Social collateral, soft information and online peer-to-peer lending: A theoretical model

ARTICLE IN PRESS

JID: EOR

[m5G;September 6, 2019;19:9]

European Journal of Operational Research xxx (xxxx) xxx

Contents lists available at ScienceDirect

European Journal of Operational Research journal homepage: www.elsevier.com/locate/ejor

Interfaces with Other Disciplines

Social collateral, soft information and online peer-to-peer lending: A theoretical model Zhengchi Liu a, Jennifer Shang b, Shin-yi Wu c,∗, Pei-yu Chen c a

School of Economics and Trade, Hunan Province Key Laboratory of Logistics Information and Simulation Technology, Hunan University, China Katz Graduate School of Business, University of Pittsburgh, United States c W. P. Carey School of Business, Arizona State University, United States b

a r t i c l e

i n f o

Article history: Received 18 October 2018 Accepted 21 August 2019 Available online xxx Keywords: Finance P2P lending Screening mechanism Social collateral Soft information

a b s t r a c t Traditional credit markets have been criticized as inefficient in allocating credits to borrowers. Powered by advanced Internet technology, online Peer-to-Peer (P2P) lending has emerged as an attractive alternative, especially for small borrowers who have limited assets and are in need of funds urgently. Although several empirical studies have examined factors influencing the micro-level lending outcome, there is a lack of understanding on the overall business model of P2P lending, especially its screening mechanism, and how it helps address the deficiency of the traditional credit market. This paper fills this void. First, we develop a theoretical model incorporating two unique features of P2P lending (soft information and social collateral) and show that in P2P, low-risk borrowers could force high-risk ones off the market under very general conditions. As a result, P2P complements traditional credit markets by serving the unserved (lowrisk borrowers with little assets) in the traditional credit markets. Second, we further identify the critical operational settings for P2P success, and the impacts of these settings on borrowers’ welfare. Overall, our model and analyses not only contribute to the literature by showing analytically that P2P and the traditional credit markets are complementary, but also provide practical guidance to P2P platform managers regarding their platform design to help reshape business strategies and enhance business opportunities. © 2019 Elsevier B.V. All rights reserved.

1. Introduction The advance of information technology has transformed the social and business environment. It has inspired Internet-based crowdfunding which becomes a valuable instrument to provide the public with convenient and quick access to capitals. Online Peerto-Peer lending (hereafter P2P) is a special case of crowdfunding. Formally, P2P refers to unsecured loans, usually not backed up by tangible collaterals, between lenders and borrowers through an online platform that provides all functions necessary to carry out loan transactions directly between lenders and borrowers. Taking advantage of emerging technologies such as cloud computing, big data and social network, P2P utilizes information sharing and searching to facilitate borrower screening. Such a platform eliminates traditional banks’ high overhead and reduces transaction time and cost. As a result, it has the potential to offer lenders higher investment returns and provides borrowers access to lowercost loans.

∗

Corresponding author. E-mail addresses: [email protected] (Z. Liu), [email protected] (J. Shang), [email protected] (S.-y. Wu), [email protected] (P.-y. Chen).

The uncollateralized nature of P2P makes it particularly attractive to small borrowers who lack assets (e.g., individuals and small firms). Without P2P, they might otherwise turn to payday lenders or credit card debt and face high interest rates and stiff fees, as evidenced by subprime lending (Adams, Einav, & Levin, 2009). For instance, Lendingclub.com reports that their borrowers on average save 33% on interest rate, compared to what they would have paid on their outstanding debt and credit cards. P2P is thus quickly gaining popularity among small borrowers, both in developed and developing countries. In fact, it has experienced rapid growth across many countries (e.g., US, UK, Canada, Japan, Italy and India), with slightly different forms since the launch of the first commercial platform, Zopa.com in 2005. The lack of collateral and hard information of the borrowers leads to information asymmetry between the lenders and the borrowers. For all types of credit markets, it is crucial to evaluate borrowers accurately and to allocate credit efficiently based on borrowers’ creditworthiness. Traditionally, credit allocation is controlled by banks as they need and possess the capability to screen borrowers and intermediate capital. However, recent banking crises have exposed the weaknesses of the traditional lending models, particularly in allocating credit to smaller borrowers. Moreover, both empirical evidences and theoretical arguments have shown

https://doi.org/10.1016/j.ejor.2019.08.038 0377-2217/© 2019 Elsevier B.V. All rights reserved.

Please cite this article as: Z. Liu, J. Shang and S.-y. Wu et al., Social collateral, soft information and online peer-to-peer lending: A theoretical model, European Journal of Operational Research, https://doi.org/10.1016/j.ejor.2019.08.038

JID: EOR 2

ARTICLE IN PRESS

[m5G;September 6, 2019;19:9]

Z. Liu, J. Shang and S.-y. Wu et al. / European Journal of Operational Research xxx (xxxx) xxx

that banks do very little screening for small borrowers and rely excessively on collateral, thereby preventing some creditworthy borrowers from obtaining loans. For example, in the United States, approximately 40% of the small business loans and almost 60% of their value are guaranteed and/or secured with personal assets (Avery, Bostic, & Samolyk, 1998). In markets with perfectly competitive banks and complete contracts, banks would offer to screen projects as a service to entrepreneurs. However, if the screening services of banks cannot be enforced by contract, banks that are highly protected by collateral may perform too little screening of the projects. Clearly, collateral and screening are substitutes from the bank’s perspective (Manove, Padilla, & Pagano, 2001). To address this challenge, P2P markets have begun to employ “social collateral”, a feature that allows borrowers to submit their social capital as collateral to enhance the creditability of unsecured loans (Karlan, Mobius, Rosenblat, & Szeidl, 2009). By using social collateral, P2P can maintain loans availability for low-risk borrowers without having to provide a high pledge. At the same time, technological advances have allowed P2P to gather and interpret the self-disclosed information and social behaviors of borrowers (Iyer et al. 2016). All this “soft information” which was not valued before plays a vital role in risk-control of P2P markets now. As an innovative market, the P2P platform’s ability to gather information and screen borrowers is key to the viability of this market. P2P lending has several properties that distinguish it from some previously explored areas in the lending markets. In particular, P2P: • • •

provides unsecured credit loans; assesses risks based on soft information; involves the third-party platform to guarantee transactions.

Given these unique properties, the screening mechanism of P2P on low-risk borrowers without sufficient assets were not addressed by the existing literature. While many empirical studies have identified other factors that affect micro-level lending outcomes, such as borrower characteristics and loan attributes (Collier et al., 2010; Freedman & Jin, 2017; Klafft, 2009; Lee et al., 2012), there is a lack of understanding on the overall business model of P2P lending, especially its screening mechanism, and how it helps address the deficiency of the traditional credit market. For P2P lending, social collateral and soft information are the most important factors in screening unsecured loans, and were not analytically investigated in the existing literature. In this research, we develop an analytical model to examine how the P2P markets help mitigate the inefficiency of the traditional lending markets through social collateral and soft information. We identify conditions under which low-risk borrowers could distinguish themselves from high-risk borrowers. Specifically, the proposed model differs from the existing literature in that it incorporates social collateral and soft information into the P2P lending model, where the borrowers have the opportunity to select a credit contract while lacking collateral. We also compare the equilibrium conditions of the traditional financial markets and the P2P markets, and show how P2P helps address the deficiency of the traditional credit market. In short, the proposed theoretical model answers three research questions: a) How does social collateral impact P2P’s loan screening? b) How does soft information impact P2P’s risk assessment? c) How do the operational variables (e.g., the loan guarantee ratio, the loan dispersion degree, and the number of users in P2P) impact the borrowers’ welfare? Few theoretical works have discussed the attributes of P2P (e.g., De Roure, Pelizzon, & Thakor, 2019 and Gao, Fan, Fang, & Lim, 2018), however we are the only one who incorporates multiple number of lenders funding a loan. Unlike the traditional “one to

