The future is not guaranteed Th f t i t t d Catherine Donnelly - PowerPoint PPT Presentation

The future is not guaranteed Th f t i t t d Catherine Donnelly Heriot-Watt University, Edinburgh, Scotland. http://www.macs.hw.ac.uk/~cd134/ November 28 2013.

Outline � Landscape � Why buy a life annuity? y y y � Alternatives � Annuity Overlay Fund � Group Self-Annuitization Scheme � Comparison

Landscape � Decline of DB schemes � Cost of life annuities � Annuity puzzle

Life annuity Life annuity Retirement choices Drawdown Drawdown

Life annuity Life annuity Alternatives Retirement choices Drawdown Drawdown

85 85 … 67 67 Drawdown (2% p.a.) 66 66 $100 $100 65 65 Consumption Consumption Assets Assets Age Age

Drawdown (2% p.a.) Assets Assets $100 $100 $102 $102 Consumption Consumption $6 $6 … Age Age 65 65 66 66 67 67 85 85

Drawdown (2% p.a.) Assets Assets $100 $100 $102 $102 $98 $98 Consumption Consumption $6 $6 $6 $6 … Age Age 65 65 66 66 67 67 85 85

Drawdown (2% p.a.) … Assets Assets $100 $100 $102 $102 $98 $98 $2 81 $2.81 … Consumption Consumption $6 $6 $6 $6 … Age Age 65 65 66 66 67 67 85 85

Life annuity (2% p.a.) With 12% loading over fair value. Pay insurer Pay insurer $100 $100 Consumption Consumption … Age Age 65 65 66 66 67 67

Life annuity (2% p.a.) With 12% loading over fair value. Pay insurer Pay insurer $100 $100 … … Consumption Consumption $6 $6 $6 $6 >+ 0 >+ 0 … Age Age 65 65 66 66 67 67 65+T 65+T

Life annuity (2% p.a.) Fair cost? With 12% loading over fair value. Pay insurer Pay insurer $100 $100 … … Consumption Consumption $6 $6 $6 $6 >+ 0 >+ 0 … Age Age 65 65 66 66 67 67 65+T 65+T

Life annuity Trust? Pay insurer Pay insurer $100 $100 … $6 $6 >+ O Consumption … Age 65 66 67 65+T Changed Need a your mind? lump sum?

Life annuity � Attractive for some, but not for all. � Can people still benefit from sharing mortality risk without buying a life annuity?

A Annuity overlay fund it l f d (Donnelly, Guillén, Nielsen 2013) Alice … Bob Drew Casey y

Annuity overlay fund Annuity overlay fund (2% p.a.) Assets $100 Mortality credit Consumption … Age 65 66 67 85

Annuity overlay fund Annuity overlay fund (2% p.a.) Assets $100 $102 Mortality $0.78 credit $6.72 Consumption … Age 65 66 67 85

Annuity overlay fund Annuity overlay fund (2% p.a.) … $34.91 Assets $100 $102 $97.98 Mortality … $0.78 $0.87 credit … $6.72 Consumption $6.72 … Age 65 66 67 85

Choose consumption Assets $100 $102 $94.63 Mortality $0.78 $0.85 credit Consumption $10 $50 … Age 65 66 67 85

Leave when you want Assets $100 $102 $97.98 Mortality $0.78 $0.87 credit Exit with $98.85 E it ith $98 85 $6.72 Consumption Age 65 66 67

Mortality credit Death Death Assets Assets Proceeds Proceeds occurs sold shared out

Mortality credit Proportional to: Instantaneous probability of death x Fund value

17:00 12:00 Mortality credit 09:00 $100 $300 Alice Bob

17:00 12:00 >+ 0 >+ 0 Mortality credit 09:00 $100 $300 Alice Bob

17:00 12:00 >+ 0 >+ 0 Mortality credit 09:00 $100 $300 Alice Bob 3q q q

17:00 $390 $10 12:00 >+ 0 >+ 0 Mortality credit 09:00 $100 $300 Alice Bob 3q q q

17:00 $100 $300 12:00 >+ 0 >+ 0 Mortality credit 09:00 $100 $300 Alice Bob 3q q q

Mortality credit � Amount and frequency depends on the group. � Mortality credit always non-negative for survivors.

