Beyond Age and Sex: Enhancing Annuity Pricing

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Beyond Age and Sex: Enhancing

Annuity Pricing

Joelle HY. Fong

The Wharton School (IRM Dept),

and CEPAR

CEPAR Demography & Longevity Workshop

University of New South Wales

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Source: Fidelity.com (http://gie.fidelity.com/estimator/gie/ownerinfo) ₂

Motivation

• Current pricing scheme of retail annuities  uneven $

returns across retirees.

• e.g. return of $0.92 per $1 invested [longer-lived person]

vs. $0.82 [average-lived].

Mitchell et al. 1999.

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Motivation

!

Consumers/ policymakers call for more flexible pricing.

!

In 2008, U.K. insurers started using postal codes,

marital status, tobacco use. (Not U.S./Canada yet).

Why not “more detailed” pricing schemes?

e.g. age, sex + BMI + educ.+ marital + health + etc.

Can more info be used in

retail annuity

pricing? Actually, YES:

 no obvious regulatory barriers (unlike pension annuity).

 insurers have ready technology (e.g. life / auto).

 impaired annuities are already underwritten.

Significant

adverse selection

in annuity mkts:

• Longer-lived people self-select into annuities.

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The Question

If

annuity providers are to use more information

in pricing,

(i) What pricing factors / risk-classes are available?

(and how will incorporating such factors improve explained

variability in mortality?)

(ii) How will it change the value of annuitization for

different demographic groups, and impact on

selection effects?

“More detailed” pricing scheme  reduce

adverse selection?

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Survival Analysis

Prior literature

- Stewart (07): Same as life insurance (No test of relevance).

- Brown/McDaid (03): race, educ, income, occupation, married,

religion, current health behavior, smoking, alcohol, and obesity.

(Ignores correlation & endogeneity).

My approach



Insurers‟ standpoint: prefer cheap-to-collect + verifiable info.

• Thus, I pre-select

„readily-measurable‟

risk factors.

• Use Gompertz proportional hazards model [and Cox].

• Inform if

less-conventional

factors (e.g. birth region, cognition)

are sig. predictors.

• Provide

ranking

of factors (vis-à-vis age & sex).

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Data: Health and Retirement Study

• U.S. biennial panel survey of adults age 50 & above, and

their households. HRS Tracker file ~ death & attrition.

• Used 9 waves:1992 – 2008. N = 9,047 individuals.

o Exclude spouse, proxies. o Nationally repres. sample. o Age 50-62 (1992) o age 66-78 (2008) o 72% survived; 21% died; 7% attrited.

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Selecting & Ranking of Factors

Simple

Pricing

Add „readily-measurable‟

Pricing Factors (PH regression)

Top 12 factors.

„More Detailed‟ Pricing

Age, sex

(Ranked using partial R

2

₎

Diabetes

Lung disease

Heart disease

Sex

Age

Marital status

High blood

Cancer

Education

BMI

Psychiatric condition

Cognition

Education

,

Marital

,

Race

,

BMI

Prior health history :

Ever-have

cancer, dia

betes, heart, lung,

stroke, arthritis, psychiatric, high

blood

Less-conventional: Birth region,

cognit

ive score

, parental

education, parental longevity

.

• Factors that are cheap-to-collect & verifiable.

• Exogenous (e.g. birth region)

; or

pre-determined (e.g. education)

;

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Estimated Hazard Ratios

Ranked covariates

Age-sex

_Pricing

More Detailed Pricing

_{(the top 12 factors)}

Age

1.09***

1.07***

Male

1.62***

1.83***

Ever-have Diabetes

2.51***

Chronic lung disease

2.33***

Heart disease

1.70***

Married

0.68***

High blood

1.45***

Cancer

2.00***

Education

0.77***

BMI (ref=normal weight):

Underweight

2.86***

Overweight

0.82***

Obese

0.85***

Major psychiatric

1.54***

Cognition (cts)

0.97***

Adjusted R

2

_6.7%

_29.7%

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Age-at-death Density Plots

How „more detailed‟ pricing schemes improve mortality

predictions:

 Insurers can distinguish across risk profiles,

0.000 0.001 0.002 0.003 0.004 55 62 69 76 83 90 97 104 111 118 Con d ition a l P rob a b ility o f d y ing Age High-longevity risk 0.000 0.001 0.002 0.003 0.004 55 62 69 76 83 90 97 104 111 118 Age Average-longevity risk 0.000 0.001 0.002 0.003 0.004 55 62 69 76 83 90 97 104 111 118 Age Low-longevity risk

 obtain tighter prediction intervals (narrower distn),

 more confident in most probable ages of death (peaks).

 Thus, better pinpoint length of expected annuity payouts.

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Impact of Detailed Pricing Schemes

If annuity providers used more information in pricing, how will it

change the annuitization values for different demographic groups?

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My approach

• A hypothetical heterogeneous cohort of 65-year old potential

annuity buyers with different sex, educ, marital, health history.

• Variety of pricing scenarios:

(

(age)

+ sex)

+ educ)

+ marital)

• Simulate annuity benefits and premiums for different buyers

~ nominal ir 6%; ω =120.

Prior literature

- E.g. Brown (01, 03), and Turra/Mitchell (08).

