Forced savings and annuitisation with crosssubsidies: a mutation of the beast. Benjamin Avanzi & Sachi Purcal Australian School of UNSW

Transcription

1 1! Forced savings and annuitisation with crosssubsidies: a mutation of the beast Benjamin Avanzi & Sachi Purcal Australian School of UNSW

2 Forced savings and annuitisation with cross-subsidies: a mutation of the beast Benjamin Avanzi 1 and Sachi Purcal 1 1 University of New South Wales Actuarial Studies, Australian School of Business b.avanzi@unsw.edu.au, s.purcal@unsw.edu.au AFIR / LIFE Colloquium München, 10 September /11 B. Avanzi, Australian School of UNSW

3 Plan Introduction: motivation Setting up the model A closed, autarkic system A tale of two cities References 2/11 B. Avanzi, Australian School of UNSW

4 Introduction: motivation Plan Introduction: motivation Setting up the model A closed, autarkic system A tale of two cities References 3/11 B. Avanzi, Australian School of UNSW

5 Introduction: motivation Background: the annuity puzzle The annuity puzzle stems from the following: economic theory (Yaari, 1965; Davidoff et al., 2005, to cite a few) suggests that annuitisation is the optimal choice of consumption flow in terms of utility but there surprisingly small demand for voluntary lifetime annuities troughout the world (Purcal and Piggott, 2008): U.K.: a big annuities market, but they are compulsory U.S.: most of tax-sheltered deferred annuities are withdrawn as lump sums Australia: only 61 annuities sold (for some AUD 11.9 mio) in 2008! (Plan for Life Research, 2008) Switzerland is an exception: the Swiss choose to annuitise... How does this system work? 3/11 B. Avanzi, Australian School of UNSW

6 Introduction: motivation A two-tiered economic approach with annuitisation and cross-subsidies a system for retirement income provision belongs to the most basic agenda of governments around the world mandating a minimum level of saving is part of a strategy to protect the old endorsed by the World Bank (1994) often, additional savings are encouraged, which leads de facto to two tiers: a tier of mandated savings (first tier), and a tier of non-mandated savings (second tier) we allow for annuitisation and cross-subsidies, which explains why both tiers are modeled together 4/11 B. Avanzi, Australian School of UNSW

7 Setting up the model Plan Introduction: motivation Setting up the model A closed, autarkic system A tale of two cities References 5/11 B. Avanzi, Australian School of UNSW

8 Setting up the model /"'('$01)!)*2'*'2&'()))))))))))))))))))))))))))'3)!4-(5,)6()"'(5267#&'()0-!2)!, 1# k # n, k!""#$#%!&'()*+!,-) w k ="'(5267#&'(>) " w k ="'(5267#&'(>) M r NM r " $!(.!5-.),!86(4,) ('(9$!(.!5-.),!86(4,).-"#$#%!&'()*+!,-) ;))))))!,)!()!((#650)63)) "# " > 0 ;)%#$*),#$)63))" < 0 ;))))))))))))))))!,)!()!((#650) "(# $ %) ;)'2)%#$*),#$) <+-)2!5-))))))))))))6,)5+-)!"5#!26!%%0)3!62)"'(8-2,6'()2!5-)3'2)!)%63-)!((#650) " # $ 5/11 B. Avanzi, Australian School of UNSW

9 Setting up the model /"'('$01)!)*2'*'2&'()))))))))))))))))))))))))))'3)!4-(5,)6()"'(5267#&'()0-!2)!, 1# k # n, k!""#$#%!&'()*+!,-) w k ="'(5267#&'(>) " w k ="'(5267#&'(>) M r NM r " $!(.!5-.),!86(4,) ('(9$!(.!5-.),!86(4,).-"#$#%!&'()*+!,-) ;))))))!,)!()!((#650)63)) "# " > 0 ;)%#$*),#$)63))" < 0 ;))))))))))))))))!,)!()!((#650) "(# $ %) ;)'2)%#$*),#$) <+-)2!5-))))))))))))6,)5+-)!"5#!26!%%0)3!62)"'(8-2,6'()2!5-)3'2)!)%63-)!((#650) " # $ 5/11 B. Avanzi, Australian School of UNSW

10 A closed, autarkic system Plan Introduction: motivation Setting up the model A closed, autarkic system A tale of two cities References 6/11 B. Avanzi, Australian School of UNSW

11 A closed, autarkic system Cross-subsidisation in the two tiers With no subsidies to or leakages from the scheme, we have r (M + NM)=rM + ρm + r NM, where ρm are the mandated savings that are converted into a lifetime annuity each year. We get r = r πm NM, where π = ρ + r r is the rate of subsidisation of M by NM. 6/11 B. Avanzi, Australian School of UNSW

