Performance of Publicly Mandated Private Pension Funds in Mexico:
Simulations with Transactions Cost
Tapen Sinha, Felípe Martínez and Constanza Barrios-Muñoz
Tapen Sinha is Seguros Comercial America Chair Professor of Risk
Management and Insurance at the Departamento Academico de Actuaria
y Seguros, Instituto Tecnologico Autonomo de Mexico (ITAM).
Felípe Martínez and Constanza Barrios-Muñoz are undergraduate
students in Actuarial Studies at ITAM.
On July 1 1997, a new privatized but compulsory retirement system came
into effect in Mexico. The new system has a complex web of contributions
by employers, employees and by the government. The retirement funds
also have a complex web of charges applied to the funds. Some funds
charge on the flow of contributions, others charge on total balance, and
yet others charge on the real rate of return earned. Thus, it is difficult to
determine which fund performs the best from the point of view of these
individual retirement account holders. We carefully analyze these complex
cases to find out which funds perform the best.
In order to perform the analysis, we develop a model of future value calculation
recursively. The usual calculation of standard future value formula does not
apply for the following reasons. (1) Charges do not apply to contributions to
the fund at a flat rate; the rate varies with the number of years in the fund.
(2) Charges on the balance of funds do not apply at a flat rate either.
(3) Charges applying on the real rate of return of the fund depends on the
nominal rate of return as well (for example, if the nominal rate of return is
equal or below the inflation rate, there are no charges).
(4) Charges do not apply to government contribution to the retirement fund
(which is in turn tied to the consumer price index with a lag of three months).
We show through simulations that the optimal strategy for individual retirement
account holder is not to stay with one fund throughout the working life. Instead,
the best option is to switch at some point. The switching point depends on a
number of factors:
(1) wage rate of the workers (and also on the growth rate of wages),
(2) real interest rate,
(3) inflation rate.