IMPACT OF DIFFERENT LIFE-CYCLE SAVING STRATEGIES AND UNEMPLOYMENT ON INDIVIDUAL SAVINGS IN DEFINED CONTRIBUTION PENSION SCHEME IN SLOVAKIA

128 2021, XXIV, 3 Finance 10.15240/ ul/001/2021-3-008 IMPACT OF DIFFERENT LIFE-CYCLE SAVING STRATEGIES AND UNEMPLOYMENT ON INDIVIDUAL SAVINGS IN DEFINED CONTRIBUTION PENSION SCHEME IN SLOVAKIA Michal Mešťan1, I an K álik2, Leoš Ša á 3, Ján Šebo4 1 Ma ej Bel Uni e si y in Banská Bys ica, Facul y o Economics, Depa men o Finance and Accoun ing, Slo akia, ORCID: 0000-0002-4974-2254, [email p o ec ed]; 2 Ma ej Bel Uni e si y in Banská Bys ica, Facul y o Economics, Depa men o Public Economics and Regional De elopmen , Slo akia, ORCID: 0000-0002-9131-7067, [email p o ec ed]; 3 Technical Uni e si y in Košice, Facul y o Economics, Depa men o Finance, Slo akia, ORCID: 0000-0001-8466-0644, [email p o ec ed]; 4 Ma ej Bel Uni e si y in Banská Bys ica, Facul y o Economics, Depa men o Public Economics and Regional De elopmen , Slo akia, ORCID: 0000-0001-7974-3285, [email p o ec ed]. Abs ac : Sea ching o he op imal sa ing s a egy is o en ied wi h he li e-cycle s a egies whe e only he age o a sa e is conside ed o se ing he alloca ion p o ile be ween equi ies and bonds. Ou a icle con ibu es o he deba e by looking a he pe o mance and adequacy isks a ising om applying age-based sa ing s a egies o sa e s in unded pension schemes. As many s udies ha e p o en he shi o he isk on o sa e s in de ined con ibu ion pension schemes unde a ious sa ing s a egies, we con ibu e o he deba e by p o iding simula ions o expec ed accumula ed sa ings ia unded pension scheme unde he a ious li e-cycle income p o iles and exis ence o unemploymen isk. Using he esampling simula ion echnique, we compa e he ixed and age-based s a egies o h ee di e en agen s wi h a ious li e-cycle income pa hs and di e en unemploymen isk. We compa e he expec ed amoun o sa ings and calcula e ela i e indica o s compa ing he expec ed mon hly bene i s, income eplacemen a e. We look closely on he impac o unemploymen on he alue o sa ings and calcula e he unemploymen ac o explaining he alue o sa ings los due o he pe iods o unemploymen . By combining li e-cycle income unc ions o indi iduals wi h di e en educa ion le el and unemploymen isk, we show ha decisions o implemen ing low isk sa ing s a egies a e subop imal and lead o a subs an ial dec ease in eplacemen a ios no only o highe income coho s bu especially o he lowes ones. A he same ime, we p o e ha employing low isk sa ing s a egy leads o he inc ease o adequacy isk especially d i en by he unemploymen isk ha is highe o lowe educa ion indi iduals. We conclude ha age-based li e-cycle sa ing s a egies, whe e he emaining sa ing ho izon is he only ac o de ining he alloca ion p o ile is no he op imal sa ing s a egy and o he ac o s should be conside ed as well when sea ching o op imal sa ing s a egy. Keywo ds: Pension sa ings, unemploymen li e-cycle income, li e-cycle s a egy. JEL Classi ica ion: D14, D15, G11, J26. APA S yle Ci a ion: Mešťan, M., K álik, I,. Ša á , L., & Šebo, J. (2021). Impac o Di e en Li e-cycle Sa ing S a egies and Unemploymen on Indi idual Sa ings in De ined Con ibu ion Pension Scheme in Slo akia. E&M Economics and Managemen , 24(3), 128–148. h ps://doi. o g/10.15240/ ul/001/2021-3-008 EM_3_2021.indd 128 8.9.2021 9:58:04 129 3, XXIV, 2021 Finance In oduc ion Indi iduals in manda o y pension sa ing (MPS) scheme in Slo akia ha e hei sa ings alloca ed mos ly in one o he pension unds – equi y o bond unds. Sa ing in only one o hese unds will be conside ed as benchma k s a egies. In ou a icle, ou goal is o compa e he p o i abili y ha can be achie ed wi h benchma k s a egies compa ed o li e-cycle sa ings s a egies. In hei case, he a io o sa ings be ween equi y and bond componen s changes dynamically, depending on he age and emaining sa ings pe iod o 40 yea s (480 mon hs). We deal wi h 3 ypes o indi iduals wi h di e en educa ion le el. In addi ion o compa ing he po en ially achie able e u ns a he end o he sa ing ho izon, we will also be in e es ed in he ola ili y o achie able e u ns and hei sp ead om he a e age wi h he selec ed sa ings s a egies. Sa e s a e ying o ge he bes alue o money, bu hey should also ake in o accoun he ac ha highe po en ial app ecia ion also en ails highe isk. The hi d key a ea on which we a e ying o ind he answe is how unemploymen will in luence he inal amoun o sa ing a he end o sa ing pe iod. In his a icle, we wo k wi h h ee le els o empi ical unemploymen a e o selec ed educa ional coho s, which we apply o he income o h ee indi iduals. 