one” credit relationship, a borrower in P2P markets usually obtains a loan from a group of lenders (Yum, Lee, & Chae, 2012). That means if the borrower breaks his promise, he will bear substantial losses of social capital. We show that the size of lenders plays a critical role in determining low-risk borrowers’ equilibrium conditions and profits. In the meantime, we model the number of users in the platform. As the existing studies suggest, network links play a role beyond a quality signal by acting as an information conduit for market participants (Iyer et al. 2016; Herzenstein, Sonenshein, & Dholakia, 2011; Lin, Prabhala, & Viswanathan, 2013; Michels, 2012). Essentially, network attributes convey positive or negative information about the borrower’s true repayment probability beyond other observable characteristics. Therefore, the network size can’t be ignored when measuring the impacts of soft information on informal lending. In answering the first research question, we find that P2P can work with the self-selection mechanism where the lenders use interest rate and social collateral as instruments to screen the borrowers’ risk type. The benchmark model of traditional credit market shows that high-risk borrowers squeeze out low-risk lowcollateral borrowers because of adverse selection and credit rationing. However, we identify general conditions of low-risk borrowers to force high-risk ones off the P2P market. In particular, when the scale of users and the loan dispersion are sufficiently large and the borrowers’ social capital is moderately high, the separating equilibrium of P2P can be achieved. This counterintuitive result is driven by the crowd-effect and network-effect which strengthen the restrictive power of social collateral. In addressing the second research question, we find that P2P’s use of soft information helps the lenders evaluate the risks more precisely. Although hard to access to hard information, the lenders can leverage soft information through the “wisdom of crowd” to predict the risks and increase the loans availability for the borrowers, which is consistent with the existing empirical studies (Freedman & Jin, 2017; Ge, Feng, Gu, & Zhang, 2017). Besides, our model also shows that the usage of soft information will loosen the lending constraint for the borrowers by reducing the collateral requirements. With regard to the third research question, we find that P2P platforms’ business strategy can actually impact borrowers’ welfare. Plenty of empirical studies have examined attributes of borrowers or lenders that influence micro-level lending outcome (Collier et al., 2010; Freedman & Jin, 2017; Klafft, 2009; Lee et al., 2012). However, there is a dearth of understanding on the strategic actions of the platforms and how they intermediate the financial transactions. Our model not only confirms the common intuition that the equilibrium interest rate of the borrowers is inversely proportional to the percentage of principals guaranteed by the platforms, we also observe that the borrowers’ equilibrium social collateral is inversely associated with the guarantee ratio, the loans’ dispersion and the number of users, while the equilibrium utility of the borrowers is positively related to these operational variables. Our contributions to the economic theory of P2P lending are threefold. First, we investigate an effective self-selection mechanism to screen borrowers in P2P markets, and analytically discern the conditions for assets-constrained borrowers to obtain loans. Second, we bridge the gap in the literature on how P2P helps mitigate the deficiency of the traditional credit market. Namely, we construct a theoretical model that incorporates the unique features of P2P: i.e. social collateral and soft information. Third, we provide insights by uniquely analyzing the interactions between the P2P’s operational decisions and borrowers’ welfare. The rest of this paper is organized as follows. Section 2 reviews the literature related to our research questions. In Sections 3, we introduce a baseline model of traditional credit markets. Section 4 presents the analysis of the model of P2P markets. Finally, the

Please cite this article as: Z. Liu, J. Shang and S.-y. Wu et al., Social collateral, soft information and online peer-to-peer lending: A theoretical model, European Journal of Operational Research, https://doi.org/10.1016/j.ejor.2019.08.038

ARTICLE IN PRESS

JID: EOR

[m5G;September 6, 2019;19:9]

Z. Liu, J. Shang and S.-y. Wu et al. / European Journal of Operational Research xxx (xxxx) xxx

concluding remarks are made in Section 5. All proofs are given in the Appendix. 2. Background and literature review Our study draws on multiple disciplines including information systems, economics, and operations. We review relevant works to identify critical features of P2P and discuss how our findings contribute to the emerging P2P literature. Financial markets are characterized by information asymmetries between lenders and borrowers. The borrowers’ private information can lead to adverse selection, wherein the lender is faced with the possibility of loss due to risk not factored at the time of lending (Stiglitz & Weiss, 1981). Stein (2002)) divides credit information into two categories: “hard” and “soft”. Hard credit information can be accurately quantified and credibly transmitted, whereas soft credit information cannot. Hard credit information has been used in traditional banking markets to alleviate information asymmetry, and collaterals have been used as an instrument to reduce adverse selection (Bester, 1985). Researchers also argue that traditional collaterals may be substituted by mechanisms such as the strength of the lending relationship. Karlan et al. (2009) suggest that network connections between individuals may be used as “social collateral” to secure informal borrowing. Just as the prospect of losing physical collateral can help secure formal lending, the possibility of losing reputation, respect, and friendships can also help secure the informal transactions. As for Small and Medium-sized Enterprises (SMEs) with insufficient financial data and physical collateral, building a judgmental rating model based on qualitative criteria (e.g., soft information) is very important to finance activities (Angilella & Mazzù, 2015; Guo, Zhou, Luo, Liu, & Xiong, 2015; Hong & Sohn, 2010; Ju & Sohn, 2014). As in other electronic markets, transaction costs are reduced in P2P by eliminating expensive bank overheads, however information asymmetry problems could become more severe than in traditional markets because most individual lenders in P2P lack financial expertise, and the lending experience takes place in a pseudonymous online environment (Ba, 20 01; Klafft, 20 09). How to address adverse selection issue in P2P is a key research topic since the long-term success of this platform depends on lenders’ willingness to provide funds continuously when requests are made by risky borrowers online (Weiss, Pelger, & Horsch, 2010). As electronic interaction spreads, it reveals new information about existing social connections and alters existing economic and social structures (Sundararajan, Provost, Oestreichersinger, & Aral, 2013). The financial markets have shown that unverifiable disclosures by borrowers, and the richness of the dialogues between lenders and borrowers tend to affect the loan outcomes, at least in terms of the likelihood of funding (Herzenstein et al., 2011; Larrimore, Jiang, Larrimore, Markowitz, & Gorski, 2011; Michaels, 2012; Sonenshein, Herzenstein, & Dholakia, 2011). Using emerging information technology, online P2P platform and lenders can easily retrieve soft information from a borrower’s social networks. Although P2P platform and potential lenders may not have access to the detailed credit history of borrowers (hard information), they are able to utilize social network information (soft information) such as the “wisdom of the crowd” (Freedman & Jin, 2017; Lee & Lee, 2012; Yum et al., 2012; Zhang & Liu, 2012). Collier and Hampshire (2010) found that borrowers’ soft information provides important signals for lenders to evaluate borrowers’ trustworthiness, which helps assess borrowers’ default risk and set interest rates. Therefore, the successful utilization of soft information as well as social collaterals can be regarded as key differences between P2P platforms and the traditional financial institutions (e.g., banks). However, the screening mechanism of P2P on low-risk borrowers without sufficient assets by using social collateral and soft

3

information were not analytically investigated in the existing literature. Research on P2P is relatively new, and has largely been empirical and mainly focused on the impact factors on individual loan’s decision. For example, Freedman and Jin (2017)), Lin et al. (2013), Weiss et al. (2010), and Iyer et al. (2016) empirically examine factors contributing to the successful funding of a loan. Our study differs from the literature as we provide a micro view of the P2P markets. We incorporate the unique features of P2P and analytically examine how soft information and social collateral collectively can provide an effective self-selection mechanism for credit screening. We also examine business strategies and provide managerial insights to P2P platforms. We find, despite without financial experts, soft information as well as social collaterals could help address adverse selection and improve credit accessibility to low risk borrowers. Given P2P markets’ ability to make sound inferences and the non-collateral-based lending structure, P2P can be of particular value to small borrowers. We show that P2P complements and adds value to the conventional lending markets. To our knowledge, only a few researches have analytically examined the P2P platforms. For example, Gao et al. (2018) proposed a data-driven investment decision-making framework for the P2P platform by evaluating the return and risk of each individual loan and formulating the investment decision in P2P lending as a portfolio optimization problem with boundary constraints. Our study investigates the P2P platform not only from a different perspective but also contribute to the literature by offering valuable insights into the relationship between the business strategies of the P2P platform and borrowers’ welfare from the view of loan viability. We analytically show why it is crucial that P2P lenders diversify their investments, and why principal guarantee was more popular for platforms in the developing countries than in the developed countries. In short, we not only highlight the screening capability of P2P but also develop insights into the conditions under which P2P will thrive. 3. Traditional credit market – The baseline model To understand if, and how, P2P may help resolve the inefficiency commonly observed in traditional credit markets, we start by presenting a baseline model depicting the traditional credit market. We then introduce P2P markets with their distinctive characteristics and show how they complement traditional credit markets by making credit more accessible to low risk borrowers with insufficient assets. The baseline model developed in this section is motivated by Bester (1985, 1987). We define a bank’s credit contract offer as γ = (R, C )= (interest rate, collateral) and model the traditional credit market accordingly. Effective contracts serve as borrowers’ self-selection mechanism and help lenders differentiate borrowers’ risks. Consider a market with many risk-neutral borrowers. Each borrower undertakes a project which requires an investment L. The borrower applies for a loan from a bank, which requires collateral C; while the borrower owns asset M. Borrower i’s project has Pi probability of success with Xi return; and 1 − Pi probability of zero return. Without loss of generality and for ease of illustration, we consider two risk types: low- and high-risk (i = l, h) borrowers. Like Stiglitz and Weiss (1981), we assume projects differ only on the mean-preserving spread of returns, while the expected returns equal: Pi Xi = X0 with Pl > Ph and Xh > Xl ; Also, X0 > L; and lenders are risk-averse, so under equal returns, loans are granted to lessrisky borrowers. For convenience, the notations necessary for this research is summarized in Table 1. The credit market is assumed to be perfectly competitive. We focus on the case C ≤ (1 + R )L, i.e. borrowers may default when the collateral (valued at C by the borrower) is less than loan repayment

