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R. Bras. Risco e Seg., Rio de Janeiro, v. 10, n. 18, p. 83-120, abr. 2014/mar. 2015 83

Variation of Prudential Limits and its Effects on the Financial and Actuarial Balance of Social Security Special SchemesLucas Andrade dos ReisBachelor Degree in Accounting from the Department of Accounting and Actuarial Sciences from the University of Brasília.http://lattes.cnpq.br/[email protected]

Benedito Leite SobrinhoActuary and Volunteer Professor at the Department of Accounting and Actuarial Sciences at the University of Brasília.http://lattes.cnpq.br/[email protected]

Diana Vaz de LimaAssistant Professor at the Department of Accounting and Actuarial Sciences at the University of Brasília. PhD in Accounting Program from the Multi-Institutional and Inter-regional Programme in Accounting UNB / UFPB / UFRN.http://lattes.cnpq.br/[email protected]

Summary

When elaborating the actuarial evaluation of Social Security Special Schemes (RPPS in its acronym in Portuguese), biometric, demographic, economic and fi nancial hypotheses must be taken in consideration. In addition, they must be consistent with the dimensioning of future commitments and in compliance with minimum standards of prudence, including interest rates and mortality tables. Bearing in mind that these parameters may vary depending on the economic environment and on the characteristics of the overall group of insured individuals, this study aims at determining how changes in prudential limits, especially those related to the choice of different mortality tables and interest rates, may impact the fi nancial and actuarial balance of the RPPS. In 2013, in order to properly address the research, simulations were made based on a theoretical group of 808 records of retired insureds along with information collected from the Statements of Actuarial Assessment Outcomes (DRAA, in its acronym in Portuguese) delivered to the Ministry of Social Security (MPS), obtained from management units of the RPPS. The results show that the change in prudential limits leads to an increase in obligations related to retirement pensions, and to negative effects in actuarial outcomes. Also, in order to preserve the fi nancial and actuarial balance of the RPPS, interest rates and actuarial hypotheses that refl ect, respectively, the investment portfolio characteristics and group of insureds of each management unit, should be adopted.

Key Words

Financial and actuarial balance. RPPS. Interest Rates. Mortality Tables.

Contents

1. Introduction. 2. Theoretical Reference. 3. Methodology. 4. Description and Analysis of Results. 5. Concluding Remarks. 6. Bibliographical References. 7. Appendices.

84 R. Bras. Risco e Seg., Rio de Janeiro, v. 10, n. 18, p. 83-120, abr. 2014/mar. 2015

Variation of Prudential Limits and its Effects on the Financial and Actuarial Balance of Social Security Special Schemes

Sinopse

Alteração dos Limites Prudenciais e seus Efeitos no Equilíbrio Financeiro e Atuarial dos Regimes Próprios de Previdência Social

Lucas Andrade dos ReisBacharel em Ciências Contábeis pelo Departamento de Ciências Contábeis e Atuariais da Universidade de Brasília.http://lattes.cnpq.br/[email protected]

Benedito Leite SobrinhoAtuário e Professor Voluntário do Departamento de Ciências Contábeis e Atuariais da Universidade de Brasília. http://lattes.cnpq.br/[email protected]

Diana Vaz de LimaProfessora Adjunta do Departamento de Ciências Contábeis e Atuariais da Universidade de Brasília. Doutora em Ciências Contábeis pelo Programa Multi-institucional e Interregional de Pós-Graduação em Ciências Contábeis UnB/UFPB/UFRN. http://lattes.cnpq.br/[email protected]

Resumo

Na elaboração da avaliação atuarial dos RPPS devem ser consideradas hipóteses biométricas, demográfi cas, econômicas e fi nanceiras adequadas ao dimensionamento dos compromissos futuros, obedecidos parâmetros mínimos de prudência, destacando-se, entre elas, as taxas de juros e as tábuas de mortalidade. Considerando que estes parâmetros podem variar dependendo do ambiente econômico e das características da massa de segurados, o presente estudo tem como objetivo verifi car como a alteração dos limites prudenciais, particularmente relacionados à escolha de diferentes tábuas de mortalidade e taxas de juros, pode impactar o equilíbrio fi nanceiro e atuarial dos RPPS. Para tratar a questão da pesquisa, foram feitas simulações tendo como base uma massa teórica de 808 registros de segurados aposentados e coletadas informações de unidades gestoras de RPPS nos Demonstrativos de Resultados da Avaliação Atuarial (DRAA) entregues ao Ministério da Previdência Social (MPS) no ano de 2013. Os resultados mostram que a alteração dos limites prudenciais gera aumento dos compromissos previdenciários e refl exos negativos nos resultados atuariais, e que para preservar o equilíbrio fi nanceiro e atuarial dos RPPS devem ser adotadas taxas de juros e hipóteses atuariais que refl itam, respectivamente, as características da carteira de investimentos e da massa de segurados de cada unidade gestora.

Palavras-Chave

Equilíbrio fi nanceiro e atuarial. RPPS. Taxas de Juros. Tábuas de Mortalidade.

Sumário

1. Introdução. 2. Referencial Teórico. 3. Metodologia. 4. Descrição e Análise dos Resultados. 5. Considerações Finais. 6. Referências bibliográfi cas. 7. Apêndices.


