Proceedings of 8th Annual London Business Research Conference
Imperial College, London, UK, 8 - 9 July, 2013, ISBN: 978-1-922069-8-3
A Stochastic Approach to Increase Replacement Rates in
Defined Contributions Pension Schemes
Denise Gómez-Hernández, and Felipe Abelardo Pérez-Sosa
The work presented here aims to show different strategies in
order to increase the replacement rate obtained by a worker at
retirement age. We assume the current accumulation model
from a representative Latin American country as Mexico and
replicate this model in order to optimize the asset allocation of
the portfolio, the amount of the contribution rate and the age of
retirement, in order to obtain a target replacement rate. The
bootstrap sampling method was applied and the results suggest
that a well-diversified portfolio, an age of retirement of 68 and a
contribution of 10% of the salary, is the most effective strategy
to follow.
Field of research: Finance
1. Introduction
Public policies on pensions have always been about keeping the balance right
between benefits and affordability, which means that even when a higher
amount of pension at retirement is desirable, it also has a cost. Nowadays, due
to a disproportional increase of pensionable periods caused by the continuous
rising of life expectancy during second half of XX century, there is a general
debate about the need for pension reforms in many countries. Therefore, to
keep this balance, a rise in the age of retirement has been proposed in order to
encourage higher savings for retirement (OECD, 2011).
Even though the pension problem is a global issue, this topic has had a
particular dynamism in Latin America since Chile changed its system in 1981
(Ham, 1996 and Bertranou, 2004). Since then, other countries from the region
have followed the Chilean example; so many Latin American countries have
similar designs in their pension schemes (Gómez and Stewart, 2008). These
reforms included funding modifications, incorporation of private initiative in
funds management and changes in general parameters, as well as retirement
age and other pension requirements (Bertranou, 2004).
In Mexico, the debate on pension reform began in early 90’s, as demographic
trends jeopardized financial sustainability of the traditional system, the country
shifted from a defined benefits scheme to a defined contribution system in 1996
(AMAFORE). The purpose of that was to eliminate design deficiencies of the
system making it consistent with demographic reality, bring financial
sustainability and to reduce fiscal charge (Villagómez and Hernández, 2009).
___________________________________________________________
Denise Gómez-Hernández, Universidad Autónoma de Querétaro. Centro Universitario, México,
Email: actdenise@gmail.com
Felipe Abelardo Pérez-Sosa, Universidad Autónoma de Querétaro. Centro Universitario,
México. Email: faps83@hotmail.com
Proceedings of 8th Annual London Business Research Conference
Imperial College, London, UK, 8 - 9 July, 2013, ISBN: 978-1-922069-8-3
Even when Mexican reform can be considered successful from a fiscal point of
view, is still far from achieving proper benefits for the workers that guarantee a
fair income for them and their families after retirement (Murillo and Venegas,
2011). So, after sixteen years of reforms to the Mexican pension system, there
are some challenges and lessons that can be learnt in other countries where
pension reforms are still controversial. For this reason, it is appropriate to
evaluate the effect of different leverages that favor better pensions at retirement
in defined contributions systems, in order to set proper pension designs that
improve workers benefits while keeping financial sustainability.
2. Literature Review
Pension plans are contracts between pension suppliers and clients of the plan,
with the purpose of giving these clients an income at their retirement (Booth et
al., 2005). There are several kinds of pension plans, but current global tendency
is to shift from unfunded defined benefit (DB) plans to funded defined
contributions (DC) schemes.
Funded plans are those where retirement pensions are equivalent to the
resources accumulated in a fund during the working period. These accumulated
funds are destined to be invested in portfolios, so asset allocation is an
important topic in these kinds of plans. Regarding DC schemes, those that are
determined by a defined formula, are in most cases a fixed percentage of the
worker's salary. Then, contributions are deposited into individual accounts and
final balance of those accounts, that includes contributions and returns, are the
resources used to finance pensions (Booth et al., 2005). These kinds of
schemes are increasing in popularity because they represent a lower risk to
pension sponsors, but have the disadvantage of not guaranteeing benefits for
their members. In other words, shifting from DB to DC plans means that risk is
transferring from the government and corporations to individuals (Blake, Cairns
and Dowd, 2001).
That risk transfer involves the natural question: will the retirement income be
enough to maintain the consumption habits of workers and their families.
