2007/08/07ARIA1 Hidden Overconfidence and Advantageous Selection Rachel J. Huang Assistant...
-
Upload
bennett-griffin -
Category
Documents
-
view
219 -
download
0
Transcript of 2007/08/07ARIA1 Hidden Overconfidence and Advantageous Selection Rachel J. Huang Assistant...
![Page 1: 2007/08/07ARIA1 Hidden Overconfidence and Advantageous Selection Rachel J. Huang Assistant Professor, Finance Department Ming Chuan University, Taipei,](https://reader036.fdocuments.us/reader036/viewer/2022062322/5697c00b1a28abf838cc82ad/html5/thumbnails/1.jpg)
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
![Page 2: 2007/08/07ARIA1 Hidden Overconfidence and Advantageous Selection Rachel J. Huang Assistant Professor, Finance Department Ming Chuan University, Taipei,](https://reader036.fdocuments.us/reader036/viewer/2022062322/5697c00b1a28abf838cc82ad/html5/thumbnails/2.jpg)
2007/08/07 ARIA 2
Agenda
1. Introduction2. Model3. Market Equilibrium4. Conclusion
![Page 3: 2007/08/07ARIA1 Hidden Overconfidence and Advantageous Selection Rachel J. Huang Assistant Professor, Finance Department Ming Chuan University, Taipei,](https://reader036.fdocuments.us/reader036/viewer/2022062322/5697c00b1a28abf838cc82ad/html5/thumbnails/3.jpg)
2007/08/07 ARIA 3
1. Introduction
![Page 4: 2007/08/07ARIA1 Hidden Overconfidence and Advantageous Selection Rachel J. Huang Assistant Professor, Finance Department Ming Chuan University, Taipei,](https://reader036.fdocuments.us/reader036/viewer/2022062322/5697c00b1a28abf838cc82ad/html5/thumbnails/4.jpg)
2007/08/07 ARIA 4
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
![Page 5: 2007/08/07ARIA1 Hidden Overconfidence and Advantageous Selection Rachel J. Huang Assistant Professor, Finance Department Ming Chuan University, Taipei,](https://reader036.fdocuments.us/reader036/viewer/2022062322/5697c00b1a28abf838cc82ad/html5/thumbnails/5.jpg)
2007/08/07 ARIA 5
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
![Page 6: 2007/08/07ARIA1 Hidden Overconfidence and Advantageous Selection Rachel J. Huang Assistant Professor, Finance Department Ming Chuan University, Taipei,](https://reader036.fdocuments.us/reader036/viewer/2022062322/5697c00b1a28abf838cc82ad/html5/thumbnails/6.jpg)
2007/08/07 ARIA 6
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.
![Page 7: 2007/08/07ARIA1 Hidden Overconfidence and Advantageous Selection Rachel J. Huang Assistant Professor, Finance Department Ming Chuan University, Taipei,](https://reader036.fdocuments.us/reader036/viewer/2022062322/5697c00b1a28abf838cc82ad/html5/thumbnails/7.jpg)
2007/08/07 ARIA 7
The Purpose
An alternative reason for advantageous selection: hidden heterogeneity in degrees of
overconfidence
![Page 8: 2007/08/07ARIA1 Hidden Overconfidence and Advantageous Selection Rachel J. Huang Assistant Professor, Finance Department Ming Chuan University, Taipei,](https://reader036.fdocuments.us/reader036/viewer/2022062322/5697c00b1a28abf838cc82ad/html5/thumbnails/8.jpg)
2007/08/07 ARIA 8
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)