Lucas Andrade dos Reis, Benedito Leite Sobrinho, Diana Vaz de Lima

Sinopsis

Alteración de los Límites Prudenciales y sus Efectos en el Equilibrio Financiero y Actuarial de los Regímenes Propios de Seguridad Social

Lucas Andrade dos ReisLicenciado en Contabilidad por el Departamento de Ciencias Contables y Actuariales de la Universidad de Brasília.http://lattes.cnpq.br/[email protected]

Benedito Leite SobrinhoActuario y Profesor Voluntario del Departamento de Ciencias Contables y Actuariales de la Universidad de Brasília.http://lattes.cnpq.br/[email protected]

Diana Vaz de LimaProfesor Asistente del Departamento de Ciencias Contables y Actuariales de la Universidad de Brasília. Doctor en Programas Contables por el Programa de Contabilidad Multi-Institucional e Inter-regional de las universidades UNB / UFPB / UFRN.http://lattes.cnpq.br/[email protected]

Resumen

Durante la elaboración de la evaluación actuarial de los RPPS, deben considerarse las hipótesis biométricas, demográfi cas, económicas y fi nancieras que sean adecuadas al dimensionamiento de los compromisos futuros, obedeciéndose los parámetros mínimos de prudencia, destacándose entre ellos, las tasas de interés y las tablas de mortalidad. Teniéndose en cuenta que estos parámetros pueden variar conforme el ambiente económico y las características de la masa de asegurados, el presente estudio tiene como objetivo verifi car cómo la alteración de los límites prudenciales, particularmente los relacionados a la elección de diferentes tablas de mortalidad y tasas de intereses, pueden impactar el equilibrio fi nanciero y actuarial de los RPPS. Para tratar la cuestión de la investigación, fueron llevadas a cabo simulaciones utilizando como base una masa teórica de 800 registros de asegurados jubilados y recolectados los datos de las unidades gestoras de los RPPS en los Demostrativos de los Resultados de la Evaluación Actuarial (DRAA) entregados al Ministerio de la Seguridad Social (MPS) en 2013. Los resultados muestran que la alteración de los límites prudenciales genera un aumento de los compromisos con el fondo de es, así como efectos negativos en los resultados actuariales, y que para preservar el equilibrio fi nanciero y actuarial de los RPPS deben adoptarse tasas de interés e hipótesis actuariales que refl ejen, respectivamente, las características de la cartera de inversión y de la masa de asegurados de cada unidad gestora.

Palabras-Clave

Equilibrio fi nanciero y actuarial; RPPS; Tasas de Interés; Tablas de Mortalidad.

Sumario

1. Introducción. 2. Marco Teórico. 3. Metodología. 4. Descripción y Análisis de los Resultados. 5. Consideraciones Finales. 6. Referencias Bibliográfi cas. 7. Apéndices.



1. Introduction According to provisions set forth in art. 40 of the 1988 Federal Constitution, active public servants working for the Federal Government, at the state, federal, or municipal levels, including respective agencies and foundations, are eligible to be part of a social security scheme based on contributions and solidarity. This is assured through contributions by the respective public entity, and by active, inactive, and retired employees, in compliance with criteria that preserve fi nancial and actuarial balance, and known as Social Security Special Scheme (RPPS).

MPS Ordinance 402 / 2008 establishes that in order to guarantee the fi nancial and actuarial balance of RPPS, the initial actuarial assessment and revaluations carried out annually should be taken into consideration if the cost of plans and benefi ts is to be kept properly organised and duly updated. These assessments are done through a technical study developed by actuary professionals whose main objective is to establish the resources needed to guarantee the payment of the benefi ts provided in the benefi t plan in a suffi cient and adequate manner.

While addressing actuarial hypotheses, the MPS Ordinance 403 / 2008 establishes that the federal entity, or the management unit of the RPPS, and the actuary professional responsible for the elaboration of the actuarial evaluation, shall jointly select the biometric, demographic, economic and fi nancial hypotheses. This selection should match the characteristics of the group of insureds and their dependents in terms of the correct dimensioning of future commitments of the RPPS, and in compliance with the minimum parameters of prudence, having as a reference the hypotheses and assumptions embodied in the Technical Actuarial Note of the respective RPPS.

The actuarial calculation uses tables of mortality to measure the likelihood of survival and death of a population, based on age at a given moment, or period of time. In addition, the actuary also uses interest rates which will work as discount rates for social security obligations, and to refl ect changes in the value of money over time.

Bearing in mind that the biometric, demographic, economic and fi nancial hypotheses may vary depending on the economic environment, and on the characteristics of the group of insureds, this study raises the following research question: to what extent the variation of prudential limits, particularly those related to the table of mortality and interest rate can affect the actuarial fi nancial balance of the RPPS?

In this sense, this study aims at determining how variations of prudential limits, particularly those related to the choice of different tables of mortality and interest rates can impact the fi nancial and actuarial balance of the RPPS.

In order to address the research question, simulations were made in 2013, based on a theoretical group of 808 records of retired insureds, and on the information collected from management units of the RPPS following the Statement of Actuarial Assessment Outcomes (DRAA, in its acronym in Portuguese) delivered to the Ministry of Social Security.



This study is limited since it analyses the planned retirements already granted to healthy individuals separately, and does not address other benefi ts such as death and retirement for persons with disabilities, or benefi ts granted to public servants in active service.

Apart from this introduction, the study is structured in four chapters. Chapter 2 presents the theoretical description of the topics in the research. Chapter 3 explains how the simulations were done. Chapter 4 explores the results obtained from the research. Chapter 5 presents the fi nal remarks.