12 Plan Introduction: motivation Setting up the model A closed, autarkic system A tale of two cities References 7/11 B. Avanzi, Australian School of UNSW

13 A taxonomy of the beast (π = ρ + r r ) /"'('$01)!)*2'*'2&'()))))))))))))))))))))))))))'3)!4-(5,)6()"'(5267#&'()0-!2)!, 1 # k # n, k!""#$#%!&'()*+!,-).-"#$#%!&'()*+!,-) w k ="'(5267#&'(>) " w k ="'(5267#&'(>) M r * NM r * $!(.!5-.),!86(4,) ('(9$!(.!5-.),!86(4,) ;))))))))))))))))!,)!()!((#650) "(# $ %) ;)'2)%#$*),#$) ;))))))))))))))))!,)!()!((#650) "(# $ %) ;)'2)%#$*),#$) <+-)2!5-))))))))))))6,)5+-)!"5#!26!%%0)3!62)"'(8-2,6'()2!5-)3'2)!)%63-)!((#650) " # $ = 0 π = 0 π> 0 π< 0 7/11 B. Avanzi, Australian School of UNSW

14 A taxonomy of the beast (π = ρ + r r ) /"'('$01)!)*2'*'2&'()))))))))))))))))))))))))))'3)!4-(5,)6()"'(5267#&'()0-!2)!, 1 # k # n, k!""#$#%!&'()*+!,-).-"#$#%!&'()*+!,-) w k >"'(5267#&'(?) " w k >"'(5267#&'(?) M r NM r " $!(.!5-.),!86(4,) ('(9$!(.!5-.),!86(4,) ;))))))))))))))))!,)!()!((#650) "(# $ %) ;)'2)%#$*),#$) ))=2',,9,#7,6.6-,)" M ;))))))))))))))))!,)!()!((#650) "(# $ %) ;)'2)%#$*),#$) <+-)2!5-))))))))))))6,)5+-)!"5#!26!%%0)3!62)"'(8-2,6'()2!5-)3'2)!)%63-)!((#650) " # $ = 0 π = 0 π> 0 π< 0 7/11 B. Avanzi, Australian School of UNSW

15 A taxonomy of the beast (π = ρ + r r ) /"'('$01)!)*2'*'2&'()))))))))))))))))))))))))))'3)!4-(5,)6()"'(5267#&'()0-!2)!, 1 # k # n, k!""#$#%!&'()*+!,-).-"#$#%!&'()*+!,-) w k >"'(5267#&'(?) " w k >"'(5267#&'(?) M r NM r " $!(.!5-.),!86(4,) ('(9$!(.!5-.),!86(4,) ;))))))))))))))))!,)!()!((#650) "(# $ %) ;)'2)%#$*),#$) ))=2',,9,#7,6.6-,) " M ;))))))))))))))))!,)!()!((#650) "(# $ %) ;)'2)%#$*),#$) <+-)2!5-))))))))))))6,)5+-)!"5#!26!%%0)3!62)"'(8-2,6'()2!5-)3'2)!)%63-)!((#650) " # $ = 0 π = 0 π> 0 π< 0 7/11 B. Avanzi, Australian School of UNSW

16 A taxonomy of the beast (π = ρ + r r ) /"'('$01)!)*2'*'2&'()))))))))))))))))))))))))))'3)!4-(5,)6()"'(5267#&'()0-!2)!, 1 # k # n, k!""#$#%!&'()*+!,-).-"#$#%!&'()*+!,-) w k >"'(5267#&'(?) " w k >"'(5267#&'(?) M NM $!(.!5-.),!86(4,) ('(9$!(.!5-.),!86(4,) =(5-2(!%) 2-.6,5267#&'() ;))))))!,)!()!((#650)) "# r r * > 0 ;))))))))))))))))!,)!()!((#650) "(# $ %) ;)'2)%#$*),#$) <+-)2!5-))))))))))))6,)5+-)!"5#!26!%%0)3!62)"'(8-2,6'()2!5-)3'2)!)%63-)!((#650) " # $ π = 0 π> 0 π< 0 7/11 B. Avanzi, Australian School of UNSW