Please cite this article as: Z. Liu, J. Shang and S.-y. Wu et al., Social collateral, soft information and online peer-to-peer lending: A theoretical model, European Journal of Operational Research, https://doi.org/10.1016/j.ejor.2019.08.038

ARTICLE IN PRESS

JID: EOR 4

[m5G;September 6, 2019;19:9]

Z. Liu, J. Shang and S.-y. Wu et al. / European Journal of Operational Research xxx (xxxx) xxx Table 1 Parameters and decision variables in our model. Category

Notation

Description

Traditional Credit Market Variables

L M Pi

Amount of investment required to undertake the project Borrowers’ available asset Probability of project success for borrower i the probability of project success of high risk borrowers. So Ph < Pl Return of borrower i’s project after success Credit contract offered by lenders to borrowers Interest rate Collateral Discount rate of the collateral to lender Expected utility of borrower i Bank’s expected utility from borrower i Total value of social capital for the borrower Social collateral Precision of risk identification by P2P platform Default-risk coefficient Number of users in the platform Number of lenders funding a loan Total fee rate of loans collected by the P2P platform Lender’s expected utility from borrower i in P2P lending % of principals guaranteed by P2P platform

Xi

γ R C

β πi ρi Online P2P Market Variables

Ms S

η μ

n m

ω εi θ

L + RL. If borrower i gets loan and his project succeeds, he repays L + RL to the bank. If his project fails, then the borrower cannot pay back the bank and he loses collateral C. Also, bank’s valuation of the collateral is β C (0 < β < 1); the deposit interest is zero; and funds for loan are sufficient. The expected utility πi of borrower i from contract γ is

πi (γ ) = Pi (Xi − LR − L ) − (1 − Pi )C.

(1)

When borrower i’s project succeeds, the bank receives interest LR. Conversely, the bank keeps collateral C but loses principal L. Thus, the bank’s expected utility ρi from borrower i’s contract γ is

ρi (γ ) = Pi LR + (1 − Pi )(βC − L ).

(2)

Given imperfect information about loan applicants, banks are unable to distinguish borrowers directly. However, they could use contracts with different interest rates and collateral requirements as a screening mechanism. Namely, effective contracts should be incentive compatible. When banks provide contract γl to lowand γh to high-risk borrowers, the contract set {γl , γh } is incentive compatible if πl (γl ) ≥ πl (γh ) and πh (γh ) ≥ πh (γl ). We analyze two cases (M ≥ Cl∗ and M < Cl∗ ). Proposition 1.

1

In the traditional credit markets,

a) When borrowers have sufficient collateral (M ≥ Cl∗ ), banks are able to screen borrowers by using contract set {γl∗ , γh∗ }, where

γ = ∗ h

 

R∗h , Ch∗



 ∗

=

γl∗ = R∗l , Cl =

1

Ph



− 1, 0 ,

 (1−β )(1−Pl )(1−Ph )

Pl (1−Ph )−β Ph (1−Pl )

,



Pl −Ph L Pl (1−Ph )−β Ph (1−Pl )

.

b) When M < Cl∗ , low-risk borrowers will drop out of the market due to adverse selection, whereas only high-risk borrowers will obtain loan. This demonstrates the inefficiency of traditional market in serving low-risk borrowers of limited-asset, which forms the base for our P2P study. In the next section, we show that P2P helps small borrowers access credit, complements and adds value to the traditional lending market.

1

Please refer to Appendix A for proof.

4. Online P2P lending market The premise of P2P lending is that people sign up on the platform (e.g., Prosper.com or Lendingclub.com) as a borrower or as an investor (i.e., lender). A borrower applies for a loan on the platform. If approved, the loan is placed on the platform for investors to fund. In the unregulated, information rich, and egalitarian P2P environment, individuals borrow money from and lend to one another based on good faith. Micro-finance theories argue that social ties can help identify risks, either because soft information can reflect the intrinsic nature of borrower ex ante, or because social capital incentivize borrowers to pay off loan ex post (Yum et al., 2012). Thus, the soft information gathered from and the social capital formed in the online networks can offer a mechanism that allows P2P platforms to screen borrowers. 4.1. Model setup We first describe how we incorporate the distinctive features of P2P in our theoretical model. Next, we examine how the distinctive features of P2P help screen borrowers lacking collaterals. Then we examine the platform strategies of P2P and how the platform design variables in P2P influence borrowers’ economic wellbeing in equilibrium market. 4.1.1. Social collateral The first differentiator of P2P from traditional lending market is that a loan is typically not backed up by a tangible collateral. Characterized by small amount, short-term and unsecured, P2P usually has no recourse for formal legal systems to enforce its contracts. Effective screening of borrowers thus becomes even more important. Ba (2001) and Egli, Ongena, and Smith (2006) establish that transacting parties are motivated to maintain good reputation due to the need of repeated businesses in the future. Such accumulated reputation forms social capital (or trust). If borrowers fail to pay off the loans, P2P platforms can easily downgrade the borrower and disclose the information online. Coupled with Internet’s fast and pervasive spread, defaults on loan may cause borrowers considerable social capital loss. Thus, social capital can serve as social collateral to secure loans, a view shared by Karlan et al. (2009). They believe potential loss of social capital incentivizes borrowers to pay back the loan. When promises are kept, the credit ratings

Please cite this article as: Z. Liu, J. Shang and S.-y. Wu et al., Social collateral, soft information and online peer-to-peer lending: A theoretical model, European Journal of Operational Research, https://doi.org/10.1016/j.ejor.2019.08.038

ARTICLE IN PRESS

JID: EOR

[m5G;September 6, 2019;19:9]

Z. Liu, J. Shang and S.-y. Wu et al. / European Journal of Operational Research xxx (xxxx) xxx

5

Fig. 1. The difference between the traditional and the P2P markets.

of the borrowers increase. We thus incorporate social capital as a unique feature in our P2P model. Besides hard credit score information, P2P borrowers may volunteer social profiles, hopefully to be viewed as a low-risk borrower and acquire low interest rate. Define S as the social capital (in monetary terms) a borrower volunteers when registering on the P2P platform; whereas the total value of social capital the borrower has is Ms (S ≤ Ms ). Conventionally, when borrowers default, they lose collaterals to the bank. In P2P, loans are collectively funded by numerous distinct lenders (Burtch, Ghose, & Wattal, 2013; Zvilichovsky, Inbar, & Barzilay, 2014). If a borrower defaults, he will lose social capital (i.e., trust) S to each of his m lenders, leading to a m × S loss (Fig. 1). In the extreme case, his loss may become n × S, where n is the number of platform members if the default information is effectively transmitted to everyone. Although n × S loss can more easily lead to a separating equilibrium, it may be unrealistic as loan default info may not be completely transparent and perceived the same by P2P lenders and non-lenders. A more realistic and conservative setting (e.g., using m instead of n) is presented below. Borrower i’s expected utility πi under contract γi is:

πi (γ ) = Pi (Xi − LR − L ) − (1 − Pi )mS.

