Prosper BDA Paper Draft 18December2009(2)-1

7/31/2019 Prosper BDA Paper Draft 18December2009(2)-1

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Borrower Decision Aid for People-to-People Lending

Lauri PuroHelsinki University of Technology

Department of Industrial Engineering and ManagementP.O. Box 5500, FIN-02015 TKK, FINLAND

Jeffrey E. TeichNew Mexico State University

Management DepartmentNew Mexico State University, Las Cruces, NM 88003, USA

Hannele WalleniusHelsinki University of Technology

Department of Industrial Engineering and ManagementP.O. Box 5500, FIN-02015 TKK, FINLAND

Jyrki Wallenius

Helsinki School of EconomicsDepartment of Business Technology

POB 1210, Helsinki 00101, [email protected]

December, 2008(Revised December 2009)

All rights reserved. This study may not be reproduced in whole or in part without theauthors' permission.


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Abstract

In setting up, and bidding in online auctions, people face difficult strategic decisions. In this

study, a Borrower Decision Aid is introduced, which will help formalize the decision making

process of the sellers, or borrowers in this case, in one particular P2P loan auction site,

Prosper.com. The vast amount of real-life bidding data available in this online auction

enables us to build new kinds of tools for decision makers. The Borrower Decision Aid helps

the borrower to quantify her strategic options, such as starting interest rate, and the amount of

loan requested. We identify which variables concerning the borrower are related to the

probability of successfully securing a loan and the final interest rate.

Keywords:people-to-people lending, decision support, reverse auctions

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Introduction

1.1 Background

Prosper.com is the first people-to-people lending marketplace, based on an online reverse

auction. In this marketplace, people make applications for loans, called listings, and then

other people make bids on these listings. The winning bidders get to fund the loan and the

interest rate is determined by the auction the more competition, the lower the interest rate.

In other words, the idea is to link the person in need of money with people willing to lend

money without an intermediating bank. Typically a loan is funded with many bidders

(lenders), because most lenders only fund $50 - $200 per each loan. Lenders bid for these

small amounts across many loans to help diversify their risk. Prosper.com was launched

publicly in February 2006, and has brokered so far over $150 million worth of loans [17],

[22].

In this study, we focus on the role of the borrower, i.e. the person who sets up the listing for a

loan. The borrower has several important strategic decisions to make, which can later

determine if she gets the loan funded or not. The purpose of this study is to provide decision

support for the borrower when making these important decisions. In the literature there are

only a few publications that discuss decision support in auctions (in general). [1], [8],

[15], [16], [23] and [25] are some examples. Their angle is different from ours, though.

Our study has significant practical importance. Currently, borrowers set their listing

parameters based on insufficient data, such as the average interest rate. In this study, we

introduce a framework to analyze the borrowers strategic decisions in terms of success

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probabilities and estimated final interest rates. A Borrower Decision Aid (BDA) is described,

which enables the borrower to evaluate her strategic options quantitatively. This is a

significant practical improvement to the current situation where Prosper.com only provides

scant advice on the starting rate and no advice on the amount of the loan.

In addition to being practically important, our study is interesting in a theoretical sense as

well. Namely, the framework and the methods used in constructing the tool are interesting

and could be used with other online auction sites.

1.2 Objectives of the Research

The main objective of this study is to develop a decision support tool for the borrowers. This

tool helps the borrowers evaluate their strategic options in quantitative terms. In more detail,

we

1. identify the most important factors that affect the outcome of the auction, that is

borrowers chances of getting the loan funded;

2. identify the most important decision variables that the borrower can change in order

to influence the outcome of the auction; and

3. develop a framework and methods to compare different strategic options in

quantitative terms.

We look at all the information available and compare it to empirical data on Prosper.com

listings. The identified factors are then divided into those which the borrower can influence

and those that are part of the credit report. Both types of variables are needed in this study,

but naturally the ones that the borrower can influence are the ones we provide advice on. We

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examine different methods of comparing strategic options and choose the best methods and

variables for the borrower decision aid. The decision support tool is then constructed and

tested. This study is limited to Prosper.com auctions only. The framework and methods of

constructing the borrower (or seller) decision aid can, however, be extended to other auction

sites as well.

1.3 Data and Research Methods

This study is based on empirical data provided by Prosper.com. Much of the data is freely

available on the Prosper.com website. However, accessing the credit records requires one to

register as a lender on the site. In total there were 312,562 listings made on Prosper.com (up

to July 2008). Prosper allows access to these listings, which form the basic population data in

our study.

The strategic decision making of the borrowers is examined with the help of multivariate

statistical analyses, in particular ordinary least-squares regression and logistic regression

analysis. The BDA itself is implemented as a website, which could be made available to the

public and/or implemented on Prospers own site or a so called third-party site.

1.4 Organization of the Paper

The first section of this study provided the background and objectives of this study. In section

2, literature related to the borrowers strategic decisions is briefly reviewed. In section 3 the

data used in this study is introduced and the borrowers basic strategic decisions are charted.

In this section, the most influential decision variables are identified for the development of

the BDA. Section 4 describes the construction of the BDA and introduces the underlying

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methods. In section 5, the BDA website is described and the two different methods of

providing support are compared. Section 6 concludes the study.

