Rationality of Investors in P2P Online Lending Platform with Guarantee Mechanism: Evidence in China

Transcription

1 Journal of Appled Fnance & Bankng, vol. 7, no. 3, 2017, ISSN: (prnt verson), (onlne) Scenpress Ltd, 2017 Ratonalty of Investors n P2P Onlne Lendng Platform wth Guarantee Mechansm: Evdence n Chna Nanfe Zhang 1 Abstract Ths paper nvestgates whether nvestors n P2P onlne lendng platforms n Chna are ratonal. In Chna, most P2P platforms run a guarantee mechansm usng loan loss provson. I take nto account the effect of the guarantee mechansm on loan's cash flow and calculate expected nternal rate of return of each loan. The emprcal results show evdence aganst ratonalty assumpton. Frstly, expected return calculated under guarantee mechansm of a loan n Chna s not only affected by systematc rsk, but also by dosyncratc rsk. Secondly, Chna P2P nvestors do not maxmze ther expected return. They take nto account other varables although ther nfluence on default and prepayment rsk s already reflected n the expected return. Conclusvely, Chna P2P nvestors are not ratonal. The guarantee mechansm mght contrbute to some of the fndngs. JEL classfcaton numbers: G110 G120 G140 G170 G210 Keywords: Ratonal expectaton, Expected return, CAPM, Guarantee mechansm 1 Introducton Whether nvestors have ratonal expectaton s an mportant topc n fnance research. Ratonal expectaton mples nvestors' ratonalty, n whch case they are able to value securtes n a ratonal way. The ntrnsc value of a securty s the sum of the dscounted cashflows t generates n each perod. Fama proposes the famous effcent market hypothess, and nvestors' ratonalty was one of ts core assumptons [1]. The captal asset prcng model (CAPM) s also based upon the assumpton that nvestors are ratonal. A major branch of emprcal fnance researches pursue to justfy or refute the ratonalty assumpton. Ths paper also ams to analyze f nvestors are ratonal, usng an exclusve dataset, a major peer-to-peer (P2P) onlne lendng platform n Chna, an emergng market, whle standard approach utlzes data from conventonal securtes n a developed market such as stock market n the Unted States. Ths paper provdes evdence that nvestors n Chna P2P platform do not form ratonal expectaton. Rsk of an asset s dvded nto two parts, systematc rsk and dosyncratc rsk. CAPM mples that only systematc rsk s prced. In other words, expected return s only 1 School of Economcs and Management, Tsnghua Unversty. Artcle Info: Receved : February 2, Revsed : March 6, Publshed onlne : May 1, 2017