(3)

From πi [Eq. (3)] and πi [Eq. (1)], we can see social capital (S) plays a similar role as tangible collateral (C) in the traditional credit market. 4.1.2. Soft information Conventionally, borrowers’ creditworthiness is assessed by banks on three factors: debt level, years of credit, and payment history (http://www.fico.com/). However, the current credit market has witnessed dramatic changes in data usage (Chui, 2013; Tsai & Wang, 2016). In the Internet era, the lending decisions are based not only on standard (hard) financial data but also on nonstandard (soft) information, drawing on experiences and behaviors. The soft information captures factors difficult to quantify, or quantifiable but not typically used by banks. For example, several institutions (e.g., Lenddo) found that borrowers’ social networks (e.g., LinkedIn or Twitter) can be a good indicator of a person’s creditworthiness and have included such data in borrower’s assessment (Rusli, 2013). Also, sometimes borrowers are asked to write a paragraph explaining why they need the loan. Instead of the content, lenders may care more about grammatical errors, as besides literacy and personality, this shows how the borrowers care and attend to details, which indirectly signals their ability to manage loan use and payment. The aggregated info online can help paint a picture of the borrower’s character. P2P distinguishes itself by its ability to collect and use soft information (e.g., network profiles, reviews and comments)

beyond hard information (e.g., debt level, payment records and credit scores). In the modern era of banking, institutions provide loans to individuals who meet qualification tests, while P2P markets allocate credits by scoring borrowers based on multiple social relationships (Herrerolopez, 2009). This view is consistent with Faia, Paiella and Monica (2017) that P2P lending is indeed an innovation in screening rather than a new service, with machine learning algorithms processing and updating information to provide information signals at low or zero cost. Furthermore, the hierarchy in P2P is entirely flat, which reduces the impediments of using and transmitting “soft” information. In screening small borrowers, the organizational structure of traditional banks does not use much subjective information when evaluating creditworthiness. In relationship banking, Berger and Udell (2002) affirm that flatter structures increase the use of soft information. P2P’s use of soft information helps lenders assess borrowers’ risk more accurately. While potential lenders may not have access to hard information, the ability to leverage soft information through the “wisdom of the crowd” (Freedman & Jin, 2017; Yum et al., 2012) is another key differentiator between the P2P platforms and traditional financial markets. We believe that the relationship between the effectiveness of soft information and the size of P2P networks will change over time. At the beginning, soft information becomes more effective as P2P networks grows in size, because more users interacting with each other will generate more soft information (e.g., chats, comments and reviews) for the platform to assess borrowers’ risk. However, the increase of users eventually leads to the increase of noise information (Shannon, 2006), which makes the effectiveness decrease without the improvement of technology. In other words, there exists an “optimal user size.” Let η be the precision of the P2P platform in differentiating high-risk borrowers from the low ones. We expect η to be an increasing and concave function of the network size n (i.e., number of users in P2P), where 0 ≤ η ≤ 1. The larger the size, the more the soft information and the higher the precision. Without loss of generality, we define:

η = η (n ) = 1 −

1 ( n = 1, 2, 3 . . . ∞). n

(4)

Borrower i’s probability of defaulting the loan (i.e., default-risk) is denoted as 1 − Pi . The default-risk gap between the high- and low-risk borrowers is:

(1 − Ph ) − (1 − Pl ) = Pl − Ph .

(5)

As soft information helps discern borrowers’ risk, we use it to improve the screening precision (η). Given (1 − Pl ) is the lower bound of default risk (by low-risk borrowers), which can be considered as the baseline risk of investment under normal conditions, the degree that the default risk of high-risk borrowers can be

Please cite this article as: Z. Liu, J. Shang and S.-y. Wu et al., Social collateral, soft information and online peer-to-peer lending: A theoretical model, European Journal of Operational Research, https://doi.org/10.1016/j.ejor.2019.08.038

ARTICLE IN PRESS

JID: EOR 6

[m5G;September 6, 2019;19:9]

Z. Liu, J. Shang and S.-y. Wu et al. / European Journal of Operational Research xxx (xxxx) xxx

Fig. 2. P2P platforms’ screening power from soft information.

discerned from low-risk borrowers is (1 − Pl ) + η (Pl − Ph ). Define the default-risk coefficient, μ, as “high-risk over low-risk”:

μ=

(1 − Pl ) + η (Pl − Ph ) 1 − Pl

=1+η

Pl − Ph , 1 − Pl

∂2μ where ∂μ ∂ n > 0, ∂ n2 < 0 and 1 ≤ μ ≤

1−Ph 1−Pl .

(6) Essentially, μ indicates

the screening power of the P2P platform and signals how much more likely a high-risk borrower will default compared to a lowrisk borrower. μ = 1 implies no screening power (η = 0) and highrisk borrowers cannot be discerned from low-risk borrowers. Note that μ could change over time according to the updated soft information accumulated over time. Iyer et al. (2016) empirically verify that the P2P market can predict a borrower’s chance of default with 45% more accurate than borrower’s exact credit score. Fig. 2 shows the relationship between screening power μ and the netP −P work size n. Given μ = 1 + (1 − 1n ) 1l −Ph (from Eqs. (4) and 6), μ becomes

1−Ph 1−Pl

l

when n is large (i.e., η = 1), which reflects the true

risk ratio between the two borrower types. It suggests with sufficient users and information, P2P Platforms can exert high level of screening power. We now discuss how P2P platforms’ screening power affects borrowers’ expected payoffs. Let μ be the “stamp” that a P2P platform will put on a high-risk borrower when he looks for funding. In order to obtain the same interest rate, R, a borrower who is stamped as high-risk borrower (high μ) would have to offer more social collateral (e.g., volunteer more specific social profiles or relationships), compared with one regarded as a low-risk borrower. Namely, the “high-risk” stamp would “magnify” his “costs” of social collateral. The requirement of social collateral will increase with μ, which signals how much more likely the high-risk borrower would default. For simplicity, we consider a linear function of requirement in terms of μ. Any convex function would make it even easier to separate low and high-risk borrowers, so a linear function represents a more “challenging” case to study. In sum, if a borrower is identified as μ times more likely to default than a low-risk borrower, then the borrower would expect to offer higher social collateral, (i.e., μ times of S that is otherwise required of low-risk borrowers) in order to obtain the same interest rate. That is, the higher the “identified” default risk, the higher the cost of borrowing. Thus, the utility πi are

πl (γ ) = Pl (Xl − LR − L ) − (1 − Pl )mS,

(7)

πh (γ ) = Ph (Xh − LR − L ) − (1 − Ph )mμS.

(8)

L. The platform connects borrowers and lenders, and generates revenue from commissions instead of the interest rate difference between the deposit and the loan like banks. The platform charges fees from both borrowers and lenders, but mainly from borrowers when their loans are funded. Assume the commission rate is ω, then the platform charges borrowers ωL. Lenders are charged an annual fee based on their user grades. For simplicity, we ignore lender’s fee as it is negligible relative to that of borrowers. In the developed countries (e.g., Europe and the U.S.), P2P usually do not guarantee lenders’ principal; investors assume the entire loss on defaulted loans. However, principal guarantee was more popular in the developing counties, like China and India. It would be interesting to examine the welfare implications of guarantee. Without loss of generality, we assume, P2P provides θ L guarantee to lenders, where θ is a percentage with 0 ≤ θ ≤ 1. Thus, the expected revenue εi of a platform providing services to borrower i is

εi = ωL − (1 − Pi )θ L.

(9)

4.2. Screening with soft information and social collateral Given loans in P2P are unsecured (i.e., no tangible collateral), we now show how soft information and social collateral help P2P screen borrowers. If borrower i fails to repay the loan, he loses the social collateral Si on each lender he defaults. An effective platform should enable self-selection, i.e. borrowers of a particular risk level would select the contract intended for them. The expected utility πi of borrower i from applying the matching contract γi can be expressed as

πl (γl ) = Pl (Xl − LRl − L ) − (1 − Pl )mSl − ωL,

(10)

πh (γh ) = Ph (Xh − LRh − L ) − (1 − Ph )μmSh − ωL.

(11)

We now examine the conditions which would support the selfselection contract (i.e., existence of separating equilibrium). Similar to the case in traditional credit market (see Appendix A), in P2P the marginal rates of substitution (MRS ) of low-risk and high-risk borrowers have the following relationship:

∂ Rl ∂ Rh (1 − Pl )m =− > MRSh (γ ) = ∂ Sl LPl ∂ Sh (1 − Ph )μm =− , μ ≥ 1 and m ≥ 1.