Literature Study

The amount of auction literature is vast. Several of the ground-breaking discoveries were

made in the 1950s and 1960s when bidding behavior was modeled using a game-theoretic

framework. The latest wave of research started after the emergence of online auctions. In

particular, the online environment enabled researchers to carry out empirical studies with data

gathered from real-life auctions (see, e.g., [3], [18], [25], [26]). This was a clear improvement

to previous laboratory studies with university students ([10], [11]).

In the traditional auction literature, the roles of the seller and the auctioneer often coincide,

although this may not be the case in online auctions. The seller is expected to be able to

choose the auction design parameters freely. Much of the literature has focused on comparing

different auction mechanisms in different situations and determining which mechanisms

provide superior profit for the seller ([19], [20]); or which mechanisms are efficient ([13]). In

online auctions the roles of the seller and the auctioneer rarely coincide. The auctioneer is the

website that facilitates the auction. The auctioneer has usually chosen some simple and

universal auction mechanism that all sellers are obliged to use. Therefore, the strategic

choices of the seller are constrained by the parameters of the chosen auction mechanism.

This, however, makes the strategic decisions of the sellers no less important, but actually this

emphasizes the importance of the few remaining decision variables at the disposal of the

seller.

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The classic decision variable of the seller is the starting price. The importance of the starting

price depends heavily on the type of item sold and the auction mechanism. The literature on

the effect of the starting price on the final price is somewhat controversial. For example, [14]

found empirical evidence stating that under some conditions having a lower starting price can

eventually lead to higher final price (in a forward auction). They suggested reduced barriers

to entry and commitment of bidders as possible reasons. The sunk search and monitoring

costs make it psychologically difficult for the bidder to walk away from the auction.

Conversely, [9] showed that the correlation between the starting price and the final price was

positive. This would mean that by entering a higher starting price, the expected final price is

higher as well. One reason they suggested was that by entering a higher starting price, the

seller is able to signal to the bidders that the item is worth at least that much. The higher

starting price leads to a higher final price also if competition among bidders is generally very

weak. In an extreme case, with just one interested buyer, the final price will equal the starting

price, and therefore the higher starting price leads to higher final price. Gilkeson and

Reynolds [9] agreed with the theory about reduced barriers to entry and commitment, but

they claimed that it would only affect the probability of the auction to succeed (i.e. the item

being sold), but not to increase the final rate. They studied eBay auctions that had a

possibility to use a secret reservation price and they proved that higher starting price leads to

lower success probability, but a higher closing price. In [18] the correlation between starting

price and final price was also found to be positive.

The tradeoff suggested by [9] provides an excellent framework for our study. The borrower

has two aims on Prosper.com. First, she wants to get her loan funded in a successful auction

event. Second, she wants the interest rate to be as low as possible. The tradeoff makes this

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decision difficult. If the borrower wants to be sure that the loan gets funded, she must settle

for a higher interest rate and a higher starting rate. But a lower starting rate may result in a

lower final rate but at a reduced probability of funding.

Prosper.com is a multi-unit auction, because the loan will normally be funded by multiple

bidders. This makes the situation even more interesting. In multi-unit auctions, the borrower

can choose the number of items (i.e. loan amount) sold in addition to the starting price. This

decision has similar kind of strategic value as the starting price. Most of the previous studies

on multi-unit auctions, however, look at the amount as a question about an optimal lot size in

repeated auctions ([2], see also [24]). On Prosper.com, however, the same borrower creates

only one or at most a couple of listings, and therefore the importance of the amount as a

strategic decision variable is further emphasized.

Strategic Decision Making of the Borrowers

This section begins by introducing the data used in this study, including an explanation of

how the Prosper.com auction site operates from the borrowers viewpoint. Next, we identify

the most important decision and credit variables that affect the outcome of the listing. These

variables will later form the heart of the Borrower Decision Aid.

1.5 An Example from Prosper.com Website

An example of a loan listing from Prosper.com is shown in Figure 1. Here the borrower is

seeking a $7,300 loan to expand a small business. There is still over 37 hours left in the

auction and the loan is already fully funded. The starting rate of the listing was 25.96% and it

has been bid down to 13%. The borrowers credit grade is C and he is a verified homeowner.

The debt-to-income ratio of the borrower is 39%. The listing includes a short description,

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where the borrower usually explains how she is planning to use the money. Additionally, the

listing may include a picture and endorsements from friends and family.

FIGURE 1 ABOUT HERE

3.2 Description of the Data Used in the Study

Prosper.com offers a unique opportunity to access a vast amount of real-life online auction

data ([22]). Prosper.com has been in operation since February 2006 and during this time until

August 2008 there have been 312,562 listings created. Our data set starts from May 2006 and

includes all non-active listings made before August 2008. The number of listings in our

sample is 293,976. From these listings 26,251 (8.4%) have been funded. This data will be

used as the basic population. The data is freely available on Prosper.com website, although

for additional credit information one must register as a lender. The data was then imported to

MS Access, where it was further analyzed.

Large amounts of data are available for every listing including what is available to registered

lenders from the credit report. In an appendix, all the factors have been listed. The most

important factors are amount requested, starting rate, credit grade, debt-to-income ratio,

duration, funding option, homeownership, and status and end date. In addition, other

demographic information is available. The credit information is pulled from Experian Scorex

Plus (SM) system, which is specialized in providing peoples credit information.