2. Regulatory Normative Guidance 1/2007, issued by the Department of Social Security and Theoretical Policies (SPPS, in its acronym in Portuguese), defi nes the RPPS as aFramework social security system established under the Brazilian federal entities to guarantee, in accordance with the law, at least the benefi ts of retirement2.1 Conceptual and and pension in case of death to all active public servants, as provided Legal Aspects in Art. 40 of the 1988 Federal Constitution. The RPPS are so named for

two reasons:

every entity of the federation can have its own RPPS, oriented towards • its public servants who hold active positions; and

it encompasses both the group provided in Article 40 of the 1988 • Federal Constitution – FC (for public servants who hold active positions, generally speaking) and in Art. 42 § 1 of the 1988 FC (for members of the Military Police Department and of the Fire Brigade in all Brazilian states and in the Federal District), also including the group provided in art. 142, § 3, section X of the 1988 FC (that addresses the military personnel of the armed forces).

Law 9,9717 / 1998 is the infra-constitutional norm that establishes general rules to govern the RPPS of the Federal Government, the states, the Federal District and municipalities. Besides the core benefi ts of retirement pensions, the RPPS may grant family, maternity, illness and hospitalisation allowances. Due to the focus of this paper, it is relevant to summarise the four RPPS retirement classes, according to Barros (2008):

a. Retirement for disability (Art. 40, § 1, Item I): derived from physical or psychological impossibility for public servants to exercise their activities;

b. Compulsory retirement (Art. 40, § 1, Item II): it is imposed by the FC for those who reach 70 years of age, based on the assumption that the employee is incapable of carrying on working at this age;



c. Voluntary retirements:I. Early retirement based on contributions and age (Art, 40, § 1, Item

III, “a”.): 10 years in the public service and fi ve years in the position he or she is at the point of retirement; time of contributions of 30 and 35 years, for women and men, respectively; and minimum age of 55 and 60, for women and men, respectively; and

II. Early retirement based on age (Art. 40, § 1, Item III, “b”.): 10 years in public service and fi ve years in the position he or she is at the point of retirement; and minimum age of 65 and 60, for women and men, respectively; and

d. Special pensions (Art. 40, § 4): These occur in cases of activities exercised exclusively under special conditions with harmful effects on health or physical integrity.

As provided in art. 40 of the 1988 Federal Constitution, amended by Constitutional Amendment 41 / 2003, particular pension schemes must observe criteria that preserve fi nancial and actuarial balance. That constitutional provision, regulated by Law 9,717 / 1998 establishes that the RPPS should be organised according to general accounting and actuarial norms.

The MPS Ordinance 403 / 2008 defi nes fi nancial balance as the guarantee of equivalence between the RPPS revenues and the liabilities in every fi nancial year; that is, the amount collected from benefi ciaries must be suffi cient to fund the benefi ts received by participants in the system. On the other hand, the actuarial balance is the guarantee of equivalence, at present value, between the estimated fl ow of revenues and projected liabilities, calculated in the long run and on an actuarial basis. Therefore, according to the MPS Ordinance 402 / 2008, both the fi nancial and actuarial balance of the RPPS should be guaranteed, following the initial actuarial assessment and reassessments annually done, to allow the organisation and revision of the plans regarding funds and benefi ts.

Another normative provision is that according to art. 4 of the MPS Ordinance 403/2008, the RPPS can adopt different funding schemes for its benefi t plan in order to keep its fi nancial and actuarial balance, namely: fi nancial system of capitalization, fi nancial system of distribution of coverage capital, and financial system of simple distribution. These schemes, according to Lima and Guimarães (2009), are the mechanisms for calculating the amounts necessary to enable the plan to have full fi nancial coverage, i.e., the full funding for its social security costs.

Moreover, based on the technical report of the actuary, the system will take into consideration the profi le of the group of insureds and the characteristics of the benefi ts to be provided, which can be of risk (such as retirement due to disability or death) or planned ones (such as voluntary retirement and mandatory retirement).



2.2 Tables of According to Ortega (1987, apud in WILBERT; LIMA; GOMES, 2013, mortality p.23), the table of mortality, also known as table of life or table of survival,

is an instrument that measures the likelihood of survival and death of a population according to age, at a given moment or period of time.

According to Oliveira et al, (2012), the fi rst ever table of mortality is from 1815, which is based on essentially actuarial concepts. It was built by Milne for the city of Carlisle, England. Since then, several other tables have been developed, and still are, for different regions and countries, due to its importance in the analysis of a variety of problems.

Oliveira et al (2012) explains that the table of mortality for a given population is an important tool for public policies, and for the fi nancing of the private sector in connection with certain services offered in the market covering a wide range of possibilities. It is also useful for actuarial and demographic studies in general. The tables are commonly used in cases of forecasting, and studies that look at demand for health services, education and with respect to the labour market, which include estimates of costs of social security and premiums in the private insurance sector.

For Sobrinho (2013), the table of mortality is a matrix that indicates the probability of death (qx) in an observed population, in ascending order of age (x), from the point of origin to that of extinction of that group. In the tables of mortality, “root of the table” is the name given to the number of living people, corresponding to the initial age (origin), while “Omega age” (ω) is the denomination for the end age, from which point there are no more survivors. It is worth noting that the tables of mortality need not necessarily start at age zero (SOBRINHO, 2013).

The MPS Ordinance 403 / 2008 establishes in Art. 6 that biometric tables should be used as references for the projection of biometric aspects of the insureds and their dependents, since they are more adequate for that group when the focus is the assessment and actuarial revaluation, in cases of survival of able and disabled individuals, and provided they do not indicate lower obligations to those achieved in the table of mortality elaborated by the Brazilian Institute of Geography and Statistics (IBGE, in its acronym in Portuguese) as the minimum survival rate limit for both sexes.

2.3 Real According to Lima, Oliveira e Silva (2013), the public entity must establishInterest Rate a discount rate for the obligations of social security benefi ts that refl ects of Actuarial the change in the value of money over time, and the currency and fi nancial Projections instrument term chosen for expressing the value of money over time must

be consistent with the currency and estimated term of the obligations of social security benefi ts.

