Beyond Age and Sex: Enhancing Annuity Pricing

Transcription

1 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 26 July 2011

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 Source: Fidelity.com ( 2

3 Motivation Significant adverse selection in annuity mkts: Longer-lived people self-select into annuities % of total loadings. (Mitchell et al. 1999; Brown 03; Finkelstein/Poterba 02).! 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. 3

4 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? 4

5 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). Transform results to age-at-death prediction intervals. 5

6 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: N = 9,047 individuals. o Exclude spouse, proxies. o Nationally repres. sample. o Age (1992) o age (2008) o 72% survived; 21% died; 7% attrited. 6

7 Selecting & Ranking of Factors Factors that are cheap-to-collect & verifiable. Exogenous (e.g. birth region); or pre-determined (e.g. education); or objectively-measured (e.g. BMI). Simple Pricing Add readily-measurable Pricing Factors (PH regression) Top 12 factors. More Detailed Pricing Age, sex Age, sex (Ranked using partial R 2 ) Education, Marital, Race, BMI Diabetes Lung disease Heart disease Prior health history : Ever-have Sex cancer, diabetes, heart, lung, Age stroke, arthritis, psychiatric, high Marital status blood High blood Cancer Less-conventional: Birth region, cognitive score, parental education, parental longevity. Education BMI Psychiatric condition Cognition 8

8 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% 9

9 Conditional Probability of dying Age-at-death Density Plots How more detailed pricing schemes improve mortality predictions: Insurers can distinguish across risk profiles, obtain tighter prediction intervals (narrower distn), more confident in most probable ages of death (peaks). Thus, better pinpoint length of expected annuity payouts. High-longevity risk Average-longevity risk Low-longevity risk Age Age Age 10

10 Impact of Detailed Pricing Schemes If annuity providers used more information in pricing, how will it change the annuitization values for different demographic groups? 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. 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 =

11 Premiums under Various Schemes Consider a $1 / month whole life annuity-due. Exp. Benefit Flow to a educated, married, female, no high blood = $152 Annuity Premiums depends on the Pricing Scheme used: Different Pricing Schemes # of pricing factors Prices ($) # of distinct premiums Age-only 1 Single price: $126 1 Age, sex 2 F: $134 M: HS-educated F: $140 Age, sex, education 3 Less-educated F: 122 HS-educated M: Less-educated M: 104 Married, HS-educated F: Unmarried, HS-educated F: Married, less-educated F: $ Age, sex, education, Unmarried, less-educated F: marital status Married, HS-educated M: Unmarried, HS-educated M: Married, less-educated M: Unmarried, less-educated M: : : : : : 12

12 Results: Financial Value (age 65, i=6%) Measured by money s worth ratio (MWR) = exp benefit / premium. e.g. MWR=0.8 : expected payouts received < premium paid. Simple pricing More detailed pricing Very long-lived: No high blood, Married, HS-educated, Females Age Age + Sex + Educ. + Marry Change in MWR -6% -5% -3% Very short-lived: High blood, Not married, less-educated, Males Change in MWR +7% +13% +15% Under more detailed pricing, shorter-lived annuity purchasers made financially better off: to ~ 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? 13

13 Financial Value (more groups) getting more $ returns getting less $ returns Simpler Pricing S1 Age-only S2 Age & sex More Detailed Pricing S3 S4 + Educ. + Marital Long-lived: No high blood, Married, High-school (HS)-educated, Females Married, HS-educated, Females HS-educated, Females Females year-olds Males Low-educated, Males Unmarried, Low-educated, Males Short-lived: High blood, Unmarried, Low-educated, Males But MWR metric does not account for risk-aversion of individuals or capture the utility gains from annuitization 14

14 Simulation: Utility-based model World with Annuities World with NO annuities To achieve same utility level V* Need $140 15

15 AEW Results getting more utility getting less utility Simpler Pricing S1 Age-only S2 Age & sex More Detailed Pricing S3 S4 + Educ. + Marital V. Long-lived: No high blood, Married, High-school (HS)-educated, Females Married, HS-educated, Females HS-educated, Females Females year-olds Males Low-educated, Males Unmarried, Low-educated, Males V. short-lived: High blood, Unmarried, Low-educated, Males Decline in AEW (for v. long-lived) -6% -5% -3% Increase in AEW (for v. short-lived) +8% +13% +15% 16

16 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 agesex; 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%. More detailed pricing Annuity markets likely to grow Help reduce adverse selection costs. 17

17 Thank you. Any feedback welcomed! 18