17 A taxonomy of the beast (π = ρ + r r ) /"'('$01)!)*2'*'2&'()))))))))))))))))))))))))))'3)!4-(5,)6()"'(5267#&'()0-!2)!, 1 # k # n, k!""#$#%!&'()*+!,-).-"#$#%!&'()*+!,-) w k?"'(5267#&'(@) " w k?"'(5267#&'(@) M r NM r " $!(.!5-.),!86(4,) ('(9$!(.!5-.),!86(4,) >',,67%-)6(5-2(!%) 2-.6,5267#&'() ;))))))!,)!()!((#650) "# ))=2',,9,#7,6.6-,)" M ;))))))))))))))))!,)!()!((#650) "(# $ %) ;)'2)%#$*),#$) <+-)2!5-))))))))))))6,)5+-)!"5#!26!%%0)3!62)"'(8-2,6'()2!5-)3'2)!)%63-)!((#650) " # $ > 0 π = 0 π> 0 π< 0 7/11 B. Avanzi, Australian School of UNSW

18 A taxonomy of the beast (π = ρ + r r ) /"'('$01)!)*2'*'2&'()))))))))))))))))))))))))))'3)!4-(5,)6()"'(5267#&'()0-!2)!, 1 # k # n, k!""#$#%!&'()*+!,-).-"#$#%!&'()*+!,-) w k?"'(5267#&'(@) " w k?"'(5267#&'(@) M r NM r " $!(.!5-.),!86(4,) ('(9$!(.!5-.),!86(4,) >(5-2(!%) 2-.6,5267#&'() ;))))))!,)!()!((#650) "# ))=2',,9,#7,6.6-,) " M ;))))))))))))))))!,)!()!((#650) "(# $ %) ;)'2)%#$*),#$) <+-)2!5-))))))))))))6,)5+-)!"5#!26!%%0)3!62)"'(8-2,6'()2!5-)3'2)!)%63-)!((#650) " # $ > 0 π = 0 π> 0 π< 0 7/11 B. Avanzi, Australian School of UNSW

19 A taxonomy of the beast (π = ρ + r r ) /"'('$01)!)*2'*'2&'()))))))))))))))))))))))))))'3)!4-(5,)6()"'(5267#&'()0-!2)!, 1 # k # n, k!""#$#%!&'()*+!,-).-"#$#%!&'()*+!,-) w k?"'(5267#&'(@) " w k?"'(5267#&'(@) M r NM r " $!(.!5-.),!86(4,) ('(9$!(.!5-.),!86(4,) >',,67%-)6(5-2(!%) 2-.6,5267#&'()63))))) " > 0 ;))))))!,)!()!((#650)63)) "# " > 0 ;)%#$*),#$)63))" < 0 ))=2',,9,#7,6.6-,)" M ;))))))))))))))))!,)!()!((#650) "(# $ %) ;)'2)%#$*),#$) <+-)2!5-))))))))))))6,)5+-)!"5#!26!%%0)3!62)"'(8-2,6'()2!5-)3'2)!)%63-)!((#650) " # $ = 0 π = 0 π> 0 π< 0 > 0 π = 0 π> 0 π< 0 8/11 B. Avanzi, Australian School of UNSW

20 A tale of two cities Plan Introduction: motivation Setting up the model A closed, autarkic system A tale of two cities References 9/11 B. Avanzi, Australian School of UNSW

21 A tale of two cities Bern: π> 0 and > 0 high level of annuitisation (Bütler, 2003) high level of savings, > GDP (Gerber and Weber, 2007) presence of a liquid marked of privately sourced annuities BUT: complex system, difficult to understand and monitor, as shown by current difficult issues the system is facing Canberra: π = 0 and = 0 annuities market is very close to being dead Swiss situation is a desired one in Canberra would it be possible to implement π> 0 and > 0? 9/11 B. Avanzi, Australian School of UNSW

22 References Plan Introduction: motivation Setting up the model A closed, autarkic system A tale of two cities References 10/11 B. Avanzi, Australian School of UNSW

23 References References I Bütler, M., 17 March Mandated annuities in Switzerland. Tech. rep., DEEP Université de Lausanne & CEPR. Davidoff, T., Brown, J. R., Diamond, P. A., Annuities and individual welfare. American Economic Review: Papers & Proceedings 95 (5), Gerber, D. S., Weber, R., Demography and investment behavior of pension funds: Evidence for Switzerland. Journal of Pension Economics and Finance 6 (3), Plan for Life Research, December The immediate annuity product and rate report. Tech. rep., Plan for Life Pty Ltd. 10/11 B. Avanzi, Australian School of UNSW

24 References References II Purcal, S., Piggott, J., Explaining low annuity demand: An optimal portfolio application to Japan. Journal of Risk & Insurance 75 (2), World Bank, Averting the Old Age Crisis: Policies to Protect the Old and Promote Growth. The World Bank, Washington, D.C. Yaari, M., Uncertain lifetime, life insurance, and the theory of the consumer. The Review of Economic Studies 32 (2), /11 B. Avanzi, Australian School of UNSW