Therefore, the discount rate refl ects the change in the value of money over time, but not the actuarial risk or the investment. It does not refl ect the specifi c credit risk of the entity either, which is supported by its creditors, nor does it refl ect the risk involved when a future experience differs from actuarial assumptions (LIMA, OLIVEIRA e SILVA, 2013).



When developing theoretical models for Social Security, Miranda (1997) found that the Government could not intervene in the process of savings accumulation, or accumulation of capital through the social security rate. In addition, any marginal increase in the social security discount rate may cause an increase in the inheritance that the agent will leave to his or her descendants.

With regards to the prudential limit, Art. 9 of the MPS Ordinance 403 / 2008 defi nes that the real interest rate used in the actuarial assessment should have the target established for the applications of the RPPS resources in the RPPS Investment Policy as a reference, with a maximum limit of 6% (six percent) per year. This threshold represents the minimum parameter for expected return on investments made by the RPPS management unit.

However, according to Lima, Oliveira e Silva (2013), nothing assures that the profi tability rate of the assets portfolio will exceed the percentage of 6% of real interest rates, something that would actually be a desirable situation since the assets would be adjusted in a percentage above the responsibilities registered in the liability side. Thus, the discount rate used to push the actuarial liabilities to the present value should be kept consistent with the profi t rate of the RPPS investments portfolio.

2.4 Actuarial The MPS Ordinance 403 / 2008 shows that the actuarial assessment Assessment is the technical study conducted by the actuary, based on biometric,

demographic and economic characteristics of the population under analysis, whose main objective is to gather the necessary resources to guarantee the payment of benefi ts provided in the plan in a suffi cient and adequate manner. The main points in a full actuarial assessment procedure include the following (FERRARI et al, 2002):

a. current values of the classes including future benefi ts and future contributions from which the total cost of each benefi t can be extracted;

b. the establishment of the cost to be charged in the year;c. the present value of the mathematical reserves, which in the language

of accounting codifi cation are called mathematical provisions;d. the definition of the costing structure, which is the allocation

of the cost between resource providers who generally speaking are the insured and his employer;

e. the actuarial cash fl ow;f. the statistics of the group of insureds, which is the object of the

assessment;g. the actuarial report.

According to Ferrari et al (2002), the components that must be taken into account when elaborating an actuarial assessment are the normative, cadastral and actuarial bases. While the normative base contains the plan of benefi ts and costing rules, the cadastral base is related to the database with information about the insureds, such as identifi cation, date of birth, gender, date of admission at the employer’s company, registry date in the social security system, salary, which is the basis for



calculating the benefi t and contribution, among others. The actuarial base is represented by parameters, technical bases and formulations used in the actuarial calculation, such as the discount rate used to calculate the present value of future benefi ts and contributions related to the plan.

The National Social Security Institute (Instituto Nacional de Seguro Social – INSS) caps the value of the highest benefi t paid by the Institute. This value will be used to calculate the contribution with regards to the pensions for insured persons who receive benefi ts above the mentioned capping limit.

With respect to the tables of mortality, the following was established: i) a general mortality table for women, which shows the annual probabilities of death from age zero to the last age, in relation to women; and ii) a general mortality table for men, which shows the annual probabilities of death from age zero to the last age, in relation to men.

The number of annuities in the year refers to the number of payments or benefi ts that will be done to the insured annually, taking also into account the annual bonus. The insured rate, in turn, corresponds to the percentage required by law to be applied over the positive difference between the amount of his or her benefi t and the amount of the capping limit of the retirement benefi ts paid by the National Social Security Institute.

3. Methodology In the formulations adopted in the actuarial basis of this work, actuarial equations were used as taught by Galé (1968), with emphasis on the3.1 Formulations commutations that facilitate the actuarial calculation as they replaceadopted the large sums of the series for quotients of easy resolution. The values

in the numerator and denominator are extracted from previously built actuarial tables, called commutation tables.

The function qx indicates the annual probability of death extracted from a table of mortality for an elderly person “x”, and px is the annual probability of survival for a person at age “x”. In the period of one year, the person may survive or die, thus the likelihood of survival and death when added together results in 100% of certainty or 1 (Equation 1).

Equation 1 px + qx = 1

Starting from Equation 1, the formula of the probability of survival can be obtained by transposing the term qx to the second side of the equation, resulting in Equation 2.

Equation 2 px = 1 – qx



The lx function indicates the number of people alive at age x, and in the fi rst age of the table there is an initial arbitrary number of living people, for example, 100,000 people. For the ages following the fi rst age of the table, the number of living people varies as seen in the following function described in Equation 3.

Equation 3 lx + n = lx + n – 1 × (1 – qx + n – 1), with n ≥ 1

The so-called Dx function is used in the calculation by commutation of a variety of actuarial functions, where i is the interest rate used in the assessment, as seen in Equation 4.

Equation 4

The so-called Nx function is also used in the calculation by commutation of different actuarial functions, as shown in Equation 5.

Equation 5

The ax function indicates the current value of a series of random annuities payable to “x” at the end of each year while the individual is living, and its commutation is shown in Equation 6.

Equation 6

q

3.2 Databases Taking into consideration the limitation of this work, the normative base was restricted to retirement benefi ts payable to healthy individuals. As for the cadastral base, it will consist of an enrolment number, date of birth, gender and value of the gross benefi t. The parameters and technical bases used in the actuarial basis are the date when the obligations will be priced, as well as the interest rate used to calculate the present value of future benefi ts and contributions related to the plan.