1. Desc ip iono Slo akDe ined Con ibu ion Pension Sa ing Scheme The Slo ak Pilla II was es ablished as a de ined con ibu ion (DC) pension sa ing scheme in 2005. Since Sep embe 2012, he en olmen is ully olun a y (in Sep embe 2012 i became manda o y) and eligible o pe sons up o 35 yea s o age. The p inciple o he unded pension is based on he accumula ion o sa ings du ing employmen and in es ing sa ings in inancial ma ke s ia special pu pose ehicles – pension unds, which a e managed and adminis a ed by Pension Fund Managemen Companies (PFMCs), licensed by he Na ional Bank o Slo akia (Ande sen e al., 2019). Acco ding o he applicable law in Slo akia ( he Ac on Old-Age Sa ing n. 43/2004), each PFMC is obliged o ope a e a leas wo pension unds which can be di ided in o wo main g oups:  Bond gua an eed manda o y pension und;  S ock non-gua an eed manda o y pension und. Each PFMC is ee o choose (mos ly based on hei business model) i i ope a es addi ional pension unds, which a e op ional. These legisla i e changes en e ed in o law on Ap il 30, 2013. Be o e his da e, each PFMC had o ope a e h ee ( espec i ely ou ) obliga o y pension unds:  Bond manda o y pension und (since Ma ch 2005);  Mixed manda o y pension und (since Ma ch 2005);  Equi y manda o y pension und (since Ma ch 2005);  Index manda o y pension und (since Ap il 2012). A e he legisla i e changes became e ec i e in May 2013, Mixed and Index pension unds became op ional, and some o PFMCs me ged hese pension unds wi h obliga o y Equi y non-gua an eed manda o y pension unds. I is impo an o say ha he i s h ee ca ego ies o pension unds a e ( om an asse managemen poin o iew) ac i ely managed pension unds, and Index pension unds a e he only unds managed passi ely. Howe e , changes in he ee policy (s ic ly egula ed) o ced p o ide s o change he in es men s a egy o pension unds owa ds being passi ely managed using mos ly ETFs as main inancial ins umen s (Ande sen e al., 2019). Indi iduals ha e he possibili y o sa e in one o wo pension unds a he same ime, i is comple ely up o a sa e how much o his own sa ings would be in es ed in one pension und o ano he . They can in es limi ed amoun o sa ings in a Bond gua an eed pension und and ano he pa in an Index non-gua an eed pension und. The e is no ee o cha ge o change his alloca ion a io o swi ch pension unds managed by he same PFMC (Ande sen e al., 2019). Lo s o indi iduals cu en ly en olled in a MPS scheme ha e hei sa ing alloca ed only in one MPF. Acco ding o Minis y o Labou , Social A ai and Family Slo ak Republic, only e y small g oup o indi iduals ha e hei sa ings spli be ween wo MPFs. Slo ak MPS scheme does no ha e p e-de ined so-called li e-cycle sa ing s a egies o indi iduals. In some Eas e n Eu ope coun ies ( o example Es onia, La ia and Li huania) PFMCs p o ide some li e- cycle pension unds o hei clien s. Acco ding o Ba nes e al. (2008) “a li e-cycle app oach o pension in es men could in ol e in es ing EM_3_2021.indd 129 8.9.2021 9:58:04 130 2021, XXIV, 3 Finance in equi y ea ly in li e, and inc easing bond holdings as e i emen app oaches. In es men in equi y ea ly in he li e cycle ensu es a long holding pe iod o equi y (e.g., 20–30 yea s), hus gi ing a po en ial o weal h accumula ion a ela i ely high e u ns and ela i ely low long- un isks, i he long- e m e u ns and isks o equi ies a e simila o wha hey ha e been his o ically. Swi ching in o bonds as e i emen app oaches means ha he holding pe iod o bonds will be ela i ely sho (e.g., 5–15 yea s), so he in es o could heo e ically bene i om he lowe isk o bonds in he sho e m, i bond e u ns and isks a e in line wi h hei his o ical p o ile. In gene al, li e-cycle can be desc ibed as an in es men app oach ha in ol es a swi ching o he po olio o e an indi idual’s li e cycle is obse ed among eal-wo ld DC plans.” Based on he cu en law in Slo akia, indi iduals can bene i om indi idual li e-cycle sa ing s a egies, which allow hem o managed hei sa ings du ing hei li e wi hou he need o c ea e a new pension und. Acco ding o Malkiel (1996), “li e cycle in es men s a egy is buil on he idea o ‘age-based in es ing’, o he no ion ha in es o s should alloca e a la ge po ion o hei long- e m in es men o equi ies o o he isky asse s when hey a e young and ha e a ela i ely long in es men ho izon, g adually shi ing his alloca ion owa ds less isky asse s as hey app oach e i emen .” This concep is discussed in pape s om Me on (2007), Ay es and Nalebu (2008), Basu e al. (2009), P au (2010), Ay es and Nalebu (2013) and Wang e al. (2017). A li e cycle s a egy does no keep i s a ge mix cons an o e ime. Ins ead, i de e minis ically changes he a ge mix ha is held in equi ies and bonds acco ding o a p ede ined ‘glide pa h’, which g adually il s he asse s mix away om equi ies and o he isky asse s owa ds less isky asse s such as bonds and cash as in es o s app oach e i emen . Fo his eason, in ou a icle we ocus on designing, es ing and compa ing li e- cycle sa ing s a egies on indi idual bases. We compa e hose s a egies wi h passi e app oach based on sa ing in one bond o equi y und. Con ibu ions o he MPS scheme a e based on he indi idual’s wage le el, which acco ding o Gu enen (2009) a ies depending on he indi idual’s educa ion, wo k expe ience, age, p e ious wage and unemploymen . Acco ding o ecen esea ch om OECD (2018), educa ion ha e huge impac o indi idual wages ac oss many de eloped coun ies – highe and be e educa ion means highe wages o indi iduals. Ka z and Mu phy (1992) con i med in hei s udy he impac