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.
Acknowledgmen s: This wo k was suppo ed
by The Slo ak Resea ch and De elopmen
Agency unde he con ac s No. APVV-19-0352.
Re e ences
Ame ican Communi y Su ey. (2014).
Ame ican Communi y Su ey Da a on
Educa ional A ainmen . Public da abase.
Ande sen, C., Ca lucci, E., Ch is o , L.,
Deinema, M., Gabau , L., Gal ai e, T., Hagen,
J., He ce, J. A., Houdmon , A., Mączyńska,
A., Manis, A., Mešťan, M., Naacke, G., Nagell,
L. S., P ache, G., Ru ecka-Gó a, J., U l, T., &
Vysniauskai e, A. (2019). Pension Sa ings:
The Real Re u n 2019 (1s ed.). B ussels: The
Eu opean Fede a ion o In es o s and Financial
Se ices Use s. h ps://be e inance.eu/wp-
con en /uploads/Pension-Sa ings-The-Real-
Re u n-2019-Edi ion-1.pd
Ay es, I., & Nalebu , B. J. (2008). Li e-
Cycle In es ing and Le e age: Buying S ock
On Ma gin Can Reduce Re i emen Risk
(NBER Wo king Pape Se ies, No. w14094).
Camb idge, MA: Na ional Bu eau o Economic
Resea ch.
Ay es, I., & Nalebu , B. J. (2013).
Di e si ica ion Ac oss Time. Jou nal o Po olio
Managemen , 39(2), 73–86. h ps://doi.
o g/10.3905/jpm.2013.39.2.073
Balco, M., Šebo, J., Mešťan, M., & Šebo á,
L. (2018). Applica ion o he Li ecycle Theo y in
Slo ak Pension Sys em. Ekonomický časopis,
66(1), 64–80.
Ba nes, F., Bell, L., & Sil a, L. C., (2008).
De ined-Con ibu ion Pension Schemes:
Risks and Ad an ages o Occupa ional
Re i emen P o ision (Repo commissioned
EM_3_2021.indd 146 8.9.2021 9:58:09
147
3, XXIV, 2021
Finance
o Oxe a). B ussels: Eu opean Fund and Asse
Managemen Associa ion (EFAMA).
Basu, A., By nes, A., & D ew, M. E. (2009).
Dynamic Li ecycle S a egies o Ta ge
Re i emen Funds (G i i h Business School
Discussion Pape s Finance, 200902). B isbane:
G i i h Uni e si y, Depa men o Accoun ing,
Finance and Economics.
Buki , I. N. M., Ismida, Y., Maulana, R.,
& Nasi , M. (2018). The in luence o wage,
age and expe ience o labo p oduc i i y in
cons uc ion wo ks in Ko a Langsa, Aceh.
In P oceedings om he Thi d In e na ional
Con e ence on Sus ainable In as uc u e and
Buil En i onmen (SIBE 2017) (MATEC Web o
Con e ences, Vol. 147). h ps://doi.o g/10.1051/
ma eccon /201814706004
Coope , D. H. (2014). The E ec o
Unemploymen Du a ion on Fu u e Ea nings
and O he Ou comes (Resea ch Depa men
Wo king Pape s, 2013 Se ies, No. 13-8).
Bos on, MA: Fede al Rese e Bank o Bos on.
EIOPA. (2020). Pan-Eu opean Pe sonal
Pension P oduc (PEPP): EIOPA’s S ochas ic
Model o a Holis ic Assessmen o he Risk
P o ile and Po en ial Pe o mance (Repo ).
F ank u am Main: Eu opean Insu ance and
Occupa ional Pensions Au ho i y.
Fe nandes, J. C. N. (2013). Li ecycle
In es men S a egies: An analysis Based on
Eu opean Da a (Doc o al disse a ion). Lisbon:
ISCTE Business School.
Galdeano, A. S., & Tu unen, J. (2005).
Real Wages and Local Unemploymen in he
Eu o A ea (Wo king Pape Se ies, No. 417).
F ank u am Main: Eu opean Cen al Bank.
Gu enen, F. (2009). An empi ical
in es iga ion o labou income p ocesses.
Re iew o Economic Dynamics, 12(1), 58–79.
h ps://doi.o g/10.1016/j. ed.2008.06.004
Gu enen, F., & Smi h, A. A. (2014). In e ing
Labou Income Risk and Pa ial Insu ance
om Economic Choices. Econome ica, 82(6),
2085–2129. h ps://doi.o g/10.3982/ECTA9446
Gu enen, F., Ka ahan, F., Ozkan, S., &
Song, J. (2015). Wha Do Da a on Millions o
U.S. Wo ke s Re eal abou Li e-Cycle Ea nings
Risk? (S a Repo No. 710). New Yo k, NY:
Fede al Rese e Bank o New Yo k
Ka z, L. F., & Mu phy, K. M. (1992).
Changes in Rela i e Wages, 1963–1987:
Supply and Demand Fac o s. The Qua e ly
Jou nal o Economics, 107(1), 35–78. h ps://
doi.o g/10.2307/2118323
Kiliano á, S., Meilche čík, I., & Še čo ič, D.