In 2013, in order to properly address the research, simulations were made based on a theoretical group of 808 records of retired insureds, along with information from the Statements of Actuarial Assessment Outcomes (DRAA, in its acronym in Portuguese) delivered to the Ministry of Social Security and collected from management units of the RPPS.



Initially, an actuarial assessment of the present value of future benefi ts (VABF) was made based on the prudential limits established in the social security legislation regarding the mortality table and interest rate. Subsequently, simulations were carried out by changing these prudential limits, in order to assess their effects on the fi nancial and actuarial balance of the RPPS.

With respect to procedures of the documental research, we analysed the mortality tables used in actuarial assessment collected from the DRAAs from the RPPS management units during the fi nancial year 2013, released by the Ministry of Social Security, as shown in Table 1.

Table 1 – Mortality tables adopted by the RPPS in 2013

Table Used Quantity of RPPS Frequency

IBGE MPS * 2011 – Both Sexes 1,782 95.5%

Other 83 4.5%

Total 1,865 100%

Source: Elaboration made by the authors using 2013 DRAA data, available at www.mps.gov.br

The data on Table 1 show that in 2013, 95.5% of RPPS management units used the IBGE 2011 * MPS general mortality table – for both sexes, therefore meeting the minimum fi gure required by the Policy Department of Social Security (SPPS, in its acronym in Portuguese).

With regards to interest rates, Table 2 shows that more than 90% of the RPPS management units adopted the percentage of 6% in 2013, which is exactly the limit established by the social security legislation.

Table 2 – Interest rates reported by RPPS in 2013

Interest rate Quantity of RPPS Frequency

6% per year 1,603 90.8%

Other 172 9.2%

Total 1,865 100%

Source: Elaboration made by the authors using 2013 DRAA data, available at www.mps.gov.br



One way of explaining the fact that this percentage is the same applied to the discount rate to bring the actuarial liabilities to the present value, is that actuaries seek to maximise the interest rate permitted by law since the higher the discount rate, the lower the present value of fl ows, and consequently, the lower the actuarial debt (LIMA, OLIVEIRA and SILVA, 2012).

3.3 Procedures in The fi rst actuarial assessment elaborated in this study aims at determining the Experimental the Current Value of Future Benefi ts (VABF, in its acronym in Portuguese), Research adopting the IBGE mortality table and the interest rate of 6% per year as minimum parameters, as established in the social security legislation, 3.3.1 Current and in practices adopted by the RPPS management units, according toAssessment fi ndings in the documental research. of the VABF through the As for the insureds, all simulations will be working with the ages reachedadoption of on 31/12/2013, and the study will be delimited for planned retirement minimum cases. The concept of a closed group was also used, which is premised parameters on the non-admission of new entrants to the initial group of insureds, so

that the group is not renewed and tends to become extinct.

With respect to the cadastral base of actuarial assessments of the work, data from every public servant were extracted, related to their identifi cation (enrolment number), date of birth, gender and value of the gross benefi t, as registered on 31/12/2013. This base will be used for all simulations of the study, as shown on Table 3.

Table 3 – Cadastral base for actuarial assessment of VABF

Enrolment Number

Date of Birth Gender VABF

1 16/03/1958 M 12,235.00

2 06/09/1957 M 12,230.97

3 24/01/1951 M 12,212.20

4 06/05/1954 M 12,183.28

5 05/09/1946 M 12,181.78

6 01/01/1954 M 12,179.16

7 16/07/1957 M 12,178.08

8 30/04/1950 M 12,174.75

9 26/04/1954 M 12,165.86

10 25/09/1057 M 12,159.92

Source: Elaboration made by the authors using theoretical group data.



As for the parameters adopted in the initial actuarial base, they observe the requirements and minimum limits established in the social security legislation, as shown on Table 4.

Table 4 – Parameters adopted in the standard actuarial base

Description ParameterFinancial Scheme Capitalization

Benefi t Retirement payable to able individuals

Assessment Date 31/12/2013

Number of benefi ts in the year 13

INSS capping limit R$ 4,390.24

General Mortality Table IBGE 2011 * MPS – both sexes

Insured’s Rate 11%

Interest rate 6% per year

Number of insureds 808


The description of the technical bases can be used for both men and women because in the table used – IBGE 2011 * MPS – both sexes have the same application, regardless of sex (Table 5).

Table 5 – Technical Bases for the calculation of retirement payments

TECHNICAL BASES – BOTH SEXESGeneral Mortality Table IBGE 2011*MPS – BOTHInterest rate: 6%

COMMUTATION TABLEx qx lx Dx Nx ax0 0.016139386 100,000 100,000 1,694,106 15.941058

1 0.001046678 98,386 92,817 1,594,106 16.174710

2 0.000665071 98,283 87,471 1,501,289 16.163157

3 0.000501358 98,218 82,465 1,413,817 16.144349

4 0.000408208 98,168 77,759 1,331,352 16.121594

5 0.000348227 98,128 73,327 1,253,593 16.095868

6 0.000307425 98,094 69,153 1,180,266 16.067564

7 0.000279687 98,064 65,218 1,111,113 16.036855

8 0.00026244 98,037 61,509 1,045,895 16.003822

9 0.000255214 98,011 58,013 984,386 15.968504

10 0.000259257 97,986 54,715 926,373 15.930936




From the constant variables in Tables 3, 4 and 5, observing minimum elements established in the social security legislation, the actuarial assessment of the elements for the calculation of the VABF (Present Value of Future Benefi ts) are summarised on Table 6.

