Payroll loans by old age and survivors pensioners : an exploratory study using the principles of actuarial mathematics

Credit activity has been growing strongly in Brazil since 2004. An important factor is personal loans to people receiving benefits from the Brazilian National Social Security Institute (INSS) with repayment by automatic deduction from their benefits. This paper investigates whether the rate of return obtained by financial institutions on these loans is the same as that on personal loans to salaried workers with automatic payroll deduction. The method to calculate these rates includes use of the actuarial mathematics’ principles, through the incorporation of a biometric risk factor associated with the borrower’s age. Employing a sample of 23 financial institutions, we compare the difference in the rates of return after considering the default costs, which are influenced by borrowers’ characteristics of two groups. The first group, composed of pensioners (both retirees and people receiving survivor pensions), is the treatment group. The control group is made up of São Paulo Municipal Government employees. The results provide significant evidence that, for the sample studied, the return obtained by financial institutions is greater on loans to social security beneficiaries.

BBR, Braz.Bus. Rev. (Engl. ed., Online), Vitória, v. 7, n. 1, Art. 4, p. 59-88, jan -apr.2010www.bbronline.com.brGraph 2 ii shows that the increase in free credit included both personal and business loans.In December 2007 and May 2008 (last figure in the graph) the balance of personal loans was, respectively, 12% and 6% higher than that of business loans.

GRAPH 2: BALANCE OF DOMESTIC LENDING(CREDIT AT THE REFERENTIAL INTEREST RATE)
Source: BCB (2002BCB ( , 2003BCB ( , 2004BCB ( , 2005BCB ( , 2006BCB ( , 2007 and Time Series/ Economic Department) Since October 1999 the Brazilian Government and the Brazilian Central Bank (BCB) have been acting together on a project to lower interest rates and the bank spread The main measures of the PJSB are in the institutional sphere, as part of the microeconomic agenda, undertaken by the Federal Government since 2003.In the view of the Central Bank, these actions are responsible for reducing the cost of credit in recent years.
Among these measures are: reduction of bank reserve requirements; improvement of the Brazilian Payment System; improvement of the Accounting Plan for Institutions of the National Financial System (COSIF); portability of banking history information (facilitating changing banks); more detailed disclosure to customers about the costs of overdraft checks; securitization of receivables; creation of the Bank Credit Note; reform of bankruptcy legislation; simplified procedures to enforce judicial awards in the Civil Procedure Code; and expansion of the system of personal loans with repayment by automatic deduction from payroll or social security benefits (together called crédito consignado, or "payroll loans").
With respect to the last item, the payroll loans system dates back to 1990, but at that time it only entailed payroll loans to civil servants.
The extension of this system to workers in the private sector and people receiving social security benefits has been very important in increasing the supply of personal loans in Brazil.
Since social security beneficiaries became eligible for this type of credit, the National Social Security Institute (INSS) has been issuing regulations to limit the repayment periods, installment values and interest rates of these loans.
In this context, in this article we investigate whether the rate of return obtained by financial institutions on payroll loans to social security beneficiaries (henceforth called INSS payroll loans) is the same as that on payroll loans to salaried workers (henceforth called payroll loans).
Analysis of the factors composing the bank spread shows that default is the only observable cost factor that varies according to the observable characteristics of the borrower in the case of payroll deduction loans.In the case of INSS deduction loans, the default cost is basically associated with the risk of the borrower's death (biometric risk), since the automatic deduction from benefits prevents borrowers from defaulting.
To isolate the factors associated with biometric risk, it is necessary to employ concepts of treatment group and control group.In this article, the treatment group consists of social security beneficiaries (retirees and receivers of survivor benefits) who have taken out automatic debit loans.
Therefore, this paper from a theoretical perspective is aligned with the contributions on credit risk, focusing on the particular case of payroll loans (automatic debit loans) in Brazil and the relevance of biometric risk as an element affecting the interest rate charged.
The control group consists of civil servants working for the São Paulo Municipal Government (PMSP).The justification for choosing this group is that it has a set of observable characteristics similar to those of the treatment group.
The default risk of the two groups is similar, given the job stability enjoyed by civil servants, with the exception of the biometric factor, since the average age of the treatment group is higher.
To carry out the study we obtained data on the nominal interest rates charged on automatic debit loans to social security beneficiaries and PMSP civil servants.We gathered the data in the first half of June 2008 from 23 financial institutions.
We addressed the research question based on an index called the Rate of Return after Default Costs (RRADC).
We obtained this by calculating the internal rate of return and incorporating the biometric risk (based on the mortality table calculated by the Brazilian Institute of Geography and Statistics -IBGE -for 2006) and the processing fee charged by the PMSP for transferring the payroll deductions to the lender financial institutions.
We found that on average, the INSS deduction loans imply higher RRADCs than payroll deduction loans to São Paulo Municipal Government employees.In other words, within the sample of banks considered, it can be stated that the rate of return they obtain is higher on INSS deduction loans than on payroll deduction loans to municipal civil servants.Payroll loans is one of the loan types available to individuals (also composed of overdraft checks, regular personal loans, mortgage loans, car loans, installment purchase of goods, credit card debt and others).
Graph 3 shows the evolution of the balance of personal loans (including all automatic debit loans), payroll deduction loans and INSS deduction loans.Takeda & Bader (2005) indicate three important dates in the evolution of payroll loans.
The first was in December 2003, when Law 10820/2003 was enacted allowing the extension to the private sector of the existing payroll loans system applicable to civil servants.
The second was May 2004, with the start of actual operation of this system for social security (INSS) beneficiaries, from which point the growth of payroll loans was fairly stable until November 2004.
The third was in December 2004, when the growth of these automatic debit loans picked up dramatically.iii .These three dates are indicated in Graph 3 by arrows 1, 2 and 3.
As can be seen in Graph 3 iv and  (2002, 2003, 2004, 2005, 2006, 2007 and   It can be seen that the policy of the INSS and Social Security Ministry was to reduce the upper limit on the allowable interest rate and the amount of each installment, relaxed somewhat by allowing a longer repayment period, to increase the available income of borrowers during the amortization period.

