the adoption of new accounting standards is not limited to a specific country.

To implement accounting standards, support of institutional environments is necessary [9]. However, as prior studies show [3,25], listed banks face a potential conflict between bank regulation and financial disclosure; therefore, how IFRS adoption influences listed banks is unclear.

Basel II is a set of guidelines that shaped the mandatory adoption of IFRS in European counties. Although replaced by Basel III, Basel II is still useful in understanding the mechanism of the banking regulations. Basel II is based on the following three pillars: (1) Minimum capital requirement that requires safer capital as banks' risky assets increase; (2) review process by a government supervisory office; (3) market discipline that relies on sophisticated investors' monitoring. For the first and second pillars, private information can be required from banks or banks' auditors. Frequently, these two pillars have priority over accounting standards [3,25]. For the third pillar, market discipline penalties include direct penalty by investor activism and indirect penalties through market prices of securities, including stock prices. Due to the high information efficiency of market prices, market discipline can reflect the bank's health information at a rate that bank supervisors cannot follow. This means that market discipline is superior to bank supervisors in reflecting the consequences of financial instruments, which are rapidly becoming increasingly complex as they undergo innovation, on the health of banks. Therefore, the importance of market discipline is in an increasing trend [7].

Banking regulations affect banks' financial reporting. Bank supervisors can require banks to disclose private information found during the review process [26,27]. Furthermore, regulatory capital requirements enhance disclosure by providing timely and extensive information that is not required by accounting standards [28]. Stringent banking regulations could conflict with accounting information in that the regulations safeguard the banking system, whereas the accounting information focuses on capital providers. Moreover, banking regulators could sacrifice the quality of accounting information to stabilize the financial system [3,28] or to avoid rapid changes in the accounting numbers to minimize the negative impact on debt contracts based on accounting information [1,25].

The influence of investor protection is the same for banks and non-financial firms. Strong investor protection provides incentives to managers to provide transparent accounting information [10,11,29]. Consequently, IFRS adoption reduces banks' cost of equity [6,30,31].

#### *2.3. IFRS Adoption in the Banking Sector*

Compared with the previous local accounting standards, IFRS adoption brought several changes. The two most important changes for this study [2,14] include an increase in fair value measurement and an increase in accounting choices.

As the fair value measure increases, the statement of financial position (balance sheet in US Generally Accepted Accounting Principles terminology) increases in relevance for equity valuation. However, the market volatility included in fair value increases the noise in measuring banks' future cash flows. Even though fair value measures do not directly rely on level 1 inputs, which are market values, level 2 or level 3 inputs of fair value measures do not alleviate the information risk because they discretionary. In sum, extended use of fair value measures increases information risks, which are unfavorable for both investors and bank regulators.

In addition, although the increase in accounting choices enhances the relevance of the statement of financial position to equity valuation, this increase could influence the banking industry negatively. The increase in accounting choices complicates verification of compliance with the debt covenants. This provides opportunities for moral hazard for both parties of the debt contract. The reduction of contractibility of accounting information could have a significant impact on capital markets, which necessitates intervention by banking regulators [3,25].

#### **3. Hypothesis Development**

Regarding IFRS adoption and banks' cost of equity, two risks should be considered. The first risk is banks' business risks, which come from operating characteristics; for example, borrowers' credit risks. The second is information risk [19,20]. Both risks increase banks' cost of equity.

Because the minimum capital regulation is applied stringently, the regulatory capital ratio efficiently reduces banks' risk [28]. This risk reduction decreases banks' cost of equity. If banks' risk is already lowered by banking regulations, IFRS adoption has little impact on the disclosure of information about banks' risks. Therefore, IFRS adoption has little impact on the cost of equity if capital regulation is strong. Based on this conjecture, I suggest the following hypotheses:

**H1:** *Banks' cost of equity decreases as the minimum capital regulation strengthens.*

#### **H2:** *Strong capital regulation weakens the impact of IFRS adoption on banks' cost of equity.*

If banking regulatory agencies have strong power, they can require private information directly from banks or banks' auditors for regulatory actions [1,28]. Therefore, bank regulation strength reduces banks' cost of equity because strong banking regulators can monitor and discipline banks.

Banking regulations have priority over financial reporting in most countries; therefore, these regulations could interfere with IFRS adoption if new accounting standards have a negative effect on the banking system. IFRS adoption increases choice among accounting rules; therefore, using accounting information for debt covenants allows for moral hazard for any one of the contracting parties in debt contracts [1]. Several banks' contracts use accounting information for debt covenants; hence, changes in accounting standards could affect banks' existing contracts. Therefore, bank supervisors have the incentive to intervene in the adoption of new accounting standards to prevent potential turmoil, which would interfere with the faithful implementation of IFRS [3,25]. The intervention of bank supervisors increases information risk of banks, which would increase bank supervisors' power. Based on this conjecture, I suggest the following hypotheses:

#### **H3:** *Banks' cost of equity decreases as the bank supervisors' power strengthens.*

#### **H4:** *IFRS adoption increases banks' cost of equity in the countries with strong banking supervisors.*

Market discipline needs a good information environment including high-quality accounting information. Country-level investor protection improves accounting quality by helping faithful financial reporting [9,29], which leads to a reduction in the cost of equity [11,30,31]. Thus, in countries with strong investor protection, IFRS adoption reduces banks' cost of equity. In relation to the institutional aspects of the banking sector, I therefore suggest the following hypothesis:

#### **H5:** *The influence of IFRS adoption on banks' cost of equity is weakened when investor protection is strengthened.*

The impact of IFRS adoption varies with the extent of changes that occur in IFRS adoption [32]. In most European countries, IFRS adoption requires more disclosure. Thus, the impact of IFRS adoption increases additional disclosure requirements. Moreover, the impact of IFRS adoption varies with the inconsistencies between IFRS and the local accounting standards implemented before IFRS adoption. Accordingly, I propose the following hypotheses.

**H6:** *The influence of IFRS adoption increases when IFRS adoption requires additional disclosures.*

**H7:** *The influence of IFRS adoption increases when inconsistencies exist between IFRS and the local accounting standards implemented before IFRS adoption.*

#### **4. Research Design**

#### *4.1. Regression Model*

I use the implied cost of equity as my proxy for expected returns because it has fewer errors than realized-return-based proxies [30,31,33] from information shocks. I average four estimates calculated using the models of Easton [34], Gode and Mohanram [35], Gebhardt et al. [36], and Claus and Thomas [37] to mitigate error in each measurement [30,31].

Studies on the effect of IFRS adoption frequently use a difference-in-differences model using voluntary adopters as the control group. This model controls for the influence that occurs simultaneously with IFRS adoption. However, except the treatment, the control group of the difference-in-differences model should be identical to the treatment group. Furthermore, only three countries have banks that adopted IFRS voluntarily. Most European banks adopt IFRS mandatorily, which means that IFRS adoption was an exogenous event for most European banks. Hence, I do not use the difference-in-differences design.

To test H1 to H5, I use the following model (1):

$$\begin{aligned} \text{CoC} &= \alpha + \beta\_1 \text{POST} + \beta\_2 \text{ENFORCE} + \beta\_3 \text{OFFICE} + \beta\_4 \text{CAPITAL} + \beta\_5 \text{POST} \text{"ENFORCE} \\ &+ \beta\_6 \text{POST} \text{"OFFICLE} + \beta\_7 \text{POST} \text{"CAPITAL} + \text{CONTROL} + \varepsilon \end{aligned} \tag{1}$$

Variable definitions are in the Appendix A. *POST* is the variable of interest. I include measures for the strength of capital regulation (*CAPITAL*), the power of bank supervisors (*OFFICE*), and the efficiency of legal enforcement (*ENFORCE*) in the regression model. *CAPITAL* and *OFFICE* are measured by The Bank Regulation and Supervision Survey 2003 conducted by the World Bank [28,38]. I centered *CAPITAL*, *OFFICE*, and *ENFORCE* by the sample mean of each variable to mitigate multicollinearity problems from biases of spurious correlations [39].

I control firm-level risks using proxies of size, return volatility, financial leverage, total capital ratio, and book-to-price ratio. Size, return volatility, and leverage are measured by the decile rank of each variable to mitigate measurement errors. I include variables to control for cross-listing on the US stock market because investor protection in the US market is stronger than it is in most European countries, but it is not affected by mandatory IFRS adoption. I also control for the annual inflation rate and the indicator variable for the adoption of IFRS 7, which could affect banks. I include the bias and dispersion of analyst forecasts to mitigate the effect of biases and the nonlinearity of the models for the implied cost of equity [37,40]. Many bank-year observations have only one one-year-ahead earnings forecast; hence, I include an indicator variable for the observations to control for potential bias and replace the dispersion of analyst forecasts with zero. I adjust the influence of the firm-level serial correlation using a firm-clustered standard error in all of the regression results in this study [41].

