enhanced annuities, individual underwriting, and adverse selection august 6, 2007 1 enhanced...

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


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


Outline

1 Introduction

2 Model Framework








4 Summary


• 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


• 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


• 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


Outline

1 Introduction

2 Model Framework








4 Summary


• 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


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


• 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


• 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


Outline

1 Introduction

2 Model Framework








4 Summary


• 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


• 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


• 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


• 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



• Distribution of profit

- With increasing quality of

the underwriting:

distribution moves to the

right expected profit

distributions become

denser volatility



• 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



Outline

1 Introduction

2 Model Framework








4 Summary


• 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


• 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


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

enhanced annuities, individual underwriting, and adverse selection august 6, 2007 1 enhanced...

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