o wo k expe ience on he p oduc i i y o indi iduals which is also ela ed o hei age (assump ion ha highe age indica e mo e wo k expe ience) and he highe wage. Buki e al. (2018) con i med ha he expe ience wo ke s in any ages will inc ease he alue o labou p oduc i i y and also shows ha he amoun o wage in luences he labou p oduc i i y oo. Galdeano and Tu unen (2005) show empi ical e idence ha eal wages a e lowe in local labou ma ke s wi h highe unemploymen . We assume ha indi iduals wi h lowe le els o educa ion a e mo e likely o expe ience unemploymen han indi iduals wi h highe le els o educa ion. The nega i e impac o unemploymen on wages should he e o e be highe o indi iduals wi h lowe le els o educa ion. The nega i e impac o unemploymen on wages is also ela ed o sa ing i sel . In he pe iod o unemploymen , he indi idual does no pay con ibu ions o he MPS scheme. The mo e pe iod o unemploymen du ing he li e o an indi idual, hen he less he will con ibu e o he sys em, which will nega i ely a ec his sa ings. Tha we ocus in he a icle on moni o ing he impac o unemploymen e ec o wages du ing ca ee o indi iduals wi h di e en le els o educa ion and also on he inal amoun o sa ings in he end o sa ing pe iod. 2. Resea ch Me hodology Desc ip ion A he beginning o he me hodology pa , we discuss in mo e de ails he o ms o con ibu ing o manda o y pension unds (MPFs). Nex pa con ains a de ailed desc ip ion o he selec ed simula ion me hod used o es ima e he u u e e u ns o equi y and bond MPFs including in la ion and desc ip ion o he sa ings scheme wi h implemen ed con ibu ions, MPFs e u ns, and a ee policy e lec ing he cu en MPFs se - up. A he end o me hodology pa , we p o ide:  explana ion o selec ed sa ing s a egies:  wo benchma k s a egies (I, II) in es ing du ing he en i e sa ing pe iod in o he equi y und (S ock (I)) o bond und (Bond (II)) only; and * wo li e-cycle in es men s a egies called as Aging I. (III) and Aging II. (IV), EM_3_2021.indd 130 8.9.2021 9:58:04 131 3, XXIV, 2021 Finance which dec ease he isky pa o sa ings as he indi idual ages;  e alua ion c i e ia o he esul s ob ained by implemen ing simula ion me hods and compa ison ma ix o each combina ion o esul s. Le us ha e a li e-cycle income unc ion (LCI) o 3 modelled indi iduals, whe e he LCI unc ions a e de ined by hei p e ious income, educa ion le el and age o an indi idual. In he a icle, we assume ha all h ee indi iduals will ha e he same leng h o sa ing pe iod se a 480 mon hs (40 yea s), which is he same as leng h o he wo king ca ee in he case o an indi idual wi h a mas e ’s deg ee. Howe e , we unde s and ha he wo king ca ee is highe han leng h o sa ing pe iod o an indi idual wi h a high school and elemen a y educa ion le el. Nex , we assume wo possible op ion:  indi iduals wi h a ull ca ee (wi hou he exis ence o unemploymen isk); and  indi iduals wi h an incomple e ca ee (wi h he exis ence o unemploymen isk). In o de o mee he a icle’s objec i es, we do no p ima ily ocus ou a en ion on whe he a longe sa ing pe iod o indi iduals wi h lowe educa ion le el can ha e a signi ican impac on he le el o accumula ed sa ings compa ed o an indi idual wi h a highe educa ion and a sho e sa ing pe iod. Ra he , we ocus on he a iance in he simula ed inal pension po s using h ee simula ion me hods. Tab. 1 p esen s he achie ed educa ion le el o each indi idual, including hei income p o iles, he ini ial mon hly wages, leng h o he sa ing pe iod exp essed in mon hs, pension sa ing scheme en y age and espec i e e i emen age exp essed in mon hs. We should s ess ha acco ding o he Social Insu ance Ac N. 461/2003, he e i emen age o indi iduals will be di e en due o he mechanism ha ies he e i emen age o he li e-expec ancy o a e i ing coho . An indi idual wi h an elemen a y educa ion le el joins he pension sa ing scheme in 2018 as a 16-yea s- old, howe e an indi idual wi h a mas e ’s deg ee en e ing he labou ma ke in ha same yea (2018) is al eady 24 yea s old. This na u ally implies ha an indi idual wi h mas e ’s deg ee will ha e a e i emen age lowe han an indi idual wi h Elemen a y educa ion when en e ing he labou ma ke in he same yea . Fo a compa abili y o he esul s, we uni ied he pension scheme en y age and hus we can expec he same e i emen age o all modeled indi iduals. Es ima ion o li e-cycle income o analysed indi iduals is ealized using he li e ime income unc ion p esen ed by Gu enen (2009) and Gu enen and Smi h (2014) and de ailed o he condi ions o he Slo ak Republic by Balco e al. (2018) and Šebo e al. (2017). We ha e modi ied he LCI model and abs ain om bo h expec ed and unexpec ed shocks such as unemploymen , disabili y, ma e ni y lea e, e c. The model uses he long- e m da a om he Ame ican Communi y Su ey (ACS, 2014) when es ima ing he li e ime income unc ions, as he e is no longi udinal da a se ies o Slo akia a ailable. Ini ial wage o each indi idual wj,1 is es ima ed using he Slo ak S a is ical O ice da a (Tab. 1). Indi idual income Educa ion le el (j)Wages p o ile Ini ial mon hly wage (w1) Sa ing pe iod (T) En y age