![Page 9: 2007/08/07ARIA1 Hidden Overconfidence and Advantageous Selection Rachel J. Huang Assistant Professor, Finance Department Ming Chuan University, Taipei,](https://reader036.fdocuments.us/reader036/viewer/2022062322/5697c00b1a28abf838cc82ad/html5/thumbnails/9.jpg)
2007/08/07 ARIA 9
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
![Page 10: 2007/08/07ARIA1 Hidden Overconfidence and Advantageous Selection Rachel J. Huang Assistant Professor, Finance Department Ming Chuan University, Taipei,](https://reader036.fdocuments.us/reader036/viewer/2022062322/5697c00b1a28abf838cc82ad/html5/thumbnails/10.jpg)
2007/08/07 ARIA 10
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
![Page 11: 2007/08/07ARIA1 Hidden Overconfidence and Advantageous Selection Rachel J. Huang Assistant Professor, Finance Department Ming Chuan University, Taipei,](https://reader036.fdocuments.us/reader036/viewer/2022062322/5697c00b1a28abf838cc82ad/html5/thumbnails/11.jpg)
2007/08/07 ARIA 11
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
![Page 12: 2007/08/07ARIA1 Hidden Overconfidence and Advantageous Selection Rachel J. Huang Assistant Professor, Finance Department Ming Chuan University, Taipei,](https://reader036.fdocuments.us/reader036/viewer/2022062322/5697c00b1a28abf838cc82ad/html5/thumbnails/12.jpg)
2007/08/07 ARIA 12
Main findings
Separating, and partial pooling equilibria can exist.
Separating equilibria can predict adverse selection or advantageous selection.
![Page 13: 2007/08/07ARIA1 Hidden Overconfidence and Advantageous Selection Rachel J. Huang Assistant Professor, Finance Department Ming Chuan University, Taipei,](https://reader036.fdocuments.us/reader036/viewer/2022062322/5697c00b1a28abf838cc82ad/html5/thumbnails/13.jpg)
2007/08/07 ARIA 13
2. Model
![Page 14: 2007/08/07ARIA1 Hidden Overconfidence and Advantageous Selection Rachel J. Huang Assistant Professor, Finance Department Ming Chuan University, Taipei,](https://reader036.fdocuments.us/reader036/viewer/2022062322/5697c00b1a28abf838cc82ad/html5/thumbnails/14.jpg)
2007/08/07 ARIA 14
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
![Page 15: 2007/08/07ARIA1 Hidden Overconfidence and Advantageous Selection Rachel J. Huang Assistant Professor, Finance Department Ming Chuan University, Taipei,](https://reader036.fdocuments.us/reader036/viewer/2022062322/5697c00b1a28abf838cc82ad/html5/thumbnails/15.jpg)
2007/08/07 ARIA 15
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[)()]([
![Page 16: 2007/08/07ARIA1 Hidden Overconfidence and Advantageous Selection Rachel J. Huang Assistant Professor, Finance Department Ming Chuan University, Taipei,](https://reader036.fdocuments.us/reader036/viewer/2022062322/5697c00b1a28abf838cc82ad/html5/thumbnails/16.jpg)
2007/08/07 ARIA 16
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
![Page 17: 2007/08/07ARIA1 Hidden Overconfidence and Advantageous Selection Rachel J. Huang Assistant Professor, Finance Department Ming Chuan University, Taipei,](https://reader036.fdocuments.us/reader036/viewer/2022062322/5697c00b1a28abf838cc82ad/html5/thumbnails/17.jpg)
2007/08/07 ARIA 17
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.
