1. Enhanced Annuities, Individual Underwriting, and Adverse Selection August 6, 2007 1 Enhanced Annuities, Individual Underwriting, and Adverse Selection 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

2. Enhanced Annuities, Individual Underwriting, and Adverse Selection August 6, 2007 2 Outline 1Introduction 2Model Framework Individual Mortality Rates Individual Underwriting Model Companies and Contracts Impact of Adverse Selection 3Numerical Analyses Parameters and Methodology Selected Results 4Summary

3. Enhanced Annuities, Individual Underwriting, and Adverse Selection August 6, 2007 3 Outline 1Introduction 2Model Framework Individual Mortality Rates Individual Underwriting Model Companies and Contracts Impact of Adverse Selection 3Numerical Analyses Parameters and Methodology Selected Results 4Summary

4. Enhanced Annuities, Individual Underwriting, and Adverse Selection August 6, 2007 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

5. Enhanced Annuities, Individual Underwriting, and Adverse Selection August 6, 2007 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

6. Enhanced Annuities, Individual Underwriting, and Adverse Selection August 6, 2007 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

7. Enhanced Annuities, Individual Underwriting, and Adverse Selection August 6, 2007 7 Outline 1Introduction 2Model Framework Individual Mortality Rates Individual Underwriting Model Companies and Contracts Impact of Adverse Selection 3Numerical Analyses Parameters and Methodology Selected Results 4Summary

8. Enhanced Annuities, Individual Underwriting, and Adverse Selection August 6, 2007 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 F D 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

9. Enhanced Annuities, Individual Underwriting, and Adverse Selection August 6, 2007 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

10. Enhanced Annuities, Individual Underwriting, and Adverse Selection August 6, 2007 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 Model Framework: Model Companies and Contracts

11. Enhanced Annuities, Individual Underwriting, and Adverse Selection August 6, 2007 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

12. Enhanced Annuities, Individual Underwriting, and Adverse Selection August 6, 2007 12 Outline 1Introduction 2Model Framework Individual Mortality Rates Individual Underwriting Model Companies and Contracts Impact of Adverse Selection 3Numerical Analyses Parameters and Methodology Selected Results 4Summary

13. Enhanced Annuities, Individual Underwriting, and Adverse Selection August 6, 2007 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 F D 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

14. Enhanced Annuities, Individual Underwriting, and Adverse Selection August 6, 2007 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 (Π A, Π B or Π C ) Numerical Analyses: Parameters and Methodology

15. Enhanced Annuities, Individual Underwriting, and Adverse Selection August 6, 2007 15 Expected profit as a function of the correlation coefficient -For insurer A, E(Π A ) = 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 Numerical Analyses: Selected Results

16. Enhanced Annuities, Individual Underwriting, and Adverse Selection August 6, 2007 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

17. Enhanced Annuities, Individual Underwriting, and Adverse Selection August 6, 2007 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

18. Enhanced Annuities, Individual Underwriting, and Adverse Selection August 6, 2007 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

19. Enhanced Annuities, Individual Underwriting, and Adverse Selection August 6, 2007 19 Outline 1Introduction 2Model Framework Individual Mortality Rates Individual Underwriting Model Companies and Contracts Impact of Adverse Selection 3Numerical Analyses Parameters and Methodology Selected Results 4Summary

20. Enhanced Annuities, Individual Underwriting, and Adverse Selection August 6, 2007 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

21. Enhanced Annuities, Individual Underwriting, and Adverse Selection August 6, 2007 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

22. Enhanced Annuities, Individual Underwriting, and Adverse Selection August 6, 2007 22 Enhanced Annuities, Individual Underwriting, and Adverse Selection 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