in o MPS scheme (x1) Re i emen age (xT) Elemen a y Minimum wage 480 € in 2017 480 mon hs (40 yea s × 12 mon hs) 300 mon hs (25 yea s) 780 mon hs (65 yea s) High school A e age wage 998 € in 2017 480 mon hs (40 yea s × 12 mon hs) 300 mon hs (25 yea s) 780 mon hs (65 yea s) Mas e ’s deg ee 1.2 × a e age wage 1,198 € in 2017 480 mon hs (40 yea s × 12 mon hs) 300 mon hs (25 yea s) 780 mon hs (65 yea s) Sou ce: own Tab. 1: Inpu da a o 3 ypes o indi iduals EM_3_2021.indd 131 8.9.2021 9:58:04 132 2021, XXIV, 3 Finance w in educa ion le el j and ime is ep esen ed as w* j, , τ ep esen s in la ion a e o e ime . Le ∈ {1, 2, …, T}; T = 480 and indica es a se ial numbe o he sa ing a e. Simula ed expec ed u u e income is calcula ed as ollows: (1) whe e ω* j, deno es he eal annual wage inc ease o he indi idual wi h he app op ia e educa ion j a ime , calcula ed as: (2) Fo mula (2) is aken om he esea ch o Šebo e al. (2015) and Gu enen and Smi h (2014). y* j,x and y* j,x –1 indica e indi idual income o each educa ion le el j and age x in ime and −1, and ep esen s he acc ued labou capi al in o m o he wo k skills and expe ience. Acco ding o Coope (2014) and Gu enen e al. (2015), i an indi idual was unemployed o a ce ain pe iod, his wage does no ollow he o iginal ull-ca ee income unc ion due o he missed skills, wo king habi s, expe ience e c. When he e u ns o he labou ma ke , he can expec o nego ia e he wage lowe han his pee s wi h highe acc ued labou capi al. His nego ia ed wage is expec ed o copy only he in la ion, o in o he wo ds, he is able o nego ia e he wage ha is o he same eal alue as be o e becoming unemployed. Due o exis ence o unemploymen isk, we modi y o mula (1) as ollows: (3) whe e U indica es he employmen s a us in ime . U = 1 indica es ha an indi idual is unemployed, while U = 0 indica es ha an indi idual is employed. When indi idual is employed (U = 0), he o mula is equal o he Fig. 1: Income g ow h and unemploymen a e o 3 ypes o indi iduals Sou ce: own in R EM_3_2021.indd 132 8.9.2021 9:58:05 133 3, XXIV, 2021 Finance o mula p esen ed in o mula (1) and income unc ion in ime depends on in la ion a e as well as on acc ued labou capi al du ing he pe iod. I an indi idual is unemployed (U = 1), his income unc ion in ime changes only due o he in la ion. Le el o unemploymen a es o selec ed indi iduals wi h espec ed educa ion le el and age was ob ained om o icial da abase o S a is ics o ice o Slo ak Republic o qua e ly pe iods om 2008 ill 2018. The g aphs in Fig. 1 p esen he es ima ed income unc ions and unemploymen a es o modeled indi iduals o a de ined educa ion le el and di e en ages. Simula ions, calcula ions and hei g aphical in e p e a ion we e pe o med using R – ee so wa e en i onmen o s a is ical compu ing and g aphics. Fu he , we can easonably expec ha indi iduals con ibu e o he MPS scheme only i hey a e employed (U = 0). In he case o unemploymen (U = 1), indi idual ecei es a empo a y unemploymen bene i , bu hey do no con ibu e in o he pension scheme. In o de o es ima e he le el o con ibu ions, we de ine he wage an indi idual ecei es as w* j, and we can de ine he con ibu ion base as ollows: (4) Thus, he con ibu ions owa d he pension scheme a e ied o he wages paid and can be exp essed in ela i e e ms (con ibu ion a e). Le us ha e manda o y con ibu ions c and olun a y con ibu ions c a, owa d he pension scheme. Manda o y con ibu ion a e is se by law and olun a y con ibu ions a e based on he disc e iona y decision o an indi idual. Fo pu pose o his a icle we conside only manda o y con ibu ions based on cu en law, so he olun a y con ibu ion a e c a, o ∈ {1; 480} = 0. The manda o y con ibu ion a e c de ined o Slo ak pension scheme o ime is as ollows: c o ∈ {1; 12} = 4.50%; c o ∈ {13; 24} = 4.75%; c o ∈ {25; 36} = 5.00%; c o ∈ {37; 48} = 5.25%; c o ∈ {49; 60} = 5.50%; c o ∈ {61; 72} = 5.75%; c o ∈ {73; 480} = 6.00%. Amoun o g oss con ibu ions payed by indi idual in absolu e e ms (Cj, ) is calcula ed as ollows: (5) Fu he , we ha e o ac o in he ee policy applied o he pension scheme. The con ibu ion ee φ in Slo ak pension scheme is equal o 1.25%, ou o which 1% o con ibu ions cj, is paid o he pension asse managemen company and emaining 0.25% o he Social Insu ance Company, which adminis a es he manda o y con ibu ions. Ne con ibu ion is calcula ed as ollows: (6) Pension asse managemen companies apply wo addi ional ees – managemen ee and a pe o mance ee. P ocess o ee implemen a ion is p esen ed by Meša o á e al. (2015) whe e hey ans o med g oss e u ns s, and b, in o ne e u ns * s, and * b, as ollows: (7) (8) whe e F M ep esen s mon hly managemen ee. The managemen ee cha ged by pension asse managemen company is applied on asse s unde managemen . Le el o annual managemen ee is 0.3% p.a., so he mon hly managemen ee can be calcula ed as ollows: (9) F V ep esen s he pe o mance ee, applied by an in es men manage o gene a ing posi i e e u ns. Acco ding o he Slo ak law, he pe o mance ee can be cha ged only i he pension und closing p ice (P ) eaches new highs (High-Wa e -Ma