(2006). A Dynamic Accumula ion Model o he
Second Pilla o he Slo ak Pension Sys em.
Czech Jou nal o Economics and Finance,
65(11–12), 506–521.
Malkiel, B. G. (1996). A Random Walk
Down Wall S ee : Including a Li e-Cycle Guide
o Pe sonal In es ing (6 h ed.). New Yo k, NY:
No on.
Meliche čík, I., & Ung a sky, C. (2004).
Pension Re o m in Slo akia: Pe spec i es
o he Fiscal Deb and Pension Le el. Czech
Jou nal o Economics and Finance, 54(9–10),
391–404.
Meliche čík, I., Szűcs, G., & Vilček, I. (2015).
In es men S a egies in he Funded Pilla o he
Slo ak Pension Sys em. Ekonomický časopis,
63(2), 133–151.
Me on, R. C. (2007). The Fu u e o
Re i emen Planning. In Z. Bodie, D. McLea ey
& L. B. Siegel (Eds.), The Fu u e o Li e-Cycle
Sa ing and In es ing (2nd ed., pp. 5–18).
Cha lo es ille, VI: Resea ch Founda ion o
CFA Ins i u e. Re ie ed om h ps://www.
c ains i u e.o g/-/media/documen s/book/ -
publica ion/2008/ 2008n1.ashx
Meša o á, N., Šebo, J., & Balco, M. (2015).
Fee Policy Analysis o P i a e Pension Schemes
o Selec ed Coun ies. In P oceedings om he
Cen al Eu opean Con e ence in Finance and
Economic (pp. 413–427). He ľany, Slo akia.
Mešťan, M., K álik, I., Žo aj, M., &
Ka košiako á, N. (2018). P ojec ions o DC
scheme pension bene i s – he case o Slo akia.
In P oceedings om he Cen al Eu opean
Con e ence in Finance and Economics (pp.
170–182). He ľany, Slo akia.
Mešťan, M., K álik, I., Žo aj, M., Ka košiako á,
N., & Kabašinskas, A. (2021). P ojec ions o
pension bene i s in supplemen a y pension
sa ing scheme in Slo akia. Cen al Eu opean
Jou nal o Ope a ions Resea ch, 29, 687–712.
h ps://doi.o g/10.1007/s10100-019-00669-2
OECD. (2018). The Fu u e o Educa ion
and Skills – Educa ion 2030. Pa is: OECD.
P au, W. D. (2009). Li ecycle Funds and
Weal h Accumula ion o Re i emen : E idence
o a Mo e Conse a i e Asse Alloca ion as
Re i emen App oaches. Financial Se ices
Re iew, 19(1). h ps://doi.o g/10.2139/
ss n.1488671
Rubins ein, R. Y., & K oese, D. P. (2007).
Simula ion and he Mon e Ca lo Me hod (2nd
ed.). Hoboken, NJ: Jon Wiley & Sons.
EM_3_2021.indd 147 8.9.2021 9:58:09
148 2021, XXIV, 3
Finance
Šebo, J., Vi dzek, T., & Šebo á, L.
(2015). Sa ing S a egies Re alued: Is Bond
Pension Fund Really a Sa e Pension Vehicle?
In P oceedings o he 20 h In e na ional
Con e ence on Theo e ical and P ac ical
Aspec s o Public Finance 2015 (pp. 244–249).
P ague, Czech Republic.
Šebo, J., Meliche čík, I., Mešťan, M., &
K álik, I. (2017). Ac i e sa ings managemen
unde he old-age pension sa ing sys em (1s
ed.). B a isla a: Wol e s Kluwe .
Šebo, J. (2018). Pension Bene i S a emen
– he case o Slo akia. Pape p esen ed a he
Consume P o ec ion and Supe ision in he
Financial Se ices Con e ence, ISCAP, Po o,
June 18–19, 2018.
Shin, S., Smola ski, J. M., & Soydemi , G.
A. (2017). Hu dle Ra es and High-Wa e ma ks:
Incen i es o Res ic ions? Jou nal o
Accoun ing and Finance, 17(1), 124–143.
Vaja gah, K. F., & Shoghi, M. (2015).
Simula ion o S ochas ic di e en ial equa ion
o geome ic B ownian mo ion by quasi-Mon e
Ca lo me hod and i s applica ion in p edic ion
o o al index o s ock ma ke and alue a isk.
Ma hema ical Sciences, 9(3), 115–125. h ps://
doi.o g/10.1007/s40096-015-0158-5
Wang, L., Li, B., & Liu, B. (2017).
Unde s anding he Le e aged Li e-Cycle
In es men S a egy o De ined-Con ibu ion
Plan In es o s. Financial Planning Resea ch
Jou nal, 3(2), 12–30.
Wie sema, U. F. (2008). B ownian Mo ion
Calculus. Hoboken, NJ: John Wiley & Sons.
Appendixes:
A ailable online: h ps://u l.umb.sk/
eama icleappendixes
EM_3_2021.indd 148 8.9.2021 9:58:09