MRSl (γ ) =

LPh

4.1.3. Online P2P lending platform We have shown above how social collateral and soft information affect a borrower’s utility. We now consider the characteristics of the P2P Lending Platform (hereafter platform) for loan amount

Specifically, low-risk borrowers exhibit a higher MRS between R (interest rates) and S (social collateral). Due to different MRS between low and high-risk borrowers, it is possible for lenders to differentiate borrowers and sort them into different risk groups through the combination of interest rate and social collateral offered by borrowers. If borrowers repay the loan, lenders earn the

Please cite this article as: Z. Liu, J. Shang and S.-y. Wu et al., Social collateral, soft information and online peer-to-peer lending: A theoretical model, European Journal of Operational Research, https://doi.org/10.1016/j.ejor.2019.08.038

ARTICLE IN PRESS

JID: EOR

[m5G;September 6, 2019;19:9]

Z. Liu, J. Shang and S.-y. Wu et al. / European Journal of Operational Research xxx (xxxx) xxx

7

profit of the interest LR; otherwise lenders lose the principal L and receive guaranteed compensation θ L. In equilibrium, lenders still receive zero rents (i.e., zero expected profits). Without loss of generality, we assume each lender contributes equally to the principal. Thus, a lender’s expected utility (ρi ) from contract γi is

ρl (γl ) = 1/m[Pl LRl − (1 − Pl )(1 − θ )L] = 0,

(12)

ρh (γh ) = 1/m[Ph LRh − (1 − Ph )(1 − θ )L] = 0.

(13)

In a separating equilibrium, we can easily show that a low-risk borrower strongly prefers a contract with low interest rate (i.e., incentive compatibility constraint for low risk borrowers is automatically satisfied). But we need to ensure that the high-risk borrowers would not prefer the contract intended for low-risk borrowers, thus the binding condition to derive the optimal separating equilibrium should be

    πh R¯ ∗h , Sh∗ = πh R¯ ∗l , Sl∗ .

(14)

Fig. 3. The economic meaning of Proposition 2.

We have proved that in the traditional credit market, the optimal contract to the society entails Ch∗ = 0 in a separating equilibrium (See Appendix B). Following the same logic, we can show

Sh∗ = 0.

(15)

Specifically, a sustainable equilibrium will be one in which a high-risk borrower would not offer any social collateral (i.e., they would choose not to provide soft information on their social network) and not be served in such a market. This is because even though the social collaterals are valuable to the borrowers, they are worthless to the lenders. Therefore, a sustainable equilibrium is when the separating equilibrium is achieved, in which high risk borrowers who could not repay the loan will be screened out. Specifically, only low-risk borrowers will be served as they are willing to offer social collateral in exchange for low interest rate. As a perfect competitor in the online financial markets, a P2P platform attains no supranormal revenues in the long-run. Thus, another condition necessary for separating equilibrium is

ε = ωL − (1 − Pl )θ L = 0. 

(16)

We can then find (R¯ ∗h , Sh∗ ) and ( R¯ ∗l , Sl∗ ) by solving Eqs. (10)–(16).

R¯ ∗h = (1−PhP)(1−θ ) , Sh∗ = 0 h

−Ph )(1−θ ) L R¯ ∗l = (1−Pl )P(1−θ ) , Sl∗ = (μPl m Pl (1−Ph ) l

.

(17)

To reach separating equilibrium, the collateral for low-risk borrowers (Sl∗ ) should not exceed the total amount available to them, i.e. S ≤ Ms . We thus have

Sl∗ =

(Pl − Ph )(1 − θ ) L ≤ Ms μmPl (1 − Ph )

(18)

or equivalently,

μm ≥

large. Since social screening power and loan dispersion, to some degree are under the control of P2P platforms, a P2P platform can sustain competitive advantage by ensuring the social screening power (through more users and better use of soft information) and the dispersion degree of each loan to stay above certain level.

(Pl − Ph )(1 − θ ) L . Pl (1 − Ph ) Ms

(19)

Two interesting observations are in place: (1) Eq. (18) suggests that in equilibrium, the requirement for social collateral decreases when screening power μ and loan dispersion m increases. That is, as screening power μ and loan dispersion m increases, the credit accessibility of small borrowers increases due to lower requirement of social collateral. (P −P )(1−θ ) (2) Since lP (1h −P ) MLs is determined exogenously (Pi , θ , L, and l

h

Ms ), the separating equilibrium (Eq. (17)) can be achieved as long as Eq. (19) holds. Namely, low-risk borrowers can always obtain loans from P2P when μ and m are reasonably

As μ depends on n (i.e., μ = 1 + (1 − 1n )

Pl −Ph 1−Pl ),

we can re-write

the above equation, which is necessary for the separating equilibrium, as:

m≥

(Pl − Ph )(1 − θ )(1 − Pl )L     , Pl (1 − Ph ) (1 − Pl ) + 1 − 1n (Pl − Ph ) Ms

(20)

n≥

(Pl − Ph )Pl (1 − Ph )mMs . (1 − Ph )Pl (1 − Ph )mMs − (1 − θ )(1 − Pl )(Pl − Ph )L

(21)

Except for n and m, the right-hand-sides of Eqs. (20) and (21) are determined exogenously. The separating equilibrium (Eq. (17)) can be achieved as long as Eqs. (20) and (21) hold. We will detail the roles of these platform design variables in Section 4.3. We summarize the separating equilibrium under P2P below: Proposition 2. In P2P, low-risk borrowers lacking tangible assets can use social collaterals to distinguish themselves from high-risk borrowers. When P2P satisfies Eqs. (20) and (21), lenders can screen different types of borrowers through contract set {γ¯ l∗ , γ¯ h∗ }, where

    γ¯ h∗ = R¯ ∗h , Sh∗ = (1−PhP)h(1−θ ) , 0 ,        h 1 −θ ) γ¯ l∗ = R¯ ∗l , Sl∗ = (1−Pl )Pl(1−θ ) , (μPl m−PPhl ()1(−P L , μ = 1 + 1 − 1n P1l −P . −Pl h)

The economic implication of Proposition 2 can be illustrated in Fig. 3. Ul and Uh represent the indifference curves of the low and high-risk borrowers respectively in P2P. When compared with πi (See Fig. A1 in Appendix A), πi incurs an extra service fee ωL. Thus, the curve Ui shifts downwards along the vertical axis. As MRSl > MRSh , the indifference curve of the lower risk (Ul ) are flatter than that of the higher risk (Uh ). Meanwhile, as MRSl > MRSl and MRSh > MRSl , borrowers’ indifference curves (Ul , Uh ), regardless of the risk level, are steeper than those in traditional credit market (Ul , Uh ). In Fig. 3, ρl = 0 and ρh = 0 represent the zero-profit curves of the lenders when providing loans to low and high-risk borrowers. Recall that social collaterals are valuable to the borrowers while valueless to the lenders, thus MRS between R and S of ρi = 0 is zero. Namely, the lenders’ zero-profit curves are completely parallel to the horizontal axis. Points E and F depict contract set

Please cite this article as: Z. Liu, J. Shang and S.-y. Wu et al., Social collateral, soft information and online peer-to-peer lending: A theoretical model, European Journal of Operational Research, https://doi.org/10.1016/j.ejor.2019.08.038

ARTICLE IN PRESS

JID: EOR 8

[m5G;September 6, 2019;19:9]

Z. Liu, J. Shang and S.-y. Wu et al. / European Journal of Operational Research xxx (xxxx) xxx

{γ¯ h∗ , γ¯ l∗ } of the separating equilibrium, by which lenders can suc-

cessfully screen borrowers and classify them into the right risk type. Thus, the borrowers lacking tangible assets (line M) can use social collaterals to distinguish themselves from high-risk borrowers, as long as the borrowers’ social collaterals is located between Cl∗ and Sl∗ . 4.3. Equilibrium analysis and implications for platform strategies Platform strategies and operations are important to the sustainability of the platform. Through equilibrium and comparative static analyses, we obtain three interesting propositions. Proposition 3. The equilibrium interest rate of borrowers (R¯ ∗l ) is inversely proportional to the percentage of principals guaranteed (θ ), while independent of the dispersion degree of loans (m) and the number of users on the platform (n). Taking the partial derivative of R¯ ∗l with respect to θ , m and n, we have