The terms of the loans on Prosper.com are fixed to a three year, fully amortized, unsecured

loan. The borrower can choose the loan amount freely between $1,000 and $25,000. The

average requested loan amount is $7,500 (median $5,000). The starting rate of the auction

can be set anywhere between 0% and 36%. The average starting rate is 19% (median 18%).

The starting rate naturally is very sensitive to the credit grade of the borrower. The credit

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grade (scaled between AA-HR, where AA is best and HR worst) is calculated by Experian. It

takes into account all the credit information variables and grades the borrower accordingly.

Debt-to-income ratio is calculated by dividing the borrowers total amount of debt with her

income. The ratio is limited to between 0-101%, but because the income is self-reported, this

statistic could be inaccurate.

The borrower can choose the duration of the auction from four alternatives: 3, 5, 7 and 10

days. 7 days is the most commonly used auction duration. The borrower has the option to end

the auction as soon as the loan gets funded. This practically means that the borrower is

satisfied with the starting rate and needs the money as quickly as possible. Otherwise the

auction will be open for the full duration. The status of the listing can be completed, expired,

withdrawn or cancelled. The completed status means that the listing was funded and the loan

issued. The expired status means that the auction ran its full duration but never got funded.

The withdrawn status means that at some point during the auction the borrower withdrew the

listing. The cancelled status means that Prosper.com has cancelled the auction because of

some faulty listing information. Furthermore, the listing can be active, which means that it is

currently running. In this study the active listings have been excluded.

3.3 Identifying Influential Variables

In this section we identify the most important variables that affect the success probability of

the listing by using pair wise correlation tests. In order to perform the tests some of the

variables had to be transformed. The most important transformation was done to the Status

variable. This was transformed into a dummy variable. The status completed was entered as

1 and expired, withdrawn and cancelled as 0. We do not know the reasons behind the

borrowers withdrawal decision. However, the number of withdrawn listings is very

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significant, up to 30% of all listings. Therefore, we can not exclude them all. It seems that a

great majority of these listings has been withdrawn because of lack of interest by the bidders.

Only 1% of all withdrawn listings were fully funded. Apparently, some people do not want to

see their listing expire, if the bidders show only little interest in it. They would rather

withdraw it and create a new listing with different listing parameters. In total, there were

140,265 borrowers who made listings on Prosper.com. Of these people, up to 67,297 (48%)

had multiple listings. Most of the people who made multiple listings had done so because

their first listing did not get funded. Up to 77% of the people who had made multiple listings

had at least one unsuccessful listing. This further underscores the point that the borrowers

could really use a strategic decision support tool, which would help them in finding the right

listing parameters the first time.

For this part of the study, the credit grade scale AA-HR was transformed to numbers between

1 and 7. This is an unorthodox way of describing the credit grade, because the credit grade is

ordinal scaled, not interval scaled as 1-7 would suggest. Later, this problem has been solved

by calculating each credit grade individually, but this scaling allows easy preliminary

examination. The funding option was transformed into a dummy variable so that Open for

duration was entered as 1 and Close when funded as 0. The same approach was used with

the variable homeownership.

In Table 1, the correlations between different listing variables and the status dummy

variable is presented. The pair wise correlation test was performed with all reasonable

variables. Some credit information variables were omitted if they suffered from a small data

sample or if they were too much alike other variables. The variables that the borrower can

have an influence on have been presented in the first four rows of the table. The rest of the

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rows are credit information variables, which the borrower can not influence at least in the

short-run.

As a whole, the correlations are relatively small. There are a few logical reasons for this. First

of all, we have used all the data available. This enables us to see the big picture, but for

example the starting rate is very sensitive to the credit grade. For example, a 15% starting

rate might guarantee the success of the listing for an AA grade borrower, but the same

starting rate might be too low for an HR grade borrower to get her listing funded. Therefore,

in the full data set the correlations are lower than when examined one credit grade at a time.

Again particularly the starting rate, i.e. the price of the loan, is very sensitive to common

market interest rates and risk premiums. We have used data from the full two and a half years

of time. During this time the federal interest rate has varied between 2-5.25% (Federal

Reserve [7]). In addition, the recent credit crisis has increased the risk premiums

substantially. Therefore, the correlations would be higher if we would look at data from

shorter periods of time, where the market fundamentals would be similar for all listings.

The correlation analysis done with the full data set does enable us to compare the significance

of different variables. As we can see, the credit information variables have generally higher

correlations than the decision variables. This is quite logical, as people with low credit grades

have difficulties in obtaining a loan no matter how high, for example, the starting rate is. All

the correlations are statistically significant, because of the high number of observations. The

amount requested and starting rate have higher correlations than the funding option and

the duration. The signs of these correlations are in line with [9]. A higher starting rate

increases the borrowers chances of getting the loan funded (note that Prosper.com auction

mechanism is reversed in the sense that high interest rate is bad for the borrower, i.e. the

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seller, and good for bidders). Logically, a higher amount requested decreases the borrowers

chances of having a successful listing. The funding option Open for duration, entered as 1

increases the borrowers success probability, as is the case with the longer duration.

Next to the credit grade, the delinquency related variables have the second highest

correlation. The current delinquencies seem to be the most influential of these variables.

The homeownership shows some correlation and the correlation of debt-to-income ratio is

relatively low. This is the case with the variable income as well. All the signs of the

variables are logical.