To test H6 and H7, I revise model (1) by including additional disclosure requirements (*ADD*) and inconsistencies between IFRS and the local accounting standards (*INC*). I use the survey of Nobes [42] to measure *ADD* and *INC*. Nobes [42] did not focus on banks; thus, items irrelevant to banks, for example, inventory or plant assets, are included. To avoid potential measurement errors from irrelevant items, I exclude items irrelevant to bank operations from *ADD* and *INC*. I centered *ADD* and *INC* by their sample means to avoid multicollinearity problems [39]. The following are the models for H6 and H7, respectively. Model (2) and model (3) are models for testing the effects of *ADD* and *ICC*, respectively.

$$\begin{aligned} \text{CoC} &= \alpha + \beta\_1 \text{POST} + \beta\_2 \text{ENFORCE} + \beta\_3 \text{OFFICE} + \beta\_4 \text{CAPITAL} + \beta\_5 \text{POST}^\* \text{ENFORCE} \\ &+ \beta\_6 \text{POST}^\* \text{OFFITE} + \beta\_7 \text{POST}^\* \text{CAPITAL} + \beta\_8 \text{ADD} + \beta\_9 \text{POST}^\* \text{ADD} \\ &+ \beta\_{10} \text{POST}^\* \text{ENFORCE}^\* \text{ADD} + \beta\_{11} \text{POST}^\* \text{OFFICE}^\* \text{ADD} + \beta\_{12} \text{POST}^\* \text{CAPITAL}^\* \text{ADD} + \\ &\text{CONTROL} + \varepsilon \end{aligned} \tag{2}$$

$$\begin{aligned} \text{CoC} &= \alpha + \beta\_1 \text{POST} + \beta\_2 \text{ENFORCE} + \beta\_3 \text{OFFICE} + \beta\_4 \text{CAPITAL} + \beta\_5 \text{POST}^\* \text{ENFORCE} + \varepsilon \\ \beta\_6 \text{POST}^\* \text{OFF} &+ \beta\_7 \text{POST}^\* \text{CAPITAL} + \beta\_8 \text{INC} + \beta\_9 \text{POST}^\* \text{INC} + \beta\_{10} \text{POST}^\* \text{ENFOCE}^\* \text{INC} + \varepsilon \\ \beta\_{11} \text{POST}^\* \text{OFFICEF}^\* \text{INC} &+ \beta\_{12} \text{POST}^\* \text{CAPITAL}^\* \text{INC} + \text{CONTROS} + \varepsilon \end{aligned} \tag{3}$$

#### *4.2. Sample Selection*

Mandatory IFRS adoption by the European Union provides the setting for a natural experiment. Therefore, I use data from listed banks of European countries from 1995 to 2009. The observations are required to have the Standard Industry Code between 6020 and 6099. Analyst forecast data and financial data are obtained from I/B/E/S and Compustat Global, respectively. I match the stock prices and analyst forecasts of seven months after the previous fiscal-year end to make sure that precious accounting information is fully incorporated. Non-positive earnings forecasts were excluded. If three-year-ahead to five-year-ahead analyst forecasts are missing, I fill in missing values using long-term earnings growth rate forecasts. I use the average of a historical three-year payout ratio to calculate the expected dividend payout ratio. If the payout ratio is missing, or smaller (larger) than 0 (1), I use the country-median value instead. I exclude banks that do not have observations both before and after the mandatory IFRS adoption in 2005. I classify years before 2004 as the pre-mandatory adoption period and years from 2005 as the post-mandatory adoption period [6,30,31].

Table 1 presents the composition of the final sample, which has 376 observations from 52 banks in 12 countries having 7 voluntary adopters and 45 mandatory adopters. Among the 376 observations, 52 and 324 observations are obtained from voluntary and mandatory adopters, respectively. Only three countries, namely, Germany, Greece, and Poland, have voluntary adopters. However, voluntary adopters could not provide a good benchmark for difference-in-differences tests, because they are not evenly distributed. The sample selection did not drive this result. By examining the entire Compustat Global database, I confirm that only three countries have banks that voluntarily adopted IFRS. This result implies that IFRS adoption is more like an exogenous event than an endogenous one. Furthermore, this also implies that financial reporting and banking regulations could have conflicting goals.


**Table 1.** Sample composition.


**Table 1.** *Cont.*

#### *4.3. Descriptive Statistics*

Panel A in Table 2 shows the means of the main variables for regression analyses by country. Means of implied cost of equity are from 10% to 14%, whereas means of the regulatory capital ratio are larger than 10% and lower than 14.5%. Only three countries, namely, Germany, Greece, and Poland, have banks that voluntarily adopted IFRS. This implies that, unlike non-financial industries, European banks' IFRS adoption might be regulated by banks [6,25]. Voluntary adopters have a higher regulatory capital ratio than mandatory adopters in the same countries, suggesting the possibility that sound banks choose to adopt IFRS voluntarily to indicate their financial stability. Panel B presents the descriptive statistics for the full sample.


**Table 2.** Descriptive statistics.


**Table 2.** *Cont.*

Table 3 presents the differences in bank characteristics before and after IFRS adoption. The variables in Table 3 are chosen differently from those in Panel B of Table 2, because the purpose of Table 3 is to present the changes in bank characteristics intuitively. *CoC* significantly changes after the mandatory IFRS adoption. However, this univariate test does not confirm that the difference is due to IFRS adoption.

**Table 3.** Differences in bank characteristics before and after the mandatory International Financial Reporting Standards (IFRS) adoption.


\*, \*\*, and \*\*\* indicate significance at the 10%, 5%, and 1% levels by two-tailed tests, respectively.

#### **5. Analysis Results**

#### *5.1. The Influence of IFRS Adoption and Institutional Environment on the Cost of Equity*

Table 4 documents variables for institutional environments, and Table 5 presents the estimation results of model (1). *ENFORCE*, *OFFICE*, and *CAPITAL* have negative coefficients in both full and partial sample analyses. However, the coefficient on *CAPITAL* is insignificant in the partial sample analysis. These results imply that investor protection and bank regulation reduce banks' risk in general.




\*, \*\*, and \*\*\* indicate significance at the 10%, 5%, and 1% levels by two-tailed tests, respectively. t-values are adjusted by firm cluster.

The interaction term of *POST* and *OFFICE* has positive coefficients, suggesting that banks in countries with strong regulations experience an increase in the cost of equity. Financial reporting and banking regulations conflict regarding IFRS adoption. In this case, banking regulations have priority over financial reporting [26]. Therefore, bank supervisors intervene in the IFRS adoption to suppress the negative impact of IFRS on the banking system, at least temporarily [3,25]. The intervention in IFRS adoption reduces the quality of accounting information and increases the uncertainty of banks and the cost of equity. This supports H4. However, the interaction terms of *ENFORCE* or *CAPITAL* with *POST* are insignificant; thus, H2 and H5 are not supported. The results are qualitatively consistent with the results for non-financial firms. Listed banks are also exposed to disclosure requirements; therefore, the results should be consistent with prior study [6].

#### *5.2. The Changes in Disclosure Requirements by IFRS Adoption on Cost of Equity*

Panel A of Table 6 documents the regression result of model (2). In column (A), the sign of the three-way interaction term of *ENFORCE* shows that legal enforcement facilitates the implementation of additional disclosure requirements by mandatory IFRS adoption, resulting in the decrease in banks' cost of equity. However, the coefficients on the three-way interaction terms of *CAPITAL* and *OFFICE* are insignificant. The result of the subsample period test presented in column (B) is qualitatively the same, except that the significance and magnitude are weaker. The results support the conjecture that the institutional environment for investor protection supports the implementation of IFRS adoption because it improves the relevance of accounting information on the equity valuation.


**Table 6.** The effect of changes in bank disclosures on cost of equity.


**Table 6.** *Cont.*

\*, \*\*, and \*\*\* indicate significance at the 10%, 5%, and 1% levels by two-tailed tests, respectively. t-values are adjusted by firm cluster.

Panel B of Table 6 shows the influence of the improved comparability on banks' cost of equity. I use model (3) for this test. *INC* indicates the differences between IFRS and the pre-IFRS local accounting standards. Therefore, *INC* also proxies for the improved comparability across countries. Unlike *ADD*, *INC* indicates disclosure requirement changes to the pre-existing accounting standards. Therefore, from the banking regulators' point of view, *INC* could be a threat to the debt market because it relates to compliance with debt covenants of the pre-existing debt contracts. By contrast, *ADD* is likely unrelated to the compliance with debt covenants because *ADD* indicates new disclosure requirements. The items related to *ADD* were not in the previous accounting standards; hence, those items have little impact on debt covenants. Thus, the effect of bank supervisors' intervention is related to *INC*, not to *ADD*.

The three-way interaction term of *CAPITAL* and *OFFICE* is positive. This means that mandatory IFRS adoption increases the cost of equity in countries with stringent banking regulations and where the pre-existing accounting standards change significantly. As *INC* increases, bank supervisors' incentive to intervene in the implementation of IFRS increases because the adoption decreases the contractibility of accounting information [1,3,25]. Moreover, changes in accounting standards impact the regulatory capital ratio, which potentially impacts the stability of the banking system. As a result of the intervention, accounting standards are implemented to minimize the potential negative influence on the debt markets, which increases information risks.

#### **6. Conclusions**

This study examines the effect of mandatory IFRS adoption on European banks' cost of equity. The empirical results of this study show that the impact of IFRS adoption on banks' cost of equity varies depending on institutional aspects. Strong investor protection is helpful in decreasing the cost of equity following IFRS adoption. However, banking regulation increases banks' cost of capital, especially when IFRS adoption has a strong impact on debt contracts. These results show that market monitoring and bank regulation are potentially at odds because of differences in policy objectives. Consequently, the cost of capital is affected differently by IFRS adoption in two institutional aspects.