Table 6 – Demonstrative Table of the VABF

EnrolmentNumber

Date of

BirthGender

Gross Benefi t Value

ContributionWithoutBenefi t

Net Benefi t Value

Age ax VABF

1 16/03/1958 M 12,235.00 862.92 11,372.08 56 11.571876 1,710,571.39

2 06/09/1957 M 12,230.97 862.48 11,368.49 56 11.571876 1,710,211.83

3 24/01/1951 M 12,212.20 860.42 11,351.78 63 10.087568 1,488.654.70

4 06/05/1954 M 12,183.28 857.23 11,326.05 60 10.750113 1,584,156.70

5 05/09/1946 M 12,181,78 857.07 11,324.71 67 9.122941 1,343,090.68

6 06/01/1954 M 12,179.16 856.78 11,322.38 60 10.759113 1,583.643.83

7 16/06/1957 M 12,178.08 856.66 11,321.42 56 11.671876 1,703,130.56

8 30/04/1950 M 12,174.75 856.30 11,318.45 64 9.853041 1,449,775.51

9 26/04/1954 M 12,165.86 855.32 11,310.54 60 10.759113 1,581,988.21

10 25/09/1957 M 12,159.92 854.66 11,305.26 56 11.571876 1,700,699.18

Source: Elaboration made by the authors using the theoretical group data.

3.3.2 Actuarial In an attempt to verify how changes in the prudential limits can impact assessment the fi nancial and actuarial balance of the RPPS, particularly that relatedof the VABF to the choice of different mortality tables and interest rates, this studyby means of will carry out simulations with the use of three different general mortality changing the tables and six different interest rate percentages. prudential limits With regards to mortality tables, in addition to the IBGE 2011 * MPS

general mortality table – both sexes, the AT-83M and AT 2000M tables will also be used, given that these biometric tables are commonly used in the Brazilian market to calculate the amount of revenue from retirement pensions.

As for the real maximum interest rate per year, in addition to the 6% limit established in the legislation applied to the RPPS, the percentage 4.5%, 4.75%, 5%, 5.25% and 5.5% will be used as references to percentages established for private pension funds, in the CNPS Resolution 09 / 2012, to be applied for actuarial assessments from 2012 to 2018.

It has been noted that the equity from the plan is based on the hypothetical amount of R$ 472,204,591.99 as a standard for comparison. Therefore, comparisons will be made based on a situation of equilibrium where the actuarial outcome is R$ 0.00. Tables showing the details of each of the simulations are listed in the Appendices at the end of this work.



4. Description Table 7 shows VABFs generated from the various simulations throughand Analysis the use of three separate general mortality tables, combined with various of Results interest rates.

4.1 Analysis of impacts of VABF as a result of changes in the mortality tables and interest rates

Table 7 – Assessment of VABFs with the use of various mortality tables and interest rates

INTEREST RATEMORTALITY TABLE

IBGE 2011*MPS – BOTH SEXES AT-83M AT-200M

6% per year R$ 472,204,591.99 R$ 491,820,012.16 R$ 522,294,393.11

5.5% per year R$ 491,229,940.71 R$ 512,204,295.10 R$ 545,160,494.37

5.25% per year R$ 501,247,194.66 R$ 522,950,446.00 R$ 557,248,244.19

5% per year R$ 511,622,166.73 R$ 534,089,924.33 R$ 569,802,245.95

4.75% per year R$ 522,372,011.36 R$ 545,642,053.71 R$ 582,846,573.63

4.5% per year R$ 533,514,881.40 R$ 557,627,311.60 R$ 596,406,808.22

Source: Elaboration made by the authors from simulations in the study.

By analysing the impacts of the simulations made on Table 7 in the VABFs, it became clear that there was an increase in the obligations of retirement pensions when the AT-83M and AT-2000M tables were used instead of the IBGE 2011*MPS – for both sexes, and there was also a reduction in interest rates.

4.2 Analysis of For the purposes of the analysis of the actuarial results, having asthe impact on a starting point a situation of equilibrium (actuarial results equal to actuarial R$ 0.00), each result, obtained from eighteen simulations, was calculatedresults arising using the following subtraction: equity of the plan less VABF, the resultsfrom changes of which are shown on Table 8. in the mortality tables and interest rates



Table 8 – Evaluation of the actuarial result using various mortality tables and interest rates



6% per year R$ 0.00 (R$ 19,615,420.17) (R$ 50,089,801.12)

5.5% per year (R$ 19,025,348.72) (R$ 39,999,703.11) (R$ 72,955,902.38)

5.25% per year (R$ 29,042,602.66) (R$ 50,745,854.01) (R$ 85,043,652.20)

5% per year (R$ 39,417,574.74) (R$ 61,885,332.34) (R$ 97,597,653.96)

4.75% per year (R$ 50.167,419.36) (R$ 73,437,461.72) (R$ 110,641,981.64)

4.5% per year (R$ 61,310,289.41) (R$ 85,422,719.61) (R$ 124,202,216.23)


Following that reasoning, and based on the data on Table 8, it can also be observed that there was an increase in the actuarial defi cit when the AT-83M and AT-2000M tables were used instead of the IBGE 2011*MPS – for both sexes, and there was also a reduction in interest rates.

4.3 Percentage From the data shown on Tables 7 and 8, it is possible to determine the Analysis of the percentage changes in the VABF and in the results, after changes in VABF and of mortality tables and interest rates (Table 9). the actuarial results after changes in mortality tables and interest rates

Table 9 – Percentage changes in th e VABF and in the actuarial results with the use of various mortality tables and interest rates



6% per year 100,0% 104.2% 110.6%

5.5% per year 104.0% 108.5% 115.5%

5.25% per year 106.2% 110.7% 118.0%

5% per year 108.3% 113.1% 120.7%

4.75% per year 110.6% 115.6% 123.4%

4.5% per year 113.0% 118.1% 126.3%




Taking into consideration that the equity of the plan remained constant for the calculation of results, we observed that variations in the values of VABFs and in negative results are the same.