TABLE 1 ABOUT HERE

In Table 2 the correlation analysis is repeated for two different credit grades: A and D. This

demonstrates how different the two credit grades are from each other. Now that the aggregate

credit information variable is already taken into account in the data sampling itself, we can

see that the decision variables become much more important. The correlations of the

amount and the starting rate are now relatively high. The correlations of the funding

option and the duration seem to remain at a low level. Note that the number of

observations in Table 1 is different across attributes. For example, the Debt to Income

attribute was not calculated in cases where income was not reported, or it was zero.

Now that the samples already contain information about the credit grade, the correlations of

the rest of the credit information variables are significantly lower. It would seem that the

debt-to-income ratio would have the highest correlation with success of the listing within a

credit grade. Homeownership seems to be problematic. In credit grade A there is no

correlation at all. In credit grade D the correlation is negative, which is counter-intuitive.

Owning a house seems to negatively affect the borrowers chances of getting the loan funded.

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Because of this inconsistency, this variable was omitted1. Apparently, the delinquency related

credit information variables seem to have some correlation with the success of the listing, but

this time the current delinquencies are more heavily emphasized. The amount delinquent

and delinquencies last 7 years seem to underperform the current delinquencies throughout

the data. The last credit information variable, the income, behaves very inconsistently. In

credit grade A the correlation is very small but positive. In credit grade D the correlation is

negative, which is again counter-intuitive. It could be that people expect borrowers with high

income to manage their financial situation better than credit grade D implies. The correlation

of the income variable is relatively low, perhaps because the income is self-reported and

possibly inaccurate.

TABLE 2 ABOUT HERE

Based on this analysis the most influential variables are the starting rate, amount

requested, credit grade, debt-to-income ratio and current delinquencies2. The

development of the borrower decision aid was designed with this set of variables.

Borrower Decision Aid Underlying Model

In this section we develop the Borrower Decision Aid using an underlying logistic regression

model and a query method, a brute force categorization of the database. They are alternative

models which provide information about the probability of the listing being funded given

initial parameter settings such as starting rate, loan amount, credit rating etc. The final rate

1 A reason might be that the individuals were never questioned about the size of their mortgage.

2 For further validation the correlations were rerun for two separate subsamples (July-December/2007

and January-June/2008). Our results showed that the same variables maintained their high correlations

with listing success over time as well, justifying our choice of variables for the model.

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given these parameters is also predicted via an OLS regression model. In general, the

predictions are based on the most recent six months of data, instead of the whole 2.5 years

available because the market for loans has substantially changed during that time period. The

Federal Funds rate has varied between 2-5.25% during the 2.5 years (Federal Reserve [7]).

Also the market risk premiums have fluctuated. For example the credit crisis that started in

spring 2007 has increased the risk premiums significantly. In Figure 2 we can see how the

interest rates have fluctuated on Prosper.com during the previous year for the various credit

grades.

FIGURE 2 ABOUT HERE

1.6 Logistic Regression Model

The Borrower Decision Aid (BDA) estimates the probability of getting the loan funded,

given planned listing parameters and borrowers credit information. We opted to use the

logistic regression model because normal regression does not allow a dependent variable to

be binary (listing getting funded or not). Gilkeson and Reynolds [9] used logistic regression

in their study to examine how the starting rate affected auction success. The logistic

regression is based on the cumulative logistic probability function described below (see, e.g.,

[21]).

where f(z) represents the probability of funding given the set of independent variables defined

as follows:

otherwise the logistic regression works in similar manner as the ordinary regression model.

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The logistic regression was calculated separately for all credit grades. The reason for this was

that borrowers behave very differently between the credit grades as we saw in Table 2. Thus,

by calculating the credit grades separately we can get more accurate results that match the

current credit grade specifically. Another reason for this is that the credit grade itself is an

important factor in determining whether the listing gets funded or not. However, adding it to

the model as a variable is difficult because it is ordinal scaled, not interval scaled.

The independent variables: starting rate, amount, debt-to-income ratio and current

delinquencies were chosen according to the analysis in section 3.3. In Table 3 the

coefficients of the logistic regression models have been displayed. They all have logical

signs. Increasing the starting rate increases ones chances of getting the loan funded.

Conversely, increasing the requested amount, debt-to-income ratio or current

delinquencies decreases ones chances of getting the loan funded. All the independent

variables are statistically significant. In logistic regression there is no equivalent measure for

the coefficient of determination R2. Instead we use McFaddens Pseudo-R2.

TABLE 3 ABOUT HERE

As we can see from Table 4, as we introduce new variables one after another, starting with

amount, followed by starting rate, debt-to-income ratio, and current delinquencies, the

Pseudo-R2 increases to 0.208, but adding additional independent variables does not improve

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the model significantly3. We use the query method, developed below, to cross validate the

model.

TABLE 4 ABOUT HERE

1.7 Query Method

The query method is an intuitive data-driven way of determining the success probability.

Based on the listing parameters entered by the borrower, the database is searched for similar

listings within a certain range (+/-25%) of the value of the parameter. This ensures that the

query returns an adequate number of similar kinds of listings. The current delinquencies

were queried as a binary true/false variable. Then the BDA calculates the success ratio of this

sample, i.e. how many listings got funded.

