Lifecycle Portfolio Choice with Systematic Longevity Risk and Variable Investment-Linked Deferred Annuities

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1 Lifecycle Portfolio Choice with Systematic Longevity Risk and Variable Investment-Linked Deferred Annuities Vasily Kartashov, Raimond Maurer, Olivia S. Mitchell, Ralph Rogalla Frankfurt, September 2011

2 VILDAs Variable Investment-Linked Deferred Annuities Premium is paid immediately / benefits start later at pre-specified retirement age (pension product; no bequest; inflexibility; survival credit) Retirement-Payments linked to return of underlying portfolio (bonds/stocks) Pricing depends on deferral period, loadings, mortality assumptions, and guarantees by annuity provider Guarantees by the annuity provider Investment risk: ( covered by annuitant; portfolio allocation) Individual longevity risk ( covered by insurance company; creating risk pools) Systematic longevity risk (change of mortality assumptions) Covered by insurance company ( pricing; internal/external hedging) Covered by annuitant ( updating rule for benefits)

3 Literature & Contributions LC-portfolio choice studies with life annuities: Many studies on immediate life annuities: Milevsky/Yong (2007, 2009), Horneff et al. (2008, 2009, 2010); Little research on deferred life annuities although they appear to be ubiquitous (SoSe; DB plans): Horneff et al. (2010); Milevsky (2005); Models with uncertain mortality rates: Many empirical work on mortality developments / pricing of life annuities: Lee/Carter 1992, Cairns/Blake/Dowd (2008); Milevsky et al. (2009) Little research on uncertain mortality rates in LC-portfolio choice: Horneff et al. (2010); Cocco/Gomes (2011 WP) We ask: What role of VILDAs in LC-portfolio choice? How does stochastic mortality influence individuals optimal behavior? How results depend on annuity provider s approach to systematic longevity risk? 3

4 Impact of Deferring & Investment Risk on Payouts (50:50 stock/bond allocation) 25 VILDA Payouts (% of Initial Investment) Def. Period 0 Def. Period 5 Def. Period Age Level (survival credit & investment returns) and range (investment volatility) of payouts increase with deferring period 4 Q95% Q5%

5 Management of Systematic Mortality Risk: Self-Insurance Scheme Loading (in %) % Quantile 99.90% Quantile 99.50% Quantile 99.00% Quantile 90.00% Quantile Notes: Implied loading relative to actuarial (trend adjusted) fair premium (US females) to self finance VILDA at the specified confidence level. VILDA payments start at age 67; AIR (3%) Age 5

6 Management of Systematic Mortality Risk: Participation Scheme 0,4 Cumulated Adjustment Factor 0,3 0,2 0,1 0-0,1-0,2-0,3-0,4 95% Quantile Mean 5% Quantile Age Cumulated Adjustment Factors: Difference of benefit payments between participating VILDAs (bought at age 20) and actuarial fair priced non-participating VILDAs (trend adjusted). 6

7 Multi-Period Life-Cycle Model Household (dynamic consumption utility optimizer) Decides each year how much to consume / save (stocks/bonds/vildas) CRRA utility function (no bequest motive; RRA=5, DF=0.96) Stochastic, unspanned labor income (Cocco et al high school profile) Retirement from age 67 on (public pension 40% of last salary) Uncertain time of death between age Setting 1: given mortality rates Setting 2: stochastic mortality rates by CBD (2008) 2-factor model; fitted US f.rates ( ) Incomplete life annuity markets Deferred life-annuity with investment-linked payments from age 67 on No annuity purchases after retirement/deferring age 67 Pricing / Risk management of systematic mortality risk by annuity provider Setting 2a: Self-Insurance calculating sufficient premiums (99.99% quantile pricing) Setting 2b: Participating annuities (updating rule) Numerical solution by dynamic optimization; MC Sim. 1 Mio. LifeCycles 7

8 Life Cycle Results with Deterministic/Stochastic Mortality: Mean Annuity Purchases & Payments (multiple of first labor income) Age Given Life Table (LT) Stochastic LT, Participating Stochastic LT, Nonparticipating Panel A: Annuity Purchases Panel B: Annuity Payments

9 Welfare Analysis - VILDA-related Consumption Increases (mean in %) Age Given Life Table (LT) Stochastic LT, Participating Stochastic LT, Nonparticipating Notes: Mean additional consumption (in %) at specified age that household with access to VILDAs is able to afford compared to household with no access VILDAs 9

10 Demand Side: Break-Even Loadings - VILDA Participation vs. Non-participation Wealth level ( x initial labor income) Age Notes: Loading to actuarial fair premium for non-participating VILDA compared to participating VILDA with no-loadings. 10

11 Sensitivity Analysis (for stochastic mortality): Range of VILDA-related Consumption Increases Participating VILDA Non-participating VILDA Age 5% Quantile Mean 95% Quantile 5% Quantile Mean 95% Quantile Excess consumption (in %) at specified age that household with access to VILDAs is able to afford compared to household in non-vilda world. 11

12 Conclusion VILDAs are private (funded) pensions products allowing households to participate survival credit, access to financial markets, low premiums Managing of Systematic Mortality Risk: Self-insurance of guaranteed mortality assumptions could be very expensive (unless there is an inexpensive natural hedge available). Efficiency improvement using the mortality instruments? Participation scheme is more attractive to households Even with expensive self-insurance VILDAs substantially increase the consumption over the life cycle Milevsky (2005: 110): ( ) engaging in irreversible financial transactions - that is annuitization - involving large lump sums will never be appealing to individuals regardless of (whether they grasp) the importance of longevity insurance. VILDAs to overcome the psychological barriers to voluntary annuitization?

13 Backup

14 Mean VILDA Bond Share, for Alternative Mortality Table Assumptions Age Given Life Table (LT) Stochastic LT, Participating Stochastic LT, Nonparticipating

15 Life Cycle Results with Deterministic Mortality: Annuity Purchases and Payments Age 5% Quantile Mean 95% Quantile Panel A: Annuity Purchases Panel B: Annuity Payments Money (as a multiple of initial labor income) invested in VILDAs at specified age as well as benefits (as a multiple of initial labor income) paid by accumulated VILDAs at specified age.

16 Life Cycle Results with Deterministic Mortality: VILDA-related Consumption Increases Age 5% Quantile Mean 95% Quantile Excess consumption (in %) at specified age that household with access to VILDAs is able to afford compared to household in non-vilda world.

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