The results of this study have policy implications. Unlike other industry sectors, the banking sector has a strong regulatory environment. Therefore, the incentives of banking regulators must be considered when designing a disclosure policy for the banking sector. If these incentives are ignored, a disclosure policy can be distorted; hence, the intended results cannot be obtained. Furthermore, this policy can yield results opposite to the intended ones. In addition, although market discipline is an important part of the banking regulatory system, factors that enhance market discipline can easily be weakened by bank supervisors. As market discipline has become more important because of rapid innovations in the finance sector, policy makers should carefully design policies related to the banking system.

This study also has several limitations. First, due to availability, some countries are not included in the analysis, which could cause a selection bias. Second, I incorporate only two aggregate measures of bank regulation, which are not enough to explain every detail of banking regulation. Third, the effects of specific regulatory events that occurred during my sample period are not totally addressed in this study. Fourth, this study focuses only on listed banks. Several banks are unlisted; hence, market discipline on unlisted banks should be addressed in future research settings. Finally, this study does not address the impact of IFRS adoption on several aspects other than stock price; for example, credit allocation activities. These could be examined separately in other studies.

**Funding:** This research received no external funding.

**Acknowledgments:** This study is based on one essay of my dissertation. I thank my dissertation chair Woon Oh Jung and committee members Lee-seok Hwan, Jong Hag Choi, Kyung-Ho Park, and Seung Yeon Lim for the guidance and support.

**Conflicts of Interest:** The author declares no conflict of interest.

#### **Appendix A**


**Table A1.** Variable definitions.


#### **Table A1.** *Cont.*

#### **References**


© 2020 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Article* **Peer-to-Peer Lending and Bank Risks: A Closer Look**

#### **Eunjung Yeo <sup>1</sup> and Jooyong Jun 2,\***


Received: 21 June 2020; Accepted: 25 July 2020; Published: 29 July 2020

**Abstract:** This study examined how the expansion of peer-to-peer (P2P) lending affects bank risks, particularly insolvency and illiquidity risks. We compared a benchmark case wherein banks are the only players in the loan market with a segmented market case wherein the loan market is segmented by borrowers' creditworthiness, P2P lending platforms operate only in the low-credit market segment, and banks operate in both low- and high-credit segments. For the segmented market case compared with the benchmark one, we find that, while banks' insolvency risk increases, their illiquidity risk decreases such that their overall risk also decreases. Our results imply that sustainable P2P lending requires an appropriate differentiation of roles between banks and P2P lending platforms—P2P lending platforms operate in the low-credit segment and banks' involvement in P2P lending is restricted—so that the growth of P2P lending is not adverse for bank stability.

**Keywords:** peer-to-peer lending; bank risk; insolvency risk; illiquidity risk

**JEL Classification:** G21, G23

#### **1. Introduction**

Peer-to-peer (P2P) lending—also known as FinTech credit, crowd-finance, or marketplace lending—refers to credit activities through online P2P lending platforms that provide direct matching between investors and borrowers and split loans into payment-dependent notes. (Committee on the Global Financial System (CGFS) of Bank for International Settlements (BIS) provided the differences among P2P lending business models: some simply match lenders and borrowers, while others reflect the loans on their balance sheets [1].) P2P lending often targets borrowers with low- and mid-level credit ratings, a group facing a reduced supply of bank loans since the collapse of the subprime loan markets and the global financial crisis of 2008. P2P lending has also demonstrated its usefulness in financial inclusiveness and as a substitute for bank loans by expanding its range of credit offers to borrowers with low-credit ratings [2] as well as by providing more investment opportunities for small institutions and retail investors [3].

P2P lending has grown dramatically in size and scale over the past decade, drawing attention from both investors and regulatory agencies [1,3]. On the one hand, unclear regulations and policy guidelines have sometimes plagued these platforms, hindering the application of new and innovative information technologies that could reduce intermediation costs and improve user experiences. (For example, in 2015, the Financial Supervisory Service of Korea suspended operations of the P2P lending platform "8 Percent" after concluding that the matching platform should be required to have the same certification as other financial institutions providing credit.) On the other hand, in terms of banking and financial stability, these regulations are reasonable. The lingering effects of the global financial crisis have become the "new normal," and, in reality, P2P lending platforms have at times failed to properly allocate credit. (In May 2016, the LendingClub, one of the best-known P2P

lending platforms, was accused of providing USD 22 million in loans to underqualified borrowers. Afterwards then-CEO Renaud Laplache and three other directors resigned or were dismissed.)

Direct investments through P2P lending platforms have the following characteristics. First, the notes traded via FinTech platforms are often unsecured [4,5]. Second, P2P lending platforms often subdivide loans into a number of mini-bonds (or notes) and provide aftermarket trading functionality, both of which enhance liquidity. (In some credit markets, wherein raising funds through banks may be difficult, other funding methods are gaining in popularity, such as small-scale divisions of bonds or direct investments. In the UK, for example, small- and medium-sized enterprises use so-called mini-bonds as a means of marketing and financing. These enterprises issue bonds to their customers, who can choose discounted products rather than receiving interest payments [4].) For example, by paying a fee equal to 1% of the sales price, LendingClub investors can trade their dividend notes in the associated aftermarket (the Note Trading Platform) before they expire. Third, P2P lending platforms typically provide loans for borrowers with low- and mid-level credit ratings. This group has faced a credit gap, or a reduced supply of loans from banks, since the global financial crisis.

Despite its growing popularity, the effects of P2P lending on major bank risks have not been investigated thoroughly. (CGFS [1] provide an expository note about this issue.) Direct investments via P2P lending platforms are supposed to be duration-matched, and they cannot be liquidated until the maturity date. This means that P2P lending is designed not to create a short-term liquidity problem. (In practice, however, some P2P lending platforms adopt more complicated originate-to-distribute approaches. LendingClub is an example: After investors and borrowers are matched, the investment funds raised by LendingClub are transferred to the WebBank (located in Utah, US), which originates from the loan and returns it to LendingClub. LendingClub then divides the loan into "payment-dependent notes" by units of USD 25, and distributes them to investors, the proceeds of which fund specific loans to borrowers. The principal and interest are paid to the loan note holders. Note that, if LendingClub initiated the loan directly, without going through a bank or depository agency, the activity would be considered as an unauthorized shadow banking activity.) Further, notes (of split loans) invested and traded through P2P lending platforms are mainly unsecured bonds (i.e., with no collateral). This implies that the contagious effects of loan defaults would be limited. Still, P2P lending platforms make commissions on initial loan brokerages and exchanges of notes in the associated aftermarkets, while investors mostly bear the risks of borrowers' defaults. (In this sense, P2P lending has some features of an originate-to-distribute model [6]. Phillips [7] uses the features as a basis for criticism of P2P lending.) Thus, P2P lending platforms would be more focused on increasing fee revenues than on proper evaluations of creditworthiness, leading to an increase in the proportion of non-performing loans. To the extent that P2P lending and bank loans act more as substitutes than as complements, competition between banks and P2P lending platforms may hamper banking prudence, given the aforementioned incentives.

Considering these characteristics and the aforementioned gap in the literature, we theoretically analyzed the effects of P2P lending on two major bank risks: (in)solvency risk and (il)liquidity risk. The idea of separating banks' illiquidity and insolvency risks was first introduced by Bagehot [8], who argued that the market itself cannot fully address the problems of an interim liquidity shock. Some researchers have criticized this view e.g., [9], but recent studies such as by Rochet and Vives [10] and Freixas and Ma [11] have supported it. The Bank for International Settlements also supports this view, having introduced the liquidity coverage ratio (LCR) and the net stable funding ratio (NSFR) requirements in Basel III. (LCR requires that a bank should hold adequate stock of unencumbered high-quality liquid assets to meet its liquidity needs for a 30 calendar day liquidity stress scenario [12]. NSFR is defined as the amount of available stable funding relative to the amount of required stable funding. This ratio should be at least 100% on an ongoing basis [13].)

Finally, while we let P2P lending refer to general lending activities rather than financing with a specific purpose, we want to note the study by Petruzzelli et al. [14], who focus on the role of crowdfunding in supporting sustainability-oriented initiatives. They find that in terms of economic importance, P2P lending becomes the most relevant crowd-finance form, (Lending-based crowdfunding collected a global volume of funds about \$25 billion in 2015 [14].) implying that P2P lending should be an important issue in sustainable finance. The rest of the paper proceeds as follows. Section 2 presents the theoretical background and Section 3 describes the model. Section 4 analyzes the major bank risks—insolvency and liquidity risks—by comparing two cases: in the benchmark case, only banks exist, and in the other case, both banks and P2P platforms exist. Section 5 discusses the effects of competition on bank risks, and the importance of the isolation of P2P lending from the banking sector. Section 6 concludes the paper.

#### **2. Theoretical Background**

In this study, we compared two cases: (i) the benchmark, in which only banks exist in a single loan market, and (ii) the case wherein the loan market is segmented by borrowers' creditworthiness and P2P lending platforms operate only in the low-credit segment. Our results show that compared with the benchmark case, when P2P lending platforms and banks operate in the low-credit market the (i) insolvency risk of individual banks increases; (ii) illiquidity risk of individual banks decreases; (iii) banks' total credit risk—the sum of both risks—also decreases.