![Page 18: 2007/08/07ARIA1 Hidden Overconfidence and Advantageous Selection Rachel J. Huang Assistant Professor, Finance Department Ming Chuan University, Taipei,](https://reader036.fdocuments.us/reader036/viewer/2022062322/5697c00b1a28abf838cc82ad/html5/thumbnails/18.jpg)
2007/08/07 ARIA 18
3. Market Equilibrium
![Page 19: 2007/08/07ARIA1 Hidden Overconfidence and Advantageous Selection Rachel J. Huang Assistant Professor, Finance Department Ming Chuan University, Taipei,](https://reader036.fdocuments.us/reader036/viewer/2022062322/5697c00b1a28abf838cc82ad/html5/thumbnails/19.jpg)
2007/08/07 ARIA 19
Proposition 1: No pooling
![Page 20: 2007/08/07ARIA1 Hidden Overconfidence and Advantageous Selection Rachel J. Huang Assistant Professor, Finance Department Ming Chuan University, Taipei,](https://reader036.fdocuments.us/reader036/viewer/2022062322/5697c00b1a28abf838cc82ad/html5/thumbnails/20.jpg)
2007/08/07 ARIA 20
Proposition 2 : first best separating equilibrium (advantageous selection)
![Page 21: 2007/08/07ARIA1 Hidden Overconfidence and Advantageous Selection Rachel J. Huang Assistant Professor, Finance Department Ming Chuan University, Taipei,](https://reader036.fdocuments.us/reader036/viewer/2022062322/5697c00b1a28abf838cc82ad/html5/thumbnails/21.jpg)
2007/08/07 ARIA 21
Proposition 3 : second best separating equilibrium (advantageous selection)
![Page 22: 2007/08/07ARIA1 Hidden Overconfidence and Advantageous Selection Rachel J. Huang Assistant Professor, Finance Department Ming Chuan University, Taipei,](https://reader036.fdocuments.us/reader036/viewer/2022062322/5697c00b1a28abf838cc82ad/html5/thumbnails/22.jpg)
2007/08/07 ARIA 22
Proposition 4 : partial pooling equilibrium (advantageous selection)
![Page 23: 2007/08/07ARIA1 Hidden Overconfidence and Advantageous Selection Rachel J. Huang Assistant Professor, Finance Department Ming Chuan University, Taipei,](https://reader036.fdocuments.us/reader036/viewer/2022062322/5697c00b1a28abf838cc82ad/html5/thumbnails/23.jpg)
2007/08/07 ARIA 23
Proposition 5 : separating equilibrium with linear premium
![Page 24: 2007/08/07ARIA1 Hidden Overconfidence and Advantageous Selection Rachel J. Huang Assistant Professor, Finance Department Ming Chuan University, Taipei,](https://reader036.fdocuments.us/reader036/viewer/2022062322/5697c00b1a28abf838cc82ad/html5/thumbnails/24.jpg)
2007/08/07 ARIA 24
Proposition 6 : no equilibrium
![Page 25: 2007/08/07ARIA1 Hidden Overconfidence and Advantageous Selection Rachel J. Huang Assistant Professor, Finance Department Ming Chuan University, Taipei,](https://reader036.fdocuments.us/reader036/viewer/2022062322/5697c00b1a28abf838cc82ad/html5/thumbnails/25.jpg)
2007/08/07 ARIA 25
Adverse selection: if )()( gf
![Page 26: 2007/08/07ARIA1 Hidden Overconfidence and Advantageous Selection Rachel J. Huang Assistant Professor, Finance Department Ming Chuan University, Taipei,](https://reader036.fdocuments.us/reader036/viewer/2022062322/5697c00b1a28abf838cc82ad/html5/thumbnails/26.jpg)
2007/08/07 ARIA 26
4. Conclusion
![Page 27: 2007/08/07ARIA1 Hidden Overconfidence and Advantageous Selection Rachel J. Huang Assistant Professor, Finance Department Ming Chuan University, Taipei,](https://reader036.fdocuments.us/reader036/viewer/2022062322/5697c00b1a28abf838cc82ad/html5/thumbnails/27.jpg)
2007/08/07 ARIA 27
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.
![Page 28: 2007/08/07ARIA1 Hidden Overconfidence and Advantageous Selection Rachel J. Huang Assistant Professor, Finance Department Ming Chuan University, Taipei,](https://reader036.fdocuments.us/reader036/viewer/2022062322/5697c00b1a28abf838cc82ad/html5/thumbnails/28.jpg)
2007/08/07 ARIA 28
Thank you for your attention!