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Auction Theory and Risk Load

Auction Theory and Risk Load. THE WINNER’S CURSE. Outline. Introduction Examples Theory Winner-Takes-All Auction “Best Terms” Rational Expectations. What is The Winner’s Curse?.

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Auction Theory and Risk Load

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  1. Auction Theory and Risk Load THE WINNER’S CURSE

  2. Outline • Introduction • Examples • Theory • Winner-Takes-All Auction • “Best Terms” • Rational Expectations

  3. What is The Winner’s Curse? • When several competitors bid on an item, the competitor whose bid the other side perceives as most advantageous wins the auction. This is the ”winner’s curse.“ In reinsurance terms, there are several reinsurers bidding on a contract. The reinsurer with the lowest price will ”win.“ Since the winner’s bid is the lowest, there will be a bias built into the process, even though each individual reinsurer’s bid may be an unbiased estimate.

  4. Simple Example

  5. Examples: Raw Data (sample)

  6. Results of winner-takes-all auction based on Single-SNAP study

  7. Results of winner-takes-all auction based on Single-SNAP study

  8. Theory: Winner-Takes-All Auction • True: Bias increases as number of bidders increases • Sort of True: Bias increases as variance of bid distribution increases • Asymptotically true: Marginal increase in bias decreases for each additional bidder • Probably True: Advantage of accuracy greatest when only a few bidders

  9. Theory: Winner-Takes-All Auction

  10. Theory: Winner-Takes-All Auction

  11. Implications • Bias increases as variance of bid distribution increases • Bias is greater for riskier lines • Bias increases for higher layers • Bias increases as number of bidders increases • Must make a bigger correction when there are more bidders • This goes directly against instinct

  12. Hit Ratios • All else being equal, should be 1/k • What happens when you adjust for the bias? • Hit ratio goes down • Elasticity of demand goes up as k increases • More price-sensitive when more competition • Are perceived as high-priced by the market

  13. Hit Ratios

  14. Data Underlying Hit Ratio Graphs

  15. Elasticity of demand estimates (very fishy)

  16. “Best Terms” • Bias changes radically depending on form of auction • Property fac cert per-risk uses “best terms” • Highest price from among successful bidders is given to all successful bidders

  17. Best Terms Example

  18. Best Terms • Assume three bidders, each willing to take 50% • Clearing price is median of bid distribution • No apparent bias

  19. Best Terms • Implication: More bias for smaller risks • Because take 100%

  20. Rational Expectations and Risk Load • “Rational bidders will adjust bids to eliminate bias” • Not supported by research • See “The Winner’s Curse” by Thaler • However, rules-of-thumb may have evolved to fix bias • Same way poker hands were ordered in terms of rarity before theory of probability developed • Is risk load such a rule-of-thumb?

  21. Risk Load Based on higher moments Many measures suggested Standard Deviation Variance Shortfall etc. Scale factor is subjective Some risk diversifies away Need less for small segments? Bias Based on expected value Measure is expected value . . . Scale factor is 1 Bias does not diversify away Need same for all segments Risk Load vs Auction Bias

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