MEMORANDUM Date 006-09-7 Authors Bengt von Bahr, Göran Ronge Traffc-lght a stress test for lfe nsurance provsons Fnansnspetonen P.O. Box 6750 SE-113 85 Stocholm [Sveavägen 167] Tel +46 8 787 80 00 Fax +46 8 4 13 35 fnansnspetonen@f.se www.f.se Summary Ths memorandum comprses the bass for an extended stress test wthn the traffc-lght method. The ncrease ncludes the stress of those parts of the techncal provsons that comprse nsurance rss,.e. mortalty, morbdty and lapse rss. Expense rs s also consdered. Bacground and purpose Fnansnspetonen s now developng a stress test for nsurance companes entre operatons that covers both assets and labltes. The sze of the changes n the rs assumptons wll be chosen so that they represent approxmately the 99.5 percent quantle for the possble outcomes over the term of one year. Ths memorandum proposes how the rs assumptons n lfe nsurance companes shall be stressed. For some assumptons, e.g. those that relate to long-term trend forecasts for mortalty and morbdty, the sze of these changes cannot be quantfed n ths manner. In these cases, the assumptons as they are stated n QIS from CEIOPS have prmarly been appled. Lfe nsurance companes that have accdent nsurance report t n the same manner as other non-lfe nsurance. Refer to the specal nstructons for Traffc lght Non-lfe nsurance companes. Changed assumptons for lfe nsurance The assumptons refer to assumptons made n the valuaton of techncal provsons. The stressed provsons shall consst of A best provson n accordance wth the Prudent Person Prncple An ncrease n the provson on account of a reducton n the dscount rate An ncrease n the provson on account of stressed rs assumptons 1(9)
Best provson n accordance wth the Prudent Person Prncple Today s provsons are normally safeguarded. Ths means that they nclude mplct and/or explct securty loadngs. A best provson accordng to the Prudent Person Prncple shall correspond to the expected value or the 50 percent quantle of the future dscounted payments for the company s nsurance rss. The calculatons shall be made wth adequate actuaral methods. Dscountng should be made wth a rs-free nterest rate. Reducton of the dscount rate The stressng of assumptons regardng the dscount rate s presented n the nstructons for the current desgn of the stress test for lfe nsurance companes. Ths topc s not dscussed n detal here. Stressng of other rss Instructons for stress tests relatng to mortalty rs, morbdty rs, non-lfe annuty rs and lapse rs, all of whch are ncluded under the term nsurance rs, are presented below. In addton, an expense rs s dentfed and reported separately. Rss relatng to morbdty and accdent nsurance that are classfed under non-lfe nsurance but are managed by lfe nsurance companes follow the regulatons that apply to correspondng rss wthn non-lfe nsurance companes. Assumptons regardng poltcal rss, for example fscal rs, are classfed as operatng rss and not dscussed here. Mortalty rs Random error The best estmate of mortalty outcome for the comng year may be defned as BSU = p R aggregated over all nsurances (or rather all nsured lves) n all portfolos, where p s the best estmate of the one-year mortalty probabltes and R s the best estmate of rs sums, both postve and negatve. The random error s measured wth the standard devaton for the outcome n the comng year, whch s
Sd( BSU ) = p (1 p ) R. If ths sum s dffcult to calculate, t may be approxmated by p (1 p) p( 1 p) R, where p s an average probablty, or by R, n where n s the number of rss. In order to ncrease the precson of the estmate of p, t s possble to dvde the portfolo nto subpopulatons wth more homogeneous age compostons. The average probablty shall preferably be weghted by the rs sum and may be determned from the data presented n the Actuaral Report. The random error s.58 Sd(BSU). If the company has a stop-loss, cumulatve or smlar type of rensurance, the company may modfy the above estmate of random error. The modfcaton shall be ustfed. Note It may appear llogcal n the calculaton of the random error to also nclude the outcome of the negatve rs sums. The random error should be a measurement of the sze of postve devatons from the expected value,.e. outcome that s larger than expected. Postve devatons may occur n two ways, ether an exceptonally large number of postve