2 122 Nanfe Zhang determned by systematc factors. Therefore, f t s found that the expected return of an asset s not only affected by ndvdual factors other than systematc ones, then nvestors do not form ratonal expectaton. Ratonal expectaton assumpton s the core debate between tradtonal fnance and behavoral fnance. Numerous researches test whether nvestors form ratonal expectaton. Jensen apples CAPM to calculate portfolo's rsk adjusted return for the frst tme [2]. Fama fnds that asset prce follows a random walk, and market s weakly effcent [3]. Furthermore, Fama et al. uses event study to show that US stock market s n the form of sem-strong effcency [4]. Fama frstly proposes effcent market hypothess[1]. Ths hypothess brngs about a complete new branch of emprcal fnance. However, some researchers do not beleve nvestors are ratonal, and ths opens up a whole new feld n fnance, namely behavoral fnance. In behavoral fnance, nvestors are not ratonal, and the rratonalty s systematc n the sense that t has long term effect on asset prces. Shlefer revews the theores of behavoral fnance comprehensvely [5]. Most researches make use of stock market to test f nvestors are ratonal. In late 2000s, a new form of market emerged. Onlne lendng platform, usually known as peer-to-peer (P2P), njects fresh blood nto ratonalty studes. Unlke stock markets, where the nformaton nvestors observe cannot be controlled, n P2P, all nformaton nvestors can see s lsted on the webste, consstng of clearly dvded nformaton on loan characterstcs (amount, nterest rate, term, etc.), systematc rsk relevant characterstcs (credt ratng of borrowers, etc.) and dosyncratc rsk relevant characterstcs (sex, age, etc.) Researches n P2P manly focus on the mpact of nformaton provded wth the loan on nvestors' decson. Mchels fnds that larger number of peces of voluntarly dsclosed nformaton leads to sgnfcantly lower borrowng cost [6]. Barasnska studes the role of nformaton of borrowers' sex [7]. Other papers study whether nvestors are smart n the process of lendng. Freedman and Jn fnds that nvestors systematcally underestmates credt rsk of borrowers, but can learn [8]. Duarte et al. fnd that the average expected return n US P2P market s negatve, yet nvestors stll nvest n t [9]. Iyer et al., on the contrary, show that nvestors' decson s even more accurate than credt score n dentfyng borrowers' rsk [10]. Among the aforementoned lterature, Duarte et al. tests f nvestors form ratonal expectaton n US P2P market and fnds that they do not[9]. However, P2P n Chna tremendously dffers from P2P n the US. In the US, P2P platform serves only as nformaton ntermedary. The platform s not responsble for nvestors' loss ncurred by borrowers' default. Oppostely, n Chna, P2P platform plays the dual role of nformaton and credt ntermedary. The platform supples loan nformaton and smultaneously promses a full prncpal refund to nvestors who encounter a default, namely a guarantee mechansm. Ths paper calculates the expected nternal rate of return(eirr) of each loan and fnds that n Chna nvestors do not form a ratonal expectaton, just lke the case n the US as shown by Duarte et al. [9]. In a behavoral fnance perspectve, the loan EIRR s affected by systematc rsk as well as borrowers' ndvdual rsk, whch means the loans are not properly prced. On the other hand, n a P2P research perspectve, no paper has studed the Chna-specfc guarantee mechansm's mpact on nvestors' ratonalty and the EIRR both at loan level and market level. Emprcal results show that all loans n Chna P2P platform have a postve EIRR, opposte to the case n the US. Furthermore, nvestors n Chna do not maxmze ther expected return. All of the above results provde strong evdence aganst ratonal expectaton assumpton.

3 Ratonalty of Investors n P2P Onlne Lendng Platform wth Guarantee Mechansm 123 The structure of ths paper s as follows. Secton 2 ntroduces the model. Secton 3 s data and varable descrpton. Secton 4 s emprcal results and dscusson. Secton 5 concludes. 2 Prelmnary Notes For each loan, there s one nomnal nterest rate specfed n the contract. However, nomnal nterest rate s nether the expected nor realzed rate of return, both of whch reflect more mportance. What nvestors place more weghts on should be the nomnal nterest rate adjusted by rsks nherent n loans. Two rsks exst n lendng process, default rsk and prepayment rsk. Both affect the contngent cash flow generated by the loan n each perod. An ntutve llustraton s gven below. Assume there are two loans both havng only one balloon payment. Loan A has a nomnal nterest rate of 10% and a default probablty of 0, whle loan B's nterest rate s 100% but s sure to default. Under the crcumstance of no nsurance or guarantee, t s easy to see that loan A's expected nterest rate s 10% and loan B's s -100%, snce ts borrower wll surely default. So a ratonal nvestor should choose loan A. Nomnal nterest rate barely means anythng, only provdng a benchmark. The above case s too smple. We need to specfy one return measure that can cover more general cases. Internal rate of return(irr) s a reasonable choce. IRR s usually mplemented n calculatng the net present value of cash flow generatng projects. It s the dscount rate that equates a project's net present value to zero. A loan s essentally a fxed ncome asset or project that has a fxed cash flow payment n each perod, justfyng the usage of IRR to symbolze a loan's performance. However, the cash flow of a loan s random. In each perod, the loan mght end up defaulted or prepad. Therefore before calculaton of IRR, the probablty of default and prepayment n each perod should be estmated, under whch expected IRR s calculated. The followng ntroduces the estmaton model. 2.1 Expected Internal Rate of Return Model In ths secton, I ntroduce a model calculatng rsk-adjusted expected IRR n detal. The loan can termnate any tme due to dfferent rsks as descrbed above, from ntaton to maturty. Each case s one realzaton of a path. I estmate for every loan the probablty of every possble path the loan can take. Freedman and Jn and Duarte et al. use dfferent models to calculate IRR [8][11][12][9]. Termnaton of a loan before maturty mght be due to two reasons, prepayment and default. Prepayment refers to the case the borrower pays back the remanng prncpal and nterests before maturty date once and for all, whle default the case that borrower fals to tmely pay the oblgatory nterests and ceases to pay anythng afterwards. In the P2P platform we choose, Renrenda, payment guarantee or nsurance mechansm s present, typcal n Chna P2P market. In the case of prepayment, borrower pays off the remanng prncpal as well as an addtonal 1% of remanng prncpal as penalty. In the case of default, the cash flow n that perod s zero. But the platform guarantees to pay back the remanng prncpal one month perod(month) later to the nvestor usng the loan loss provson. Ths loan loss provson s rased from borrowers. Each borrower s charged an admnstratve fee every month.