k P inciple acco ding o Shin e al., 2017). Pe o mance ee is se a 10% o he di e ence be ween new and old highs eached du ing he las 36 mon hs (3 yea s). Pe o mance ee can be calcula ed as ollows: (10) EM_3_2021.indd 133 8.9.2021 9:58:05 134 2021, XXIV, 3 Finance Many di e en simula ion app oaches can be ound in he li e a u e. The mos popula me hod is he Mon e Ca lo me hod wi h he bes i dis ibu ion (Rubins ein & K oese, 2007; Wie sema, 2008; Vaja gah & Shoghi, 2015). This app oach allows us o c ea e basically unlimi ed amoun o simula ions o almos any inancial ins umen wi h su icien ime se ies. Disad an age o his me hod is ha hey do no main ain ela ions among inancial ins umen e u ns o mac oeconomic a iables. I we wan o main ain a ela ionship be ween a iables, we could use copula unc ion wi h Mon e Ca lo simula ion me hod. I is compu a ionally and nume ically e y di icul me hod ( he di icul y inc eases wi h he numbe o simula ed pa ame e s). The simula ion me hod ha o e comes he disad an age o he Mon e Ca lo me hod and he e o e used in his a icle is called esampling. The pu pose o his me hod is o use a long his o ical ime se ies o a ious pa ame e s and simula ed he expec ed u u e pa hs wi hou des oying he ela ions among he pa ame e s. The eason why we decided o use his app oach is ha in ou model we could po en ially wo k wi h many di e en mac oeconomics indica o s as well as many di e en inancial ins umen s, so he combina ion o pa ame e s is unlimi ed. We mus choose one pa ame e which will de ine he size o he blocks. In ou model, we wo k wi h wo asse classes (equi ies and bonds) and supplemen he da a wi h he in la ion. This me hod is desc ibed in de ail by Šebo e al. (2017), Balco e al. (2018), and Mešťan e al. (2018, 2021). Resampling me hod wo ks wi h almos 100 yea s-long block o his o ical inancial da a se ies ( om Janua y 1919 o Sep embe 2018) consis ing o : Equi y e u ns ep esen ed by mon hly his o ic e u ns (di idends included) o Dow Jones Indus ial A e age 30 (DJIA 30) index since Janua y 1919 un il Decembe 2001, and since Janua y 2002 un il Sep embe 2018 we use mon hly e u ns o ETF DIA which is he exchange aded inancial ins umen designed o copy DJIA30 index pe o mance. Bond e u ns ep esen ed by mon hly his o ic e u ns o 7–10 US easu y bond (cons an ma u i y) om Janua y 1919 o Decembe 2001, and om Janua y 2002 o Sep embe 2018 we use mon hly e u ns o ETF IEF which copies he US easu y bonds wi h 7–10 yea s du a ion. In la ion a e ep esen ed by mon hly changes in US cus ome p ice index (CPI) since Janua y 1919 un il Sep embe 2018. All da ase s desc ibed abo e ha e been ex ac ed om he FRED – FED S . Louis da abase. This da ase (called block (B)) consis s o 3 columns ep esen ed by mon hly in la ion changes, equi y and bond mon hly e u ns o a gi en pe iod. We di ide his o iginal block o da a in o 36 sho e blocks o da a based on he business cycle (expansion, con ac ion) using he Na ional Bu eau o Economic Resea ch me hodology, which p o ides in o ma ion on US Business Cycle and Expansions and Con ac ions. We ge 18 expansion blocks (BG) and 18 con ac ion blocks (BD). Then we s a gene a ing 480-mon hs (40-yea ) long blocks con aining mon hly e u ns o equi ies, bonds and in la ion. Combining expansion and con ac ion blocks, we ge 1,000 new da a se ies o bonds, equi ies and in la ion, which gi es he o al numbe o simula ions. We ma k mon hly o ecas ed e u n o equi ies s, , o bonds as b, and o in la ion a e as τ . Based on he analysis o he pension unds’ po olio s uc u es (Manaze Uspo .sk, 2018), we can easonably expec han almos 99% o he po olios consis om ETFs acking one o mo e equi y and/o bond indices. Fo pu pose o his a icle we will conside ha equi y MPF und will in es 100% o he po olio in o equi ies and bond MPF und will in es 100% o he po olio in bonds. In o de o p esen easonable esul s o simula ions, we p esen h ee scena ios – neu al, op imis ic and pessimis ic. Neu al scena io is ep esen ed by he 50 h pe cen ile o all simula ions esul s, nega i e and posi i e scena io is ep esen ed by he 10 h, espec i ely 90 h, pe cen ile. The e is no speci ic na ional egula ion on he me hodology o simula ion me hods in his scheme. Fo his eason, he pe cen iles ha e been se acco ding o he Slo ak egula ion on Pension Bene i S a emen o supplemen a y pension und p o ide s in supplemen a y pension scheme in Slo akia s a ing om 2019. In o de o calcula e expec ed pension sa ings, we apply ou di e en sa ing s a egies – wo benchma k s a egies and wo li e-cycle s a egies. Benchma k s a egies a e ma ked as S ock (I) and Bond (II) s a egy. EM_3_2021.indd 134 8.9.2021 9:58:06 135 3, XXIV, 2021 Finance Unde he s a egy (I), indi iduals alloca e weI s, = 100% o hei sa ings exclusi ely o he equi ies (bonds weigh s a e weI b, = 0%), unde he s a egy (II), hey alloca e weII b, = 100% o hei sa ings exclusi ely o bonds (equi ies weigh s a e weII s, = 0%). The emaining wo sa ing s a egies, Aging I. (III) and Aging II. (IV), a e based on a dynamic change in he indi idual sa ings alloca ion a