⎧ ¯∗ ∂ Rl 1 − Pl ⎪ ⎪ =− <0 ⎪ ⎪ ∂θ Pl ⎪ ⎨ ∗ ∂ R¯ l . =0 ⎪ ∂m ⎪ ⎪ ⎪ ⎪ ⎩ ∂ R¯ ∗l =0 ∂n

The equilibrium interest rate decreases when the ratio of principals guaranteed increases. This is intuitive, as the interest rate represents the risk of the loan. Traditionally, the bank is the only victim when the loan defaults. However, in P2P, the platform could share the risk of lenders by guaranteeing portion of the principals from loss when facing default (θ > 0). Higher θ implies more risk is transferred from the lenders to the P2P platform. Thus, high θ leads to low interest rate since interest rate is an indicator of lender’s risk. In contrast, the dispersion degree (m) and the number of users (n) have no influence on the risk-transferring pattern of the loan, so the interest rate is independent of m and n. Proposition 4. The equilibrium social collateral of borrowers (Sl∗ ) is inversely proportional to the guarantee (θ ), the dispersion degree of loans (m) and the number of platform users (n). Taking the partial derivative of Sl∗ with respect to θ , m and n, we have

⎧ ∗ ∂ Sl (Pl − Ph ) ⎪ ⎪ ⎪ ∂θ = − μmPl (1 − Ph ) L < 0 ⎪ ⎪ ⎨ ∂ S∗ ( P − P ) (1 − θ ) l =− l 2 h L<0 . ∂ m μm Pl (1 − Ph ) ⎪ ⎪ ⎪ 2 ∗ ⎪ (Pl − Ph ) (1 − θ ) ⎪ ⎩ ∂ Sl = − L<0 ∂n μ2 n2 mPl (1 − Ph )(1 − Pl )

From Section 4.2, we know that the equilibrium social collateral (Sl∗ ) signifies the borrowers’ accessibility to loans, where the smaller the social collateral required, the lower the hurdle for the borrowers to receive funds from P2P markets. Here, ∂ Sl∗ /∂ θ < 0 suggests that the social collateral requirement decreases with the guarantee of principals. In other words, the borrower’s accessibility to loans increases if the P2P platform is willing to provide more guarantee. Principal guarantee was more popular for the P2P platforms in the developing countries, such as India and China than in the developed countries; in fact most P2P platforms in US do not provide guarantees at all. As the platforms are only recently established in developing countries, borrowers in the online community often have low social capitals. Thus, guarantees by the platform help reduce the barriers for small borrowers, especially SMEs, to access the fund.

Similarly, ∂ Sl∗ /∂ m < 0 and ∂ Sl∗ /∂ n < 0 indicate that the social collateral requirement decreases with the dispersion degree and the number of platform users. The dispersion of loans exacerbates borrower’s loss of social collaterals at default and makes it more costly for high-risk borrowers to mimic low-risk ones. This in turn increases the screening capability of P2P platforms. Also, as the users grow, the online network produces more soft information, which enhances the differentiating power of borrowers with different risk levels. Thus, a platform with higher loan dispersion and more users will have higher screening ability, which in turn reduces the hurdle of social collateral requirement, allowing low-risk borrowers to have a better chance of obtaining loans without the need of offering many social collaterals. This finding is important as it suggests that as the P2P lending platform grows in size, it is able to serve more customers by reducing the social collateral requirement. 

Proposition 5. The equilibrium utility of borrowers (πl ∗ ) is positively associated with the guarantee rate (θ ), the dispersion degree of loans (m) and the number of users on the platform (n). ∗

Taking the partial derivative of π  l with respect to θ , m and n, we have

⎧  ∂πl ∗ (Pl − Ph ) ⎪ ⎪ = L>0 ⎪ ⎪ ∂θ μ Pl (1 − Ph ) ⎪ ⎪ ⎨ ∗ ∂πl (P − Ph )(1 − θ ) = l L>0 . ⎪ ∂m μmPl (1 − Ph ) ⎪ ⎪  ⎪ ⎪ ∂π ∗ (P − P )2 1 − θ ) ⎪ ⎩ l = l 2 2h ( L>0 ∂n μ n Pl (1 − Ph ) 

∂ πl ∗ /∂ θ > 0 suggests that borrowers’ expected utility in the

separating equilibrium increases with guarantees. This is reasonable as the interest rate will decrease with guarantees (Proposition 3). Lower interest rates undoubtedly improve borrowers’ utility. Thus, providing guarantee to lenders not only benefits lenders (risk-sharing) but also borrowers, hence attracting more borrowers.  ∂ πl ∗ /∂ m > 0 suggests that borrowers’ expected utility correlates positively with the loan’s dispersion degree. As mentioned above, the dispersion of loans exacerbates the loss of social collaterals at default and makes it more costly for high-risk borrowers to mimic low-risk ones. This increases the screening ability of P2P and platforms thus should encourage lenders to diversify their investment as widely as possible. This result explain why, for example, both Lending Club and Prosper (the top two US P2P platforms) have very low minimum investment requirement in each loan ($25), and they encourage investors to spread the investment across as many “Notes” as possible. Particularly, they encourage that “no Note is more than 1% (and preferably less) of your total P2P investing portfolio” (Lendingclub.com and Renton 2011). Essentially, a loan should be funded by numerous lenders, as diversification is an effective way to spread investor’s risk. While it is well-known that investors benefit from diversification, our model analytically shows that diversification (high degree of dispersion of lender’s loans) improves the well-being of borrowers and make P2P more attractive.  Finally, πl ∗ /∂ n > 0 indicates that borrowers’ expected utility increases with the number of users on the platform. This suggests that borrowers benefit when additional users join the network. This is because as the platform accumulates more users and soft information and increases its screening capability, low risk borrowers are more likely to be distinguished from high-risk borrowers, which would lower the investor’s risk and the interest rate. In other words, P2P market exhibits network effects. Namely, larger n leads to higher borrower’s welfare, which in turn makes the

Please cite this article as: Z. Liu, J. Shang and S.-y. Wu et al., Social collateral, soft information and online peer-to-peer lending: A theoretical model, European Journal of Operational Research, https://doi.org/10.1016/j.ejor.2019.08.038

JID: EOR

ARTICLE IN PRESS

[m5G;September 6, 2019;19:9]

Z. Liu, J. Shang and S.-y. Wu et al. / European Journal of Operational Research xxx (xxxx) xxx

platform more appealing to potential borrowers and hence attracts even more users to the platform. In summary, we have shown that the benefits of P2P increases with principal guarantee ratio (θ ), loan dispersion (m), and number of users (n). These are also the instruments P2P platforms can maneuver to improve their competitiveness. In the initial stage when only a few users are with the platform, offering guarantee to principals, even though it entails risks to the platform, may be the most effective operations strategy. This is because guarantees will not only appeal to lenders and attract investors to participate in the platforms, but also will increase borrowers’ utility and attract more borrowers to join. As a result, the number of lenders and borrowers will grow, so will the dispersion degree of loan (m). Higher n and m further improve the attractiveness and competitiveness of the P2P platforms in the long run. This explains why in some developing countries, startup P2Ps provided high guarantee ratio at the early stage of the business, in some case even up to 100%, as they aimed to attract user base quickly. Once the platforms have attracted enough users, they gradually reduced the principal guaranteed and let the loan dispersion and user volumes take over the strategic role of improving attractiveness and competitiveness. For example, i2ifunding.com in India initially offered up to 100% principal protection at the early stage of their business, but no longer did so recently (https://www.i2ifunding.com/ p2p- lending- principal- protection- terms).