4 124 Nanfe Zhang I defne Ptp to be probablty that a loan s prepad n month t condtonal on the loan not termnatng before month t, Ptd probablty that the borrower defaults n month t condtonal on the loan not termnatng before month t, and P tc probablty otherwse condtonal on the loan not termnatng before month t. It s easly seen that: P P P 1 tp td tc A loan can termnate n every month before maturty T because of default or prepayment, totalng 2( T 1) paths. In the last month, or month T, t wll ether termnate naturally or default, totalng 2 paths. Therefore, there are 2( T 1) 2 2T possble paths for a loan wth maturty T. For each path, we wll use the condtonal probablty to recursvely calculate the uncondtonal probablty. I denote the uncondtonal probablty for a loan to termnate n month t (t<t) Q tk ( k p, d), where p stands for prepayment and d default. Usng probablty theory, Q tk ( P t u 1 uc ) P tk In the fnal month, Q ( P ) P Tk T u1 uc,( t 1,2,..., T 1) Tk Each path corresponds to a net present value of loan at month 0. There are three scenaros: a. Prepayment n month t (t<t). t PAYMENT REMAININGP RINCIPAL *1.01 NPVtp AMOUNT u t u1 (1 r) (1 r) The last term s the penalty of prepayment. b. Default n month t. t 1 PAYMENT REMAININGP RINCIPAL NPV tp AMOUNT u t 1 u 1 (1 r) (1 r) In month t, there s no cash flow, whereas Renrenda wll refund the remanng prncpal n month t+1. c. Natural termnaton n month T. NPV Tc AMOUNT T PAYMENT u u 1 (1 r) Combned wth Q tk, E ( NPV ) Q NPV tk tk t, k Equatng E(NPV) zero, r can be solved numercally. Annualzng r by multplyng r by 12, I get the expected IRR. I argue expected IRR should be the core rate of return a ratonal and sophstcated nvestor pays attenton to, snce t already ncorporate all relevant systematc and unsystematc nformaton n the process of calbratng the probabltes, as wll be covered later.

5 Ratonalty of Investors n P2P Onlne Lendng Platform wth Guarantee Mechansm Probablty Estmaton Model In ths secton, I descrbe the calbraton of the condtonal probabltes. It s trval to calculate the uncondtonal probabltes gven condtonal ones. More specfcally, I estmate the condtonal probablty for each of three cases (c=censored, p=prepayment, d=default) n month t gven the loan survves to month t. Multnomal logstc regresson s appled n the followng form: Ptp et ln( ) 11 12loancharacterstcs 13 progresst 14loancharacterstcs progresst 1 t P tc Ptd et ln( ) 21 22loancharacterstcs 23 progresst 24loancharacterstcs progresst 2t Ptc The dependent varables are a par of odds rato, whch are ratos of condtonal probablty of prepayment or default n month t to a benchmark condtonal probablty that loan s censored or normally progresses n month t. All loan characterstcs avalable are ncluded n the model. I also add a progress varable that s month t dvded by term T to account for the possble tme varyng model structure, and nteracton terms between progress and loan characterstcs. I run the regresson to get all the coeffcents and plug them back n the model to generate all condtonal probabltes: Pˆ tp ln( ) ˆ ˆ loancharacterstcs ˆ progress ˆ t loancharacterstcs progresst tp Pˆ tc Pˆ td et ln( ) ˆ ˆ loancharacterstcs ˆ progress ˆ t loancharacterstcs progresst td Pˆ tc And usng smple math, I have Pˆ Pˆ Pˆ tp td tc e e e tp tp tp e tp e e td e 1 e td td td Data and Varables Descrpton Data descrpton Ths paper's data comes from a large P2P platform, Renrenda, n Chna. Renrenda was establshed n The sample perod starts n January 2011 and ends n February There are loans n the sample. I use all the sample to calbrate the multnomal logt model and estmate the expected IRR for each loan. However, only data before August 2012 are used to study whether nvestors are ratonal, snce n August 2012 Renrenda launched a manual loan screenng mechansm. The platform nvaldates some loans based on some unknown crtera. As a result, a certan amount of loans contaned n the data are not really seen by nvestors. To study whether nvestors are ratonal when