CREDIT'S COST DETEMINANTS
The cost of bank credit is basically determined by banks' funding cost plus the bank spread.The bank spread is the difference between the interest rate paid to depositors or other funding sources and the rate charged to borrowers (COSTA & NAKANE, 2004).
According to Costa & Nakane (2004), the domestic funding cost in Brazil is based on the Selic rate (benchmark rate) and the bank spread is composed of two elements, called cost factors and margin factors.
Cost factors consist of the operational and administrative costs associated with banking activity and the regulatory costs of financial intermediation.These cost factors are: • operational and administrative costs.Troster [200-] states that banking activity, because of its sophistication, requires highly trained workers, advanced technology and complex infrastructure, making these costs high.
• reserve requirement cost.The reserve requirements on cash deposits, term and passbook savings account deposits affect the spread by reducing the total amount of funds available for lending.
• cross subsidies.According to Nakane (2003), the existence of directed lending at subsidized rates (e.g., crop loans and mortgages) means that part of the spread charged on non-directed credit reflects an element of compensation by these transactions.
• cost of the Credit Guarantee Fund (FGC).This fund is formed by contributions from financial institutions and is intended to protect investors and accountholders against intervention, extrajudicial liquidation, bankruptcy or insolvency of banks.It is financed by a levy of 0.0125% on guaranteed deposits (maximum of R$ 60 thousand), limited at 2% of the total of these accounts.This affects the bank intermediation cost by reducing the volume of resources available for loans.2005) add that the growth rate of industrial output affected negatively both high default rates and by reduced demand for credit.
• legal risk.Troster [200-] observes that the inefficient judicial system (with costly and slow proceedings) aggravates default costs.Costa & Mello (2006), in studying the effects of a decision by the Superior Tribunal of Justice (the highest court for non-constitutional matters) in July 2004 that held payroll loans to be illegal (a decision later overturned), found evidence that this decision had a negative impact by increasing the interest rate on loans and reducing the volume of credit offered by banks.
The second element, margin factor, refers to the remuneration of the bank's capital, that is, the gains from intermediation activity, net of the inherent costs of this activity.The determinants of the margin factor are: • competition.According to Oreiro & Paula (2005), despite the recent increase in banking concentration (and resulting reduction of competition) in Brazil, the evidence of the effect of this higher concentration on the bank spread does not appear to be conclusive.A similar view was expressed by Nakane (2003), who showed that in the period from 1994 to June 2003 the number of banks in Brazil fell from 246 to 164.
However, he cited three works that had rejected the hypothesis that Brazilian banks behave as if there was perfect competition, but also rejected the hypothesis that they behave as a cartel or in collusion.
• opportunity cost.Banks can invest the funds on deposit in public bonds, which interest rate yield an high real return in the last years.,.
• transfer cost.According to Nakane (2003), types of credit tied to maintenance of bank accounts, such as overdraft checks for individuals and guarantee accounts for businesses, are typical of situations where customers are tied to a particular bank, due to the difficulty of transferring their banking history and reputation data to competing institutions.
As a result of these high transfer costs, the interest rates charged on these types of credit are markedly higher than on loan types where this does not occur.The Brazilian Central Bank (BCB, 2006) published the composition of the bank spread shown in Table 3.The figures in this table should be analyzed with care, since they show the composition of the spread, not its dynamic.
For example, the greater participation in 2006 than in 2005 of the "default" item in the total spread can be explained either by an increase in default or a relative reduction of one of more of the other components.
It can be seen that the spread is mainly explained by administrative costs and loan default, and that in more recent years the latter grew in importance.An important point here is that default is the only observable cost factor that varies according to borrowers' characteristics.