Annuity overlay fund Annuity overlay fund - features � Any heterogeneous group � Contribution upon death � Actuarially fair at all times

Annuity overlay fund Annuity overlay fund - implications � Individuals retain investment control � Individuals decide how much to consume � Split investment from mortality: cost transparency p y

Numerical experiments � How willing are you to accept the mortality credit volatility? � Assume Black-Scholes financial market: � Risk-free interest rate r > 0 . � Risky asset price dynamics: dS t = μ S t dt + σ S t dZ t

Numerical experiments

Numerical experiments Return due to Return due to Small i investment in t t i mortality risk t lit i k change financial market sharing in wealth

Numerical experiments As number of members becomes infinite, Return due to Return due to Small investment in i t t i mortality risk t lit i k change financial market sharing in wealth

Numerical experiments As number of members becomes infinite, Instantaneous probability of death Instantaneous probability of death Return due to Return due to Small i investment in t t i mortality risk t lit i k change financial market sharing in wealth

Numerical experiments Insurer’s equivalent to infinite fund Cost Cost Return due to Return due to Small i investment in t t i mortality t lit change financial market pooling in wealth

Numerical experiments Finite annuity overlay fund: Insurer equivalent to infinite annuity overlay fund: su e equ v e o e u y ove y u d:

Numerical experiments

Numerical experiments 30 Young savers Old Spenders 25 25 20 Wealth 15 W 10 5 0 30 40 50 60 70 80 Age in years

Numerical experiments Participants Total number of Breakeven costs participants in fund (% of wealth) Old Spenders 300 <0.5% p.a. Young Savers Young Savers 300 300 <0.05% p.a. 0.05% p.a. Combined portfolio 300 < 0.75% p.a.

Practical questions � Purpose of the fund? � Conditions on fund exit and/or withdrawals? � Conditions on investment strategies? � Determination of mortality probabilities. y p � Asset sales upon death – legal issues/time. � Asset valuations – e g illiquid assets Asset valuations e.g. illiquid assets.

Group self annuitization (GSA) Group self-annuitization (GSA) scheme (Piggott, Valdez and Detzel 2005) � Purpose: provide consumption stream to participants. � Similar to a life annuity, without the guarantee.

Casey Drew GSA GSA fund Bob … Alice GSA

GSA – participant’s view Pay scheme Pay scheme $100 $100 … … Consumption Consumption $6.72 $6 72 $6 72 $6.72 >+ 0 >+ 0 … Age Age 65 65 66 66 67 67 65+T 65+T

GSA– scheme perspective … Assets Assets $10 000 $10,000 $10 200 $10,200 $9 723 $9,723 $1,618 $1 618 … … Payments out Payments out $667 $667 $662 $662 $281 $281 … Age Age 65 65 66 66 67 67 85 85

GSA � Share mortality risk. � Same investment strategy for all participants.

GSA calculation For each participant, This year’s consumption payment y p p y = Last year’s consumption payment y p p y x Mortality adjustment Mortality adjustment x Investment return adjustment Investment return adjustment

GSA calculation For each participant, This year’s consumption payment y p p y = Last year’s consumption payment y p p y Same Same x adjustment for all Mortality adjustment Mortality adjustment participants x Investment return adjustment Investment return adjustment

GSA calculation � Adjustments compare actual experience over the year to expected experience over the year

GSA - features � Any heterogeneous group � Contribution upfront: pays consumption stream � Not actuarially fair but may be only significant y y y g for highly heterogeneous groups (Sabin 2010, Donnelly 2013).

GSA - implications � Assets centrally managed � Consumption calculation pre-determined � Cost transparency

Quick comparison � Life annuity contract � Annuity overlay fund � Group self-annuitization (GSA) scheme

Quick comparison Life annuity GSA Annuity overlay Who bears Insurer Group Group mortality risk? � � � Mortality pooling? (Indirect) (Direct) (Direct) � � � Mortality guarantee?

Quick comparison Life annuity GSA Annuity overlay Who bears Insurer Individual Individual investment risk? � � � Investment guarantee? Premium/ Upfront Upfront Upon death contribution paid

Quick comparison Life annuity GSA Annuity overlay � � � Consumption stream? (individual’s choice) � � � Lump sum withdrawals? � � � Exit before death?

Quick comparison Life annuity GSA Annuity overlay � � � Costs transparent? � � � Individual investment control � � Actuarially fair? ?

Conclusion � Practical implementation. � Further questions: can we share investment risk across time? � Challenge: construct robust, transparent, g , p , easy-to-understand pension schemes.