6 126 Nanfe Zhang makng nvestng decsons, I have to make sure that all data I use are actually seen by nvestors. In the loans, were not fully bd and loans were fully bd. Some of the fully bd loans were nvaldated by the platform, leavng loans for model calbraton. As for the ratonal expectaton analyss part, we use all loans, fully bd or not, from January 2011 to August 2012, totalng loans Varable descrpton Core dependent varable: FundngSuccess: 1 f a borrower gets the money and 0 otherwse. Independent Varables: Loan specfc characterstcs: Amount (n 1000s): Amount of the loan dvded by Interest: Annualzed nomnal nterest. Term: Maturty of a loan n months. Borrower-specfc characterstcs: Gender: 1 f male and 0 f female. Age: Age of borrower. IsVoc: 1 f borrower has a vocatonal college degree and 0 otherwse. IsUnGrad: 1 f borrower has a bachelor's degree and 0 otherwse. IsPoGrad: 1 f borrower has a master or PhD degree and 0 otherwse. IsDvorced: 1 f borrower s dvorced and 0 otherwse. IsMarred: 1 f borrower s marred and 0 otherwse. Lne of work relevant dummes: A group of dummes that are 1 f borrower s n a correspondng lne of work and 0 otherwse. Lne of work ncludes caterng, real estate, publc affars, charty, constructon, transportaton, educaton, fnance or law, retal, meda, energy, agrculture, sport or art, medcal, entertanment, government, and manufacture. WorkExp: Years of workng of borrower. 1 f no more than 1 year. 2 f more than 1 year and no more than 3 years. 3 f more than 3 years and no more than 5 years. 4 f more than 5 years. Income: 1 f borrower's ncome s lower than RMB f between RMB 1000 and f between RMB 2000 and f between RMB 5000 and f between RMB and f between RMB and f hgher than House: 1 f borrower has at least one house and 0 otherwse. Mortgate: 1 f borrower s n a mortgage contract and 0 otherwse. Credt specfc characterstcs: CR: Credt ratng of borrower by Renrenda, ncludng AA, A, B, C, D, E, HR n a descendng order. CR take the value of 6 for AA, 5 for A, 4 for B, 3 for C, 2 for D, 1 for E and 0 for HR. Applcaton: Hstorcal total number of loans borrower has appled. Success: Hstorcal number of successes n borrowng. PadLoan: Hstorcal number of loans fully pad off by borrower. TotalLendng (n 1000s): Hstorcal amount of loans borrowed.

7 Ratonalty of Investors n P2P Onlne Lendng Platform wth Guarantee Mechansm 127 Termnaton relevant: Prepayment: 1 f termnated due to prepayment and 0 otherwse. Default: 1 f termnated due to default and 0 otherwse. Tertme: Months before termnaton. Terprogress: Months before termnaton as a percentage of loan term. Table 1 s the summary statstcs for two samples, panel A for multnomal logt sample and panel B for ratonal expectaton sample. Table 1: Summary statstcs Frst second thrd Panel A Varable Name N Mean Standard Devaton Mn Medum Max Skewness amount term age appled success cleared totallendng gender svoc sungrad spograd sdvorced smarred st sres sreales spublc scharty sconstr strans sedu sfnlaw sretal smeda senergy sagr ssportart smed sent sgov smanuf workexp CR prepayment default censored tertme terprogress

8 128 Nanfe Zhang Panel B Varable Name N Mean Standard Devaton Mn Medum Max Skewness Amount Term Age Income House mortgage #appled #success #cleared Totallendng Gender Isvoc Isungrad Ispograd Isdvorced Ismarred Ist Isres Isreales Ispublc Ischarty Isconstr Istrans Isedu Isfnlaw Isretal Ismeda Isenergy Isagr Issportart Ismed Isent Isgov Ismanuf Workexp CR Fundngsuccess Interest Man Results 3.1 Dstrbuton of Expected IRR Expected IRR of each loan s calculated as llustrated above. In the default/prepayment rate estmaton model, loan's nomnal nterest rate s not ncluded, due to endogenety concern, for nterest rate s consdered to reflect default/prepayment rsk. As robustness check, I also repeat the procedure ncludng nomnal nterest rate. And the results are smlar. The results of logt regresson are not the man focus n ths paper thus not presented. But they are avalable upon request. The relatonshp between expected IRR and nomnal nterest rate n Chna s of man nterest n ths secton. A large dsparty between Chna and US P2P lendng platform s the exstence of a guarantee mechansm n the former. In the US, wthout the guarantee, f