io o e he sa ing pe iod. We speak abou so called li e-cycle sa ing s a egies ha use de- isking o e ime depending bo h on he indi idual age o he o e all emaining leng h o sa ing pe iod. The signi icance o li e-cycle sa ing s a egies in he case o long- e m sa ings (including e i emen sa ings) was exp essed by se e al au ho s Me on (2007), Ay es and Nalebu (2008), Basu e al. (2009) o Ay es and Nalebu (2013). Fe nandes (2013) highligh s he impo ance o li e-cycle s a egies as ollows: acco ding o li ecycle s a egies, po olio’s exposu e o isky asse s should decline and in es o s should alloca e mo e capi al o iskless asse s as hey ge olde . We check i ou esul s suppo wo a gumen s behind li ecycle s a egies. The i s pa o he p e ious sen ence claims ha equi ies ou pe o m bonds in he long e m and he second one ha he isk o equi y dec eases in he long e m. Aim o hese s a egies is o educe expec ed isk h ough educing exposu e o iskie asse s on an asse -weigh ed basis o e he li ecycle, dec ease po en ial ola ili y o sa ings close o he e i emen and deli e highe e u n (accumula ed weal h) o indi idual compa ed o any di e en s a egy. The li e-cycle sa ing s a egy (III) is based on indi idual’s cu en age and ollow he simple equi y alloca ion ule ‘100 − age’. As he age is exp essed in mon hs (no yea s), equi ies alloca ion a io is calcula ed as ollows: (11) and espec i e bond alloca ion a io is calcu la- ed as ollows: (12) Second li e-cycle sa ing s a egy (IV) is based on he leng h o a emaining sa ing pe iod, no on he age o an indi idual. In ou case, he de- isking is ealized du ing he sa ing ho izon. The equi y alloca ion a io is exp essed as ollows: (13) Fig. 2: Leng h o economic cycles om Janua y 1919 o Sep embe 2018 Sou ce: own based on da a om NBER, FRED, Thomson Reu e s Eikon, Mo nings a Di ec and Finance Yahoo EM_3_2021.indd 135 8.9.2021 9:58:06 136 2021, XXIV, 3 Finance and espec i e bond alloca ion a io is calcula- ed as ollows: (14) In o de o espec legal es ic ions on equi y alloca ion in Slo ak pension scheme, we ha e implemen ed he mechanism limi s he equi y alloca ion based on ollowing ules: (15) The alue o sa ings a he end o sa ing pe iod o speci ic sa ing s a egy is ep esen ed by Si j,T , whe e Cj, is explained by o mula (5), can be calcula ed as ollows: (16) and i indica es a se ial numbe o sa ing s a egy whe e i ∈ {I, II, III, IV}. We assume ha new con ibu ions Cj, a e in es ed a he beginning o he each sa ing pe iod ( ). I means, ha he i s con ibu ion is in es ed o a pe iod o 480 mon hs, second con ibu ion is in es ed 479 mon hs and he las one is in es ed only o 1 mon h. Cu en egula ion on Pension Bene i S a emen in Slo akia uses o mula (12) wi h T – ins ead o T – + 1. Using T – app oach compa ed o he T – + 1 app oach logically sligh ly unde es ima e he inal alue o sa ings. Based on he abo e-men ioned me hodology, we a emp o answe he ollowing scien i ic ques ions: Which sa ing s a egy deli e highe e u ns o accumula ed weal h in he end o he sa ing pe iod? Does li e-cycle sa ing s a egies dec ease po en ial isk/ ola ili y a he end o sa ing pe iod and deli e highe sa ing pe o mance han he benchma k s a egies? How does he exis ence o unemploymen a ec he inal alue o sa ings o modeled indi iduals? Final me hodological pa ocuses on he e alua ion o achie ed esul s and should p o ide he solid g ound o he discussion pa . The i s e alua ion indica o is he sa ings pe o mance SPi j,T o each indi idual j and each sa ing s a egy i. I can be iewed as a a io o inal sa ings and paid con ibu ions. Sa ings pe o mance indica o , as p esen ed by Šebo e al. (2017) and Mešťan e al. (2021), is calcula ed as ollows: (17) Second indica o (used by Kiliano á e al., 2006; and la e Meliche čík e al., 2015) is he mon hly e i emen indica o (MRIi j,T), which indica es he numbe o mon hs du ing which an indi idual j will ecei e pension o each s a egy i which is equal o his las p e- e i emen wage. Mon hly e i emen indica o has an in e es ing in e p e a ion alue, as i allows an indi idual o modi y his consump ion beha iou based on expec ed mon hly pension bene i s. I he desi ed indi idual eplacemen a io is applied, he indica o can be di ided by he desi ed eplacemen a io and i p o ides he numbe o mon hs, ha he inal pension po can co e a ce ain eplacemen a io o he las income o an indi idual. MRIi j,T could be calcula ed as ollows: (18) Thi d indica o is called indi idual eplacemen a io (IRRi j,T). This a io old us a io be ween he indi idual las wage in ime o e i emen and expec ed pension bene i . In op imal case, his a io should be 1 o 100% (o i we mul iply his a io by 100). I his a io is equal 1.0, he pension bene i is equaled as hei las wage be o e e i emen and hei s anda ds o li ing will no dec ease. Bu i his a io is 0.5, hen i means ha an indi idual will ha e esou ces o co e only hal wha he could a o d om his las pay. We calcula e i as ollows: (19) EM_3_2021.indd 136 8.9.2021 9:58:07 143 3, XXIV, 2021 Finance (III) as well as Aging II. (IV). Due o he ela i ely low unemploymen isk o an