The Cost of Minimum Pension Guarantee

Tapen Sinha, ING Chair Professor, ITAM and Professor, University of Nottingham, UK

tapen@itam.mx

What is the problem we study? Governments often promise a minimum level

of benefits under an accumulation scheme If future does not turn out to be rosy, what is

the likelihood that the government has to foot the bill of this guarantee? How much would it cost?

Using the actual experience of the past eight years, and including actual features of the Mexican system, we calculate the probability distribution of such promises

The Chilean Experience

To make the reform in Chile in 1981 more acceptable, the Chilean government issued a guarantee of a minimum pension

At the time, the calculations indicated that very few people will actually fall back on it

Two unexpected outcomes First, instead of a 80-90% density, the average

worker had 50-60% density Second, the management fees ate up between 20

and 25% of contributions

Pension System in Mexico

Investment Regime

Minimum Pension Guarantee

Model

Results

Conclusions

Current Mexican pension regime (for the formal sector)

In 1997, Mexico moved from a defined benefits system (a la US Social Security) to a defined contribution system (a la Chile)

The system is publicly mandated but funds are privately managed

The funds are called AFORES (Administradoras de Fondos para el Retiro)

There are three components to each fund: government component, private compulsory component and private voluntary component

There is a government contribution

There is also a government guarantee

Contribution is 6.5% of the base salary (SBC)There are three component

Worker

Employer

1.125%

Monthly Contribution as percentage of SBC

5.150%

0.225%

6.5%

Govt

TOTAL

Other Contributions

This is called Cuota Social (cs). 5.5% of minimum wage indexed for inflation

Each individual can also make voluntary contribution to the system. But such funds are maintained separately

Note: There is an upper limit to the SBC equivalent to 25 times the minimum wage

Pension System in Mexico

Investment Regime

Minimum Pension Guarantee

Model

Results

Conclusions

Investment regime under the new system

The AFORES invest in special funds called SIEFORES.

Until 2004, the SIEFORES had extremely restricted investment regimes. For example, investment in anything other than high grade inflation protected bonds were not allowed

In January 2005, new investments were allowed such as foreign bonds in currencies other than pesos as well as in other instruments provided that capital is protected from erosion (through synthetic instruments such as futures and options)

ACTUAL INVESTMENT STRUCTURE IN THE PENSION SYSTEM

SIEFORE-1

SIEFORE-2

Allowed Financial Instruments & Limits Affiliated Workers

Debt Instruments with inflation protection – lower limit 51%

Foreign Debt – up to 20%

Assigned Workes

Workers over 56 years old

Workers who choose to invest under this SIEFORE

Foreign Instruments – up to 20%

Equity Notes – up to 15%

Workers under 56 years

  SIEFORE Fund 1 SIEFORE Fund 2

Type 

Upper Limit

 Upper Limit

Government bonds √ 100% √ 100%

Private debt with ratings mxA-1+ and mxAAA1 √ 100% √ 100%

Private debt with ratings mxA-1 and mxAA[1] √ 35% √ 35%

Private debt with ratings mxA-2 and mxA1 √ 5% √ 5%

Value of foreign debt √ 20%    

Foreign debt     √ 20%

Structured notes with capital protection     √ 15%

[1] Private debt with ratings by Standard & Poor’s

Pension System in Mexico

Investment Regime

Minimum Pension Guarantee

Model

Results

Conclusions

The nature of minimum pension guarantee

The government promises to pay a minimum level of benefits if the amount of money accumulated in the worker’s account does not reach certain minimum value

What does the government promise?