rs sums or an exceptonally small number of negatve rs sums occur. The random error shall therefore be calculated on the bass of the entre portfolo of rs sums. Parameter errors The techncal nsurance provson shall be estmated usng the mortalty assumptons that comprse the best estmate accordng to the Prudent Person Prncple. Ths provson s desgnated as BA. Wth respect to the choce of mortalty assumptons, the followng apples. The company shall apply assumptons regardng current and future mortalty to ts portfolo on the bass of experence from ts own and smlar nsurance populatons. If ths nformaton s not deemed to be suffcently relable, the company may apply the M06 mortalty table prepared by the Swedsh Insurance Federaton as ts best estmate. Durng the test perod n the fall of 006, the M90 mortalty table may be appled for the same purpose. Some comparatve estmates from mortalty stressng are reported n Appendx 1. These show that a general factor reducton n mortalty by approxmately 0 percent corresponds to an ncreased expected lfespan for a 65-year-old (both male and female) of years. Correspondngly, a factor ncrease n mortalty means that the probablty that a 40-year-old des before the age of 65 ncreases by 8-1%. CEIOPS uses smlar technques n Solvency II. The stressng s mplemented by calculatng the provson wth other mortalty assumptons as follows: 3
The one-year mortalty probablty s ncreased by 0% n all ages The one-year mortalty probablty s reduced by 0% n all ages These provsons are desgnated as SA + and SA -, respectvely. + max SA BA; SA BA;0. The parameter error s ( ) The mortalty rs s the sum of the random error and the parameter error. Morbdty rs Morbdty rs refers to the nsurance rs wthn long-term llness nsurance and waver of premum nsurance. Random error The best estmate of the morbdty outcome for the comng year may be defned as BSU = p P q Q r R, where the frst sum ncludes all nsurances except ongong cases of llness, the second all ongong cases of llness pror to the end of the qualfyng perod and the thrd all cases of llness n payment. p s the best estmate of the one-year probablty of llness ncdence and P s the correspondng estmate of the rs sum. q s the best estmate of the probablty that the llness wll termnate wthn one year for those cases of llness that are n the qualfyng perod and Q s the correspondng estmate of the released rs sum. r s the best estmate of the probablty that cases of llness n payment wll termnate wthn one year and R s the correspondng estmate of the released rs sum. Note: In some companes, the llness s frst regstered when payments wll begn. In such cases, the above qq terms may be approxmated or placed n pp terms. Insurances that nclude benefts wth varyng qualfyng perods should be dvded nto correspondng portfolo components. The random error s measured wth the standard devaton for the outcome n the comng year, whch s 4
Sd( BSU ) = p (1 p ) P + q (1 q ) Q + r (1 r ) R. If these sums are dffcult to calculate, they may be approxmated n a smlar manner as descrbed n Mortalty rs. The random error s.58 Sd(BSU). If the company has a stop-loss, cumulatve or smlar type of rensurance, the company may modfy the above estmate of random error. The modfcaton shall be ustfed. Parameter errors The techncal nsurance provson shall be estmated usng the assumptons that comprse the best estmate accordng to the Prudent Person Prncple. The same prncples apply here as for parameter errors n Mortalty rs. Ths provson s desgnated as BA. The stressng s mplemented by applyng the followng other assumptons: ncreased one-year probabltes of llness ncdence by 50% reduced probabltes by 0% at all tmes that the llness has termnated. If the company apples a run off functon λ(x,t), ths shall be ncreased such that [1- λ(x,t)] s replaced by 0.8 [1- λ(x,t)] for all ages x and duratons t. the degrees of nvaldty (the relatonshp between actual leave of absence due to llness and full-tme leave of absence due to llness), gr, s ncreased such that (1-gr) s replaced by 0.8 (1-gr) Ths provson s desgnated as SA. The parameter error s SA BA. Appendx shows the aggregated morbdty outcomes for lfe nsurance companes durng the years 00-005 n accordance wth the Actuaral Report. Ths data partly verfes the stress test levels that are currently recommended. The morbdty rs s the sum of the random error and the parameter error. Annutes emanatng from non-lfe nsurance ( non-lfe annutes ) Random error 5