Therefore, according to the changes presented on Table 9, and keeping the interest rate at 6% per year, it is possible to conclude that by simply using the AT-83M table there was an increase of 4.2% both in the obligations with retirement pensions and in the results. And when the AT-2000M table is used, this increase goes up to 10.6%.

Furthermore, the study showed that the reduction of interest rates caused an impact on the obligations with retirement pensions for each of the three general mortality tables. By fi xing the IBGE 2011*MPS – for both sexes table and with a reduction in interest rates to 6%, the results show an increase in the percentage of the VABF, and defi cits equal to 4%, 6.2%, 8, 3%, 10.6% and 13%, corresponding to the rates 5.5% per year, 5.25% per year, 5% per year, 4.75% per year and 4.5% per year, respectively.

By keeping the IBGE 2011*MPS table – for both sexes as a base and with 6% of interest rate, a similar analysis can be done using the AT-83M and AT-2000M tables, with their respective interest rates. For example, by replacing the standard comparative table with the AT-83M table, using an interest rate of 5% per year, there is an increase of 8.5% in the VABF and in the actuarial results. However, if this replacement was made with the AT-2000M table at 4.5% per year, the increase would be of 26.3%.

5. Final This study aims at determining how changes in the prudential limits can Remarks impact the fi nancial and actuarial balance of the RPPS, particularly when

different mortality tables and interest rates apply.

According to the documental research of the 2013 DRAA, 95.5% of RPPS management units uses the IBGE 2011 * MPS table – for both sexes, which is the minimum required by the supervisory body. In addition, 90.8% of the RPPS had their actuarial assessment carried out based on the actual interest rate of 6% per year, which is the maximum value for prudential rate.

Therefore, the results show that in most RPPS there is a commitment towards fi nancial and actuarial balance which is kept with the use of mortality tables and interest rates, which are in accordance with the prudential limits established in the social security legislation, without taking into consideration the specifi cities of the group of insureds and the investment portfolio characteristics of its own management unit.

By analysing to what extent the change in prudential limits can affect the fi nancial and actuarial balance of the RPPS, the results of experimental research show that the simple change from the IBGE 2011 table to the AT-83M table generated an increase of 4.2% for both the obligations with retirement pensions and actuarial results. When we consider the change from the IBGE table to the AT-2000M table, the increase goes to 10.6%.



With respect to interest rates, even with the maintenance of the 2011 IBGE mortality table, the percentages ranged from 4% (for an interest rate of 5.5% per year) to 13% (for an interest rate of 4.5% per year), which is evidence that any change in the interest rate has a direct impact on the outcome obtained.

By performing combined analysis with a variation in the mortality table and interest rates, it becomes clear that any simulation that changes the prudential limits leads to an increase in obligations with retirement pensions and subsequent effects on the actuarial outcomes, which will require an extraordinary increase in contributions to cover any defi cits and consequent restoration of the fi nancial and actuarial balance.

Despite the fact that the fi ndings in this study show that most RPPS management units use mortality tables and interest rates in accordance with the prudential limits established in retirement pensions legislation, one must bear in mind that in order to preserve the fi nancial and actuarial balance of RPPS, interest rates and actuarial assumptions should match the characteristics of investment portfolios and of the group of insureds for each management unit.

In terms of future research, we suggest that a focus should be given to empirical studies to assess the sustainability of RPPS taking into consideration other actuarial hypotheses, or even evaluating the RPPS in relation to other benefi ts, such as pension due to death, annuities for individuals with disabilities, or benefi ts to be granted to public servants in active service.

6. Bibliographical References

BARROS, Clemilton da Silva. O rol de benefícios dos regimes próprios de previdência social e as aposentadorias em espécie. Conteúdo Jurídico, Brasília-DF: 23 set. 2008. Disponível em: <http://www.conteudojuridico.com.br/?artigos&ver=2.21155&seo=1>. Acesso em: 21 mai. 2014. BRASIL. Conselho Nacional de Previdência Complementar. Resolução CNPC nº 09, de 29 de novembro de 2012. Altera a Resolução nº 18, de 28 de março de 2006, do Conselho de Gestão de Previdência Complementar, que estabelece parâmetros técnico-atuariais para estruturação de plano de benefícios de entidades fechadas de previdência complementar, e dá outras providências. Diário Ofi cial [da] República Federativa do Brasil, Poder Executivo, Brasília, DF, 23 de janeiro de 2013, Seção 1. _______. Constituição da República Federativa do Brasil/Constituição (1988). Texto constitucional de 5 de outubro de 1988 com as alterações. Brasília: Câmara dos Deputados, 2005. _______. Ministério da Previdência Social. Portaria Ministerial nº 402, de 10 de dezembro de 2008. Disciplina, parâmetros e as diretrizes gerais para organização e funcionamento dos regimes próprios de previdência social dos servidores públicos ocupantes de cargos efetivos da União, dos Estados, do Distrito Federal e dos Municípios, em cumprimento das Leis nºs 9.717, de 1998, e 10.887, de 2004. Diário Ofi cial [da] República Federativa do Brasil, Poder Executivo, Brasília, DF, 11 de dezembro de 2008, Seção 1.