5. Conclusion The emergence of P2P and its unique feature of unsecured loans has the potential to influence the credit viability of small borrowers without tangible assets. Before P2P is available, some creditworthy individuals are limited to some costly finance sources because they cannot get fund from banks without tangible collateral. The absence of collateral and hard information leads to information asymmetry between the lenders and the borrowers, resulting in inefficiency of traditional lending markets. However, P2P allows the collateral to be substituted by borrowers’ social capital and leverages the soft information through the “wisdom of crowd.” These unique features make it possible for P2P to complement traditional financial institutions and improve access to credit, especially for small borrowers. In this paper, we provide a micro and analytical investigation on the viability and sustainability of this emerging financial platform and the key design variables that affect its performance. Our model shows that social collateral makes the self-selection mechanism applicable to the borrowers without tangible collateral and its performance is contingent on the scale of users and the loan dispersion. It is interesting to observe that low-risk borrowers squeeze out high-risk ones in P2P markets, while the opposite is true in the traditional credit markets. Note that although the potential of social collateral in screening borrowers’ type has been discussed in the previous studies (Karlan et al., 2009; Paal & Wiseman, 2011), we analytically identified the general conditions under which social collateral works, which hitherto has not been explored in the literature. We further demonstrate that soft information enhances the screening power of P2P and relieves the collateral burden for lowrisk borrowers. While empirical studies (e.g. Iyer et al. 2016; Freedman & Jin, 2017; Ge et al., 2017) have examined the relationship between soft information and the interest rate, and the default risk of borrowers, the uniqueness of our work lies in modeling the soft information analytically and ingeniously measuring it with the scale of users. We observed that the more users in P2P platforms, the less the social collateral required when separating equilibrium is achieved.

9

Our research also identifies the critical operational settings (the principal guarantee ratio, the loan dispersion degree and the number of users in the network) for P2P’s success, and their positive association with borrowers’ utility. Different from empirical study that examines the factors impacting borrowing outcome (Collier et al., 2010; Freedman & Jin, 2017; Klafft, 2009; Lee et al., 2012), we analytically examine the relationship between the platform design and the borrowers’ economic wellbeing. Compared with the analytical works by De et al., 2019 and Gao et al., 2018, our P2P study focuses on different perspectives and consider the extra dimension of the platform’s strategy with much more extensive analytical modeling. The findings of this study provide insights for various players in the P2P markets, including the lenders, the borrowers and the P2P platforms. For the lenders, our analysis suggests that unsophisticated individuals should value the signal role of soft information and interpret the nonstandard information collectively to solve the screening problem. As for the borrowers, we find that low-risk borrowers without sufficient assets can potently distinguish themselves by providing social collateral. Our model also provides practical guidance to the P2P platform managers regarding their platform design to help not only reshape their business strategies but also enhance their business opportunities. Overall, our paper substantiate why P2P is widely termed “social lending” and under what conditions it is viable. We validate that online platforms indeed could facilitate the utilization of social networks, and benefit both the P2P lenders and borrowers. This is especially interesting as such relationships are selforganizing and impose little cost to the marketplace. Acknowledgement This work is supported by National Natural Science Foundation of China [grant nos. 71771081, 71420107027]; and Natural Science Foundation of Hunan Province, China [grant no. 2017JJ2037]. Appendix A. Proof of Proposition 1 Case I: Sufficient collateral and perfect screening We first consider the case when borrowers have sufficient collaterals, i.e. M > C. Institutions (e.g., banks) can screen borrowers following the sequence in Fig. A1. From Eq. (1), borrower i’s marginal rate of substitution MRSi under γ is: MRSi (γ ) = ∂∂ CR = −

(1−Pi )

1 LPi 2

LPi

. Clearly, MRSl > MRSh under γ . Further, we have

∂ MRSi (γ ) = ∂ Pi

> 0, indicating borrowers with a low default risk exhibit a

higher MRS between R and C. They prefer (low R, high C) than those with a higher default risk. Thus, when borrowers have sufficient collateral, banks can use R and C to sort borrowers into different risk groups. As a perfect competitor in the credit market, the long term profit for banks is zero when providing loans in either contract γl∗ or γh∗ :

    ρh R∗h , Ch∗ = Ph LR∗h + (1 − Ph) βCh∗ − L = 0, ρl R∗l , Cl∗ = Pl LR∗l + (1 − Pl ) βCl∗ − L = 0.

Fig. A1. The timeline of the screening game.

Please cite this article as: Z. Liu, J. Shang and S.-y. Wu et al., Social collateral, soft information and online peer-to-peer lending: A theoretical model, European Journal of Operational Research, https://doi.org/10.1016/j.ejor.2019.08.038

ARTICLE IN PRESS

JID: EOR 10

[m5G;September 6, 2019;19:9]

Z. Liu, J. Shang and S.-y. Wu et al. / European Journal of Operational Research xxx (xxxx) xxx

Fig. A2. Illustration of the separating equilibrium.

Fig. A3. Borrowers’ available collateral and the separating equilibrium.

Besides, in equilibrium, low-risk borrowers will strictly prefer γl∗ , while the high-risk borrowers are indifferent between γl∗ and γh∗ given sufficient collaterals (the binding condition). Thus we have

π



∗ ∗ h Rh , Ch



=π



∗ ∗ h Rl , Cl



.

The optimal contract, which maximizes the sum of both lenders’ and borrowers’ welfare, involves

Ch∗ = 0. In another word, high-risk borrowers will not be served in the market. This is because collaterals are discounted at rate β when transferred from borrowers to banks, making any collateral inefficient. See the Mathematical proof of Ch∗ = 0 in Appendix B. We can then solve (R∗l , Cl∗ ) and (R∗h , Ch∗ ) through Eqs. (A1)– (A4):



R∗h =

R∗l =

1 Ph 1 Pl



− 1, Ch∗ = 0 β (Pl −Ph )(Pl −1 ) Ph (Pl −1 )β +Pl (1−Ph )



− Pl + 1 , Cl∗ =

Pl −Ph L Ph (Pl −1 )β +Pl (1−Ph )

.

Fig. A2 illustrates the separating equilibrium. Ul and Uh represent the indifference curves of the borrowers with low and high risk, respectively. Each curve shows the combination of collateral and interest rate that gives the borrower equal utility. As low-risk borrowers are willing to accept a higher collateral for lower interest rates than those with high risk, their indifference curves are flatter. We denote ρl = 0 (ρh = 0) as the zero-profit curves for contract γl (γh ). On the zero-profit curve, the bank’s marginal rate of substitution MRSρ between R and C is equal to MRSρ (γ ) = ∂∂ CR = −

(1−Pi ) LPi

β . Therefore, MRSρ > MRSi , as 0 < β < 1. Namely, banks’

zero-profit curves are flatter than borrowers’ indifference curves on a given loan contract γ . The high-risk borrowers are indifferent between A and B, as they are on the same curve Uh . Thus, high-risk borrowers are not motivated to mimic the low-risk borrowers to seek lower interest rates. The credit market reaches a separating equilibrium and banks can successfully discern borrowers of different risk types. That is, perfect screening can be achieved when borrowers have sufficient collaterals. However, these conclusions are premised on borrowers’ ability to provide the required collaterals (M ≥ Cl∗ ), which could be difficult to satisfy by Small and Medium Enterprises (SMEs) as they often lack collateral assets. In the following, we show that the separating equilibrium may not exist when borrowers have insufficient collateral.

Case II: Insufficient collateral and imperfect screening Borrowers’ collaterals are often limited (M < Cl∗ ), i.e. M is on the left of point B in Fig. A3. Thus, if there exists γD for low-risk borrowers to distinguish themselves from high-risk ones in the separating equilibrium, point D would be: (i) on the left of M; (ii) on the zero-profit curve ρl = 0. Hence, the only possible locations for D would be below Uh . It implies that high-risk borrowers (point A) will mimic low-risk ones to accept γD (point D), as doing so would enhance utility. Rationally, high-risk borrowers will pretend to be low-risk ones and choose the same contract as low-risk borrowers. As a result, banks cannot design a contract to differentiate borrowers’ risk types. The separating equilibrium {γl∗ , γh∗ } under the case of sufficient collaterals thus may not exist. Because of adverse selection (i.e., high- and low-risk borrowers cannot be separated), low-risk borrowers, who lack collaterals to distinguish themselves, will drop out of the market (Stiglitz & Weiss, 1981). By substituting Cl∗ for the collateral condition M ≥ Cl∗ , we have

Pl − Ph M ≥ . L Pl (1 − Ph ) − β Ph (1 − Pl ) It implies that low-risk borrowers can obtain loans from the credit market when the collateral to loan ratio is greater than a specific value. On the contrary, if M < Cl∗ , low-risk borrowers would drop out of the credit market. Appendix B. Mathematical proof of C∗h = 0 Borrower i’s expected utility in contract γ = (R, C ) is

πi (γ ) = Pi (Xi − LR − L ) − (1 − Pi )C. When contracting with borrower i, Banks’ expected utility is

ρi (γ ) = Pi LR + (1 − Pi )(βC − L ). The social welfare Wi of loan γ is

Wi = ρi (γ ) + πi (γ ) = Pi LR + (1 − Pi )(β C − L ) + Pi (Xi − LR − L ) − (1 − Pi )C = (1 − Pi )(β − 1 )C − (1 − Pi )L + Pi (Xi − L ). Taking the partial of the social welfare Wi with respect to C, we have

∂ Wi = (1 − Pi )(β − 1 ) < 0. ∂C

As β − 1 < 0 and 1 − Pi > 0, the social welfare of the loan is negatively correlated with collateral C. Theoretically, there exist

Please cite this article as: Z. Liu, J. Shang and S.-y. Wu et al., Social collateral, soft information and online peer-to-peer lending: A theoretical model, European Journal of Operational Research, https://doi.org/10.1016/j.ejor.2019.08.038

JID: EOR

ARTICLE IN PRESS Z. Liu, J. Shang and S.-y. Wu et al. / European Journal of Operational Research xxx (xxxx) xxx

various pairs of contracts

γl∗ = (R∗l , Cl∗ ) and γh∗ = (R∗h , Ch∗ ), Cl∗ = Ch∗ + C, which satisfy the condition of the separating equilibrium. Obviously, the social welfare of loans (γl∗ ,γh∗ ) achieves the maximum level when Ch∗ reaches the minimal value 0.