The logistic regression can calculate the precise success probability with exact listing

parameters, whereas the query method takes a set of listings which have relatively similar

listing parameters. The query method requires vast amounts of data (i.e., listings) to work

properly. When there are not enough similar listings, the reliability of the query method

quickly decreases. This problem arises when the given listing parameters are less frequently

used. As stated previously, all the methods use 6 months of data. For the query method,

however, the data sample is extended to 12 months if the number of similar listings is below

20. The user of the BDA will naturally be alerted when the sample period is increased to 12

months.

3 For further validation the logistic regression model was recalculated with out-of-sample data. Results

using data from July-December 2007 showed that the same variables remained significant in the model

and no additional variables that would have improved the model significantly were found in the 7-

12/2007 sample either. In other words, the model structure remains consistent over time, although the

individual regression coefficients require regular updating for current market conditions.

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1.8 Regression Model for the Final Rate

The final rate of the listing was estimated with an ordinary regression model. In Table 5 the

correlations between the regression variables have been calculated for credit grade A. The

correlation was highest between the final rate and the starting rate. The correlation

between the final rate and the amount is also high. The debt-to-income ratio and current

delinquencies have lower correlations with the final rate, but they are still statistically

significant. There is a risk of multicollinearity in the model, because the correlation between

the independent variables starting rate and amount is 0.55. Both variables are vital for the

model and therefore neither one was omitted.

TABLE 5 ABOUT HERE

The regression model is similar to the logistic regression model, but this time the dependent

variable is the final rate. The final rate is a continuous variable and therefore an OLS

regression model is appropriate.

The results of the regression model, presented separately for different credit grades, can be

seen in Table 6. Each regression coefficient is presented with the corresponding p-value

associated with the t-test. Almost all of the variables are statistically significant with 5%

significance level. There are two exceptions: the variable amount in credit grade C and the

variable debt-to-income ratio in credit grade HR.

The R2 is between 0.5-0.7. The number of observations is quite equally distributed among the

credit grades. The number of observations is much smaller than in the logistic regression,

because here we can use only completed listings. In the last column of Table 6, the final rate

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estimates have been calculated with the following listing parameters: starting rate 18%,

amount $5,000, debt-to-income ratio 40% and zero current delinquencies. As we can

see, the final rate estimate quickly increases as the credit grade becomes worse. As a whole

the regression model predicts the final rate reasonably well. Looking at the associated

residual plots, it appears there is unequal (increasing) variance associated with some of the

variables implying heteroskedasticity, in particular when outside the range of common

values. However because we are not calculating prediction intervals in the BDA (point

estimates are still unbiased), this appears less serious.

TABLE 6 ABOUT HERE

4.4 Comparison of Query and Logistic Regression Methods

As a brief cross validation between the query method and the logistic regression method, we

have produced Figures 3 and 4. In Figure 3 the BDA was run with listing parameters: credit

grade A, debt-to-income ratio 40%, zero current delinquencies and $5,000 requested

amount. The starting rate was increased from 1% up to 30%. In general, the two methods

provide similar results. Within reasonable starting rates between 9-17% the results are very

similar. For low starting rates (below 7%), the success rate estimates are unreliable for both

methods, and probably actually are close to zero. For higher starting rates (above 17%), the

actual success rates are probably in between the results produced by the two methods.

FIGURE 3 ABOUT HERE

In Figure 4, the analysis is repeated, but this time the starting rate was fixed to 15% and the

amount was changed from $1,000 to $25,000. Again, the results of both methods are very

similar, the query method providing an upper bound and the logistic regression a lower bound

for the success rate. The query method has some fluctuations when the number of

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observations is very small. This is just one cross-section of the data; however on average the

two methods should produce similar results.

FIGURE 4 ABOUT HERE

Borrower Decision Aid Website

The BDA was implemented as a website. On the website the borrower enters the blank fields

in the borrower information window as seen in Figure 5. Then they click Estimate and

the results for an example are presented on their screens below. First, the tool prints the

listing parameters that the borrower entered and shows the search criteria for the query

method. Then a sensitivity table is presented, where the borrower can see how the estimated

final rate and estimated success probability change with different requested amounts and

starting rates. In this case, the estimated final rate with the given parameters was 11.65% and

the success probability 0.46. These figures were calculated based on the regression models.

By increasing the starting rate by 1%, the borrower can increase her chances of getting the

loan funded to 0.50 but the final rate increases to 12.15%. By decreasing the requested

amount, however, the borrower can increase the success probability to 0.50 and decrease

the final rate to 11.50%. In the table, some other combinations have also been calculated

allowing the borrower to decide the best option, or, repeat and recalculate.

Below the sensitivity table, there are more detailed results. First, we can see the search

criteria used by the query method. Then there is the final rate estimate with coefficient of

determination and number of observations. Next, the tool calculates the estimated final rate

according to the regression model as presented in section 1.8. In this case the estimate is

11.63%, which is significantly below the starting rate of 15%. Below the estimated final rate,

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the tool presents the R2, and number of observations used in constructing the model. These

basic regression diagnostics give some indication of the reliability of the results.

The next analysis is the logistic regression. Here the BDA calculates the estimated success

probability of the listing. In this case the probability of the listing getting funded is 46%.