RESEARCH PROBLEM
The supply of personal credit in Brazil in recent years has grown substantially, and automatic debit loans have played an important role in this development.Therefore, it is interesting to perform a quantitative analysis of the characteristics and conditions for granting these loans to social security beneficiaries.
The literature has shown, for example, that credit and economic growth are positively correlated (for example, see De Gregorio & Guidotti, 1995 vi ).
Nevertheless, in Brazil little research has been done on payroll loans in general.
The few works published on this type of credit generally focus on the interest rates charged, using econometric models, and have not been very conclusive vii .
Given the relevance of the theme (the recent growth of the number and volume by value of automatic deduction loans to social security beneficiaries, their reflections on the policies of the Social Security Ministry and the recognized importance of the credit channel to wage and economic growth) and the shortage of works on the subject, we believe the present study is timely.
Our aim is to investigate whether the rate of return on INSS deduction loans is the same as that obtained on payroll deduction loans.By rate of return we mean the real return obtained by financial institutions after considering the costs and possible additional fees charged on loan transactions.
The novelty of the empirical part of this study is the incorporation of the cost represented by biometric risk, that is, the risk that the borrower will die before paying back the loan.
This risk is particularly relevant in the case of social security beneficiaries, since they are obviously on average older than other groups and have a higher probability of dying.For this it is necessary to incorporate an actuarial mathematical exercise into the usual financial mathematical calculation, represented by the granting and repayment of loans.This actuarial aspect is described in the next section.