First, regarding insolvency risk, borrowers in the low-credit segment would choose higher-risk, higher-return projects because the interest rate applied to the low-credit market segment would be higher than that applied to the benchmark case, as in Boyd and De Nicolo [15]. As a result, the likelihood of borrowers' defaults on individual bank loans increases in the low-credit segment, leading to higher insolvency risk. Second, regarding illiquidity risk, the proportion of protected deposits in a bank's deposit portfolio would increase with loan market segmentation, as a result of banks substituting for P2P lending platforms. This would lower the level of critical cash flow that would prevent a bank run, resulting in a lower illiquidity risk. Third, in the segmented market case, a bank's combined credit risk is smaller than that in the benchmark case, implying that the decreased illiquidity risk would be great enough to cancel out the increased insolvency risk.

We further investigated the effect of competition and the implication of the separation of P2P lending and banking and find that competition is more likely to reduce the combined credit risk in the segmented market case than in the benchmark case. This result also implies that once banks begin to participate in P2P lending, either directly or indirectly, it would adversely affect the combined risk because it would lessen the competition in the segmented market case. Our results imply that sustainable P2P lending requires an appropriate separation of roles between banks and P2P lending platforms. If P2P lending platforms and banks are differentiated in their roles for separate market segments, the spread of the former may not pose a significant problem in terms of bank risks. Regulatory agencies, however, would have to limit P2P lending platforms' brokerage of mini-bonds or notes outside their associated aftermarkets. At the same time, they may have to prevent banks or their subsidiaries from joining the trades of split notes in the aftermarkets of P2P lending platforms and let the banks focus on the high-credit market segments and protected deposits business.

Before the mid-2000s, studies on inter-bank competition focused on analyzing the impact of competition on financial stability [16–18]. Often, as competition increases, banks become more risk-seeking (See Carletti [19] for more details on previous studies on bank competition and financial stability). However, recent studies have suggested that this is not necessarily the case [15,20,21]. The U-shaped relationship between bank competition and bank failure has been confirmed by both theoretical [15] and empirical analyses [21]. These studies are traditional, homogeneous inter-bank competition analyses, and they do not involve financial institutions that do not follow the deposit-loan model.

More recent studies have investigated the coexistence of P2P lending platforms and banks. Thakor and Merton [22] suggested that banks have a stronger incentive to manage a trust, but P2P lending platforms tend to experience more adverse effects from a loss of trust. De Roure et al. [23]

found that P2P lenders tend to be bottom fishers, P2P loans are riskier, and the risk-adjusted interest rates for P2P loans are lower than those for bank loans. Tang [24] found that P2P platforms are essentially substitutes for banks and mostly serve the same borrower population, despite their unique potential. Finally, Vallee and Zeng [25] and Balyuk [26] studied the informational role of P2P lending and its relationship with investors and banks, respectively.

A strand of the recent banking literature has adopted global games, which are games of incomplete information wherein each player obtains a private signal about the true state with a small amount of noise, and his/her higher-order beliefs also affect the outcome [27,28]. Goldstein and Pauzner [29] and Rochet and Vives [10] are two well-known global game-based bank run models. Goldstein and Pauzner [29] directly extend the Bryant–Diamond–Dybvig (BDD) model [30,31] by incorporating the actual interim liquidity needs of consumer-depositors. Our study is close to Rochet and Vives [10] and Freixas and Ma [11], who focus on depositors' speculative runs on unprotected bank deposits. Nevertheless, it is distinct because we extend the model to incorporate the situation wherein heterogeneous types of financial institutions co-exist in the market.

In addition to the finance literature, studies such as Cusumano [32], Einav et al. [33], and Sundararajan [34] emphasize the positive aspects of competition in platform economies, which open the chance of entry for small players and enhance efficiency. However, their focus is often the sharing of horizontally diversified, and sometimes idle, "physical" facilities. Due to this difference, there are limitations to applying the implications to the case of P2P lending in the current paper.

To the best of our knowledge, this study is one of the first works, if not the first, to implement a full theoretical analysis of the effects of the competition between P2P lending platform and banks on bank failure risks, specifically in the strand of microeconomic banking literature such as Rochet and Vives [10], Goldstein and Pauzner [29] and Freixas and Ma [11], which consider only homogeneous banks. This study also provides related policy implications that it is necessary for a regulatory authority to supervise the P2P lending platforms separately from the existing banking sector to promote the sustainable development of alternative lending.

#### **3. Model**

We follow the basic settings and notations of Freixas and Ma [11], (Freixas and Ma [11] can also be regarded as an extension of the BDD model, which is the de facto standard model and the starting point in the microeconomics of banking.) with modifications, extensions, and clarifications where necessary.

#### *3.1. Players and Settings*

As per the standard Bryant–Diamond–Dybvig (BDD) model, we consider a one-good, three-period (*t* = 0, 1, 2) economy wherein all agents are assumed to be risk-neutral. There are two types of investors: *depositors* who deposit their liquidity in banks, and *P2P lenders* who lend directly to entrepreneurs (borrowers) via P2P lending platforms and hold these entrepreneurs' loan notes. Similar to the BDD model, depositors are assumed to be homogeneous. At *t* = 1, the depositors decide whether to withdraw their deposits early, and the lenders trade notes amongst themselves in the accompanying aftermarket. When depositors withdraw their deposits early at *t* = 1, they incur a penalty. (In Rochet and Vives [10], unprotected deposits are mostly wholesale deposits such as certificates of deposit, and early withdrawals stop the rolling over of these deposits.) However, unlike the BDD model, we do not consider any unanticipated consumption needs at *t* = 1, which are likely to be covered by protected demand deposits such as checking accounts. We assume that depositors are interested only in the rates of return from their investments, as modeled in Rochet and Vives [10] for example, and that their decisions on the early withdrawal of their deposits solely depend on their speculation on the likelihood of realization of the promised return at *t* = 2.

P2P lending platforms do not take deposits; they only match lenders and borrowers and earn fee revenue per match. Loans via P2P lending platforms are split into payment-dependent *notes* and can be traded in the accompanying aftermarkets at *t* = 1, similar to that in the (incomplete) market example of Diamond and Dybvig [31]. We assume that trades of notes occur only between P2P lenders, limiting the effects of trades within P2P lending platforms and preventing the "hacking" of the market e.g., [35]. Moreover, we assume that banks cannot identify a borrower's type, default risk, or creditworthiness. However, we assume that P2P platforms, with their new technology, can correctly identify whether a borrower's type is higher or lower than a threshold.

Borrowers are entrepreneurs who are cashless but have long-term and productive, yet potentially risky, projects classified by their type *b* ∈ (0, *B*], with a higher *b* indicating the safer entrepreneur. Each entrepreneur's project requires a unit of the loan at *t* = 0 which is to be paid back with the gross rate of return from the loan *r*(> 1), when the project is completed at *t* = 2. There is a threshold type *B*ˆ such that *<sup>B</sup>*<sup>ˆ</sup> <sup>&</sup>gt; 1/(*<sup>x</sup>* <sup>−</sup> *<sup>r</sup>*). Here, *<sup>x</sup>* denotes the gross rate of return from an entrepreneur's successful project. Borrowers of *<sup>b</sup>* <sup>&</sup>lt; *<sup>B</sup>*<sup>ˆ</sup> and *<sup>b</sup>* <sup>≥</sup> *<sup>B</sup>*<sup>ˆ</sup> are classified as Group 1 and Group 2, respectively. We assume that there exists a difference in the maximum value of *r* for Group 1 and for Group 2, respectively, which the borrowers in each group are willing to accept. Banks are supposed to be unable to identify which group a potential borrower belongs to. In contrast, P2P lending platforms, often considered to have more advanced technology, are supposed to correctly identify whether a borrower is in Group 1 or Group 2, although not the exact value of *b*, which creates the possibility of market segmentation.

A bank's portfolio of deposits at *t* = 0, 1 + *F*, consists of the following: *F* is the portion of demand deposit, given the amount of loan is normalized as one, in the benchmark case with banks only, and *F*- in the case of P2P lending platforms also operate. (For the remainder of the paper, we use the same approach using the apostrophe.) At *t* = 2, the sum of the liquidity reserve and recouped loan with return *D* (and *D*- ), *F* + *D* (and *F*- + *D*- ), must be delivered to depositors if the bank is solvent where *D* > 1 (and *D*- > 1). *F* + *D* is the promised, but not all of it is necessarily protected. Note that, although not exactly the same, *F* is related to the liquidity reserve; a higher value of *F* implies that the proportion of savings deposits is lower. We assume that there is no equity in the bank's portfolio. For simplicity, we assume that if a bank fails at *t* = 2, it returns nothing but *F* (and *F*- ) to the depositors. As Diamond [36] noted, increased participation in direct financing causes the banking sector to shrink, primarily through the reduced holdings of long-term assets, implying the possibility of *F*- > *F*. Finally, we assume that the size of deposits is less than the demand for loans, causing excess demand for loans.

A P2P lending platform does not have a depository function (i.e., *F* = 0) and it only matches P2P lenders and borrowers. We assume that all P2P lenders are homogeneous: every P2P lender has an equal share of the loans given to all borrowers such that each P2P lender has the same homogeneous loan portfolio. We also assume that the (average) investment at *t* = 0 is normalized as 1. Thus, a P2P lender's ex-post gross rate of return at *t* = 2 is the cash flow generated from successful loans. When banks and credit markets co-exist, we assume that no cross-participation—depositors' purchase of notes or lenders' purchase of loan claims—is allowed at *t* = 1. Thus, any transaction that occurs in the secondary markets attached to P2P platforms does not affect the money market. Finally, we assume that all rates are exogenous unless specified.