- Under

mortality heterogeneity

(e.g. 67-yr olds with different sex, educ, race)

,

 Ǝ dispersion in financial value (and utility-adj value) of annuities

between different groups under

age-only pricing

.

 Shorter-lived get

lower money‟s worth. Transfer of resources.

 Disp. reduce if

actuarially fair pricing

for every separate group.

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Premiums under Various Schemes

Consider a $1 / month whole life annuity-due.

Exp. Benefit Flow

to a educated, married, female, no high blood = $152

12 Different Pricing Schemes # of pricing factors Prices ($) # of distinct premiums

Age-only 1 Single price: $126 1

Age, sex 2 F:

M:

$134

117 2

Age, sex, education 3

HS-educated F: Less-educated F: HS-educated M: Less-educated M: $140 122 125 104 4

Age, sex, education,

marital status 4 Married, HS-educated F: Unmarried, HS-educated F: Married, less-educated F: Unmarried, less-educated F: Married, HS-educated M: Unmarried, HS-educated M: Married, less-educated M: Unmarried, less-educated M: $145 129 129 111 128 110 109 91 8 : : : : :

Annuity Premiums

depends on the Pricing Scheme used:

Different Pricing Schemes # of pricing factors Prices ($) # of distinct premiums

Age-only 1 Single price: $126 1

Age, sex 2 F:

M:

$134

117 2

Age, sex, education 3

HS-educated F: Less-educated F: HS-educated M: Less-educated M: $140 122 125 104 4

Age, sex, education,

marital status 4 Married, HS-educated F: Unmarried, HS-educated F: Married, less-educated F: Unmarried, less-educated F: Married, HS-educated M: Unmarried, HS-educated M: Married, less-educated M: Unmarried, less-educated M: $145 129 129 111 128 110 109 91 8 : : : : :

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Results: Financial Value

(age 65, i=6%)

Simple pricing More detailed pricing Age Age + Sex + Educ. + Marry Very long-lived: No high blood,

Married, HS-educated, Females 1.204 1.133 1.081 1.047

Change in MWR -6% -5% -3%

Very short-lived: High blood, Not

married, less-educated, Males 0.645 0.693 0.780 0.893

Change in MWR +7% +13% +15%

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 Under more detailed pricing, shorter-lived annuity purchasers made

financially better off:

 0.693 to 0.893 ~ 30% gain just by adding 2 pricing factors !

 Longer-lived made worse off but still MWR >1.

 Uneven effect: gains for SL >> losses for LL. Why?

• Measured by money‟s worth ratio (MWR) = exp benefit / premium.

• e.g. MWR=0.8 : expected payouts received < premium paid.

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Financial Value (more groups)

Simpler Pricing More Detailed Pricing

S1 Age-only

S2 Age & sex

S3 + Educ.

S4 + Marital

Long-lived: No high blood, Married,

High-school (HS)-educated, Females 1.204 1.133 1.081 1.047 Married, HS-educated, Females 1.150 1.082 1.032 1.000

HS-educated, Females 1.114 1.048 1.000

-Females 1.062 1.000 -

-65-year-olds 1.000 - -

-Males 0.931 1.000 -

-Low-educated, Males 0.827 0.889 1.000 -Unmarried, Low-educated, Males 0.722 0.775 0.873 1.000 Short-lived: High blood, Unmarried,

Low-educated, Males 0.645 0.693 0.780 0.893

getting more $ returns getting less $ returns

• But MWR metric does not account for risk-aversion of individuals

or capture the utility gains from annuitization…

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Simulation: Utility-based model

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World with Annuities

World with NO annuities

To achieve same utility level V*

Need $140

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AEW Results

16 getting less utility getting more utility

Simpler Pricing More Detailed Pricing S1

Age-only

S2 Age & sex

S3 + Educ.

S4 + Marital V. Long-lived: No high blood, Married,

High-school (HS)-educated, Females 1.592 1.495 1.421 1.374 Married, HS-educated, Females 1.583 1.488 1.415 1.368

HS-educated, Females 1.577 1.482 1.411

-Females 1.568 1.474 -

-65-year-olds 1.552 - -

-Males 1.527 1.644 -

-Low-educated, Males 1.471 1.586 1.791 -Unmarried, Low-educated, Males 1.406 1.512 1.709 1.972 V. short-lived: High blood, Unmarried,

Low-educated, Males 1.342 1.445 1.633 1.882

Decline in AEW (for v. long-lived) -6% -5% -3%

Increase in AEW (for v. short-lived) +8% +13% +15%

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Summary

(i) What pricing factors / risk-classes are available?

-

Some cheap-to-collect ‘readily-measurable’ factors are strong predictors.

-

Esp. education, BMI, cognition, prior health history.

-

R2 improves by 4 – 5 times when 10 factors added.

-

Improved age-at-death predictions: sharper peaks, narrow distn

.

(ii) How value of annuitization for different demographic groups change &

implication for adverse selection?

2 effects may occur :

1. Shorter-lived groups may be sufficiently induced to buy annuities.

• MWR: substantial financial gains 29% just by adding 2 factors to

age-sex; enjoy decent MWR values of 0.8 to 0.9.

• AEW: achieve attractive utility gains of about 30%.

2. Longer-lived groups incentivized to remain in annuity market.

• not severely penalized by higher prem. Modest fin /utility losses ~8%.

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“More detailed” pricing  Annuity markets likely to grow 

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