References Adams, W., Einav, L., & Levin, J. (2009). Liquidity constraints and imperfect information in subprime lending. American Economic Review, 99(1), 49–84. Angilella, S., & Mazzù, S. (2015). The financing of innovative SMEs: A multicriteria credit rating model. European Journal of Operational Research, 244(2), 540–554. Avery, R. B., Bostic, R. W., & Samolyk, K. A. (1998). The role of personal wealth in small business finance. Journal of Banking & Finance, 22(6–8), 1019–1061. Ba, Sulin (2001). Establishing online trust through a community responsibility system. Decision Support Systems, 31(3), 323–336. Berger, A. N., & Udell, G. F. (2002). Small business credit availability and relationship lending: The importance of bank organisational structure. The Economic Journal, 112(477), F32–F53. Bester, H. (1985). Screening vs. rationing in credit markets with imperfect information. American Economic Review, 75(4), 850–855. Bester, H. (1987). The role of collateral in credit markets with imperfect information. European Economic Review, 31(4), 887–899. Burtch, G., Ghose, A., & Wattal, S. (2013). An empirical examination of the antecedents and consequences of contribution patterns in crowd-funded markets. Information Systems Research, 24(3), 499–519. Chui, M. (2013). Social media to boost financial services. InFinance: The Magazine for Finsia Members, 127(2), 34–36. Collier, B. C., & Hampshire, R. (2010). Sending mixed signals: Multilevel reputation effects in peer-to-peer lending markets. In Proceedings of the ACM conference on Computer supported cooperative work (pp. 197–206). ACM. De Roure, C., Pelizzon, L., & Thakor, A. V. (2019). P2p lenders versus banks: cream Cream skimming or bottom fishing?SAFE Working Paper No. 206. Egli, D., Ongena, S., & Smith, D. C. (2006). On the sequencing of projects, reputation building, and relationship finance. Finance Research Letters, 3(1), 23–39. Faia, Paiella, & Monica (2017). P2P lending: Information externalities, social networks and loans’ substitution Social Science Electronic Publishing. Freedman, S., & Jin, G. Z. (2017). The information value of online social networks: Lessons from peer-to-peer lending. International Journal of Industrial Organization, 51(2), 185–222. Gao, G., Fan, Z., Fang, X., & Lim, Y. (2018). Optimal stackelberg strategies for supply chain finance based on online peer-to-peer lending. European Journal of Operational Research, 267(2), 585–597. Ge, R., Feng, J., Gu, B., & Zhang, P. (2017). Predicting and deterring default with social media information in peer-to-peer lending. Journal of Management Information Systems, 34(2), 401–424. Guo, Y., Zhou, W., Luo, C., Liu, C., & Xiong, H. (2015). Instance-based credit risk assessment for investment decisions in P2P lending. European Journal of Operational Research, 249(2), 417–426. Herrerolopez, S. (2009). Social interactions in P2P lending. Workshop on Social Network Mining & Analysis. DBLP.

[m5G;September 6, 2019;19:9] 11

Herzenstein, M., Sonenshein, S., & Dholakia, U. M. (2011). Tell me a good story and I may lend you money: The role of narratives in peer-to-peer lending decisions. Journal of Marketing Research, 48(SPL), S138–S149. Hong, S. K., & Sohn, S. Y. (2010). Support vector machines for default prediction of SMEs based on technology credit. European Journal of Operational Research, 201(3), 838–846. Iyer, R., Khwaja, A. I., Luttmer, E. F., & Shue, K. (2016). Screening peers softly: Inferring the quality of small borrowers. Management Science, 62(6), 1554–1577. Ju, Y. H., & Sohn, S. Y. (2014). Updating a credit-scoring model based on new attributes without realization of actual data. European Journal of Operational Research, 234(1), 119–126. Karlan, D., Mobius, M., Rosenblat, T., & Szeidl, A. (2009). Trust and social collateral. Quarterly Journal of Economics, 124(3), 1307–1361. Klafft, M. (2009). Online peer-to-peer lending: A lenders’ perspective. Social Science Electronic Publishing, 2(2), 81–87. Larrimore, L., Jiang, L., Larrimore, J., Markowitz, D., & Gorski, S. (2011). Peer to peer lending: The relationship between language features, trustworthiness, and persuasion success. Journal of Applied Communication Research, 39(1), 19–37. Lee, E., & Lee, B. (2012). Herding behavior in online P2P lending: An empirical investigation. Electronic Commerce Research and Applications, 11(5), 495–503. Lin, M., Prabhala, N. R., & Viswanathan, S. (2013). Judging borrowers by the company they keep: Friendship networks and information asymmetry in online peer– to-peer lending. Management Science, 59(1), 17–35. Manove, M., Padilla, A. J., & Pagano, M. (2001). Collateral versus project screening: A model of lazy banks. Rand Journal of Economics, 32(4), 726–744. Michels, J. (2012). Do unverifiable disclosures matter? Evidence from peer-to-peer lending. The Accounting Review, 87(4), 1385–1413. Paal, B., & Wiseman, T. (2011). Group insurance and lending with endogenous social collateral. Journal of Development Economics, 94(1), 30–40. Rusli, E. M. (2013). Bad credit? Start tweeting. Wall Street Journal. https://www.wsj. com/articles/SB10 0 01424127887324883604578396852612756398. Shannon, C. E. (2006). Communication in the presence of noise. Proceedings of the IRE, 37(1), 10–21. Sonenshein, S., Herzenstein, M., & Dholakia, U. M. (2011). How accounts shape lending decisions through fostering perceived trustworthiness. Organizational Behavior and Human Decision Processes, 115(1), 69–84. Stein, J. C. (2002). Information production and capital allocation: Decentralized vs. hierarchical firms. Journal of Finance, 57(5), 1891–1921. Stiglitz, J. E., & Weiss, A. (1981). Credit rationing in markets with imperfect information. American Economic Review, 71(3), 393–410. Sundararajan, A., Provost, F., Oestreichersinger, G., & Aral, S. (2013). Information in digital, economic, and social networks. Information Systems Research, 24(4), 883–905. Tsai, M. F., & Wang, C. J. (2016). On the risk prediction and analysis of soft information in finance reports. European Journal of Operational Research, 257(1), 243–250. Weiss, G.N., Pelger, K., & Horsch, A. (2010). Mitigating adverse selection in p2p lending–empirical evidence from prosper.com. Available at SSRN 1650774. Yum, H., Lee, B., & Chae, M. (2012). From the wisdom of crowds to my own judgment in microfinance through online peer-to-peer lending platforms. Electronic Commerce Research and Applications, 11(5), 469–483. Zhang, J., & Liu, P. (2012). Rational herding in microloan markets. Management Science, 58(5), 892–912. Zvilichovsky, D., Inbar, Y., & Barzilay, O. (2014). Playing both sides of the market: success Success and reciprocity on crowdfunding platforms. Available at SSRN 2304101.

Please cite this article as: Z. Liu, J. Shang and S.-y. Wu et al., Social collateral, soft information and online peer-to-peer lending: A theoretical model, European Journal of Operational Research, https://doi.org/10.1016/j.ejor.2019.08.038