The Federal Government promises the equivalent of one minimum wage to any worker who has contributed to the new system for 1250 weeks or 24 years (even if it is not continuous)

The government promises to pay an annuity of one minimum salary for life for each worker in the system

A digression on minimum wage Real Minimum Wage 1944-2005

0

10

20

30

40

50

60

1943 1953 1963 1973 1983 1993 2003

Although small today, the number of people who become beneficiaries of this promise is rising

Source: IMSS data

Number of people entitled to minimum pension guaranteethousands,2005

Government burden of such a guarantee isrising...(millions of pesos)

1997 1999 2001 2003 2005 1998 2000 2002 2004

4.34

3.5

2.8

2.2

1.7

1.3.9

.19

86

66

49

35

25

17

8

1 to 3 MW

4 to 5 MW

6 to 10 MW

More than 10 MW

....and this will continue to rise because the workers under the regime largely have low wages (with over half earning no more than 3 times the minimum wage)

M.W.= Minimum Waves

Source: IMSS

55.68%

20.65%

15.06%8.6%

Salary level of workers under the IMSS system2004

Pension System in Mexico

Investment Regime

Minimum Pension Guarantee

Model to Calculate the Cost of the M.P.G.

Results

Conclusions

The model is as follows: The first element describes the distribution of the variable rate of return, the second describes the law of motion, the third is a contribution at each period taking into account the commission charged

),( 2MMMt Normalr

ttftr

t CVrVV Mte )1)(1(1

csVComAFOREC ttit )065(. ,

Equity Returns

Accumulation

Contribution

No commission

The rate of return is the actual rate that prevailed during 1997-2005 in Mexico

= 0.00757452 equivalent of 9.48% annual

= 7.12315%

Adjusted Log Likelihood = 135.017

For the riskless rate, we took the real rate of return of Bondes182 (a government bond with inflation indexation)

rf = 4.63% annual

Monthly rate of return of the Mexican broad market index IPC was indeed Normal during 1997-2005

-3

-2

-1

0

1

2

3

-.20 -.15 -.10 -.05 .00 .05 .10 .15 .20

IPC

Nor

mal

Qua

ntile

Theoretical Quantile-Quantile

Underlying assumptions for running simulations

- Retirement Age. 65 years

- Contribution period. 25 and 40 years respectively

- Contribution Rate. 6.5% of base salary

- Contribution frequency. Monthly

- Commissions. We use the actual and projected commission structure

taking into account the loyalty discounts offered by some AFORES

- Inflation. We calculate everything in real terms

Measuring the guarantee costWe can conceptually think of the guarantee cost as an implicit put option for the government at the retirement age

Where

PMG: Price of a contingent annuity that pays the equivalent of one minimum salary in real terms

VT: Funds accumulated in the worker’s individual account at retirement

Payoff (T) = max{ PMG – VT , 0}

PMGVT

Pa

yo

ff

We could value the option using traditional Black Scholes option pricing model (it requires risk neutral valuation and the assumption of complete contingent markets)

Simulation

Cashflows

Average

1,000 realizations of the final amount for each level of salary assuming different levels of investment in equity

We calculate the present value for each trajectory

The average payment is the value of the option

We need to calculate the single premium contingent annuity of one minimum salary (the government guarantee)

The net premium for such an annuity is calculated using the following euqation

)1(*))1.9(.*( )12()12(97 smfääSMP xxy

Where

SM97: Minimum salary current in 1997 but brought forward to 2005

f : Administrative and acquisition fee 1%

sm: Security Margin of 2%

We also assume that at retirement the worker is married and his spouse is

four years younger than him (average in Mexico)

*We use the mortality table used by the Mexican Social Security

Pension System in Mexico

Investment Regime

Minimum Pension Guarantee

Model to Calculate the Cost of the M.P.G.

