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Winner's curse

M&A / Merger Model

In an auction for a commonly valued asset, the winner is the most optimistic bidder and therefore tends to overpay.

Also written: winners curse, the winners curse

Suppose several bidders each estimate the value of the same asset, and their estimates are unbiased, meaning they are as likely to be too high as too low. The average estimate is then right. The auction, however, does not sell to the average view. It sells to whoever is highest, and the highest of several unbiased estimates is biased upward. The winner overpays by roughly the size of the largest error in the room.

Nothing irrational has happened, which is what makes the result worth knowing. The usual explanation offered in interviews, that bidders get carried away and abandon their reservation price, describes a different and less interesting phenomenon. The curse is a selection effect and it survives perfectly disciplined bidders.

It gets worse as the field grows, because the largest error in a bigger sample is bigger. The remedy is to shade the bid, meaning to bid deliberately below your own estimate, and to shade further the more bidders you expect. This is why a disciplined buyer expects to lose most of the processes it enters, and why winning a very broad auction is not by itself evidence of a good deal.

The condition matters. The curse is a common value phenomenon, where the asset is worth roughly the same to everyone: a loan portfolio, an oil field, a licence. Where value is genuinely private, a strategic buyer paying more for synergies only it can realise is not making an estimation error at all. So the same observation, that the winner outbid everyone else, is a warning in one setting and a rational outcome in the other.

Worked example

Illustrative. Five bidders estimate 80, 90, 100, 110 and 120 for a portfolio truly worth 100. As a group they are exactly right, and the winner still pays 120 and is 20 down on day one.

Run the same auction with three bidders estimating 90, 100 and 110 and the winner pays 110, so the overpayment halves to 10.

To break even, the top bidder needed to bid 100, twenty below its own honest estimate. That gap is the shading the winner's curse demands.

Taught in context in M&A III: Deal Design, Auctions and Hostile SituationsSee the three modules that are free to read

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