Unfortunately, there is not an ultimate answer for that question until the worker
actually retires, when of course it is too late. That is why an evaluation of
pension plans, especially DC schemes, is a very important matter and the
appropriate way to do this is by testing a pension plan with a stochastic
simulation. This method consists of generating a probabilistic range of
outcomes for the value of the pension fund at any given future date, considering
various assumptions. It is possible to compare pension plans with a defined
target at a certain degree of probability (Blake et al., 2001).
The purpose of this paper is, then, to use the bootstrap sampling method, in
order to generate 10,000 simulations of the value of the fund for each analyzed
scenario. This method is used when a limited number of data is available and it
consists in generating a subsample of the data set (Gómez Hernández, 2008).
Booth et al. (2005) defines this method as a simple and powerful tool, in which
projections are estimated with random variables from empirical data that
represent an approximation of their true distribution.
Proceedings of 8th Annual London Business Research Conference
Imperial College, London, UK, 8 - 9 July, 2013, ISBN: 978-1-922069-28-3
3. Methodology and Model
Defined contribution (DC) pension schemes are based on the value of the sum
accumulated in the fund during the accumulation phase. The value of the sum is
a result of contributions and investment returns, and normally, accumulation
phase refers to the member's working life (Blake, 2006). Booth et al. (2005)
proposes that funds in real currency should be projected as in (1).
( )
( )(
)
(
) ∑ ( )(
)
(1)
Where:
( ) = Projected fund after periods in real units
( ) = Real contribution paid at end of period
= Projected real investment return per period
= Number of periods up to retirement age
= Expense fraction for contributions
In this paper, we adopt a scheme where the only existing charges are on assets
under managementi, then formula (2) applies for our accumulated fund, which is
taken from (1) with some modifications for our purpose.
(
)(
)
(2)
Where:
Accumulated fund until period
Real rate of return at period used to project the value of the fund
The weighted average charge on assets under management
The value of the contribution at period
DC plans rely on the money purchase principle, which means that the money
accumulated is equivalent to the received benefits at retirement. In that sense, it
is important to notice that any value should be expressed in real terms, due to
the fact that nominal units can give an exaggerated impression of the value of
future benefits that do not correspond to the actual purchasing power of money
(Booth et al., 2005).
Is important to notice that no DC pension plan can achieve a target pension
outcome, but it is possible to use stochastic simulation to project it with an
acceptable probabilistic degree of confidence (Blake et al., 2001).
3
Proceedings of 8th Annual London Business Research Conference
Imperial College, London, UK, 8 - 9 July, 2013, ISBN: 978-1-922069-8-3
4. Assumptions
The assumptions that we use to perform our simulations are based on Formula
(2) and they are as follows:




An initial value of the fund of zero (the individual starts with no money in
his or her account)
The weighted average charge on assets under management is assumed
to be 0.0123 per annum as in the current Mexican pension system
(CONSAR, 2013).
For the accumulation period, we assume an individual starts working at
the age of 20 making contributions until his retirement. In this case,
retirement age is set at 65 years, which is the official retirement age in 16
of 30 OECD countries, including Mexico.
The most common approach for contributions in DC plans is to pay fixed
percentages of the worker's salary (Booth et al., 2005). For this model,
contributions are estimated according to general Mexican legal
dispositions, which are made every two months as follows:
o Employers: 5.150% of workers base income.
o Workers: 1.125% of base income.
o Government: 0.225% of workers base income.
Then, bimonthly contributions are determined as in (3):
(
)
(3)
Where is the monthly base income of the worker at period . For this
model, the initial income assumed is $566.67 US dollars per month,
which is the average monthly wage in Mexico, according to OECD
(2011).
To this initial income, the yearly effect of real salary increase is added, as
in (4):
(
)
(4)
0.0035 is the yearly average increase in Mexican salaries from 2000 to
2012, according to the Real Index of Minimal Salaries published by
Mexican Central Bank. This period was chosen due that in recent years
Mexican economy had a controlled inflation that is expected to remain.
4.1 Projected real investment return
In order to estimate the investment return for the model, contributions are
invested in a portfolio with 4 different assets: Mexican equity, Mexican bonds,
International equity and International bonds. These are the traditional
investment assets for Mexican pension funds. In order to obtain historical rates
of return on these assets, we obtained the Prices and Quotations Index of
Mexican Stock Exchange, Treasury Certificates for 28 days issued by Mexican
Proceedings of 8th Annual London Business Research Conference
Imperial College, London, UK, 8 - 9 July, 2013, ISBN: 978-1-922069-28-3
government, Standard & Poors 500 index and Treasury Bills for three months
issued by U.S. Treasury, respectively.
