2007/08/07 ARIA 1

Hidden Overconfidence and Advantageous Selection

Rachel J. HuangAssistant Professor, Finance Department

Ming Chuan University, Taipei, TaiwanYu-Jane Liu

Professor, Department of FinanceNational Cheng Chi University, Taipei, Taiwan

Larry Y. TzengProfessor, Department of Finance

National Taiwan University, Taipei, Taiwan

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Agenda

1. Introduction2. Model3. Market Equilibrium4. Conclusion

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1. Introduction

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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, rev

erse mortgages, medigap insurance

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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

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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 insura

nce There should exist other factors which

induce advantageous selection.

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The Purpose

An alternative reason for advantageous selection: hidden heterogeneity in degrees of

overconfidence

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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)

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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

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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

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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 indivi

duals will purchase more coverage than the more optimistic individuals

Two dimension: Jeleva and Villeneuve (2004, ET)

Monopoly

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Main findings

Separating, and partial pooling equilibria can exist.

Separating equilibria can predict adverse selection or advantageous selection.

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2. Model

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Assumptions and Notations (1/2)

Competitive insurance market Two types of customers: those who is overconfident (ty

pe 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

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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

iiiiiiiiiii FQpWUFQpQLWUFEU )()](1[)()]([

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Investment in Self-protection

r type will invest in self-protection iff

o type will invest in self-protection iff

Assume Δo <0

0)]()(][)([ fQpWUQpQLWUf rrrrrr

[ ( ( )) ( )][ ( ) ( )] 0o o o o o og f g U W L Q p Q U W p Q f

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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.

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3. Market Equilibrium

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Proposition 1: No pooling

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Proposition 2 : first best separating equilibrium (advantageous selection)

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Proposition 3 : second best separating equilibrium (advantageous selection)

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Proposition 4 : partial pooling equilibrium (advantageous selection)

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Proposition 5 : separating equilibrium with linear premium

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Proposition 6 : no equilibrium

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Adverse selection: if )()( gf

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4. Conclusion

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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.

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Thank you for your attention!