The best estmate of the non-lfe annutes outcome for the comng year may be defned as BSU = p R aggregated across all non-lfe annutes, where p represents the best estmates of the one-year mortalty probabltes and R s the best estmate of (negatvely released) rs sums. The random error s measured wth the standard devaton for the outcome n the comng year, whch s Sd( BSU ) = p (1 p ) R. If ths sum s dffcult to calculate, t may be approxmated n a smlar manner as descrbed n Mortalty rs. The random error s.58 Sd(BSU). Parameter errors The techncal nsurance provson shall be estmated usng the assumptons that comprse the best estmate accordng to the Prudent Person Prncple. The same prncples apply here as for parameter errors n Mortalty rs. Ths provson s desgnated as BA. The stressng s mplemented by calculatng the provson wth a mortalty assumpton such that the one-year mortalty probablty s 0% lower n all ages. Ths provson s desgnated as SA. The parameter error s SA BA. The non-lfe annuty rs s the sum of the random error and the parameter error. Lapse rs Lapse ncludes pad-up polces, cessaton of premum payments, surrenders and transfers. Lapse rs s measured by the quanttes V = the techncal provson for those nsurances that may be surrendered wthn ths meanng and where lapse sgnfes a cost for the company 6
F = the company s mplct or explct recevable clams through exstng nsurances for polcyholders and agents. Allowances for cancellaton lablty should be made here. F = deferred acquston costs (DAC) Lapse rs s 0.005 V + 0.1 F Total lfe nsurance rs The total lfe nsurance rs LR s defned as LR = r, Korr r, R r R where Korr s the followng correlaton matrx, r and stand for row and column, respectvely, and R r and R are the prevously calculated rss. Korr Mortalty Morbdty Non-lfe Lapse annutes Mortalty 1 Morbdty 0.5 1 Non-lfe 0.5 0 1 annutes Lapse 0.5 0 0 1 Expense rs Ths rs shall be reported separately and shall not be ncluded under the term nsurance rs. The expense rs s measured by K = the company s annual fxed costs, defned as operatng expenses plus clams adustment costs mnus acquston costs. The expense rs s calculated as 0.1 K. Expense rs and nsurance rs are assumed to have a correlaton coeffcent of 0.5 when calculatng the total rs. *********************************************************** Appendx 1 Examples of stressed mortalty assumptons The followng table presents a comparson of the stressng between QIS and ths memorandum for P(40,65) = the probablty that a 40-year-old wll de before the age of 65 E(65) = the expected remanng lfespan for a 65-year-old The startng pont s the M90 mortalty table and the stress tests have been mplemented by multplyng the mortalty ntensty by a factor. 7
Factor P(40,65) E(65) Female Male Female Male 0.8 5.30% 7.98% 7.78.69 0.9 5.94% 8.93% 6.73 1.71 1 6.57% 9.88% 5.80 0.84 1.1 7.1% 10.81% 4.97 0.07 1. 7.84% 11.73% 4.1 19.38 0.8855 +1 year 0.7854 + years 0.893 +1 year 0.7986 + years 1.1050 + 10% 1.14 + 0% 1,1031 + 10% 1,081 + 0% +1 year and + years ndcates the ncrease n expected lfespan n relaton to M90 +10% and +0% ndcate the ncrease n probabltes for mortalty and lfespan n relaton to M90 ************************************************************ Appendx The followng lst was compled from the reports ncluded n the Actuaral Report from 00-005. It ncludes reportng of long-term llness nsurance and premum exempton nsurance for all lfe nsurance companes excludng Alecta. Illness ncdence Rato 00 003 004 005 Results (rs premums - -9% -4% -16% 13% (provson for llness ncdence + IBNR)) / rs premums 61% 74% 81% 7% Run off Result (actual run off estmated run off) / estmated run off Total Total result / revenue (rs premums + actual run off) -38% -5% 11% 6% The table shows that the assumptons regardng llness ncdence were sgnfcantly underestmated for the years 00 and 003. The values for 001 demonstrate an even greater underestmaton (but are not reported n the above table). 8
Even f the run off shows postve results, the table shows that a stress test of llness ncdence should defntely be tested at a 50% level. Possble connectons to mproved run off shall not be assumed; rather the test level can be lowered. 9