All the returns were used in monthly real terms, as well as salaries.
Nevertheless, unlike Mexican securities, inflation on international assets is not a
relevant issue for local workers, as a change in the price of another country
does not affect the purchasing power in the current one. Hence, in this model
only international returns are kept in nominal values. Also we assume that
differences between inflation rates would be reflected in exchange rates and
fund managers would only change their currency positions when exchange rate
is favorable, due to the long term nature of pension funds.
Once all the data is in a comparable monthly series, the task is to select the
proper values for each period for the model. To do this, Blake (2006) proposes
that DC schemes should be designed with a degree of probability, and that the
appropriate way to do this is through a stochastic simulation. That means that a
large range of outcomes should be generated for the value of the pension at
any given future date. In this sense, real investment return for each period is
selected randomly from real data series, by using the bootstrap sampling
method. Then, 10,000 simulations are obtained to calculate the mean value of
the fund projected.
4.2 Asset Allocation
The asset allocation used in our model was according to the Mexican regulation
available, which depends on an age group as shown in Table 1.
Table 1
Average asset allocation for age group
Age group (t)
Asset
< 36 37 to 45 46 to 59 60 >
Mexican Equity (
)
14%
12%
9%
2%
Mexican Bonds (
)
66%
73%
77%
93%
International Equity (
) 17%
13%
11%
2%
International Bonds (
) 2%
2%
2%
3%
Total
100% 100%
100% 100%
Reference: CONSAR (2012a)
Therefore, for our investment portfolio model, the real investment return for
each period will be calculated as in (8):
(8)
( )
[
][
]
Where:
( ) = Projected real investment return for investment portfolio at period
5
Proceedings of 8th Annual London Business Research Conference
Imperial College, London, UK, 8 - 9 July, 2013, ISBN: 978-1-922069-8-3
= % of the portfolio invested in Mexican equity, according to the age of the
worker at period .
= % of the portfolio invested in Mexican bonds, according to the age of
the worker at period .
= % of the portfolio invested in international equity, according to the age of
the worker at period .
= % of the portfolio invested in international bonds, according to the age of
the worker at period .
= Random value of Mexican equity real return for period
= Random value of Mexican bonds real return for period
= Random value of International equity real return for period
= Random value of International bonds real return for period
5. Findings
5.1 Projected fund and replacement rate
The final balance of the fund was calculated using the bootstrap sampling
method with 10,000 simulations. The results are shown in Table 2.
Table 2
Projected fund
Value
Mean of the final balance
of the fund (usd)
Standard deviation
Number of simulations
$43,207
$10,064
10,000
As the final balance of the fund does not reflect the purchasing power of the
worker at retirement, the replacement rate is calculated as in OECD (2011), to
show the level of pensions in retirement relative to earnings when working, as in
(9) (Institute of actuaries, 1980):
(
̈
(
)
)(
)
(9)
Where:
= Projected fund after periods in real units
)
̈
= Actuarial annuity rate at age 65 payable monthly
= Base income of the worker at final period
= Insurance company charges on the conversion of the final balance of the
fund to a monthly pension, assumed to be 3%ii.
(
Then, the mean of the final balance of the fund, by using the assumptions
stated before, becomes a replacement rate of 39.71%.This means that, a
worker that starts working and contributing to his or her pension fund at age 20
and retires at age 65, can expect to obtain only 40% per month of his or her
Proceedings of 8th Annual London Business Research Conference
Imperial College, London, UK, 8 - 9 July, 2013, ISBN: 978-1-922069-28-3
salary at retirement for life, if we are using the Mexican pension system’s
regulations.
In the following sections, a sensitivity analysis is performed, in order to increase
the replacement rate obtained in this section.
5.2 Changes in asset allocation
As stated previously, the current asset allocation in Mexican pension funds is
shown in Table 1. Nevertheless, this does not mean that those weights are the
optimal ones for building portfolios that drive the best performance of the funds.
In order to determine an optimal portfolio that derives in a higher replacement
rate than our previous result, Table 4 shows the value at risk for each of the
returns on assets by using historical data at a 5%.