METHODOLOGY
To obtain the rate of return on a banking transaction, in the case here an INSS deduction loan, it is necessary to ascertain the revenues from the transaction and compare them ex post with the associated costs and expenses.
However, the objective of this study is to compare the rate of return on INSS deduction loans with that on payroll deduction loans.In other words, the methodological path is to consider the social security beneficiaries (retires and receivers of survivor benefits) as the treatment group, as defined by Wooldridge (2002, Ch. 18).
The next step is to find a control group.Ideally this group should contain a set of individuals with observable characteristics as near as possible to those of the treatment group, with the exception of one, which will serve as an element to identify and differentiate the two groups.The more homogeneous these two groups are, the more adequate the methodology.
For this reason, attention should first be focused on the characteristics of the credit market, as presented in the preceding sections.
Then attention should be turned to finding the factors that differentiate the costs of payroll loans to social security beneficiaries and those of payroll loans to salaried employees.
Analysis of the factors composing the bank spread, presented in the previous section and summarized in Table 3, shows that default is the only observable cost factor that varies according to the borrowers' characteristics.
All other components of the spread are related to the characteristics of other agents (federal government and banking system) and the legal-institutional framework, all of which are independent of the borrowers' characteristics.
Besides this, we assume these other components homogeneously affect those receiving payroll loans (whether social security beneficiaries or salaried employees), and thus do not justify differences in the rate of return obtained by banks on these transactions.
Therefore, the cost factor we focus on here to compare the rates of return on the two types of payroll loans is default.In the case of payroll loans to social security beneficiaries (treatment group), the default cost is basically associated with the risk the borrower will die before paying off the loan (biometric risk), since the automatic deduction from benefits rules out default.
As a control group (for comparison and evaluation of the result) we chose payroll borrowers made up of employees of the São Paulo Municipal Government (PMSP).The justification for this choice is that this group has very similar observable characteristics as the treatment group.
The control group's default risk is similar, given the job stability enjoyed by civil servants, except for the biometric factor.
As can be seen in Table 4, which presents the restrictions of municipal legislation on payroll deduction loans to PMSP employees, these are no stricter than on loans to social security beneficiaries (Table 2).
In other words, the characteristic that differentiates the rates of return on loans to the treatment group and the control group is biometric risk.
This difference is due to the fact that the average age of active civil servants is substantially lower than that of social security beneficiaries, which should be reflected in the cost of default.

The Model
As already discussed, only examining the possible cost of default given by the biometric risk of both groups leads to the inference that there is a difference in the rate of return between the treatment and control groups, since all other cost factors can be considered equal for both groups.
To test hypotheses H 0 and H 1 , we calculated what we call the Rate of Return after Default Costs (RRADC), obtained by calculating the internal rate of return (IRR), plus the biometric risk (and the possible risk factor this represents for each group) and the transfer fee (TF) charged by the PMSP on the loan payments transferred to the lending banks.
Equation 1 shows the calculation of the IRR without including the biometric risk and transfer fee.In it, AM t is the amount the monthly installment to be paid in month t, LV is the loan value, n is the number of monthly installments and IRR is the internal rate of return, which equals the present value of the AM t installments at the contracted value LV.
The loan is fully amortized x , meaning all the payments are equal (no balloon payment).In this case the amount of the installments AM is calculated according to equation 2 xi , where j is the nominal interest rate charged by the bank (shown in Table 5), TF is the transfer fee and the expression (1 -TF) makes AM represent the amount actually received by the bank.
In other words, this gives the expected value of each installment, based on the probability that the borrower will survive over the life of the loan.
As presented by Vilanova (1969, Ch. I and II) and Parmenter (1999, Ch. 7), this probability, which represents the biometric risk factor, designated by the terms t P x according to standard actuarial notation, is given by equation 3, in which l x is the number or living persons (survivors) of a determined cohort with age x and l x+t indicates the number of living persons (survivors) of this same cohort with age x + t.
The values of l x employed to calculate the biometric risk factor t P x were obtained from the mortality table calculated and disclosed by the Brazilian Institute of Geography and Statistics (IBGE, 2006), which is used by the INSS to calculate the "social security factor" xii .The segment of this table used in this study is presented in Table 10 of the Appendix.
Given the relatively short loan maturities and the fact the payments are monthly, it is necessary to perform an additional calculation based on this mortality table, since it only presents annual values of l x and here we need monthly values.
We estimated the monthly values of l x by an ordinary least squares (OLL) regression, employing the annual data for l x calculated by the IBGE ( 2006) for people 30 to 80 years old.The model estimated is presented in equation 4.
The age, utilized to estimate the number of survivors (l x ), was included in the model up to the third degree to enable capturing the curve's non-linearity and to obtain good fit with the real data.