indi idual wi h he mas e ’s deg ee (see he Fig. 1), he simula ion esul s unde he ull employmen and unde he exis ence o unemploymen isk deli e ed almos simila esul s (see Tab. 4). Unlike he p e ious wo indi iduals wi h lowe educa ion le els, an indi idual wi h a mas e ’s deg ee could ace he unemploymen du a ion o only 21 mon hs, which is less han 2 yea s o e he whole wo king ca ee . As can be seen in Fig. 1, an indi idual wi h a mas e ’s deg ee could ace he highes unemploymen isk (almos 30%) only du ing he i s 1–2 yea s a e g adua ion. La e in he ca ee , he unemploymen isk alls signi ican ly, which gi es he oppo uni y o he pension po o ise s eadily wi h no signi ican in e up ion o e he emaining wo king ca ee as he unemploymen a e o he emaining age coho s dec eases and oscilla es a ound 5%. Tab. 4 p esen s he esul s o indica o s o each s a egy. We obse e simila dis ibu ion o sa ings pe o mance simula ions as in he p e ious wo educa ional coho s. As he e a e no majo in e up ions in he con ibu ions, he indica o s o eplacemen a io as well as MRI a e on a e age highe compa ed o he lowe educa ed indi iduals. We e e o he Appendix 3 o mo e de ailed esul s o each analyzed indica o . I should be no ed, ha he e is a hand ul o esea ches in es iga ing pension sa ing p ocess unde a ious isk ac o s, including unemploymen . Howe e , mos o he au ho s ac o in he e ec o unemploymen , bu ocus ei he on compa ing sa ing and/o in es men s a egies wi hin DC schemes (EIOPA, 2020; Šebo e al., 2017, 2015; Wang e al., 2017; Fe nandes, 2013; Meliche čík e al., 2015; Basu e al., 2009) o he e ec o unemploymen on li e-cycle income p ocesses (Buki e al., 2018; Galdeano & Tu unen, 2005; Gu enen, 2009; Gu enen & Smi h, 2014; Gu enen e al., 2015; Ka z & Mu phy, 1992). The e is no s aigh o wa d esea ch ha would analyze he impac o educa ion-speci ic unemploymen Fig. 5: Sa ing pe o mance dis ibu ion o each sa ing s a egy wi hou and wi h he unemploymen isk o an indi idual wi h mas e ’s deg ee educa ion le el Sou ce: own in R EM_3_2021.indd 143 8.9.2021 9:58:09 144 2021, XXIV, 3 Finance U = 0 U = 1 U = 0 – U = 1 U = 1/U0 – 1 Con ibu ions ∑T =1 Cj, 110,493.03€ (33,512.97€)* 107,763.60€ (32,738.60€)* −2,569.30€ (−800.39€)* −2.39% Las wage w* j,T 5,749.10€ (1,722.42€) 5,615.91€ (1,686.39€) −113.54€ (−36.03€) −2.09% Mon hs o unemploymen – 21 (4.46)** – – S ock (S a egy I) Sa ing Si j,T 332,114.25€ (99,684.43€)* 311,421.26€ (93,490.40€)* −19,351.24€ (−5,863.50€)* −6.09% Pension bene i PBi j,T 1,323.59€ (397.28€)* 1,241.12€ (372.59€)* −77,12€ (−23.37€)* −6.09% Sa ing pe o mance SPi j,T 2.05 (1.56)** 1.93 (1.50)** −0.11 −3.77% IRRi j,T 0.23 (0.12)** 0.22 (0.12)** −0.01 −4.06% MRIi j,T 57.87 (31.31)** 55.46 (30.04)** −2.29 −4.06% Unemploymen e ec UEi j,T –596.53€ (363,24€)** – – Bond (S a egy II) Sa ing Si j,T 231,200.12€ (70,167.32€)* 217,229.53€ (65,900.40€)* −13,781.01€ (−4,231.60€)* −6.07% Pension bene i PBi j,T 921.41€ (279.64€)* 865.73€ (262.64€)* −54.92€ (−16.86€)* −6.07% Sa ing pe o mance SPi j,T 1.08 (0.46)** 0.99 (0.44)** −0.08 −3.75% IRRi j,T 0.16 (0.04)** 0.15 (0.04)** −0.01 −4.04% MRIi j,T 40.74 (10.28)** 39.07 (9.88)** −1.64 −4.04% Unemploymen e ec UEi j,T –415.04€ (138.09€)** – – Aging I. (S a egy III) Sa ing Si j,T 278,715.33€ (85,087.01€)* 261,172.90€ (79,992.50€)* −16,647.95€ (−5,136.70€)* −6.08% Pension bene i PBi j,T 1,110.77€ (339.10€)* 1,040.86€ (318.80 €)* −66.35€ (−20.47€)* −6.08% Sa ing pe o mance SPi j,T 1.56 (0.80)** 1.46 (0.77)** −0.10 −3.77% IRRi j,T 0.20 (0.06)** 0.19 (0.06)** −0.01 −4.06% MRIi j,T 49.4 (16.23)** 47.46 (15.58)** −2.00 −4.06% Unemploymen e ec UEi j,T –509.04€ (213.42€)** – – Tab. 4: A e age esul s o each s a egy o an indi idual wi h mas e ’s deg ee educa ion le el – Pa 1 EM_3_2021.indd 144 8.9.2021 9:58:09 145 3, XXIV, 2021 Finance on he e minal alue o pension sa ings and hus ou pape p o ides mo e insigh in o he u u e esea ch in he a ea o sea ching o an op imal sa ing s a egy unde he exis ence o unemploymen o agmen ed con ibu ions unde mode n employmen con ac s ( eelance s, pa - ime jobs, e c). Conclusion The aim o he pape was o show, on he example o h ee indi iduals wi h di e en educa ion le els, he expec ed pe o mance o applying wo s a egies using a passi e app oach o sa ing and in es ing (S ock (I) and Bond (II) and wo li e-cycle s a egies (Aging I. (III) and Aging II. (IV)), which a e based on a dynamic de e mina ion o he sa ings a io be ween sha es and bonds o e ime. Only ew au ho s ha e analyzed he impac o unemploymen on he le el o sa ings unde a ious in es men s a egies. Ou app oach en iches he exis ing esea ch by es ima ing he expec ed li e-cycle income and unemploymen ajec o ies o h ee di e en educa ional and income coho s. The i s educa ional coho is ep esen ed by an indi idual wi h an elemen a y educa ion, who o e he li e-cycle ecei es he minimum wage, which is close o 60% o an a e age wage, and is exposed o he high p obabili ies o being unemployed o e he wo king ca ee . The second indi idual is ep esen ed by a high school educa ion and his li