The Winner's Curse in Lending: Why Approvals Disappoint

A lender whose test lets through 30% of bad applicants expects a default rate of 3.57% on what it approves. If applicants can try three lenders, it gets 6.81%, because the approved pool now includes the applicants its competitors correctly turned down. The test did not change and no one misrepresented anything. The market structure alone produced the losses, and it is strongest exactly where lenders most want to grow.

Winning the applicants others turned down

In 1971, three petroleum engineers at Atlantic Richfield noticed that companies winning offshore oil leases at auction were earning poor returns on them. Their explanation became known as the winner's curse: when many bidders estimate the value of the same uncertain asset, the winner is the one whose estimate was most optimistic, and the most optimistic estimate is, on average, too high. Winning is itself evidence of having overestimated.

Lending has the same structure. An applicant who can apply to several lenders is, in effect, being valued by each of them. The lenders that approve are disproportionately the ones whose assessment erred in the applicant's favor. Broecker formalized this for credit in 1990: when lenders screen independently with imperfect tests, each lender's approved pool contains applicants rejected by its competitors, and the more competitors there are, the worse that pool becomes.

The curse does not require anyone to lie or any test to get worse. It is produced by the market structure alone, which is why lenders with sound models can still be surprised by their losses.

The curse, worked

Take an applicant pool in which 10% would default. Each lender runs a test that approves 90% of good applicants and 30% of bad ones, with errors independent across lenders. Applicants apply to lenders in turn until one approves them.

Number of lenders the applicant can try	Share of applicants eventually approved	Default rate among approved loans
1	84.0%	3.57%
2	94.2%	5.41%
3	96.5%	6.81%
5	98.3%	8.46%
10	99.7%	9.75%

With three lenders, a bad applicant has a 66% chance that at least one test will pass them, against 30% with one. A good applicant was already approved 90% of the time, so competition adds few good borrowers and many bad ones. With ten lenders, screening has almost no effect: the approved book defaults at 9.75%, close to the 10% of the unscreened pool.

A lender that validated its model on its own historical approvals, priced for 3.57% and then entered a market with two active competitors would underprice by roughly three percentage points of loss. Per our counterfactual analysis, nothing in its own data would reveal why, because the counterfactual, how the same applicants would have performed absent competition, is never observed.

Why shared data softens the curse

The curse depends on lenders making different mistakes. If every lender used the same test with the same errors, an applicant rejected by one would be rejected by all, and trying more lenders would not help a bad applicant at all. The approved default rate would stay at 3.57% however many lenders competed.

• Common bureau scores correlate errors. Much of consumer lending relies on the same few scores from the same files, which limits the curse but, per our assessment monoculture analysis, concentrates a different risk: everyone misjudges the same applicants together.
• Proprietary data decorrelates errors. A lender with information no one else has makes different mistakes. That can help or hurt it: it wins applicants others misjudged as risky, but also attracts those others correctly rejected and it wrongly accepts.
• Inquiries partially reveal the search. Per our credit inquiry analysis, multiple recent inquiries are a visible trace of an applicant shopping across lenders, which is part of why they predict default.

This creates a tension in model strategy. Differentiated data is valuable, but only to the lender that is more accurate than its competitors, not merely different. A lender whose novel signal is noisier than the market's will specialize in exactly the applicants the market has already correctly identified as risky.

Where the curse is strongest

Setting	Why the curse bites
Entering a new market or state	Incumbents have screened the pool for years; the entrant sees what they declined. Shaffer found evidence consistent with this in higher loan losses at newly chartered banks.
Online lending with instant decisions	Applying elsewhere is costless and fast, so applicants try many lenders.
Loan marketplaces and comparison sites	Applications are distributed to many lenders at once; the ones that accept are the ones whose models were most favorable.
Thin-file and new-to-credit applicants	Tests are least accurate where data is scarcest, so errors are largest and least correlated.
Small business credit after a bank decline	An applicant declined by its bank and approved by an alternative lender is, by construction, an applicant one informed lender judged negatively.

Per our new state launch analysis and cold start analysis, the first cohorts in a new market typically perform worse than models predict, and the winner's curse is one reason that does not require the model to be wrong about anyone it has seen before.

How lenders respond

In auctions, sophisticated bidders shade their bids below their estimate to account for the curse. Lenders have equivalents.

• Price for the competitive pool, not the test. Expected losses should be estimated from performance in the market as it exists, not from the test's accuracy on an uncontested sample.
• Tighten where search is cheap. Higher cutoffs in channels where applicants can try many lenders, such as marketplaces, are the lending equivalent of bid shading.
• Use search signals. Inquiry velocity and, per our stacking detection analysis, simultaneous applications are direct evidence of where an applicant sits in the search process.
• Prefer information that improves accuracy, not just difference. Per our soft information analysis, relationship knowledge is the classic example of information that lets a lender be right where others are wrong.
• Enter gradually. Small initial cohorts reveal the competitive pool's actual performance before volume makes the lesson expensive.

The case that the curse is overstated

• Most applicants do not shop much. Survey evidence in consumer credit finds many borrowers apply to one or two lenders, limiting the number of independent draws.
• Tests are highly correlated in practice. Shared bureau data means much of the error is common, not independent.
• Lenders already observe outcomes in the competitive pool. A lender with years of performance data in a competitive market has priced the curse implicitly, even if it never named it.
• Competition has offsetting benefits. It lowers prices for good borrowers who do shop and pushes lenders toward better information.

These points limit the curse in mature, data-rich markets; they do not remove it where it matters most. The settings in which the curse is strongest, new markets, thin files and instant online decisions, are exactly the settings where shopping is cheap, errors are large and historical data is short. Per our acceptance selection analysis, a related selection operates after approval, as applicants with better offers elsewhere decline, so the two effects compound.

Testable implications

• Loss rates should rise with the number of active lenders in a market among otherwise similar borrowers, especially in segments with thin data.
• Entrants' early cohorts should underperform incumbents' cohorts with matched observable characteristics, with the gap narrowing as the entrant builds data.
• Approved applicants with recent declines elsewhere should default more than observably similar applicants without them.
• The exit of a major lender should improve incumbents' performance in the segments where the exiting lender was active, since fewer independent tests now stand between bad applicants and approval.

The third implication is the one most lenders can test with data they already hold. Per our reject inference analysis, the applicants a lender declined and who were later funded elsewhere are observable through bureau data, and the mirror image, approved applicants recently declined elsewhere, is the population the winner's curse predicts will disappoint.

Frequently asked questions

References

1. Capen, E. C., Clapp, R. V., & Campbell, W. M. (1971). Competitive Bidding in High-Risk Situations. Journal of Petroleum Technology, 23(6), 641–653.
2. Thaler, R. H. (1988). Anomalies: The Winner's Curse. Journal of Economic Perspectives, 2(1), 191–202.
3. Broecker, T. (1990). Credit-Worthiness Tests and Interbank Competition. Econometrica, 58(2), 429–452.
4. Riordan, M. H. (1993). Competition and Bank Performance: A Theoretical Perspective. In C. Mayer & X. Vives (Eds.), Capital Markets and Financial Intermediation. Cambridge University Press.
5. Shaffer, S. (1998). The Winner's Curse in Banking. Journal of Financial Intermediation, 7(4), 359–392.

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This analysis is educational and does not constitute investment, credit or legal advice. Applicant pools, test accuracies, default rates and the sequential application model are stylized illustrations and do not describe any particular lender, market or model. Real lender errors are partly correlated, which moderates the effects shown.