GRAPH 5: AVERAGE OF THE RRADCS OF THE FINANCIAL INSTITUTIONS (BY BORROWER'S AGE AND LOAN TERM)
Source: Authors' calculations (Tables 7 and 8) Some considerations can be made based on the results of Tables 7 and 8.As explained in the methodology section, the RRADC index does not represent the bank's actual rate of return.This means that in the case of the sample analyzed, a change in the controllable variables appears not to affect the fact the rate of return obtained by banks on INSS deduction loans is higher than that on payroll deduction loans to PMSP employees.
Therefore, we it is reasonable to affirm that the differences observed in Tables 7 and 8 hold for Table 9, with different parameters.
This is probably a reflection of the fact the loan value is not a relevant explanatory variable to differentiate the two groups, which strengthens the importance of incorporating the biometric risk factor.

FINAL COMMENTS
In this article we sought to incorporate and quantify the role of biometric risk in loans to social security beneficiaries secured by deduction from future benefits.To do this, we employed a control group, composed of São Paulo Municipal Government employees.
The results obtained do not indicate rejection of the alternative hypothesis (H 1 ), meaning that for the sample analyzed the rate of return obtained by banks on INSS deduction loans is different (and higher) than the rate obtained on automatic debit loans to other individuals.
This means that the financial institutions in the sample analyzed obtain more profit from payroll loans to INSS beneficiaries than from payroll loans to São Paulo municipal employees.
These results are relevant for the formulation of public policies by the Social Security Ministry, particularly with respect to the maximum interest rates that banks can charge on automatic debit loans to social security beneficiaries.
The results are also important to clarify to interested groups and to society at large the different treatment with respect to profit margins given by banks to the two groups of customers.
Nevertheless, care should be taken in any attempt to generalize the conclusions reached, since they are highly dependent on the sample and the control group utilized in this study.
Given the importance that INSS deduction loans have gained within the personal loan category in recent years, payroll loans deserves further empirical study, which could corroborate the results presented here.to 15% and established IOF of 0.38% of the loan value.vi The authors found a positive empirical relationship between the level of credit and growth of per capita GDP.
vii According to Rodrigues et al. (2006), payroll loans is an important factor in the reduction of the rates charged on personal loans.In turn, Barros, Fagundes & Cavalcante (2007) concluded that the persistence of high interest rates on payroll loans is due to the high administrative costs, mainly derived from payment of commissions to correspondent banks.viii On April 30, 2008, banks were forbidden to charge loan origination fees on any type of loan, according to National Monetary Council Resolution 3518/07.ix The names of the financial institutions have been omitted.Note that the numbering in Tables 5, 7 and 8 is mutually consistent.x The deduction from the equation to calculate the installments for a fully amortized loan can be found in any basic financial mathematics book, such as Bruni & Fama (2002).xi The result of this equation does not completely reflect the installments the borrower actually pays, because it does not include the IOF (tax on financial operations).However, the absence of the IOF does not distort the final results because it represents a cost to the borrower, not to the bank, so it does not affect the bank's rate of return.
xii The social security benefits is defined by a "social security factor", which consider the age and life expectancy of the beneficiary.xiii Such a high R 2 value is evidence of the existence of high multicollinearity of the explanatory variables.However, as pointed out by Wooldridge (2003, Ch. 3), multicollinearity is not such a serious problem, since it does not violate any of the assumptions of the OLS model, particularly that the estimators are not biased.xiv The latest date disclosed by Dataprev resulted in an average term of 31 months, but this precedes the extension of the maximum term to 60 months.For this reason, we decided to simulate data for terms of 36 and 60 months, also considering that some financial institutions charge different interest rates for loan periods.
of 2004, Brazil has experienced strong growth (averaging 10% a year as a proportion of GDP) in the balance of free credit (as opposed to directed lending under government programs).Starting in 2006 there was a sharp reduction of the average interest rate on such credit transactions, which fell from 54% a year in January 2006 to 44% in January 2008.These figures are shown in Graph 1 i .GRAPH 1: INTEREST RATE, SPREAD AND FREE CREDIT/GDP Source: BCB (Time Series/Economic Department)