#### *3.2. Timing of Game*

At *t* = 0, loans are jointly financed by a continuum of investors. For simplicity, a P2P lender is homogeneous and assumed to hold split notes of all types of borrowers' loans, in the same way as (unprotected) deposits are diversified via bank.

At *t* = 1, an investor, indexed by *i*, receives a private noisy signal *si* = *θ* + *<sup>i</sup>* about a random cashflow generated from the (unit) loan portfolio, denoted by *θ*. Here, *<sup>i</sup>* is i.i.d. and follows a probability distribution with zero mean and a small but non-zero standard deviation of *σ*. Each depositor who chooses to withdraw his/her deposit early will recover *qD*(< *D*/*R* or *q* < 1/*R*) by paying an early withdrawal penalty of (1 − *q*)*D* where *q* ∈ (0, 1) is the proportion of a deposit that one can recover from early withdrawal, given that the bank has not failed at *t* = 1. Similarly, at *t* = 1,

lenders decide whether to sell or buy the diversified notes in the aftermarket. Both depositors' and P2P lenders' decisions at *t* = 1 depend on their observations of private signals.

Provided an early withdrawal of savings deposit (or loan) is requested, the bank should liquidate its long-term financial claims with discount, which generates an expected cash flow of *θ* multiplied by the discount factor <sup>1</sup> <sup>1</sup>+*<sup>λ</sup>* where *λ* is the discount rate. (This can be regarded as the haircut rate of the financial products in the money market. During the repo run in the last global financial crisis of 2007–2008, the average haircut on bilateral repo transactions, except for U.S. Treasuries, rose from zero in early 2007 to almost 50% at the peak of the crisis in late 2008 [37].) We assume <sup>1</sup> <sup>1</sup>+*<sup>λ</sup>* ≤ *q*, which means that a bank's early liquidation of long-term assets is costlier than a depositor's early liquidation of short-term assets or deposits. If the bank's ex-post cash flow at *t* = 2 (i.e., which is the sum of the recovered loan and the value of its remaining assets) is less than the amount to be redeemed, bank failure occurs.

In case of lending via P2P lending platforms, the notes are assumed to be traded within the associated aftermarkets where lenders are randomly matched and trade their notes; if lender *i* and *j*, whose signals satisfy *si* > *sj* without loss of generality, are matched, then *j* sells her/his (portfolio of) notes to *i* at *sj*. (In fact, only a fraction of the notes and not the whole portfolio would be traded in the aftermarkets. This assumption helps to avoid theoretical problems with the measurement from abusing the law of large numbers. This setting also implies that no speculative trade in the sense of Harrison and Kreps [38] would occur.) Thus, the traded notes would be "discounted" proportional to the risk or standard deviation. (For example, if we assume that noise *<sup>j</sup>* follows *N*(0, *σ*2), the amount of the discount can be approximated as *σ*/ <sup>√</sup>3.) Note that based on our assumptions, which limit the effects of trades within associated P2P lending platforms, transactions in aftermarkets do not have any spillover effect in the banking sector.

At *t* = 2, if the bank is solvent, it delivers the promised amount *F* + *D* (and *F*- + *D*- ), and *F* (and *F*- ) otherwise. For investments via P2P lending platforms, the cash flow generated from loans (excluding non-performing loans) is recovered for an individual lender *i*.

#### *3.3. Borrowers' Type and Market Segmentation*

Although P2P lending platforms seek to maximize the number of matches between lenders and borrowers, we argue that P2P lending platform eventually match loans only for borrowers in Group 1, and segment the loan market, based on the empirical findings by De Roure et al. [23], Tang [24]. (In this study, we combined the finding from De Roure et al. [23]—P2P lenders tend to be bottom fishers and P2P loans are riskier, with that from Tang [24]—P2P lending platforms are essential substitutes for banks, as a stylized fact for our setting. We also want to note that [39] observe a similar kind of vertical separation of the hospitality market after the entry of Airbnb. In a separate study, we investigated a condition for this type of endogenous market segmentation to occur. The key idea is that when the loan supply from banks fails to clear the loan demand due to external conditions (e.g., prudence regulation and credit rationing), the P2P lending platform can choose to either (i) compete in both market segments with a single rate, or (ii) let banks cover *everyone* in the high-credit market and capture the bigger excess loan demand as well as compete only in the low-credit market. In some cases, choosing the latter is better for P2P lending platforms.) Henceforth, we use Market 1 to denote the market segment for low-credit borrowers (Group 1) and Market 2 to denote high-credit borrowers (Group 2). When the loan market is segmented, the gross rate of return from a loan in Market 2, denoted by *r*2, is supposed to be lower than that in Market 1, denoted by *r*1, namely *r*<sup>1</sup> > *r*2.

Similar to the early withdrawal of unprotected deposits, the P2P lending notes can be traded at *t* = 1 with a discount proportional to the standard deviation of private signal *σ*. Because we assume that investors would not switch between banks and P2P platforms at *t* = 1, (For example, without this assumption, depositors of unprotected bank deposits could withdraw early and purchase the notes at *t* = 1.) trades in the aftermarkets do not have any influence on the banking sector. Table 1 summarizes the investment characteristics classified by institutional settings, timing, decision, and cash flows.


**Table 1.** Timing, decision, and cash flows for different institutional settings.

#### *3.4. Cash Flow from Loans*

We adopt the result of the cash flow model by Freixas and Ma [11] which derives the probability of success according to the type of borrower *b* as follows

$$\Pr(b) = \begin{cases} 1 & \text{if } \quad b \in [1/(\pi - r), B] \\ \quad b(\pi - r) & \text{if } \quad b \in (0, 1/(\pi - r)). \end{cases}$$

Note that there exists a unique threshold type of entrepreneur that determines whether a loan is risk-free or risky. Assume that *b* follows a uniform distribution *U*(0, *B*] and that *B* is sufficiently high so that loans would be riskless for a large proportion of borrowers. In the same loan market, (or market segment), banks and P2P lending platforms are assumed to treat borrowers equally. That is, differentiating the rate on loans for each type of borrowers is impossible. The ratio of risk-free to total loans is derived as

$$a \equiv \left( B - 1/\left( \mathbf{x} - r \right) \right) / B \;= 1 - 1/\left( B(\mathbf{x} - r) \right). \tag{1}$$

The greater the value of *α*, the more secure is the loan portfolio.

Equation (2) is the first derivative of *α* with respect to *r*, represented as

$$
\partial \mathfrak{a} / \partial r = -1 / (B(\mathfrak{x} - r)^2) < 0,\tag{2}
$$

implying that as the exogenous gross rate of return on loan *r* increases, the proportion of risk-free loans *α* decreases.

Let *γ* be the ratio of *non-performing* loans to risky loans. From a unit loan provided to borrowers, the total cash flow generated referred to as *θ*, can be expressed as

$$
\theta \equiv ar + (1 - r)[0 \cdot \gamma + r \cdot (1 - \gamma)] \, = \, r - (1 - a)r\gamma. \tag{3}
$$

We assume that *γ* follows a uniform distribution *U*[0, 1]. (Freixas and Ma [11] show that *γ* follows a uniform distribution between 0 and 1 if entrepreneurs know the exact value of *b*; moreover, *b* follows a uniform distribution (0, *B*]; and their utility functions are a specific form of the quadratic function. However, we use the result as an exogenous condition due to the symmetric uninformedness of entrepreneur types in our model, and the negative, deterministic correlation between entrepreneur type and the gross rate of return from a project.) Then, the expected value of the ratio of the non-performing loan to the risky loan, *E*(*γ*), is 1/2. (Consequently, the volatility of the cash flow is determined only by the ratio of risk-free loans, *α*.) and the expected gross rate of return from loans, which is also the expected gross rate of return from investment via P2P lending platforms, is (1 + *α*)*r*/2.

Finally, it should be noted that not all of the entrepreneurs would be able to get a loan from banks regardless of their types without P2P lending for the following reasons. First, the canonical credit rationing problem e.g., ref. [40] can occur: all type of borrowers want to get a loan with a given gross rate of return less than *rL*, and some of them are even willing to pay higher rates, but the loan supply is less than the demand. Second, we have assumed that the amount of deposits is not sufficient to cover the entire demand for loans. Note that only one of these two constraints is binding.

#### **4. Comparison of Risks**

Following Rochet and Vives [10] and Freixas and Ma [11], we consider only speculative runs by depositors and treat (in)solvency risk and (il)liquidity risk separately. We first use the case wherein only banks exist as a benchmark and compare the result with that of the segmented market case with both banks and P2P lending platforms; furthermore, we investigate how individual risks and total credit risk change under different circumstances.