_______. Ministério da Previdência Social. Portaria Ministerial nº 403, de 10 de dezembro de 2008. Dispõe sobre as normas aplicáveis às avaliações e reavaliações atuariais dos Regimes Próprios de Previdência Social – RPPS da União, dos Estados, do Distrito Federal e dos Municípios, defi ne parâmetros para a segregação da massa e dá outras providências. Diário Ofi cial [da] República Federativa do Brasil, Poder Executivo, Brasília, DF, 11 de dezembro de 2008, Seção 1. FERRARI, A. et al. Regime próprio de previdência dos servidores: como implementar? Uma visão prática e teórica. Brasília: MPAS. Coleção Previdência Social. Série Estudos, 2002. v.17. GALÉ, José González. Elementos de Calculo Actuarial. 4. ed. Buenos Aires: Macchi, 1968. LIMA, Diana Vaz de. V.; OLIVEIRA, F. V.; SILVA, C. A. T. Efeito da taxa de desconto na sustentabilidade dos Regimes Próprios de Previdência Social. Informe de Previdência Social. Brasília, v. 24, nº 5, p. 3-23, maio 2012. LIMA, Diana Vaz de; GUIMARÃES, Otoni Gonçalves. Contabilidade Aplicada aos Regimes Próprios de Previdência Social. Brasília: MPS, 2009. MIRANDA, Rogério Boueri. Três Modelos Teóricos para a Previdência Social. Texto para Discussão nº 516. Brasília: IPEA, 1997. Disponível em http://desafi os2.ipea.gov.br/ pub/td/1997/td_0516.pdf, consultado em 10/2/2014. OLIVEIRA, Mário de. et al. Tábuas biométricas de mortalidade e sobrevivência: experiência do mercado segurador brasileiro – 2010. Rio de Janeiro: Funenseg, 2012. ORTEGA, Antonio. Tablas de mortalidad. San José, Costa Rica: Centro Latino Americano de Demografi a, 1987. SOBRINHO, Benedito Leite. Atuária Básica. Brasília: UnB/CCA, 2013, 90 p. Apostila. WILBERT, Marcelo Driemeyer; LIMA, Diana Vaz de; GOMES, Marília Miranda Forte. O Impacto da Utilização de Diferentes Tábuas de Mortalidade nas Estimativas de Pagamento de Benefícios no RGPS. Revista Brasileira de Risco e Seguro, Rio de Janeiro, v. 8, nº 16, p. 19-40, maio-out. 2013.



7. Appendices

Appendix A – IBGE 2011 * MPS Table – Both Sexes (Interest Rate = 6%)

CURRENT VALUE OF BENEFITS GRANTEDFinancial Scheme: CapitalizationBenefi t: Retirement paid to able individualsAssessment date: 31/12/2013Number of benefi ts in a year: 13INNS capping limit: 4,390,24General Mortality Table: IBGE 2011 * MPS – BOTH SEXESInsured’s rate: 11%Interest rate: 6.00% per yearNumber of insureds: 808

FINANCIAL ACTUARIAL BALANCE

Equity of the Plan R$ 472.204.591,99

VABF R$ 472.204.591,99

Balance Result R$ 0,00

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Appendix B – IBGE 2011 * MPS Table – Both Sexes (Interest Rate = 5.5%)




VABF R$ 491.229.940,71

Balance Result (R$ 19.025.348,72)

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Appendix C – IBGE 2011 * MPS Table – Both Sexes (Interest Rate = 5.25%)




VABF R$ 501.247.194,65


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Appendix D – IBGE 2011 * MPS Table – Both Sexes (Interest Rate = 5%)




VABF R$ 511.622.166,73


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Appendix E – IBGE 2011 * MPS Table – Both Sexes (Interest Rate = 4.75%)




VABF R$ 522.372.011,35


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Appendix F – IBGE 2011 * MPS Table – Both Sexes (Interest Rate = 4.5%)




VABF R$ 533.514.881,40


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Appendix G – AT – 83 M Table (Interest Rate = 6%)

CURRENT VALUE OF BENEFITS GRANTEDFinancial Scheme: CapitalizationBenefi t: Retirement paid to able individualsAssessment date: 31/12/2013Number of benefi ts in a year: 13INNS capping limit: 4,390,24General Mortality Table: AT 83 MInsured’s rate: 11%Interest rate: 6.00% per yearNumber of insureds: 808



VABF R$ 491.820.012,16


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Appendix H – AT – 83 M Table (Interest Rate = 5.5%)




VABF R$ 512.204.295,10


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Appendix I – AT – 83 M Table (Interest Rate = 5.25%)




VABF R$ 522.950.446,00


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Appendix J – AT – 83 M Table (Interest Rate = 5%)




VABF R$ 534.089.924,33


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Appendix K – AT – 83 M Table (Interest Rate = 4.75%)




VABF R$ 545.642.053,71


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Appendix L – AT – 83 M Table (Interest Rate = 4.5%)




VABF R$ 557.627.311,60


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Appendix M – AT – 2000 M Table (Interest Rate = 6%)




VABF R$ 522.294.393,11


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Appendix N – AT – 2000 M Table (Interest Rate = 5.50%)




VABF R$ 545.160.494,37


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Appendix O – AT – 2000 M Table (Interest Rate = 5.25%)




VABF R$ 557.248.244,19


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Appendix P – AT – 2000 M Table (Interest Rate = 5%)




VABF R$ 569.802.245,95


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Appendix Q – AT – 2000 M Table (Interest Rate = 4.75%)




VABF R$ 582.846.573,63


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Appendix R – AT – 2000 M Table (Interest Rate = 4.5%)




VABF R$ 596.406.808,22


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Variation of Prudential Limits and its Effects on the Financial …rbrs.com.br/arquivos/rbrs_18_4.pdf · Variation of Prudential Limits and its Effects on the Financial and Actuarial