Scale of Longevity Risks for Pension and Life Annuity Providers. Henry JIN, BEng, MCom Centre for Pension and Superannuation, UNSW

Transcription

1

2 Scale of Longeviy Risks for Pension and Life Annuiy Providers Henry JIN BEng MCom Cenre for Pension and Superannuaion UNSW

3 Ouline Norman Cohen s criique moivaion of he paper Mahemaical framework Force of Longeviy Longeviy Risk Premium Longeviy Risk vs. Invesmen Risk Numerical Eamples Empirical Evidence of Force of Longeviy UK and AUS Longeviy Risk for Ausralian Male age 60 Discussion and Conclusion

4 Norman Cohen s criique FT 9 Feb 2004 Was he acuarial profession asleep a he wheel? Given he scale of he crisis in he pensions indusry - for i is no jus on longeviy ha acuaries go i wrong bu on invesmen and funding as well - i is a wonder ha he profession has no come in for he opprobrium given o say accounans acuaries have consisenly underesimaed human longeviy. -- Norman Cohen 9 Feb 2004 Financial Times

5 Was he criique fair? Wha acuaries did? Friedland 1998 had a summary of a day-long discussion among epers iled impac of moraliy improvemen on Social Securiy: Canada Meico and he U.S. on Ocober Khalaf-Allah 2002 buil a model o projec fuure moraliy improvemen in erm of reducion facors for UK. Lin and Co 2004 also discussed he securiisaion of he longeviy risks in life annuiies. Ausralian Governmen Acuary published Moraliy Improvemen Facor in Ausralian Life Table and

6 Wha was missing? Need o add concep of longeviy in acuarial ebook Need o compare and manage he longeviy risk ogeher wih invesmen risk in a more sysemaic way Scale of he measuremen This Paper Correlaion o invesmen Ne Paper

7 Mahemaical Framework Coninuous Survival Funcion: Force of Longeviy S S = 1 υ S S Force of Moraliy S S = 1 μ [ ] = υ μ d S n n S n 0 ep / [ ] = d d r a ϖ υ μ ep 0

8 Mahemaical Framework Discree Condiional Survival Probabiliy P = S 1 / S Condiional Force of Longeviy a a ξ = 1 P P ϖ 65 ϖ 65 k 1 = ep r1 k k p = ep r1 k P65 m2004 m k = 1 k = 1 m= ϖ 65 ϖ 65 k 1 = ep r2 k k p = ep r2k P65 m2044 m k = 1 k = 1 m= Eremely Simplified Assumpion ξ 65 m n m = ξ a k 1 [ r2 40 ξ k] ϖ = ep P65 m2004 m k = 1 m= 0 a r = a r 40ξ 2 Longeviy Risk Premium indeaion

9 Longeviy vs. Invesmen Fundamenal driver of he longeviy risk is ξ which is a weighed average of he condiional forces of longeviy over age 65 and beyond. The longeviy risk premium is 40ξ which implies ha he longeviy risk usually increases wih epanding horizon. The longeviy effec in life annuiy pricing is somehow equivalen o he case of reduced rae of invesmen reurn which implies ha longeviy risk could be measured in a similar way of invesmen risk. Alernaively he concep of longeviy indeaion can be used so ha an annuiy sold in 2044 would be equivalen o an indeed annuiy sold in 2004 indeed by 40ξ per annum.

10 Equivalen Longeviy Term Srucure ELTS Now move on o a more fleible eample where neiher erm srucure nor longeviy improvemen is fla any more. Two Alernaive Assumpions: [ 65 m2004 ] P 65 m2004 m = ep μ m ξ 65 m n m = ξ 65 m a ϖ 65 k = k = 1 m 0 ep [ RF 2044 m 40 ξ 65 m μ65 m2004 m ] = Then he longeviy adjusmen in annuiy pricing would be agains forward rae erm srucure. ELTS

11 Empirical Longeviy Evidence in Ausralia Annual improvemen of p Male 80 Male 70 Male Horizon Source: Auhor s Calculaion. Ausralian Life Table

12 Equivalen Longeviy Term Srucure UK and AUS Annual Longeviy Term Srucure UK Male UK Female AUS Male AUS Female Age Source: auhor s calculaion based on ALT and UK Inerim Life Table

13 Accumulaive Effec of Longeviy Risk 50% 7% 45% 40% 35% Longeviy Risk Longeviy Risk Premium 6% 5% Longeviy Risk % 30% 25% 20% 15% 4% 3% 2% Longeviy Risk Premium % 10% 1% 5% 0% 0% Updaing Lag years Source: Auhor s calculaion. The risk free erm srucure as of 31 May 2004 is used. The moraliy benchmark is he cohorised life able for Ausralian male aged 60 from ALT

14 Conclusions Force of Longeviy is he key concep o bring longeviy and invesmen ogeher which can be easily offse agains erm srucure in life annuiy pricing. Longeviy eperiences in UK and AUS over he las wo decades coincide closely. Forces of longeviy over reiremen ages are quie consisen over ime while he bigger conribuions of longeviy observed over he older ages. The weighed average annual force of longeviy would be in he order of 0.1% for male cohor aged 60 in 2004 and around half for female. Longeviy risks accumulae proporionaely over ime. Mos of he eposure o longeviy shorfall can be reduced by updaing he cohorised life ables on a regular basis.

15 Furher Discussions Diversificaion is possible if we can undersand he correlaion paern beween hese risks. The diverging longeviy rends in China and Russia over las decade migh be a good eample of he negaive correlaion beween invesmen risk and longeviy risk. An empirical sudy of he correlaion beween longeviy and invesmen in differen sages of business cycle migh be an ineresing opic. Bu i is beyond he scope of his paper.

16 Any Quesion??