Swiss ReAuction Theory and Risk Load (Chris Svendsgaard, DUO Armonk) Z 1 Auction Theory and Risk Load THE WINNER’S CURSE

Swiss ReAuction Theory and Risk Load (Chris Svendsgaard, DUO Armonk) Z 2 Outline Introduction Examples Theory –Winner-Takes-All Auction –“Best Terms” –Rational Expectations

Swiss ReAuction Theory and Risk Load (Chris Svendsgaard, DUO Armonk) Z 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.

Swiss ReAuction Theory and Risk Load (Chris Svendsgaard, DUO Armonk) Z 4 Simple Example

Swiss ReAuction Theory and Risk Load (Chris Svendsgaard, DUO Armonk) Z 5 Examples: Raw Data (sample)

Swiss ReAuction Theory and Risk Load (Chris Svendsgaard, DUO Armonk) Z 6 Results of winner-takes-all auction based on Single-SNAP study

Swiss ReAuction Theory and Risk Load (Chris Svendsgaard, DUO Armonk) Z 7 Results of winner-takes-all auction based on Single-SNAP study

Swiss ReAuction Theory and Risk Load (Chris Svendsgaard, DUO Armonk) Z 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

Swiss ReAuction Theory and Risk Load (Chris Svendsgaard, DUO Armonk) Z 9 Theory: Winner-Takes-All Auction

Swiss ReAuction Theory and Risk Load (Chris Svendsgaard, DUO Armonk) Z 10 Theory: Winner-Takes-All Auction

Swiss ReAuction Theory and Risk Load (Chris Svendsgaard, DUO Armonk) Z 11

Swiss ReAuction Theory and Risk Load (Chris Svendsgaard, DUO Armonk) Z 12 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

Swiss ReAuction Theory and Risk Load (Chris Svendsgaard, DUO Armonk) Z 13 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

Swiss ReAuction Theory and Risk Load (Chris Svendsgaard, DUO Armonk) Z 14 Hit Ratios

Swiss ReAuction Theory and Risk Load (Chris Svendsgaard, DUO Armonk) Z 15

Swiss ReAuction Theory and Risk Load (Chris Svendsgaard, DUO Armonk) Z 16

Swiss ReAuction Theory and Risk Load (Chris Svendsgaard, DUO Armonk) Z 17 Data Underlying Hit Ratio Graphs

Swiss ReAuction Theory and Risk Load (Chris Svendsgaard, DUO Armonk) Z 18 Elasticity of demand estimates (very fishy)

Swiss ReAuction Theory and Risk Load (Chris Svendsgaard, DUO Armonk) Z 19 “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

Swiss ReAuction Theory and Risk Load (Chris Svendsgaard, DUO Armonk) Z 20 Best Terms Example

Swiss ReAuction Theory and Risk Load (Chris Svendsgaard, DUO Armonk) Z 21 Best Terms Assume three bidders, each willing to take 50% –Clearing price is median of bid distribution –No apparent bias

Swiss ReAuction Theory and Risk Load (Chris Svendsgaard, DUO Armonk) Z 22 Best Terms Implication: More bias for smaller risks –Because take 100%

Swiss ReAuction Theory and Risk Load (Chris Svendsgaard, DUO Armonk) Z 23 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?

Swiss ReAuction Theory and Risk Load (Chris Svendsgaard, DUO Armonk) Z 24 Risk Load vs Auction Bias 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