#### *4.1. Insolvency Risk*

#### 4.1.1. Benchmark: Only Banks Exist

Insolvency occurs if the ex-post cash flow *θ* from the unit loan is smaller than the total amount of bank deposits *F* + *D* that must be paid back at *t* = 2. That is if inequality condition,

$$
\theta \,\, = \, r - (1 - a)r\gamma \ge F + D\_\prime \,\, \tag{4}
$$

is *not* satisfied, the bank can be considered as insolvent. From Equation (4), the critical level of the loan loss for determining solvency, *γSR*, is derived as

$$
\gamma\_{SR} = (r - (F + D)) / ((1 - a)r). \tag{5}
$$

Note that *γ* follows a uniform distribution in [0, 1]. The (in)solvency risk, or the probability that a bank faces the solvency problem, is denoted by *ρSR* and derived as *ρSR* ≡ 1 − *γSR*. By simple rearrangement in terms of the market gross rate of return from the loan, this is expressed as

$$
\rho\_{SR} \equiv 1 - \gamma\_{SR} = (\mathbf{F} + \mathbf{D} - ar) / (1 - a)r \tag{6}
$$

#### 4.1.2. Co-Existence of Banks and P2P Lending Platforms

Now, we investigate the segmented market case of banks and P2P lending platforms co-existing in the low-credit market segment (Market 1) while only banks exist in the high-credit one (Market 2). Unlike a bank, a P2P lending platform itself does not face the problem of insolvency, as the lenders directly take on the default risk of their loans. The cash flow condition for the bank's soundness is now represented as

$$
\hat{\theta} = \frac{\beta \hat{B}}{B} [r\_1 - (1 - a\_1)r\_1 \gamma] + \frac{B - \hat{B}}{B} r\_2 \ge F' + D' \tag{7}
$$

where *β* is the share of applicants for whom banks provide a loan in Market 1, which satisfies

$$\frac{r\_2}{r\_1} = \frac{B - \beta \hat{B}}{B - \hat{B}} \frac{1 + \omega\_1}{2}$$

such that the expected cash flows from both a unit loan via banks and via P2P lending are the same. Note that *<sup>α</sup>*<sup>1</sup> = (*B*<sup>ˆ</sup> <sup>−</sup> 1/(*<sup>x</sup>* <sup>−</sup> *<sup>r</sup>*1))/*B*<sup>ˆ</sup> <sup>&</sup>lt; *<sup>α</sup>*, and *<sup>α</sup>*<sup>2</sup> <sup>=</sup> 1.

From Equation (7), in the segmented market case, the critical level of loan loss, denoted by *γ*ˆ*SR*, is derived as

$$\hat{\gamma}\_{SR} = \frac{\beta r\_1 + (B - \hat{B})r\_2/\hat{B} - B(F' + D')/\hat{B}}{\beta (1 - \alpha\_1) r\_1}. \tag{8}$$

The change in the bank's profit from the benchmark is represented by

$$\delta(r - (F + D)) = \hat{r} - (F' + D') \tag{9}$$

where *r*ˆ = *<sup>B</sup>*<sup>ˆ</sup> *<sup>B</sup> <sup>β</sup>r*<sup>1</sup> <sup>+</sup> (*B*−*B*ˆ) *<sup>B</sup> r*2, which is supposed to be less than *r* due to competition, represents the bank's gross rate of return, or revenue, on unit loan from both market segments, and *δ*(< 1) reflects the decrease in the bank's loan–deposit margin compared with the benchmark case. Given the assumptions and Equation (8), the following inequality

$$\gamma\_{SR} = \frac{\delta(r - (F + D))}{\hat{B}/B(1 - a\_1)\beta r\_1} = \frac{B\delta r(1 - a)}{\hat{B}\beta r\_1(1 - a\_1)}\gamma\_{SR} = \frac{\delta r(\mathbf{x} - r\_1)}{\beta r\_1(\mathbf{x} - r)}\gamma\_{SR} < \gamma\_{SR}$$

is sufficiently satisfied if *β* is not sufficiently smaller than *δ*, implying that the impact of P2P lending on banks' profit reduction is greater than that on their market share in the low-credit segment.

To facilitate comparison with the benchmark results, suppose that *F* + *D* = *F*- + *D*- = *R*, which means that the future value of the normalized deposit portfolio in the benchmark case and that in the segmented market case are the same. Note that, in this case, the amount of the protected bank deposit, denoted by *F*- , is greater than that in the benchmark case (i.e., *F*- > *F*) due to the lower rate of return on loan and, consequently, savings deposits. Then, from *r*ˆ − (*F*- + *D*- ) <sup>&</sup>lt; *<sup>r</sup>* <sup>−</sup> (*<sup>F</sup>* <sup>+</sup> *<sup>D</sup>*) + *<sup>B</sup>*ˆ(*<sup>β</sup>* <sup>−</sup> <sup>1</sup>)*r*1/*B*, Equation (9) leads to the following inequality

$$(1 - \delta)(r - (F + D)) > (1 - \beta)r\_1 \hat{B}/B.)$$

Given that *Br*<sup>ˆ</sup> 1/*<sup>B</sup>* <sup>&</sup>gt; 1/2, and *<sup>r</sup>* <sup>−</sup> (*<sup>F</sup>* <sup>+</sup> *<sup>D</sup>*), which is the loan–deposit spread, would not be greater than 1/2 in any reasonable case, 1 − *δ* must be greater than 1 − *β*, or *β* > *δ*. Thus, given that *F* + *D* = *F*- + *D*- = *R*, the insolvency risk of a bank, *ρ*ˆ*SR* = 1 − *γ*ˆ*SR*, is greater than that in the benchmark, *ρSR*, which leads to the following proposition.

**Proposition 1.** *When a loan market is segmented by borrowers' capability and when P2P lending platforms and banks operate simultaneously in the low-credit segment, an individual bank's insolvency risk is greater than that in the benchmark case.*

#### *4.2. Liquidity Risk*

#### 4.2.1. Benchmark: Only Banks Exist

We now examine the case of bank failure due to insufficient liquidity caused by depositors' early withdrawal. This situation can occur when a bank is forced to liquidate its long-term assets due to the early withdrawal of many depositors at *t* = 1, even though in the absence of early withdrawals, the bank would not face a soundness problem and it could repay the debt sufficiently at *t* = 2.

Let *q* be the proportion of a deposit that one can recover from early withdrawal at *t* = 1, and let *λ*, satisfying 1/(1 + *λ*) < *q* as assumed above, be the discount rate applied to a bank's (long-term) loan sold at *t* = 1, which would generate cash flow *θ* without the early withdrawal request. The condition that the liquidity problem never occurs at *t* = 1 is expressed as

$$\theta/(1+\lambda) > qD\_{\prime}$$

implying that the present value of cash flow *θ* discounted by 1 + *λ* is greater than the highest possible recovered amount in early withdrawal.

Let *L* be the ratio of depositors who take early withdrawals, or run, at *t* = 1. In this case, the level of *L* at which the bank can survive at *t* = 1 but experiences failure at *t* = 2 is determined by the following inequality

$$(1 - L)D > \theta - F - L(1 + \lambda)qD. \tag{10}$$

The liquidity risk arises when the deposit to be returned at *t* = 2 is greater than the remaining liquidity from the cash flow *θ*, deducted by the protected deposit *F*, and by the liquidity that has flowed out due to early withdrawal at *t* = 1, *L*(1 + *λ*)*qD*. The probability of each depositor's belief that a bank will *not* fail at *t* = 2 due to illiquidity is the probability that *L does not satisfy* Equation (10), which is

$$\Pr\left(L \le \frac{\theta - F - D}{[(1 + \lambda)q - 1]D} = L^\*\right). \tag{11}$$

Whether a depositor *i* chooses to withdraw early at *t* = 1 or not is influenced by his/her private signal, *si* = *θ* + *i*, and his/her forecasts about other depositors' behavior, which are reflected by *L*. Note that depositor *i*'s strategy is influenced by other depositors' *belief* on *L* upon observing his/her private signal *si*. Then, ultimately, this depositor must consider the *belief on other depositors' beliefs*, which violates the common knowledge assumption and corresponds with the setting of a global game [28].

Following convention, we first apply the *Laplacian property* [28] to our setting: any investor *i*'s *belief* about the ratio of early withdrawal *L* follows *U*[0, 1]. Depositors are supposed to use the switching strategy, which is proven to be optimal if the Laplacian Property is satisfied [28]. If depositor *i* chooses a switching strategy, he/she chooses either to run if the signal is below a certain threshold level or to wait until maturity.

The threshold level of the cash flow for an early withdrawal decision, referred to as *s*∗, is determined when the expected value of the early withdrawal at *t* = 1 equals that of the maturity withdrawal at *t* = 2, or

$$qD = \Pr(\text{survive at } t = 2 | \text{s } = s^\*) \cdot D\_{\text{est}}$$

given that Pr(survive at *t* = 1|*s* = *s*∗) = 1, or *αr* > (1 + *λ*)*qD*. Given that the Laplacian Property is satisfied, in a Perfect Bayesian Equilibrium, the likelihood of other investors' decision to run would behave like a random variable drawn from the uniform distribution of *U*[0, 1]. (Moving away from the switching point, this belief may not actually be uniform. However, according to Morris and Shin [28], as long as the payoff advantage of running on the bank is decreasing in *θ*, the Laplacian action coincides with the equilibrium action.) From the Equation (11), we can infer that

$$\Pr(\text{survive at } t = 2 | s = s^\*) = \Pr(L \le L^\*) = (\theta - F - D) / ([(1 + \lambda)q - 1]D)$$

as *L* follows *U*[0, 1]. Note that the probability of solvency at *t* = 2 is continuous. Thus, the expected payoff from waiting is also continuous and monotone decreasing in *L*, and thus, monotone increasing in *θ*. The threshold cash flow level *θ*∗, under which a bank run may occur, is derived as

$$
\theta^\* = F + D + q[(1+\lambda)q - 1]D.\tag{12}
$$

Note that *s*<sup>∗</sup> is *uniquely* determined, *s*<sup>∗</sup> = *θ*∗. Let *θ* = *F* + *D*, and ¯ *θ* = *F* + (1 + *λ*)*qD*, which satisfy *θ* < *θ*<sup>∗</sup> < ¯ *<sup>θ</sup>*. Then, a depositor has to run for any *<sup>L</sup>* <sup>∈</sup> [0, 1] if *<sup>θ</sup>* <sup>&</sup>lt; *<sup>θ</sup>* and wait if *<sup>θ</sup>* <sup>&</sup>gt; ¯ *θ*, which means that the *limit dominance property* [28] is satisfied. Thus, we can conclude that our setting of the global game satisfies all the required properties in Proposition 2.1 of Morris and Shin [28] for the existence of a unique switching strategy *s*∗ = *θ*∗. (While not incorrect, the explanation of the global game model in Freixas and Ma [11] uses the setting of Carlsson and Van Damme [27], where the state variable is an unbounded real number (i.e., *θ* ∈ **R**) and neither upper nor lower dominance exists.)