VaR
Mexican
Equity
VaR (5%)
-11.76%
VaR
VaR (5%)
< 36
-2.43%
Table 4
Value at Risk
Mexican
Bonds
-2.45%
International International
Equity
Bonds
-7.78%
0.00%
Portfolio for age group
37 to 45
46 to 59
-2.25%
-2.14%
60 >
-2.27%
Table 4 shows that with a probability of 5%, our portfolio can obtain a real return
on Mexican equities of -11.76% or less, -2.45% or less in Mexican bonds, 7.78% or less in international equities and no loss on international bonds. Also,
according to the age group of the worker, he or she can expect a 5% probability
a return of -2.43% or less when is 36 years old or less, -2.25% or less when he
or she is from 37 to 45 years of age, and so on. The conclusion is that
international bonds are far more stable than the other assets used and also,
that the portfolio of the age group 46-59 is one that provides less of a loss.
According to portfolio theory, portfolio optimization is about maximizing the
expected return with an acceptable risk, or to minimize the risk with a target
expected return (Ross, Westerfield and Jaffe, 2000). In that sense, our following
simulations of the optimal portfolios were optimized assuming 2 strategies:
1) Maximize their returns keeping the original standard deviations.
2) Minimize their standard deviations keeping the original returns.
The results of the optimization by making changes in the asset allocation based
on both strategies for each portfolio are shown in Figure 1.
7
Proceedings of 8th Annual London Business Research Conference
Imperial College, London, UK, 8 - 9 July, 2013, ISBN: 978-1-922069-8-3
Figure 1:
Changes in asset allocation for different optimization strategies
Portfolios for < 36
Portfolios for 37 to 45
100%
100%
90%
90%
80%
80%
70%
70%
60%
60%
50%
50%
40%
40%
30%
30%
20%
20%
10%
10%
0%
0%
wIB
Original
2%
Strategy 1
35%
Strategy 2
41%
wIB
Original
2%
Strategy 1
39%
Strategy 2
49%
wIE
17%
22%
20%
wIE
13%
20%
17%
wMB
66%
26%
24%
wMB
73%
24%
20%
wME
14%
17%
16%
wME
12%
16%
14%
Portfolios for 46 to 59
Portfolios for 60 >
100%
100%
90%
90%
80%
80%
70%
70%
60%
60%
50%
50%
40%
40%
30%
30%
20%
20%
10%
10%
0%
0%
Original
3%
Strategy 1
3%
Strategy 2
80%
2%
2%
6%
93%
91%
8%
4%
5%
wIB
Original
2%
Strategy 1
42%
Strategy 2
56%
wIB
wIE
11%
19%
14%
wIE
wMB
77%
23%
18%
wMB
wME
9%
16%
12%
wME
2%
The results in Figure 1 show that current portfolios invest a higher weight in
Mexican bonds than the 2 optimization strategies suggested before. Results for
strategy 1 and 2 show that a higher percentage of investment should be made
on international bonds, in order to either maximize returns or minimize the
standard deviation of the portfolio. There is only one exception, the portfolio for
the last group of age assuming strategy 1, shows that the maximum amount of
the portfolio should be invested on Mexican Bonds, rather than on International
ones. This is because when maximizing returns keeping the original standard of
deviation, Mexican Bonds give higher returns than the other assets for that
particular group of age. In order to analyze further these results, the value at
risk of the portfolios obtained assuming the two strategies, are shown in Table
5.
Proceedings of 8th Annual London Business Research Conference
Imperial College, London, UK, 8 - 9 July, 2013, ISBN: 978-1-922069-28-3
Table 5:
Value at Risk for optimal portfolios
Portfolios for< 36
Portfolios for 37 to 45
Original Strategy 1 Strategy 2 Original Strategy 1 Strategy 2
VaR (5%) -2.43%
-2.39%
-2.15%
-2.25%
-2.21%
-1.80%
Portfolios for 46 to 59
Portfolios for 60 >
Original Strategy 1 Strategy 2 Original Strategy 1 Strategy 2
VaR (5%)
-2.14%
-2.10%
-1.51%
-2.27%
-2.19%
-0.57%
Table 5 shows that with a probability of 5%, the portfolio with the original asset
allocation for workers younger than 36 can obtain a return of -2.43% or less. On
the other hand, if strategy 1 is assumed a -2.39% or less return is obtained, and
so on. The lowest loss can be achieved with portfolios for workers older than 60
with asset allocation according to strategy 2, where with a 5% probability a
return of -0.57% or less is obtained.
The accumulation model was run again assuming the optimal portfolios
obtained from the original strategy, the strategies 1 and 2 and we added a
mixed strategy; in order to find which one drives the highest replacement rate.
