Exploring Auction Models for Peer-to-Peer Lending
A study says in the emerging market for peer-to-peer loans, the auction method that’s used can make an important difference to the borrower.
The market for real estate loans crashed three years ago and still has not recovered. But another financial market — peer-to-peer lending — has boomed, and was expected to increase to $5.8 billion last year, an increase of nearly 800% since 2007.
Peer-to-peer lending brings borrowers and potential lenders together without the participation of a traditional financial institution. It is also known as social lending, a name that speaks to the perception that it offers a chance for individuals and small businesses that could not obtain affordable financing in the conventional market to get loans at the best possible rates.
But is the reverse auction method, used until recently by Prosper, the largest online peer-to-peer lending group, the best way to deliver that result? That’s the question asked by Nicolas Lambert of Stanford GSB and two colleagues in a research paper.
The answer: It is not. When compared to a competing style of auction known as the Vickrey–Clarke–Groves (VCG) auction, the Prosper auction “can lead to much larger payments for the borrower than the VCG mechanism,” the researchers found. Even when the VCG auction doesn’t perform as well for the borrower, the downside tends to be relatively small.
The paper, Auctions for Social Lending: A Theoretical Analysis, was written by Ning Chen, of the Nanyang Technological University of Singapore; Arpita Ghosh, of Yahoo Research, and Lambert, assistant professor of economics.
Prosper, which calls itself the “eBay for Loans,” claims a membership of nearly 1.1 million and has funded personal loans worth $228 million. Until late last year it conducted online auctions in which borrowers created loan listings, specifying the amount of money they want to borrow, and a reserve interest — the highest rate they are willing to pay.
Potential lenders vet the various borrowers for credit worthiness and establish (but don’t divulge) the lowest rate at which they would fund the loan. The auction starts at the lender’s reserve rate (which is known to everyone) and continues as lenders bid lower and lower — in effect, a reverse auction.
Because lenders like to spread their risk, they often are only willing to fund part of a loan, which means that many auctions have multiple “winners,” lenders who will loan the money.
Although Prosper moved away from the auction model after research for Lambert’s paper was completed, the research makes an important theoretical contribution to the understanding of social lending, a growing part of internet-based commerce that has had little academic scrutiny. In fact, the authors believe it is the first paper to analyze the theory behind auction mechanisms used in social lending. Prosper-style auctions are used in other venues, including the sale of online advertising, and by other social-lending sites, which means the work has additional practical value.
Prosper now evaluates the credit worthiness of applicants for new loans, gives them a score, and sets a reasonable interest rate for the loan. Lenders have access to that information and can choose to fund all or part of the loan without an auction.
The company revised its methodology because some prospective lenders and borrowers, perhaps overly excited by the auction, submitted or accepted bids that were significantly out of sync with the credit worthiness of proposed transactions, Prosper founder and CEO Chris Larson, MBA ’91, said in an interview with Stanford Business magazine. The move to a fixed-rate system tripled the company’s closure rate to 90%, he said.
The VCG auction has two essential properties that distinguish it from other auction models:
- First, it is efficient. Situations are economically efficient if there is a balance between benefit and loss and no one can be made better off without making someone else worse off. In the case of the VCG auction, there is no waste of value, an attractive feature for a system that claims to be social.
- Second, it is “truthful.” Lenders have an incentive to bid their actual reserve interest rate; that is, the cheapest rate they would be willing to accept. This makes it easy to predict the auction’s outcome, and the optimal bidding strategy is an obvious one to all lenders. In other auction designs, such as in Prosper, lenders typically act strategically and declare a rate often higher than the minimum, in hopes of getting a better deal.
The outcome of the auction Prosper used at the time is determined using the concept of a Nash equilibrium. Bids are at equilibrium when no lender can increase his revenue by changing his bid. But the Prosper auction is not truthful so participants do not know the true reserve rates of the other players. Therefore, the Prosper auction has many equilibria that yield very different auction outcomes, making it difficult to predict exactly how much the borrower ends up paying.
Instead, the analysis yields a range of plausible payments for the borrower — one payment for each equilibrium. The paper shows that in the VCG auction the borrower never pays much more than in the Prosper auction, and in many instances can pay significantly less.
Even so, the VCG model is not used as often as the model suggests.
In a simple VCG auction where there can only be one winner, the highest bidder wins, but the price paid is the second-highest bid. However, the pricing rule becomes much more complex when there are multiple winners, as in the case of social lending. This may explain why social lending companies have been reluctant to use the VCG auction, the researchers said.
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