Let *μ* = 1 + *q*[(1 + *λ*)*q* − 1] > 1 for simplicity of notation. If the bank becomes illiquid, despite it being solvent at *t* = 2, and a run on the bank would occur, the range of cash flow would be

$$F + D < \theta \le F + \mu D.$$

Similar to *ρSR*, we can define the probability of (il)liquidity risk, *ρLR*, as

$$
\rho\_{LR} = \frac{(\mu - 1)D}{(1 - a)r}.\tag{13}
$$

The total credit risk of a bank, *ρTR* = *Pr*(*θ* < *θ*∗), is the sum of the insolvency risk *ρSR* and the illiquidity risk *ρLR*, which is derived as

$$
\rho\_{TR} = \frac{(\text{F} + \mu D) - ar}{(1 - a)r}.\tag{14}
$$

4.2.2. Co-Existence of Banks and P2P Lending Platforms

Again, we investigate the segmented market case, in which P2P lending platforms enter and operate in the low-credit market segment (Market 1). Considering that loans in the high-credit segment (Market 2) are supposed to be riskless and early withdrawal is not likely to occur, we focus only on Market 1.

Note that the trades of notes in the associated aftermarket at *t* = 1 do not influence depositors outside P2P lending platforms. Then, we can adapt Equation (10), which describes the condition for the illiquidity problem for an otherwise solvent bank, for the segmented market case as

$$(\hat{B}/B)(1-L)D' \ge \hat{\theta} - F' - L(\hat{B}/B)(1+\lambda)qD'.$$

The threshold cash flow that makes early withdrawal and waiting indifferent without actual insolvency, ˆ *θ*∗, is then derived as

$$\hat{\theta}^{\*} = F' + (\hat{B}/B)(1 + q[(1+\lambda)q - 1])D' = F' + \mu(\hat{B}/B)D'.\tag{15}$$

Given the assumptions, we find that the cash flow threshold level ˆ *θ*∗ is lower than *θ*∗, derived from the benchmark case. The liquidity risk in the segmented market case is derived as

$$\rho\_{LR} = \frac{F' + \mu(\mathring{\mathcal{B}}/\mathcal{B})D' - (F' + D')}{(\mathring{\mathcal{B}}/\mathcal{B})(1 - u\_1)r\_1} = \frac{(\mu - (\mathcal{B}/\mathring{\mathcal{B}}))D'}{(1 - u\_1)r\_1} \tag{16}$$

In the worst case, the cash flow would be generated only from risk-free loans. Given that *B* > *B*ˆ, *D*-< *D*, *α*<sup>1</sup> < *α*, and *r* < *r*1, we derive the following proposition.

**Proposition 2.** *The probability of a bank's (il)liquidity risk is lower when the market is segmented by borrower types and banks compete with P2P platforms than that in the benchmark case, or when ρ*ˆ*LR* < *ρLR.*

As in the benchmark case, the total credit risk of a bank in the segmented market case, *ρ*ˆ*TR* = Pr(ˆ *θ* < ˆ *θ*∗), the sum of the insolvency risk, *ρ*ˆ*SR*, and the illiquidity risk, *ρ*ˆ*LR*, is derived as

$$\begin{split} \boldsymbol{\rho}\_{TR} &= \boldsymbol{\rho}\_{SR} + \boldsymbol{\rho}\_{LR} = 1 - \frac{\delta \mathcal{B}(\boldsymbol{r} - (\boldsymbol{F} + \boldsymbol{D}))}{\beta \hat{\mathcal{B}} (1 - a\_1) r\_1} + \frac{(\mu - (\boldsymbol{B}/\hat{\mathcal{B}})) \boldsymbol{D}'}{(1 - a\_1) r\_1} \\ &< 1 - \frac{\mathcal{B}(\boldsymbol{r} - (\boldsymbol{F}' + \boldsymbol{D}'))}{\hat{\mathcal{B}} (1 - a\_1) r\_1} + \frac{(\mu - 1) \boldsymbol{D}'}{(1 - a\_1) r\_1} = \frac{(1 - a\_1) r\_1}{(1 - a\_1) r\_1} - \frac{\mathcal{B}(\boldsymbol{r} - (\boldsymbol{F}' + \boldsymbol{D}'))}{\hat{\mathcal{B}} (1 - a\_1) r\_1} + \frac{(\mu - 1) \boldsymbol{D}'}{(1 - a\_1) r\_1}, \end{split} \tag{17}$$

by assuming *β* > *δ*. The right-hand side of Equation (17) is less than *ρTR* = (*F* + *μD* − *αr*)/((1 − *α*)*r*) if the inequality

$$\frac{\hat{B}}{B}(1-\alpha\_1)r\_1 + F' + D' - r + \frac{\hat{B}}{B}(\mu - 1)D' < \frac{r\_1(\varkappa - r)}{r(\varkappa - r\_1)}(F + \mu D - \varkappa r)$$

is satisfied, which can be rewritten as

$$\frac{r\_1}{B(\mathbf{x} - r\_1)} + F' + D' - r + \frac{\mathcal{B}}{B}(\mu - 1)D' < \frac{r\_1(\mathbf{x} - r)}{r(\mathbf{x} - r\_1)}(F + D - r + (\mu - 1)D) + \frac{r\_1}{\hat{B}(\mathbf{x} - r\_1)}\tag{18}$$

Given A3, *D*- < *D* and *B*ˆ < *B*, we can conclude that the inequality condition of Equation (18) is always satisfied, which leads to Proposition 3

**Proposition 3.** *Given the assumptions, the total credit risk of a bank is lower when the loan market is segmented by borrower types and P2P lending platforms operate in the low-credit market segment than that in the benchmark case.*

The insolvency risk rises when the loan market is segmented by credit ratings because banks as well as P2P lending platforms charge higher interest rates in the low-credit segment than they would in the benchmark case, which leads borrowers to choose high-risk, high-return projects, as in Boyd and De Nicolo [15]. In contrast, the decrease in illiquidity risk occurs because the ratio of protected deposits in a bank's portfolio would be higher in the segmented market case. Then, the effect of lowering the cash flow threshold that would trigger a bank run would dominate the effect from the increase in the ratio of risky loans in the low-credit market segment. Note that our model is mainly designed for analyzing the risks of individual institutions; it is not suitable for contagion or systemic risk. Still, our result implies that expecting a minimal impact from P2P lending on contagion and systemic risk in the banking sector is not overstretching. (Freixas and Ma [11] used the same global game approach for the analysis of system risk with strong assumptions about the contagion; it is a simultaneous, non-sequential event that affects only the discount rate.)

Note that our results are mainly derived from the assumptions that (i) P2P lending platforms operate only in the segmented market for borrowers with low-credit ratings while banks operate in both the low- and high-credit market segments; (ii) lending is direct and loans are treated as split notes (non-secured mini-bonds); (iii) only lenders can trade split notes in the associated aftermarket.

#### **5. Extension**

#### *5.1. Competition Effects*

Two common effects of competition on the soundness of banks are (i) the risk-shifting effect, which is the result of lower risk-seeking tendencies among borrowers as loan rates decline with intensified competition, and (ii) the buffer-reduction effect, which is the lowered capacity of banks to absorb loan loss as loan–deposit margins decline with intensified competition and deteriorating profitability. The effect of competition on the soundness of banks mainly depends on which effect dominates. As the benchmark for this discussion, we again adopt the results of Freixas and Ma [11], which we summarize as follows.

Considering that the risk-free loan ratio *α* is also a function of the gross rate of return from a loan *r*, the first derivative of the benchmark insolvency risk *ρSR* is as follows:

$$\frac{\partial \rho\_{SR}}{\partial r} = \frac{-1}{(1-a)^2 r^2} \frac{\partial a}{\partial r} (r^2 - \mathfrak{x}(F+D)). \tag{19}$$

Equation (2) shows that *α* is monotonically decreasing in *r*. Thus, the insolvency risk *ρSR* increase in *<sup>r</sup>*, or declines as the competition intensifies, only when *<sup>r</sup>*<sup>2</sup> − *<sup>x</sup>*(*<sup>F</sup>* + *<sup>D</sup>*) > 0, which is a necessary and sufficient condition. In other words, given that all other conditions remain the same, competition in the loan market initially reduces banks' rates of return on loans and contributes to the reduction of insolvency risk. However, once the rate falls below a threshold (or *<sup>r</sup>*<sup>2</sup> − *<sup>x</sup>*(*<sup>F</sup>* + *<sup>D</sup>*) < 0), it leads to decreased buffering capital and increased insolvency risk. The first derivative of the illiquidity risk *ρLR* with respect to *r* in the benchmark case is as follows:

$$\frac{\partial \rho\_{LR}}{\partial r} = (\mu - 1) \frac{-D}{(1 - a)^2 r^2} \left( \frac{\partial (1 - a)}{\partial r} r + (1 - a) \right) < 0. \tag{20}$$

As competition intensifies, the rate of return on loan *r* decreases and, consequently, the illiquidity risk increases.