Again, the regression diagnostics, i.e. the Pseudo-R2 and the number of observations used in

constructing the particular logistic regression model, have been attached to the regression

results. The final analysis is the query method. Here the BDA queries the database for similar

listings as the one entered by the borrower. The search criteria were shown in the very

beginning of the results box. In this case there were in total 51 similar listings of which 24

were funded. The implied success probability is 47%, which is very close to the one given by

the logistic regression method. Finally, the 51 similar listings have been printed individually

(only the first four are shown in the figure). The borrower can then manually check what kind

of listings people have made previously and the result.

FIGURE 5 ABOUT HERE

Conclusions

The main objective of this study was to develop a decision support tool for the borrowers in a

P2P reverse auction lending environment. The underlying tool is based on regression models

and data driven query methods. The tool enables the borrowers to evaluate their strategic

options in quantitative terms. We found that there is a trade-off between having a low final

rate and getting the loan funded, as the previous literature had suggested. In order to have a

low final rate, the borrower must choose a lower starting rate. This, however, decreases the

borrowers chances of getting the loan funded. Therefore, the borrower must consider these

two factors and make the difficult tradeoff decision about the targeted final rate and the

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acceptable risk in terms of success probability. The Borrower Decision Aid (BDA) quantifies

this decision by calculating the estimated success probability and the estimated final rate. In

addition, the borrower can fine-tune both the success probability and the estimated final rate

by changing the loan amount. By requesting a smaller loan amount the success probability

increases and the final rate decreases. If the borrower is not able to find a satisfying starting

rate that would have acceptable success probability combined with suitable final rate, she

must decrease the loan amount.

The BDA assists the borrower to see the listing parameters in a strategic context and provides

useful quantitative information to support the final decision. As such the BDA naturally

works only with P2P lending sites similar to Prosper.com. However, the methods used in

constructing the tool could be used in other contexts as well. Firstly, the BDA could be

extended to other online auctions with sufficient data available. The auctions would not have

to be multi-unit, but the success probability could be attached, for example to exceeding the

secret reservation price (used, for example, on eBay; see [12]). The final rate estimate is

naturally even more widely applicable. A reliable estimate of the final price would be useful

for the seller in any auction. The availability of data is probably the biggest constraint in

expanding the use of the BDA.

One of the benefits for auction sites to provide access to their raw auction data is the possible

development of third party sites providing tools to the general public. Prosper has already

benefited from this aspect of their philosophy and will continue to do so. We have provided

our BDA to Prosper, and they are considering implementing our tool on their site.

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Acknowledgement: This research was supported by the Academy of Finland grant

number #121980.

References

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in Iterative Combinatorial Auctions, Inf Syst Research 16, 2005, 169185.

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Auctions, CITM Working Paper 96-WP-1019, 1996.

[3] P. Bajari and A. Hortasu, The Winners Curse, Reserve Prices, and Endogeneous Entry:

Empirical Insights from eBay Auctions, RAND Journal of Economics34 (2), 2003,

329-355.

[4] Borrower Decision Aid, 2008, http://www.tikkunekut.org/prosper/index.php/, viewed

September 10th 2008.

[5] Erics Credit Community website, Prosper Loan Growth Last 24 Months,

http://www.ericscc.com/stats/prosper-loan-growth/, viewed September 5 th 2008.

[6] Erics Credit Community website, Lender Interest Rate History,

http://www.ericscc.com/stats/interest-rate-history/, viewed September 5 th 2008.

[7] Federal Reserve, Open Market Operations, http://www.federalreserve.gov/fomc/

fundsrate.htm, viewed September 5th 2008.

[8] J. Gallien and L.M. Wein, A Smart Market for Industrial Procurement with

Capacity Constraints, Management Science 51, 2005, 7691.

[9] J.H. Gilkeson and K. Reynolds, Determinants of Internet Auction Success and Closing

Price: An Exploratory Study, Psychology & Marketing 20 (6), 2004, 537-566.

[10] R.M. Harstad, Dominant Strategy Adoption and Bidders Experience with Pricing Rules,

Experimental Economics 3, 2000, 261-280.

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http://www.federalreserve.gov/fomc/%20fundsrate.htmhttp://www.federalreserve.gov/fomc/%20fundsrate.htmhttp://www.federalreserve.gov/fomc/%20fundsrate.htmhttp://www.federalreserve.gov/fomc/%20fundsrate.htmhttp://www.federalreserve.gov/fomc/%20fundsrate.htm


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[11] J.H. Kagel, R.M. Harstad, and D. Levin, Information Impact and Allocation Rules in

Auctions with Affiliated Private Values: A Laboratory Study, Econometrica 55 (6),

1987, 1275-1304.

[12] R. Katkar and D. Reiley, Public versus Secret Reserves in Auctions: Results from a

Pokemon Field Experiment, NBER Working Paper No. W8183, 2001, Available at

SSRN: http://ssrn.com/abstract=264437.

[13] R.J. Kauffman, T.J. Spaulding, and C.A. Wood, Are Online Auction Markets Efficient?

An Empirical Study of Market Liquidity and Abnormal Returns, Decision Support

Systems48 (1), 2009, 3-13.

[14] G. Ku, A.D. Galinsky and J.K. Murnighan, Starting Low but Ending High: A Reversal

of the Anchoring Effect in Auctions, Journal of Personality and Social Psychology

90 (6), 2006, 975-986.