e-cycle income s a s below he a e age wage, while du ing he p oduc i i y peak eaches a highe wage han he economy a e age and la e in a ca ee p e e s job s abili y and hus accep lowe inc eases o wages. O e all, du ing he en i e wo king ca ee , his wage s ood a he a e age. The las indi idual holds he mas e ’s deg ee, while his li e-cycle income is on a e age a 1.25 he a e age wage. Again, his wage s a s below he a e age and has a s eepe g ow h du ing he i s wo hi ds o his ca ee . La e on, he p e e s job s abili y and accep s lowe wage inc eases. Bo h highe educa ion le el indi iduals ace lowe unemploymen isks o e he li e-cycle, which u ned in o smalle di e ences in he sa ings pe o mance o bo h scena ios (wi h and wi hou unemploymen isk). We ha e o mula ed h ee esea ch ques ions and ollowing conclusions can be d awn based on he pe o med simula ion and esea ch. O he 4 selec ed s a egies, an indi idual, ega dless o his/he educa ion, can expec he highes pension po by applying he S ock (I) s a egy ha in es s all con ibu ions in o he equi y und. In ui i ely and in he line wi h many p e ious pape s, his isky s a egy deli e s high dispe sion o expec ed e u ns. Li e-cycle s a egies, Aging I. (III) and Aging II. (IV), a e a comp omise be ween he pe o mance and associa ed down-side isk ep esen ed by he s anda d de ia ion o e u ns. These s a egies equi e an ac i e U = 0 U = 1 U = 0 – U = 1 U = 1/U0 – 1 Aging II. (S a egy IV) Sa ing Si j,T 270,849.33€ (80,160.78€)* 254,105.97€ (75,124.50€)* −16,011.48€ (−4,840.50€)* −6.09% Pension bene i PBi j,T 1,079.43€ (319.47€)* 1,012.70€ (299.40€)* −63.81€ (−19.29€)* −6.09% Sa ing pe o mance SPi j,T 1.37 (0.67)** 1.28 (0.64)** −0.09 −3.78% IRRi j,T 0.19 (0.06)** 0.18 (0.05)** −0.01 −4.07% MRIi j,T 46.54 (14.32)** 44.62 (13.73)** −1.89 −4.07% Unemploymen e ec UEi j,T –490.17€ (193.47€)** – – Sou ce: own in R No e: * p esen ed in eal e ms (discoun ed by in la ion); ** ep esen s a s anda d de ia ion (S dDe ) om he a e age. Tab. 4: A e age esul s o each s a egy o an indi idual wi h mas e ’s deg ee educa ion le el – Pa 2 EM_3_2021.indd 145 8.9.2021 9:58:09 146 2021, XXIV, 3 Finance app oach, howe e he ac i i y is equi ed on an annual basis. A sligh ly highe pe o mance o all h ee indi iduals was achie ed by applying he Aging I. (III) s a egy compa ed o he Aging II. (IV) s a egy. The ad an age o li e- cycle s a egies is ha hey a e less agg essi e wi h signi ican ly less dispe sion o e u ns. The lowes pe o mance has been obse ed by applying he Bond (II) s a egy, which uses a passi e alloca ion o con ibu ions exclusi ely o he leas ola ile inancial ins umen s such as bonds. Li e-cycle s a egies ailed o p o ide a single indi idual wi h a highe pe o mance han he S ock (I) s a egy, bu bo h ha e achie ed highe pe o mance han he second Bond (II) s a egy. His og ams o pe o mance dis ibu ion a he end o a sa ing ho izon p o ides he e idence ha he li e-cycle s a egies b ing less ola ili y o an indi idual han he S ock (I) s a egy, while he Bond (II) s a egy is he leas ola ile s a egy. Looking a he esul s o all he s a egies applied o all h ee indi iduals, one can obse e he igh skewed dis ibu ion, which indica es ha in all s a egies, an indi idual can expec below a e age esul s wi h a chance o achie ing abno mal sa ings pe o mance in a ew (ex emes), cases especially o S ock (I) s a egy. The hi d and pe haps he mos aluable ques ion, we ied o answe , is how he isk o unemploymen a ec s he accumula ed alue o sa ing o indi iduals wi h di e en li e-cycle income pa hs. Based on he esul s o ou model, we can conclude ha he impac o unemploymen is he g ea e he longe an indi idual is unemployed. Howe e , he impac is g ea e when he unemploymen occu s a he beginning o he wo king ca ee . This is due o he los e ec o compound in e es , which is in line wi h many p e ious esea ch indings. As he unemploymen isk is U-shaped o e he wo king ca ee , we can expec di ec nonlinea ela ion be ween he inal alue o sa ings and he leng h o unemploymen . When ying o unde s and he impac o unemploymen isk on he inal alue o sa ings, one should ca e ully conside he pe iods o wo king ca ee , when unemploymen occu s. I a pe son is unemployed a he beginning o he sa ing ho izon, he does no con ibu e o he pension sys em and he e o e he loses he compound in e es e ec on ini ial con ibu ions e en i he alue o ini ial con ibu ions is small due o he lowe wage a he beginning o he wo king ca ee . The impac o unemploymen on inal alue o sa ings dec eases when he unemploymen isk occu s la e in he ca ee . I indi iduals con ibu e egula ly o 30 yea s, especially o e he las 10 yea s, and would ha e been unemployed o some ime, hen his would ha e had a signi ican ly lowe impac on his inal alue o sa ings han he non-con ibu ion pe iod ha occu s ea ly in his ca ee . Howe e , we ealize ha he pape has no speci ically ocused on he impac o unemploymen wi h ega d o he pe iod o unemploymen , and he e o e we lea e his in e es ing ques ion open o u he esea ch. 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