Finally, from Equation (14), we conclude that the total credit risk *ρTR* increases with respect to *<sup>r</sup>* if and only if *<sup>r</sup>*<sup>2</sup> − *<sup>x</sup>*(*<sup>F</sup>* + *<sup>μ</sup>D*) > 0. In other words, under the threshold level, *<sup>r</sup>*˜ = *x*(*<sup>F</sup>* + *<sup>μ</sup>D*), the risk-shifting effect no longer dominates the buffer reduction effect, or competition causes the total credit risk to be higher.

Now, we examine the segmented market case. Suppose the rate of return on a loan in Market 2, *r*2, is fixed, and we focus on the rate of return on a loan in Market 1, *r*1, and the competition effects in the low-credit market segment between banks and P2P lending platforms. Equation (8) implies that *γ*ˆ*SR* monotone decreases in *r*<sup>1</sup> in a way that is similar to the benchmark case. That is, the insolvency risk of a bank, *ρ*ˆ*SR* = 1 − *γ*ˆ*SR*, decreases, and competition reduces the insolvency risk until *r*<sup>1</sup> reaches the threshold level. However, the risk then increases if the interest rate further decreases below the threshold level. From Equation (16), we conclude that competition in Market 1 reduces the illiquidity risk of a bank.

The effect on a bank's total credit risk is similar to that observed in the benchmark case. Instead of the exact threshold rate of return from a loan, we use the approximation derived from Equation (18) to determine the threshold level as

$$r\_1^2 > \varkappa\_1(F' + (1 + \hat{B}/B(\mu - 1))D').$$

Given that *x*<sup>1</sup> > *x*, and *F*- + (<sup>1</sup> <sup>+</sup> *<sup>B</sup>*ˆ/*B*(*<sup>μ</sup>* <sup>−</sup> <sup>1</sup>))*D*- < *F* + *μD*, whether the threshold value of *r*1, *r*˜ <sup>1</sup> = *x*1(*F*- + (<sup>1</sup> <sup>+</sup> *<sup>B</sup>*ˆ/*B*(*<sup>μ</sup>* <sup>−</sup> <sup>1</sup>))*D*-), is greater or not than that of the benchmark case *r*˜ depends on the values of these variables.

Proposition 4 shows that the threshold rate of return on a loan in Market 1 is likely to be lower than that in the benchmark case. That is, the risk-shifting effect—the upside—is likely to dominate the buffer-reduction effect—the downside—for a lower level of threshold rate in the segmented market case than in the benchmark case.

**Proposition 4.** *Given F* + *D* = *F*- + *D*- *, the threshold rate of Market 1 in the segmented market case, r*˜ 1*, is lower than r, the threshold rate in the benchmark case (i.e.,* ˜ *r*˜ <sup>1</sup> < *r).* ˜

**Proof.** We want to show that *x*1(*F*- + (<sup>1</sup> <sup>+</sup> *<sup>B</sup>*ˆ/*B*(*<sup>μ</sup>* <sup>−</sup> <sup>1</sup>))*D*- ) < *x*(*F* + *μD*). Given that *x*<sup>1</sup> ≈ *x*, we can rewrite the inequality as

$$F' - F' = D - D' < \mu D - D' - \hat{B}(\mu - 1)D'/B\_{\nu}$$

which leads to

$$
\triangle(\mu - 1)D'/B < (\mu - 1)D.
$$

As *B*ˆ/*B* < 1 and *D*-< *D*, we conclude that the inequality holds true.

Proposition 4 also implies that competition is more likely to reduce the combined credit risk in the segmented market case than in the benchmark case.

#### *5.2. Implication for the Separation of P2P Lending and Banking*

So far in our analysis, we have strictly limited bank participation in P2P lending and assumed that only individual lenders can buy split notes and trade them in an associated aftermarket. Given the stringent regulations that prohibit shadow banking that includes P2P lending, it is doubtful that P2P lending platforms would be allowed to take deposits or mediate loans for borrowers with high credit ratings. In contrast, banks could use their subsidiaries and invest in and/or trade payment-dependent notes via P2P lending platforms, (For example, as stated in Vallee and Zeng [25], financial institutions like banks could combine their information with that of P2P lending platforms and use this higher-quality information to purchase split notes) or they could even operate their own P2P lending platforms.

Once banks begin purchasing split notes via P2P lending platforms, they would replace the "loans" that the banks would otherwise provide. These could also be used as another source of interim liquidity in the aftermarket, which would be less conspicuous to monitoring authorities than the money market. From the analysis of competition effects in the previous subsection, however, we expect that reduced competition in the low-credit market segment, along with the lax separation of P2P lending and banking, would lead to a higher rate of return on loan *r*1. It would also increase an individual bank's liquidity and total credit risk.

Another possibility is the banks' direct participation in P2P lending. From the perspective (and within the limitations) of our model, unlike banks purchasing split notes via P2P lending platforms, competition in the low-credit market segment (Market 1) would not decrease, although banks would now hold more payment-dependent split notes. If banks choose to buy more notes in the aftermarket after observing their private signals, their liquidity reserves would decrease, which would lead to a higher rate of the haircut in the money market, as suggested by the higher discount rate *λ*. If a bank chooses to sell more notes in the aftermarket, the sales themselves would decrease the expected value of the split notes. This would be bad news for the bank, which could, in turn, lead to an increase in the probability of a run on an otherwise solvent bank. In all, allowing banks to participate in P2P lending would counter the purpose of Basel III, which requires stronger prudential regulation of bank liquidity.

#### **6. Concluding Remarks**

Since the global financial crisis of 2007–2008, direct finance via P2P lending has emerged and rapidly grown as a new vehicle for borrowers without high credit ratings, especially among households and small- and mid-sized enterprises. The growth of P2P lending may have two countervailing effects on banking. One is that banks are less exposed to risky loans and interim liquidity needs, which tend to be better served by P2P lending platforms and their associated aftermarkets. The other is that banks must compete against P2P lending platforms, reducing the liquidity buffers that they need to maintain solvency.

In this study, we investigated the effects of P2P lending on major bank risks: (in)solvency risk and (il)liquidity risk. Specifically, considering the characteristics of direct investments through P2P lending platforms, we compared two cases: (i) the benchmark case, in which only banks exist in a single loan market, and (ii) a segmented market case in which the loan market is segmented by borrowers' creditworthiness, P2P lending platforms operate only in the low-credit segment, and banks operate in both low-and high-credit segments. For the segmented market case, as compared with the benchmark one, we find that while banks' insolvency risk increases, their illiquidity risk decreases such that their overall risk also decreases.

We also find that competition between banks and P2P lending platforms is more likely to reduce the combined credit risk, the sum of (in)solvency, and (il)liquidity risks, in the segmented market case than in the benchmark one. This result implies that once banks begin to participate in P2P lending either directly or indirectly, it would create an adverse effect on the combined risk because it would lessen the competition in the segmented market case. In all, sustainable P2P lending requires an appropriate differentiation of roles between the banking sector and P2P lending so that P2P lending platforms focus more on borrowers with low-credit ratings, while banks focus more on the high-credit market segment and protected deposits.

To the best of our knowledge, this study is one of the first works, if not the first, to implement a full theoretical analysis of the effects of the competition between P2P lending platform and banks on bank failure risks, specifically in the strand of microeconomic banking literature such as Rochet and Vives [10], Freixas and Ma [11], Goldstein and Pauzner [29].

Note that our results are valid only if P2P lending platforms adhere to more primitive, direct forms of financing (e.g., issuing and circulating payment-dependent notes), without handling shadow deposits, derivatives or secured loans. If these platforms expand their business scope and develop more highly leveraged or complex products strongly linked to and affected by other markets and tradings, the implications of the results would be investigated. This is because our assumption that the effects of aftermarket trades of notes stay within the scope of P2P lending platforms would be no longer valid. Finally, we do not fully examine the strategic behaviors of P2P lending platforms in this study. Apart from filling this gap, future studies can (i) empirically investigate how P2P lending platforms affect bank risks under different regulatory frameworks in different economies, and (ii) explore how the role of P2P lending platforms differs from that of banks in advanced economies.

**Author Contributions:** For this research article, contributing roles are as follows: Conceptualization, E.Y. and J.J.; formal analysis, E.Y. and J.J.; funding acquisition, E.Y.; investigation, J.J.; methodology, J.J.; project administration, E.Y.; writing—original draft, J.J.; writing—review and editing, E.Y. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Financial Stability Division of Bank of Korea, National Research Foundation of Korea funded by the Ministry of Education (NRF-2018S1A5A2A01035483), and Fulbright Mid-Career Researcher Scholarship.

**Acknowledgments:** We thank Inho Lee, Takeshi Nakata and, specifically, Yun Woo Park for helpful comments and suggestions.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

#### **Abbreviations**

The following abbreviations are used in this manuscript:

P2P Peer-to-Peer

BDD Bryant–Diamond–Dybvig

#### **References**


© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

*Article*