[15] A.M. Kwasnica, J.O. Ledyard, D. Porter and C. DeMartini, A New and Improved

Design for Multiobjective Iterative Auctions, Management Science 51, 2005, 419

434.

[16] R. Leskel, J. Teich, H. Wallenius and J. Wallenius, Decision Support for Multi-Unit

Combinatorial Bundle Auctions, Decision Support Systems 43 (2), 2007, 420-434.

[17] A. Lin and J. Teich, P2P Lending A Credit Revolution?, New Mexico Business

Outlook, NMSU College of Business, July 2006.

[18] D. Lucking-Reiley, D. Bryan, N. Prasad, and D. Reeves, Pennies from eBay: The

Determinants of Price in Online Auctions, Journal of Industrial Economics 55 (2),

2007, 223-233.

[19] R.P. McAfee and J. McMillan, Auctions and Bidding, Journal of Economic Literature25

(2), 1987, 699-738.

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http://ssrn.com/abstract=264437http://www.sciencedirect.com/science/journal/01679236http://www.sciencedirect.com/science?_ob=PublicationURL&_tockey=%23TOC%235878%232007%23999569997%23644001%23FLA%23&_cdi=5878&_pubType=J&view=c&_auth=y&_acct=C000040838&_version=1&_urlVersion=0&_userid=736613&md5=700c518901bb8e20b0cf82f1a35f730ehttp://ssrn.com/abstract=264437http://www.sciencedirect.com/science/journal/01679236http://www.sciencedirect.com/science?_ob=PublicationURL&_tockey=%23TOC%235878%232007%23999569997%23644001%23FLA%23&_cdi=5878&_pubType=J&view=c&_auth=y&_acct=C000040838&_version=1&_urlVersion=0&_userid=736613&md5=700c518901bb8e20b0cf82f1a35f730e


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[20] P.R. Milgrom R.J. Weber, A Theory of Auctions and Competitive Bidding,

Econometrica 50 (5), 1982, 1098-1122.

[21] R.S. Pindyck and D.L. Rubinfeld, Econometric Models and Economic Forecasts

(McGraw-Hill, Boston, 1997).

[22] Prosper.com, Listing Summary for Listing Number #385755, 2008, http://www.

prosper.com/lend/listing.aspx?listingID=385755/, viewed September 5th 2008.

[23] T. Sueyoshi and G.R. Tadiparthi, An Agent-Based Decision Support System for

Wholesale Electricity Markets, Decision Support Systems 44 (2), 2008, 425-446.

[24] J.E. Teich, H. Wallenius, J. Wallenius, and A. Zaitsev, A Multi-Attribute e-Auction

Mechanism for Procurement: Theoretical Foundations, EJOR175 (1), 2006, 90-100.

[25] D. Van Heijst, R. Potharst and M. Van Wezel, A Support System for Predicting eBay

End Prices, Decision Support Systems 44 (4), 2008, 970-982.

[26] J. Zhang, The Roles of Players and Reputation: Evidence from eBay Online Auctions,

Decision Support Systems 42 (3), 2006, 1800-1818.

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Appendix: Listing Factors and Additional Credit Information

Listing Factor Description

Amount Funded The sum of bid amounts or requested amountif fully funded

Amount Remaining The amount still remaining unfundedAmount Requested The amount requested in the listing

Bid Count The number of bids on this listing

Borrower City The home city of the borrower

Borrower Starting Rate The starting rate of the listing

Borrower State The home state of the borrower

Category One of the following:Not availableDebt consolidationHome improvementBusiness loanPersonal loanStudent loanAuto loanOther

Creation Date The date the listing was created

Credit Grade The credit grade of the borrower AA-HR

Debt-to-Income Ratio The debt-to-income ratio of the borrower

Description The description about the listing written bythe borrower

Duration The duration of the listing

End Date The date when the listing ends

Funding Option One of the following:

Open for durationClose when funded

Group Key The identifier code of the group in which theborrower is a member of

Is Borrower Homeowner Specifies if the borrower is a verifiedhomeowner

Key The identifier code of the listing

Lender Rate The final interest rate of the listing

Member Key The identifier code of the borrower

Start Date The starting time of the listing

Status One of the following:Active

WithdrawnExpiredCompletedCancelledPending Verification

Title The title of the listing

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Additional Credit Information Description

Amount Delinquent The amount delinquent at the time the listingwas created

Bankcard Utilization The percentage of available revolving credit

that is utilized at the time the listing wascreated

Borrower Occupation The occupation of the borrower

Current Credit Lines The number of credit lines

Current Delinquencies The number of current delinquencies

Date Pulled The date when the credit information waspulled

Delinquencies Last 7 Years The number of delinquencies in the last 7years

Employment Status The employment status of the borrower

First Recorded Line of Credit The date of the first recorded credit line of the borrower

Income The annual income range of the borrower 0 Not displayed1 $0 or unable to verify2 - $1 24,9993 - $25,000 49,9994 - $50,000 74,9995 - $75,000 99,9996 - $100,000+7 Not employed

Inquiries Last 6 Months The number of inquiries in the last 6 months

Length Status Months The length of the employment status inmonths

Open Credit Lines The number of open credit lines

Public Records Last 10 Years The number of public records in the last 10years

Public Records Last 12 months The number of public records in the last 12months

Revolving Credit Balance Amount of revolving credit balance

Total Credit Lines The number of total credit lines

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Figure 1 Screen image from one listing on Prosper.com (Prosper.com, Used with

