Swiss ReWinner’s Curse Chris Svendsgaard1 THE WINNER’S CURSE

Swiss ReWinner’s Curse Chris Svendsgaard2 Outline Basic model Implications of the basic model Questions that can be explored using this model Rational expectations and risk load

Swiss ReWinner’s Curse Chris Svendsgaard3 Winner’s Curse Basic Model You, and (k - 1) competitors, bid to reinsure a risk Bids are independent, identically distributed, unbiased estimates of the correct price Lowest bid wins the deal

Swiss ReWinner’s Curse Chris Svendsgaard4

Swiss ReWinner’s Curse Chris Svendsgaard5 Implications of the basic model Winning bid will be biased Bias increases as variance of bid distribution increases –Greater bias for risky lines, high layers Bias increases as number of bidders increases –At a decreasing rate

Swiss ReWinner’s Curse Chris Svendsgaard6 Questions that can be explored using this model The benefit (and cost) of being more accurate Different auction mechanisms –“Best Terms” State Farm makes money using those rates--why can’t we? Why renewal business is more profitable A-priori loss ratios (Murphy’s Law)

Swiss ReWinner’s Curse Chris Svendsgaard7 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 ReWinner’s Curse Chris Svendsgaard8 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 –Don’t need for some segments? Bias –Based on expected value –Measure is expected value –. –Scale factor is 1 –Bias does not diversify away –Need for all segments

Swiss ReWinner’s Curse Chris Svendsgaard9 Risk Load vs Auction Bias (continued) Risk Load –Does not depend on the number of competitors –Probably should depend on how good you are at pricing, but not 100% clear how Bias –Depends on the number of competitors –Depends directly on how accurate your pricing is

Swiss ReWinner’s Curse Chris Svendsgaard10 Auction Theory and Risk Load THE END

Swiss ReWinner’s Curse Chris Svendsgaard11 Appendix 1: Simple Example

Swiss ReWinner’s Curse Chris Svendsgaard12 Appendix 2: More Realistic Examples Swiss Re in-house comparison of individual risk cat models SR model (“Single SNAP”) and two vendor models Standard risk in different locations (165 for EQ, 66 for Wind) “Correct Price” is average of three models at location Winning bid is lowest of three models at location Note that all three models have been changed since this study

Swiss ReWinner’s Curse Chris Svendsgaard13 Examples: Raw Data (sample)

Swiss ReWinner’s Curse Chris Svendsgaard14 Results of winner-takes-all auction based on Single-SNAP study

Swiss ReWinner’s Curse Chris Svendsgaard15 Results of winner-takes-all auction based on Single-SNAP study

Swiss ReWinner’s Curse Chris Svendsgaard16 Appendix 3: Accuracy Being more accurate reduces your bias If you are perfectly accurate, you will suffer no bias –BUT hit ratio goes from 1/k to 1/[2^(k-1)] (assuming symmetric bid distributions) Or does it? How do people correct for bias in practice? Would you put some bias back in to get your volume up?

Swiss ReWinner’s Curse Chris Svendsgaard17 Appendix 4: “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 ReWinner’s Curse Chris Svendsgaard18 Best Terms Example

Swiss ReWinner’s Curse Chris Svendsgaard19 Best Terms Assume three bidders, each willing to take 50% –Clearing price is median of bid distribution –No apparent bias

Swiss ReWinner’s Curse Chris Svendsgaard20 Best Terms Implication: More bias for smaller risks –Because take 100%

Swiss ReWinner’s Curse Chris Svendsgaard21 References –Look for Auction Theory bibliography by Paul Klemperer The Winner’s Curse: Paradoxes and Anomalies of Economic Life –Richard H. Thaler –Princeton University Press, 1992

Swiss ReWinner’s Curse Chris Svendsgaard22 Thanks and a tip o’ the hat to Shaun Wang for encouragement Rob Downs for collaboration Isaac Mashitz and Gary Patrik for comments Gene Gaydos for original idea