This mixed strategy assumes that fund managers follow strategy 1 for workers
younger than 46, and strategy 2 for workers from that age until 60. Again, the
exercise was repeated 10,000 times by using the bootstrap sampling model.
Figure 2, shows the results for the 4 different strategies assumed.
Figure 2:
Replacement rates for different investment strategies
43%
44%
43%
42%
41%
41%
40%
40%
40%
39%
38%
Original
Strategy 1
Strategy 2
Mixed strategy
It can be seen from Figure 2, that the original strategy and the one that
minimizes the risk, give similar results. Also, that the highest replacement rate is
achieved when maximizing the returns at a certain level of risk, but not by
9
Proceedings of 8th Annual London Business Research Conference
Imperial College, London, UK, 8 - 9 July, 2013, ISBN: 978-1-922069-8-3
much. However, evidence shows that an excessive conservative investment
approach is not the most effective path for replacement return purposes,
comparing with the return maximization strategy.
Results in Figure 2 confirm that Mexican pension funds must be more
diversified and increase its weights in international securities, which in the long
run would be more convenient for workers according to replacement rates
comparison. It is important to keep in mind that investment strategies for
Mexican pension funds are strictly regulated by law, so any implementation of
these recommendations must be encouraged from official agencies in order to
be effectively applied.
Nevertheless, even when it was found that is possible to improve replacement
rates by optimization investment portfolios, actual impact of asset allocation in
replacement rate is not enough to guarantee that workers could keep their
consumption habits on their retirement, so other leverages are analyzed further.
5.3 Changes in retirement age
OECD (2011) points out that a main topic in pension systems sustainability is
that current pensionable ages are not proportional to actual life expectancy, and
this is why actively encourages its members to retire later. According to that
suggestion, our projection model was modified in its accumulation period, in
order to find the tradeoff between an additional working year and the
replacement rate.
Then, a new sensitivity analysis was performed by assuming the optimal asset
allocation found in the previous analysis, which corresponds to the strategy of
maximizing returns while keeping the original standard deviation of the portfolio
(strategy 1). The results are shown in Figure 3 and show the tradeoff between
the replacement rate and the age of retirement. This shows that an additional
working year from age 65 until 69, represents an average increase of 1.36 base
points on the replacement rate.
Proceedings of 8th Annual London Business Research Conference
Imperial College, London, UK, 8 - 9 July, 2013, ISBN: 978-1-922069-28-3
Figure 3:
Replacement rate for different retirement ages using the optimal
investment strategy
49%
49%
47%
48%
47%
46%
46%
44%
45%
43%
44%
43%
42%
41%
40%
65
66
67
68
69
As Gustman and Steinmeier (2012) rightly point out, the decision to work an
additional year relies in the balance among present and future benefits
perceived by the worker. The OECD (2011) states that previous research on
retirement incentives such as the one by Gruber and Wise (1998, 1999),
Blöndal and Scarpetta (1999) and Duval (2003); emphasizes that the worker will
be motivated on increasing his or her retirement age if his or her pension rate
increases also.
5.4 Changes in contributions
As is seen in (2), the amount of contributions is a highly relevant component for
pension funds (Solís, 2006). Even when the most part of the contributions to
Mexican pension systems are mandatory (CONSAR, 2012b), it is possible to
increase the fund value through voluntary saving. In this section, the impact of
additional contributions in the projected fund is analyzed by using the bootstrap
sampling method again. Also, the asset allocation assumed is the one that
drives to a higher replacement rate (strategy 1).
The results show that an additional contribution of 1% of workers salary
represents an average increase of 6.57 base points on the replacement rate
obtained (see Figure 4).
11
Proceedings of 8th Annual London Business Research Conference
Imperial College, London, UK, 8 - 9 July, 2013, ISBN: 978-1-922069-8-3
Figure 4:
Replacement rate for different contributions using the optimal investment
strategy
69%
63%
70%
56%
60%
50%
49%
43%
40%
30%
20%
10%
0%
6.5%
7.5%
8.5%
9.5%
10.5%
Villagómez and Hernández (2009) point out that even when a rise in mandatory
contributions could drive into a substitution effect of private savings, in
developing countries this is not common. The reason for that is because of the
need for liquidity in emergency situations. Additionally, complementing the
increase of retirement contributions with a proper financial education could
enforce workers to recognize their pension funds as part of their actual wealth.