Permission, 2008)

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Figure 2 Interest rates by credit grades on Prosper.com (Eric's credit community,

2008b)

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Query Method vs. Logistic Regression Method (Starting Rate)

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

0 % 5 % 10 % 15 % 20 % 25 % 30 %

Starting Rate

SuccessRate

0

10

20

30

40

50

60

70

No

ofListings

No of Listings

Query

Logistic Regression

Figure 3 Query method compared against logistic regression method

Query Method vs. Logistic Regression Method (Amount)

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

0 5000 10000 15000 20000 25000

Amount

SuccessRate

0

20

40

60

80

100

120

140

160

180

200

No

ofListings

No of Listings

Query

Logistic regression

Figure 4 Query method compared against logistic regression method

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Figure 5 Example Screen Image of Borrower Decision Aid (Borrower Decision Aid,

2008)

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Table 1 Pairwise correlation tests between success of the listing and listing

characteristics

Correlation P-Value Observations

Amount Requested -0.06 0.0000 293976Starting Rate 0.06 0.0000 293976Funding Option 0.03 0.0000 293976

Duration 0.02 0.0000 293976

Credit Grade* -0.28 0.0000 293976

Debt-to-Income Ratio -0.04 0.0000 274246Homeownership 0.07 0.0000 293976

Current Delinquencies -0.14 0.0000 291732Delinquencies last 7 years -0.10 0.0000 291732

Amount Delinquent -0.06 0.0000 220252Income 0.03 0.0000 293976

* Credit grade AA-HR transformed into interval scale of 1-7

Table 2 Pairwise correlation between success of the listing and listing characteristics in

credit grades A and D

Credit Grade A Credit Grade D

Correlation P-

Value

Obs. Correlation P-

Value

Obs.

Amount Requested -0.24 0.0000 11073 -0.18 0.0000 43234Starting Rate 0.11 0.0000 11073 0.17 0.0000 43234

Funding Option -0.02 0.0441 11073 -0.04 0.0000 43234Duration 0.03 0.0006 11073 0.02 0.0003 43234

Debt-to-Income Ratio -0.09 0.0000 9501 -0.05 0.0000 40033Homeownership 0.00 0.9947 11073 -0.03 0.0000 43234

Current Delinquencies -0.04 0.0000 11035 -0.07 0.0000 42985Delinquencies last 7 years -0.01 0.2484 11035 -0.04 0.0000 42985

Amount Delinquent -0.01 0.2286 9568 -0.04 0.0000 37174

Income 0.02 0.0091 11073 -0.05 0.0000 43234

Table 3 Logistic regression coefficients and Pseudo-R2s

Credit Grade Pseudo-R2 Observations

Constant Starting rate Amount DTI Delinquencies

AA -0.291 14.990 -0.000140 -0.83481 -0.788 0.170 2844A -0.773 16.895 -0.000156 -2.68859 -0.617 0.208 3562

B -0.911 10.544 -0.000167 -0.93690 -0.528 0.166 5682

C -0.356 7.177 -0.000268 -2.20924 -0.403 0.191 9610

D -1.184 5.514 -0.000273 -1.34284 -0.399 0.162 12482

E -3.271 11.204 -0.000652 -1.53234 -0.195 0.218 11436

HR -3.424 9.357 -0.000846 -0.62510 -0.139 0.206 21908

Coefficients

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Table 4 Improvement in Pseudo-R2 when the number of variables is increased

Explanatory

Variable

Pseudo-

R2

Amount 0.076

Starting Rate 0.122DTI 0.170CurrentDelinquencies 0.208All possible 0.214

Data from credit grade A

Table 5 Pairwise correlation table for regression variables in credit grade A

FinalRate Amount StartingRate DTI

FinalRate 1

Amount 0.5618 1

StartingRate 0.8218 0.5496 1

DTI 0.2155 0.0999 0.1927 1

CurrentDelinquencies 0.1601 -0.1152 0.1695 -0.0647

Table 6 Regression model for the final rate

Starting rate Amount DTI CurrentDeli Constant R2 Obs FinalRate Estimate

AA 0.316 0.00017 0.005 0.750 3.659 0.639 1022 10.38

p-value 0.000 0.000 0.000 0.000 0.000A 0.527 0.00013 0.009 0.391 2.717 0.693 931 13.18

0.000 0.000 0.000 0.000 0.000

B 0.494 0.00014 0.004 0.330 4.624 0.565 1280 14.37

p-value 0.000 0.000 0.040 0.000 0.000

C 0.739 0.00006 0.008 0.390 0.443 0.665 1535 14.34

p-value 0.000 0.081 0.019 0.000 0.190

D 0.683 -0.0002 0.010 0.380 3.713 0.546 1284 15.33

p-value 0.000 0.000 0.013 0.000 0.000

E 0.840 0.00045 0.023 0.284 -1.005 0.509 536 17.31

p-value 0.000 0.002 0.048 0.000 0.436

HR 0.870 0.00045 0.004 0.120 -0.260 0.676 484 17.82

p-value 0.000 0.009 0.455 0.002 0.796

Documents

Prosper BDA Paper Draft 18December2009(2)-1