9 Ratonalty of Investors n P2P Onlne Lendng Platform wth Guarantee Mechansm 129 borrower defaults, nvestor wll lose everythng, havng a return of -100%. Therefore, t s possble for a loan to have a negatve expected return. However n Chna onlne lendng market, snce each loan s protected aganst default by the platform, t s mpossble for a loan's expected return to be negatve, zero at least. In the case of default, expected IRR of a loan s smaller than ts nomnal nterest rate undoubtedly. Investor only loses one nterest payment at the month of default, for the remanng prncpal refund s one month later. Whereas n the case of prepayment, expected IRR can even be larger than ts nomnal nterest rate thanks to the penalty of 1%. It s natural to nfer that the expected IRR n Chna P2P lendng market to be postve and hghly correlated wth nomnal nterest rate. Fgure 1 plots the dstrbuton of expected IRR and nomnal nterest rate. The relatonshp s as expected. The emprcal probablty densty functon of expected IRR s more leftward than that of nomnal nterest rate. Fgure 2 plots the dstrbuton of nomnal nterest rate n excess of expected IRR, and Table 2 presents some statstcs of the dfference. In most cases, the dfference s postve, mplyng a larger nomnal nterest rate than expected IRR. But sometmes prepayment penalty drves expected IRR hgher than nomnal nterest rate. On average, the dfference s 0.52%. And the dfference s skewed to the rght. Fgure 1: Emprcal dstrbuton of expected IRR and nomnal nterest

10 130 Nanfe Zhang Fgure 2: Emprcal dstrbuton of dfference between nomnal nterest and expected IRR Also, the expected IRR n Chna P2P market as a whole s postve, on the contrary to Duarte et al. (2014)'s fndng of a negatve overall expected IRR n US market. I have to pont out that my fndng does not mplcate hgher qualty n Chna onlne loan assets than n the US. The postve expected IRR n Chna s smply a drect result of guarantee mechansm. Ths places more unpredctablty n nvestors' behavor, n that they do not have that hgh an ncentve as n the US market to do the rsk return analyss. Everythng they lose wll be compensated. Therefore, ratonal expectaton n Chna market remans a puzzle even though that n the US s already studed by many researchers. Table 2: Statstcs for dfference of nterests N Mean Mn Medum Max Skewness Influence Factors of Expected IRR Based on the assumpton that nvestors have ratonal expectaton, accordng to the renowned captal asset prcng model, rsk-adjusted expected return only depends on the systematc rsk of the portfolo nstead of dosyncratc rsk. I am to use Chna P2P market to study f Chna P2P nvestors form ratonal expectaton. Frst I have to dentfy proxes for systematc rsks. Takng nto account Duarte et al. (2014)'s choce, I use borrower's credt ratng, hstorcal borrowng records, educaton, ncome, workng experence and loan specfc characterstcs to proxy systematc rsk of a loan. Other varables represent dosyncratc rsk. Expected IRR s then regressed on both systematc factors and dosyncratc factors. The regresson model s expresson (1).

11 Ratonalty of Investors n P2P Onlne Lendng Platform wth Guarantee Mechansm 131 ExpectedIRR SystematcFactors IdosyncratcFactors (1) If nvestors are ratonal, when controllng all systematc factors from above, other varables should be nsgnfcant. What ndvdual rsk has mpact on should be the dfference between nomnal nterest rate and expected IRR. Expected IRR should be solely drven by systematc factors. Table 3 dsplays the regresson result. Table 3: Expected returns determnants under guarantee mechansm (A) (B) (C) Varable Coeffcent P Value Coeffcent P Value Coeffcent P Value Intercept < < <.0001 age < gender < < <.0001 sdvorced < < <.0001 smarred < < <.0001 st < < <.0001 sres < <.0001 sreales spublc scharty sconstr strans sedu sfnlaw < < <.0001 sretal < < <.0001 smeda < < senergy < < <.0001 sagr < < <.0001 ssportart smed sent < < <.0001 sgov < < <.0001 smanuf < < <.0001 CR appled E success < <.0001 cleared < <.0001 totallendng amount < <.0001 term < <.0001 ncome house <.0001 mortgage <.0001 workexp <.0001 svoc sungrad <.0001 spograd <.0001 Adjusted R Num. of Obs F test 74.94(p<0.0001) (p<0.0001) (p<0.0001) Panel A ncludes only dosyncratc factors, panel B adds hard nformaton systematc factors from the platform and panel C adds all other systematc factors. After controllng for systematc factors, expected IRR s stll sgnfcantly affected by ndvdual factors