br GRAPH 3: BALANCE OF CREDIT TRANSACTIONS -INDIVIDUALS (NOMINAL VALUES) Source
: DATAPREV, BCB Time Series/DEPEC) In December 2005 INSS deduction loans represented 34% of all automatic debit loans, and in December 2007 this figure was 35%.

Table 1 : Annual variation of credit transaction balances -individuals (%) Period
Table 2 shows the main rules for INSS deduction loans in force as of December 2007 until July 2008.

GRAPH 4: PAYROLL LOANS -INSS Source
: DATAPREV Note.Dataprev (the INSS database) does not have data for May 2006 and July 2007.

Table 4 : Rules on payroll loans to São Paulo Municipal Government employees (in effect as of April 2008) Item Maximum value
At the time the study was conducted, 56 banks had agreements with the INSS for deducting loan repayments, allowing them to extend payroll loans to social security beneficiaries.
Therefore, we examine the following hypotheses, null (H 0 ) and alternative (H 1 ): H 0 : Given the biometric risk (default by death), the rate of return obtained by banks on INSS deduction loans is equal to the rate of return on payroll loans to PMSP The data were gathered in the first half of June 2008 from 23 banks and are presented in Table 5. ix BBR, Braz.Bus.Rev. (Engl.ed., Online), Vitória, v. 7, n. 1, Art. 4, p. 59-88, jan -apr.2010www.bbronline.com.brHowever, it is necessary to consider that the PMSP deducts 2% of the installment transferred to the bank as a processing fee and to evaluate to what point this cost reduces the banks' rate of return on these loans, and at the same time to what point the greater biometric risk reduces the rate of return on loans to INSS beneficiaries.

Table 11 -Continued Values of l x and t P x estimated according to the approximation presented in
Fixed interest is the average rate (fixed in advance) charged on credit transactions with non-directed resources at the referential interest rate (the weighted average rate calculated by the Central Bank from a sample of most financial institutions).Analogously, the fixed spread is the average spread charged on credit transactions with free resources at the referential rate (fixed in advance).iiThe numbers refer to loans regulated by BCB Circular 2957 of December 30, 1999.The data are expressed in constant values of May 2008, updated by us according to the consumer price index (IPCA).iiiThe fact that many banks only managed to conclude agreements with the INSS for transfer of the deductions at the end of October 2004 can perhaps explain this acceleration.ivThe balances in the graph were updated by the consumer price index (IPCA) accumulated through December 2007.vPIS is the Contribution to the Social Integration Fund, COFINS is the Contribution to Finance Social Security, IOF is the Tax on Financial Transactions, IR is Income Tax and CSLL is Social Contribution on Net Profits."Contributions" are taxes whose revenues are earmarkedfor specific purposes instead of going into the general fund.In January 2008, when the CPMF (a of 0.38% on checks and other financial transfers) was not extended by the Senate, the government, to counteract the loss of revenue, increased the CSLL rate for financial institutions from 9% BBR, Braz.Bus.Rev.(Engl.ed., Online),Vitória, v. 7, n. 1, Art. 4, p. 59-88, jan -apr.2010www.bbronline.com.briThe expression Free Credit refers to the non-directed credit of the financial system, except with financial intermediaries.GDP is estimated by the Central Bank for 12 months at prices of the indicated month, using data from the IBGE, deflated by the centered IGP-DI (general market price index).BBR, Braz.Bus.Rev. (Engl.ed., Online), Vitória, v. 7, n. 1, Art. 4, p. 59-88, jan -apr.2010www.bbronline.com.brprovisional levy