1. 2007/08/07ARIA1 Hidden Overconfidence and Advantageous Selection Rachel J. Huang Assistant Professor, Finance Department Ming Chuan University, Taipei, Taiwan Yu-Jane Liu Professor, Department of Finance National Cheng Chi University, Taipei, Taiwan Larry Y. Tzeng Professor, Department of Finance National Taiwan University, Taipei, Taiwan

2. 2007/08/07ARIA2 Agenda 1. Introduction 2. Model 3. Market Equilibrium 4. Conclusion

3. 2007/08/07ARIA3 1. Introduction

4. 2007/08/07ARIA4 Motivation (1/3) Relation between RISK TYPE and INSURANCE COVERAGE ADVERSE selection: Theoretical prediction: positive Empirical evidence is mixed: positive: health insurance, annuities negative: life insurance, long-term care insurance, reverse mortgages, medigap insurance

5. 2007/08/07ARIA5 Motivation (2/3) ADVANTAGEOUS selection (de Meza and Webb, 2001) explained by heterogeneous (hidden) degree of risk aversion more risk-averse implies more insurance more risk-averse might imply more self- protection, i.e. lower risk type

6. 2007/08/07ARIA6 Motivation (3/3) Empirical evidence on the sign of the negative relationship between degree of risk aversion and risk type is mixed negative: long-term care insurance positive: automobile and Medigap insurance There should exist other factors which induce advantageous selection.

7. 2007/08/07ARIA7 The Purpose An alternative reason for advantageous selection: hidden heterogeneity in degrees of overconfidence

8. 2007/08/07ARIA8 Overconfidence Why? Svenson (1981): Half the drivers in Taxes judged themselves to be among the safest 20%, and 88% believed themselves to be safer than the median driver. What? Optimistic on risk probability Langer (1975), Weinstein (1980) and Larwood and Whittaker (1977) show that CEOs tend to underestimate the failure of investment projects. “ Bad things cannot happen to me. ” Optimistic on information quality Daniel, Hirshleifer and Subrahmanyam (1998), Gervais and Odean (2001), and Gervais, Heaton, and Odean (2005)

9. 2007/08/07ARIA9 Intuition overconfidence might imply less insurance might also imply less self-protection, i.e. high risk type => negative correlation between risk type and insurance coverage

10. 2007/08/07ARIA10 Most Related Literature (1/2) Model setting: de Meza and Webb (2001, Rand) Hidden information cause different types of individuals. De Meza and Webb: degree of risk aversion Our: degree of overconfidence The ex ante objective loss probabilities of different type of individuals are the same. Different type of individuals would make different decisions on the investment for self-protection to reduce the loss probability. One dimension approach

11. 2007/08/07ARIA11 Most Related Literature (2/2) Heterogeneous risk perception One dimension: Koufopoulos (2002, working) Oligopoly market Main findings: two types of separating equilibrium advantageous selection One risk type in equilibrium but the less optimistic individuals will purchase more coverage than the more optimistic individuals Two dimension: Jeleva and Villeneuve (2004, ET) Monopoly

12. 2007/08/07ARIA12 Main findings Separating, and partial pooling equilibria can exist. Separating equilibria can predict adverse selection or advantageous selection.

13. 2007/08/07ARIA13 2. Model

14. 2007/08/07ARIA14 Assumptions and Notations (1/2) Competitive insurance market Two types of customers: those who is overconfident (type o) and those who don't (type r) with proportion θ They have the same objective probability of loss: π(F)=π or π(f)<π depending on investment in self-protection F ∈ {0,f} Subjective belief of loss probability r type: π or π(f) o type: g(π ) or g(π(f) ) g’>0, g(π(F) ) < g(π ) g(π )< π(f) Hidden information about types of customers and hidden action

15. 2007/08/07ARIA15 Assumptions and Notations (2/2) The expected utility of the type i insured is where W : initial wealth L : loss size p : premium rate Q : coverage

16. 2007/08/07ARIA16 Investment in Self-protection r type will invest in self-protection iff o type will invest in self-protection iff Assume Δ o <0

17. 2007/08/07ARIA17 Game structure Stage 1 Insurers make binding offers of insurance contracts specifying coverage Q and premium rate p. Stage 2 Individuals choose either a contract from the set of contracts offered or no contract. If the same contract is offered by two insurers, individuals toss a fair coin. Stage 3 Individuals choose whether or not to invest in self-protection.

18. 2007/08/07ARIA18 3. Market Equilibrium

19. 2007/08/07ARIA19 Proposition 1: No pooling

20. 2007/08/07ARIA20 Proposition 2 : first best separating equilibrium (advantageous selection)

21. 2007/08/07ARIA21 Proposition 3 : second best separating equilibrium (advantageous selection)

22. 2007/08/07ARIA22 Proposition 4 : partial pooling equilibrium (advantageous selection)

23. 2007/08/07ARIA23 Proposition 5 : separating equilibrium with linear premium

24. 2007/08/07ARIA24 Proposition 6 : no equilibrium

25. 2007/08/07ARIA25 Adverse selection: if

26. 2007/08/07ARIA26 4. Conclusion

27. 2007/08/07ARIA27 Contribution and findings Our paper provides a theoretical model of hidden overconfidence to explain advantageous selection in the insurance market. We demonstrate that: Separating (partial pooling) contracts in a form of advantageous selection is equilibrium when the deviation in belief of the loss probability between the rational type of insured and the overconfident type of insured is relatively large. neither the rational type of insured nor the overconfident type of insured expend any effort to reduce the loss probability, and both purchase insurance at the same premium rate, when the deviation in belief of the loss probability between the rational type of insured and the overconfident type of insured is relatively small. Separating contracts in a form of adverse selection is equilibrium when the degree of overconfidence of the overconfident type insured is less severe.

28. 2007/08/07ARIA28 Thank you for your attention!