12 132 Nanfe Zhang cross-sectonally. Elder borrowers mply lower expected IRR. Loan of a male borrower has lower expected IRR than that of a female one. Loan of a sngle borrower has hgher expected IRR than that of a marred or dvorced borrower. These are just a few examples of sgnfcant nfluence of dosyncratc rsk. The emprcal evdence s aganst ratonal expectaton assumpton. Expected IRR s not only correlated wth systematc rsk, but also dosyncratc rsk. Loans are not properly prced due to nvestors rratonalty. The reason behnd the result mght be the guarantee mechansm reducng the dfference of nomnal nterest rate and expected IRR, blurrng the rsk return structure of the loan. In other words, no matter how much rsk s nherent n a loan, the expected IRR wll be close to the nomnal nterest rate because of guarantee mechansm. 3.3 Investors' Decson Although the loans n Chna P2P market are not properly prced, t does not mean that nvestors are rratonal when makng nvestment decson. For a expected return maxmzng, ratonal and sophstcated nvestor, she can stll only use systematc nformaton to make decson. Therefore, I regress the dummy varable of a successful loan transacton on expected IRR as well as other varables. The equaton s expresson (2) and (3), and t s desgned to study when controllng expected IRR, whether other varables stll sgnfcantly affect the probablty that a representatve nvestor nvests n the loan. Pr( FundngSuccess ) log( ) 1 Pr( FundngSuccess ) Pr( FundngSuccess ) log( ) 1 Pr( FundngSuccess ) EIRR EIRR 1 Varables 22 2 (2) (3) If nvestors n Chna have ratonal expectaton and maxmze ther expected return, then expected IRR should have a postve mpact on the probablty of loan beng funded. Furthermore, controllng for expected IRR, other varables should be jontly nsgnfcant. And f t s the most mportant factor n nvestor's decson, regresson coeffcent of expected IRR should be robust and reman sgnfcantly postve whchever other factors controlled. More specfcally, comparng to the benchmark model merely ncludng expected IRR as explanatory varable, models that nclude expected IRR as well as other varables do not have a sgnfcant ncrease n explanatory power. The result of the regresson s gven n Table 4. Panel A only ncludes expected IRR as ndependent varable, panel B adds dosyncratc varables and panel C contans both systematc and dosyncratc varables. Table 4: Investors' decson under guarantee mechansm

13 Ratonalty of Investors n P2P Onlne Lendng Platform wth Guarantee Mechansm 133 (A) (B) (C) Varable Coeffcent P value Coeffcent P value P value P value Intercept < < <.0001 rr < < <.0001 age < <.0001 gender sdvorced smarred < <.0001 st < sres sreales spublc scharty sconstr strans sedu < sfnlaw < sretal < smeda senergy sagr ssportart <.0001 smed sent < sgov < <.0001 smanuf 0.36 < <.0001 CR <.0001 appled success <.0001 cleared totallendng amount term <.0001 ncome <.0001 house mortgage workexp <.0001 svoc <.0001 sungrad <.0001 spograd L Lkelhood rato test D.F Confdence 95% 99% 95% 99% Ch-square From panel A, expected IRR has a sgnfcantly negatve mpact on the probablty a loan beng funded. Investors do not am for hgh expected return. When controllng for all other varables, as n panel C, the nfluence of expected IRR turns sgnfcantly postve. For example, for two loans havng the same expected IRR, one wth a male borrower wll be less lkely to be fully funded than one wth a female borrower. Ths s evdence that nvestors' rratonally prefer female borrowers to male ones. By 'rratonally', I mean the preference does not rse from return dfference but from nvestors' taste. As a whole, expected IRR s not even robust across dfferent model specfcatons. Investors' stll take nto account other factors, despte the rsks of other factors already ncorporated nto

