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Multistage allocation problem for Mexican pension funds.

Andrés García-Medina1,2, Norberto A Hernández-Leandro2, Graciela González Farías3

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Target Date Fund (TDF) strategies applied to Mexican pension systems show similar investment glide-paths across various forecasting models. The GARCH(1,1) model with a fixed covariance matrix offered the best risk-return trade-off.

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Area of Science:

  • Financial Economics
  • Pension Fund Management
  • Quantitative Finance

Background:

  • The Mexican pension system operates under a specific regulatory framework influencing investment strategies.
  • Target Date Funds (TDFs) are increasingly utilized for retirement planning, requiring robust allocation models.
  • Multistage allocation problems necessitate sophisticated approaches to manage risk and return over time.

Purpose of the Study:

  • To solve the multistage allocation problem for the Mexican pension system using TDF strategies.
  • To analyze investment trajectories (glide-paths) across 14 heterogeneous assets over a 161-quarter horizon.
  • To evaluate the impact of different forecasting models and covariance matrix estimations on TDF performance.

Main Methods:

  • Employed Target Date Fund (TDF) strategy within regulatory constraints.
  • Estimated expected returns using GARCH(1,1), EGARCH(1,1), and GJR-GARCH(1,1) models.
  • Utilized a stationary block bootstrap as a benchmark and assessed fixed historical and DCC-GARCH(1,1) covariance matrices.
  • Quantified asymmetric dependencies using transfer entropy.

Main Results:

  • Observed highly similar glide-paths across various forecasting models, indicating robustness of the TDF structure.
  • Identified the GARCH(1,1) model with a fixed historical covariance matrix as yielding the highest Sharpe ratio.
  • Confirmed that glide-paths transition from risky assets to bonds over time, as expected.

Conclusions:

  • The proposed methodology is computationally efficient and suitable for realistic TDF implementation in pension systems.
  • Investment strategy structure remains consistent regardless of the specific forecasting model used.
  • Optimal risk-return trade-off achieved with GARCH(1,1) and a fixed covariance matrix highlights its effectiveness.