Results

Conclusions

50%

100%

25%

75%

5 MW3 MW

10 MW 25 MW

1 MW

0

0.2

0.4

0.6

0.8

1

*Measured in multiples of minimum wage

PROBABILITY TO EXERCISE THE GUARANTEE UNDER THE ASSUMPTION THAT THE WORKER CONTRIBUTES TO THE SYSTEM DURING 40 YEARS

Probability

Income* Equity Fraction

 MARKETLambda

Percentage Invested in Equity

INCOME* 0% 25% 50% 75% 100%

1 1.000 0.549 0.268 0.224 0.231

2 1.000 0.103 0.103 0.115 0.142

3 0 0.008 0.024 0.055 0.087

5 0 0 0.005 0.022 0.042

10 0 0 0 0.003 0.009

25 0 0 0 0 0

WHEN WE REDUCE THE CONTRIBUTION TIME TO 25 YEARS, THE RESULTS CHANGE DRAMATICALLY

 MARKET Lambda

Percentage Invested in Equity

INCOME*0% 25% 50% 75% 100%

1 1.000 1.000 0.967 0.829 0.728

2 1.000 1.000 0.863 0.680 0.603

3 1.000 1.000 0.694 0.499 0.443

5 1.000 0.893 0.327 0.284 0.297

10 0 0 0.034 0.058 0.099

25 0 0 0 0.001 0.0060

50%

100%

25%

75%

5 MW3 MW

10 MW 25 MW

1 MW

0

0.2

0.4

0.6

0.8

1

Equity Fraction

Income*

Probability

*Measured in multiples of minimum wage

Option value

N

SF

PROBPNSFi

BSi

BSBSi

,

,

PROBBS Probability of exercising the MPG

option for the workers whose base salary is BSBS Base salary

SFi,BS Final accumulated sum for indvidual i with initial salary BS

PN Net premium cost for the MPGN Number of times the experiment is conducted.

15%

50%

75%

100%

5 MW

10 MW

1 MW3 MW

25 MW

50,000

100,000

150,000

200,000

250,000

Equity Fraction

Income*

Option Price

We also calculate the cost of the option for the government

 MARKET Lambda

Percentage Invested in Equity

INCOME*0% 25% 50% 75% 100%

1 216 201 158 127 116

2 181 161 103 85 81

3 147 119 63 50 54

5 78 42 21 24 32

10 0 0 1 3 7

25 0 0 0 .073 .256

Option price, 25 yearsthousands

*Measured in multiples of minimum wage

The cost of this promise can be 0.5-2% of GDP foreverWhat can the government do to minimize this problem? It can encourage people to invest larger proportion in stocks rather than bonds (by setting the default option)

It can change the contribution rate (currently set at 6.5% of the salary) to something higher (and that will make it similar to other countries in the region

What we DO know from the simulations is that even by eliminating management fees for the low income workers, it will not make a big difference in government liabilities (neither will modest rise in income)

Wage Equation Estimated

4.6

4.65

4.7

4.75

4.8

4.85

4.9

4.95

5

5.05

5.1

5.15

20 25 30 35 40 45 50 55 60 65

Age

log

(Wa

ge)

male

female

48.22 years

Wage Equation Estimated

4.6

4.65

4.7

4.75

4.8

4.85

4.9

4.95

5

5.05

5.1

5.15

20 25 30 35 40 45 50 55 60 65

Age

log

(Wa

ge)

male

female

48.22 years

Time

Wage

Young

Old

Observations from data….that leads to….

1997 2005

20s 30s 40s 50s 60s

Wage…the following lifetime wage profile

0.7

0.9

1.1

1.3

1.5

1.7

1.9

2.1

2.3

Mar-97 Aug-98 Dec-99 May-01 Sep-02 Feb-04

m60m55m50m45m40m35m30m25m20m15

Males in Quintile 3

Time

Wage rate Stylized Fact

Men in 20s

Men in 30s

Men in 40s

Men in 50s

Pension System in Mexico

Investment Regime

Minimum Pension Guarantee

Model to Calculate the Cost of the M.P.G.

Results

Conclusions

CONCLUSIONS

Minimum pension guarantee is present to serve a social purpose: protecting low income individuals from falling into poverty

But it also binds the government to future costs High commission (between 20% and 30% of contribution)

directly affect the minimum pension guarantee: therefore, governments should seriously consider strategies for reducing commissions

The capital protection regulation currently in place does not eliminate all downside risks

While allowing for investment in broad stock indexes can increase upside for the workers, it can significantly increase the burden for the government especially for low income workers