5.5 An integrated strategy
After evaluating the effects of different leverages of replacement rate, the next
task is to integrate the best practices of each of them in a single fund, in order
to get a significant improvement in the amount of pension. To achieve this, the
model was run from a stochastic approach as in previous exercises, but
assuming different scenarios for the amount of the contribution and the
retirement age. In all of them, the asset allocation was determined according to
the strategy of maximization of returns and both, the rate of contribution and the
retirement age, were increased to achieve a replacement rate of at least 75%.
Results are shown in Figure 5.
Proceedings of 8th Annual London Business Research Conference
Imperial College, London, UK, 8 - 9 July, 2013, ISBN: 978-1-922069-28-3
Figure 5:
Replacement rate for different contribution and retirement ages scenarios
using the maximum return method
Retirement age: 68
Retirement age: 69
78%
80%
76%
80%
75%
75%
71%
69%
70%
70%
65%
65%
60%
60%
Contributions:
9.5%
Contributions:
10.5%
Contributions: Contributions:
9.5%
10.5%
As can be seen in Figure 5, projections show that the replacement rate target of
75% can be achieved when contributions are 10.5% of workers salary and
retirement age is 68. A higher replacement rate of 78% can be achieved by
working an additional year until age 69, with the same level of contributions. In
both cases funds must be invested in internationally diversified portfolios,
according to a return maximization strategy as explained in section 5.2.
Otherwise, pensions in retirement could be much lower than income of active
workers, and possible insufficient for keeping their desirable consumption
habits.
6. Summary and Conclusions
The simulations shown in this paper prove that, from a statistical approach, the
replacement rates for pension funds can be improved from 40% to almost 80%,
by increasing the amount of contribution and the age of retirement from the
current ones in Latin America countries as Mexico. Also, to obtain this result, an
optimal portfolio should be constructed by assuming the actual portfolio theory.
First of all, it was observed that an excessive asset allocation in Mexican bonds
is not the optimal choice. On the contrary, well diversified portfolios, with a
proper balance of international securities proved to be the most effective
strategy. Is important to notice that any pension system should take in to
consideration investment opportunities of a globalized world, then developed
countries could take advantage of higher returns from emerging economies, at
the same time that pension funds from developing countries could benefit from
lower risk securities taken from more stable economies. In any case,
international diversification shows to be the optimal strategy for pension funds.
13
Proceedings of 8th Annual London Business Research Conference
Imperial College, London, UK, 8 - 9 July, 2013, ISBN: 978-1-922069-8-3
A second issue is the retirement age. Working longer is not desirable, but is
necessary. OECD has been arguing so from many years due to demographic
trends. That is the main reason why pension systems of many countries are
facing financial difficulties. With this exercise it has been proved that from a
statistical approach, the retirement age in order to achieve a replacement rate
of 75% should be 68 years old in a Defined Contribution scheme. To encourage
longer working lives, is suggested the design of proper incentives to workers, in
order to perceive real benefits of working an additional year and to reduce costs
of delaying retirement.
Finally, contributions must rise. At least in Mexico, current contributions are
much lower than required to achieve a desirable replacement rate. As voluntary
savings for retirement are also low, it would be necessary to increase
mandatory contributions from 6.5% to 10.5% of workers salary, so they could
get a replacement rate of 75% or more. A way to smooth social disagreement of
this measure is to dispose additional contributions in a liquid subaccount, due to
people often saving for emergency purposes, so availability is considered an
important requirement. Also, this proposal could encourage workers to engage
in their retirement fund, so they actually consider it as part of their personal
wealth.
The proposal of increasing Mexican contributions over 10% of salary is not
senseless compared with other Latin American countries. For example,
contributions in Uruguay are 15% of base salary, in El Salvador are 10.3% and
in Bolivia, Chile and Peru are of 10%. Also, is important to notice that with
exception of Chile and Peru, those countries have lower than average earnings
than Mexico (Corvera, Lartigue and Madero, 2006).
Notes
i
In this paper we use the Mexican Pension System as a reference to perform
our simulations, then only charges on assets under management are assumed
in our model.
ii
Average of charges from insurance companies in Mexico.
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AMAFORE nd, Antecedentes: la reforma de 1997. Consulted on September
30th, 2011 fromhttp://www.amafore.org/antecedentes-la-reforma-de-1997
Banco de México nd, Estadísticas. Consulted on February 28th, 2013 from:
http://www.banxico.org.mx/estadisticas/index.html
Bertranou, FM 2004, 'Sistemas de jubilaciones y pensiones en América Latina:
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