enhanced annuities, individual underwriting, and adverse selection august 6, 2007 1 enhanced...
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August 6, 2007 Enhanced Annuities, Individual Underwriting, and Adverse Selection 1
Enhanced Annuities, Individual Underwriting, Enhanced Annuities, Individual Underwriting,
and Adverse Selectionand Adverse Selection
A Solution for the Annuity Puzzle?A Solution for the Annuity Puzzle?
Presentation at the ARIA 2007 Annual Meeting
Quebec City, Canada, August 2007
Gudrun Hoermann, Institute of Insurance Economics, University of St. Gallen
Jochen Russ, Institute for Financial and Actuarial Science, Ulm
August 6, 2007 Enhanced Annuities, Individual Underwriting, and Adverse Selection 2
Outline
1 Introduction
2 Model Framework
• Individual Mortality Rates
• Individual Underwriting
• Model Companies and Contracts
• Impact of Adverse Selection
3 Numerical Analyses
• Parameters and Methodology
• Selected Results
4 Summary
August 6, 2007 Enhanced Annuities, Individual Underwriting, and Adverse Selection 3
Outline
1 Introduction
2 Model Framework
• Individual Mortality Rates
• Individual Underwriting
• Model Companies and Contracts
• Impact of Adverse Selection
3 Numerical Analyses
• Parameters and Methodology
• Selected Results
4 Summary
August 6, 2007 Enhanced Annuities, Individual Underwriting, and Adverse Selection 4
• The value for money of a so-called standard annuity is the higher, the
longer the life expectancy of an insured person at the time of
annuitization
- Annuity depends only on age and gender of insured
Could be a (partial) explanation for the so-called annuity puzzle
• In many countries, there exist tax incentives for annuitization of old-age
provision contracts
- Sometimes even tax-sheltered or state subsidized products where
annuitization is compulsory
With reduced life expectancy only choice between annuitization at
“unfair” rates and lump sum benefit with tax disadvantage
Low acceptance of annuities in the population
Introduction
August 6, 2007 Enhanced Annuities, Individual Underwriting, and Adverse Selection 5
• Solution: Enhanced Annuities
• Annuity is the larger, the lower the insured´s life expectancy
• Complement to “preferred“ products
• Still very uncommon in many insurance markets
• Implementation by individual underwriting at the time the contract is
taken out (immediate annuity) or at the end of the deferment period
(deferred annuity)
• Advantage: “fair deal“ for everybody
Acceptance of annuities should increase
Introduction
August 6, 2007 Enhanced Annuities, Individual Underwriting, and Adverse Selection 6
• Existing literature about Enhanced Annuities: primarily practical issues
- Market development, size and potential
- Different product types
- Description of possible underwriting methodology
- Tax issues; distribution channels; reinsurance; etc.
- Ainslie (2000): Determination of portion of pensioners buying Enhanced Annuities instead of standard annuities (adverse selection)
- Emphasis of risk of underwriting Enhanced Annuities
• To our knowledge:
- No model for the individual underwriting of Enhanced Annuities and the quality of such an underwriting
- No quantitative analyses of the effects on the insurer´s profit/loss
- No quantitative analyses of the effects of adverse selection
Introduction
August 6, 2007 Enhanced Annuities, Individual Underwriting, and Adverse Selection 7
Outline
1 Introduction
2 Model Framework
• Individual Mortality Rates
• Individual Underwriting
• Model Companies and Contracts
• Impact of Adverse Selection
3 Numerical Analyses
• Parameters and Methodology
• Selected Results
4 Summary
August 6, 2007 Enhanced Annuities, Individual Underwriting, and Adverse Selection 8
• We assume that each person has individual mortality rates
- Individual frailty factor d applied on standard mortality table
- Frailty factor d realization of random variable D
• “Typical“ requirements for the distribution FD of the frailty factor in the population
- Continuous
- Domain d ≥ 0
- Probability density function:
“flat” at zero
- Right-skewed
- Expected value = 1
Model Framework: Individual Mortality Rates
August 6, 2007 Enhanced Annuities, Individual Underwriting, and Adverse Selection 9
Model Framework: Individual Underwriting
• The insurer performs individual underwriting on each insured
- Result of the underwriting: estimate for the insured´s frailty factor d
Determines the mortality rates used in the pricing of the contract (pricing rates)
- realisation of the random variable
- and D identically distributed (i.e. no systematic underwriting error)
- and D positively correlated with correlation coefficient
which is a measure for the quality of the individual underwriting
would imply the hypothetical case of perfect underwriting
• Individual underwriting model: continuous and symmetric
ˆ D,D
10 ρ
d̂ D̂
D̂
D̂
ˆD,Dρ =1
d̂
August 6, 2007 Enhanced Annuities, Individual Underwriting, and Adverse Selection 10
• Three model companies
- Insurer A: Only standard annuities
Pricing mortality rates = standard table
- Insurer B: Individual underwriting
Pricing mortality rates = estimation for frailty factor applied on
standard table
Correlation between the distributions explained above
determines quality of the individual underwriting
- Insurer C: Perfect individual underwriting
Special case of insurer B for
• Portfolio of individual insureds of same age and gender
• Each insured purchases an annuity that is priced with the
corresponding insurer´s pricing rates
- Simple immediate lifelong annuity for a single premium
ˆD,Dρ
Model Framework: Model Companies and Contracts
ˆD,Dρ =1
August 6, 2007 Enhanced Annuities, Individual Underwriting, and Adverse Selection 11
• To analyze the effect of adverse selection we assume the following
- A certain percentage s (selection intensity) of all insureds with a
frailty factor d beyond some threshold d* (selection barrier), i.e.