14 134 Nanfe Zhang expected IRR. Furthermore, by comparng the explanatory power of dfferent models wth panel (A) model beng the benchmark, t s easly seen that addng other varables sgnfcantly decrease -2*log-lkelhood, n that the statstcs of lkelhood rato test are both larger than the ch-square crtcal values. The null hypothess that none of the other varables except expected IRR have any mpact on nvestors' decson are rejected. That means nvestors n Chna consder a great deal of nformaton besdes expected return of the loan. To conclude, nvestors n Chna do not form ratonal expectaton. 3.4 Dscusson The lack of robustness n expected IRR n Chna P2P market mght result from the guarantee mechansm. Investors mght get confused when they make ther decson. Even f they are ratonal, nvestors mght not be clear about how to nterpret the mpact of the guarantee on future cash flows. Some of them mght choose to beleve that the platform wll actually fulfll ts responsblty when borrower defaults, but some mght not. Those who could not completely trust the platform wll put lttle weght on the guarantee effect when makng decson, n other words a complete dfferent expected IRR wll be observed. Therefore, t s natural for the expected IRR effect to be not robust gven that some nvestors beleve n t whereas others do not. But gven the good record of Renrenda, where all defaulted loans are refunded by the platform, t mght stll be more ratonal for nvestors to gve credt to the guarantee mechansm. 5 Concluson Whether nvestors for ratonal expectaton s an mportant ssue both n tradtonal and behavoral fnance research. If nvestors are ratonal, then accordng to CAPM model, the expected IRR of loan should only be affected by systematc rsk nstead of dosyncratc rsk. Ths paper s especally nterested n Chna P2P nvestors' ratonalty. In Chna, P2P s one of the hottest topc n web fnance. Furthermore, unlke the case n the US, Chna P2P platforms have a guarantee mechansm that pays back all remanng prncpal for a defaulted loan to nvestors. What effect the mechansm may have on nvestors s unknown. No other research has used a market wth guarantee mechansm to study nvestors' ratonalty. Ths paper bulds a multnomal logstc model to ncorporate the default/prepayment rsk n each month for each loan and computes the expected IRR, or rsk-adjusted return, of every loan. The result shows that n a platform wth guarantee mechansm, the dfference of expected IRR and nomnal nterest rate s partcularly small. Expected return of a loan s not only affected by systematc rsk but also dosyncratc rsk, not n accordance wth CAPM. Besdes, nvestors take nto consderaton other rsk factors along wth expected IRR, although the return-relevant nfluence of the rsk factors s already ncorporated n the latter. All emprcal results gve evdence to the fact that Chna P2P nvestors are not ratonal. References

15 Ratonalty of Investors n P2P Onlne Lendng Platform wth Guarantee Mechansm 135 [1] E. Fama, Effcent captal markets: a revew of theory and emprcal work, Journal of Fnance, 25(2), (1970), [2] M. Jensen, The performance of mutual funds n the perod , Journal of Fnance, 23(2), (1967), [3] E. Fama, The behavor of stock market prces, Journal of Busness, 38(1), (1965), [4] E. Fama, L. Fsher, M. Jensen and R. Roll, The adjustment of stock prces to new nformaton, Internatonal Economc Revew, 10(1), (1969), [5] A. Shlefer, Ineffcent markets, Oxford Unversty Press, Oxford, [6] J. Mchels, Do unverfable dsclosures matter? Evdence from peer-to-peer lendng, Accountng Revew, 87(4), (2012), [7] N. Barasnska, Does gender affect nvestors' appette for rsk? Evdence from peer-to-peer lendng, DIW Dscusson Paper 1125, (2011). [8] S. Freedman and G. Jn, Learnng by dong wth asymmetrc nformaton: evdence from prosper.com, NBER Workng Paper W16855, (2011). [9] J. Duarte, S. Segel and L. Young, To lend or not to lend: revealed atttudes towards gender, ethncty, weght, and age n the U.S., SSRN Workng Paper , (2015). [10] R. Iyer, A. Khwaja, E. Luttmer and K. Shue, Screenng peers softly: nferrng the qualty of small borrowers, Management Scence, 62(6), (2015), [11] S. Freedman and G. Jn, Do socal networks solve nformaton problems for peer-to-peer lendng? Evdence from Prosper.com, SSRN Workng Paper , (2008). [12] S. Freedman and G. Jn, The sgnalng value of onlne socal networks: lessons from peer-to-peer lendng, NBER Workng Paper W19820, (2014).