d > d*, prefer Enhanced Annuities to standard annuity products
This results in a modified mortality distribution for insurer A
In particular, average mortality rate decreases
The profit/loss situation worsens
Model Framework: Impact of Adverse Selection
August 6, 2007 Enhanced Annuities, Individual Underwriting, and Adverse Selection 12
Outline
1 Introduction
2 Model Framework
• Individual Mortality Rates
• Individual Underwriting
• Model Companies and Contracts
• Impact of Adverse Selection
3 Numerical Analyses
• Parameters and Methodology
• Selected Results
4 Summary
August 6, 2007 Enhanced Annuities, Individual Underwriting, and Adverse Selection 13
• Specification of parameters:
- Standard annuitant mortality table “DAV 2004 R” of the German
Society of Actuaries
- No costs and no safety loadings in the annuity product
This allows us to focus on the pure effects of the individual
underwriting
- Distribution FD of frailty factors in the population: Gamma (2; 0.25; 0.5)
Based on the “typical requirements” described above
- 100 male insureds aged 65
- Technical (=guaranteed) interest rate of 2.25%; no surplus
- When selection effects are analyzed, we assume that a certain
percentage of people with a frailty factor > 1.5 turn away from insurer
A
Numerical Analyses: Parameters and Methodology
August 6, 2007 Enhanced Annuities, Individual Underwriting, and Adverse Selection 14
• We perform 10,000 Monte Carlo simulations
- In each simulation path, we generate for each person
The individual frailty factor (determining the individual mortality)
o Gamma distribution
The result of the underwriting (insurer´s estimation of frailty factor)
o Correlated gamma distribution
The time of death of the insured
o Based on the individual mortality
- This completely determines the cash-flow stream of the insurer
- Thus, we get (a Monte Carlo estimate for) the distribution of the
insurer´s profit/loss (ΠA , ΠB or ΠC)
Numerical Analyses: Parameters and Methodology
August 6, 2007 Enhanced Annuities, Individual Underwriting, and Adverse Selection 15
• Expected profit as a function
of the correlation coefficient
- For insurer A, E(ΠA) = 0 by
calibration
- Expected profit of insurer
B is increasing in the
quality of the individual
underwriting
- Expected profit of insurer
B exceeds expected profit
of insurer A even for
rather poor quality of the
individual underwriting-0.2%
0.0%
0.2%
0.4%
0.6%
0.8%
1.0%
1.2%
1.4%
1.6%
1.8%
0.0 0.2 0.4 0.6 0.8 1.0
Correlation coefficient
Percentage ofpremium volume
A B C
Numerical Analyses: Selected Results
August 6, 2007 Enhanced Annuities, Individual Underwriting, and Adverse Selection 16
• Volatility of profit as a function
of the correlation coefficient
- For low correlation
coefficients volatility of
insurer B exceeds A
- Better quality of
underwriting reduces
standard deviation
- For correlations above
0.4, both, expected profit
higher and volatility lower
than for insurer A
Numerical Analyses: Selected Results
August 6, 2007 Enhanced Annuities, Individual Underwriting, and Adverse Selection 17
• Distribution of profit
- With increasing quality of
the underwriting:
distribution moves to the
right expected profit
distributions become
denser volatility
Numerical Analyses: Selected Results
August 6, 2007 Enhanced Annuities, Individual Underwriting, and Adverse Selection 18
• Considering selection effects:
Expected profit as a function
of the “selection intensity”
(d* = 1.5)
- Selection effects cause a
systematic loss for insurer
A
- The loss increases as the
number of good risks
turning away from insurer
A increases
Numerical Analyses: Selected Results
August 6, 2007 Enhanced Annuities, Individual Underwriting, and Adverse Selection 19
Outline
1 Introduction
2 Model Framework
• Individual Mortality Rates
• Individual Underwriting
• Model Companies and Contracts
• Impact of Adverse Selection
3 Numerical Analyses
• Parameters and Methodology
• Selected Results
4 Summary
August 6, 2007 Enhanced Annuities, Individual Underwriting, and Adverse Selection 20
• Enhanced Annuities
- pay higher benefits to persons with decreased health status
- hence offer the same value-for-money for everybody
- are therefore also attractive for persons with a less than average life
expectancy
which is particularly important when tax incentives for
annuitization are given
- could thus increase the acceptance of annuity products
what – under certain assumptions - can be shown to be beneficial
for seniors.
Summary
August 6, 2007 Enhanced Annuities, Individual Underwriting, and Adverse Selection 21
• From an insurer´s point of view
- Even if the underwriting is only “right on average”, Enhanced
Annuities would increase expected profitability
- The advantage increases in the quality of underwriting
- Insurer’s profit volatility decreases in the quality of the underwriting
- Selection effects cause significant negative effects on a standard
insurer if competitors offer Enhanced Annuities
• Enhanced Annuities have positive effects on an insurer´s risk profile
- Even under rather week assumptions for the quality of the
underwriting
Summary
August 6, 2007 Enhanced Annuities, Individual Underwriting, and Adverse Selection 22
Enhanced Annuities, Individual Underwriting, Enhanced Annuities, Individual Underwriting,
and Adverse Selectionand Adverse Selection
A Solution for the Annuity Puzzle?A Solution for the Annuity Puzzle?
THANK YOU VERY MUCH!
Gudrun Hoermann, Institute of Insurance Economics, University of St. Gallen
Jochen Russ, Institute for Financial and Actuarial Science, Ulm