Multistage allocation problem for Mexican pension funds

The problem of multistage allocation is solved using the Target Date Fund (TDF) strategy subject to a set of restrictions which model the latest regulatory framework of the Mexican pension system. The investment trajectory or glide-path for a representative set of 14 assets of heterogeneous characteristics is studied during a 161 quarters long horizon. The expected returns are estimated by the GARCH(1,1), EGARCH(1,1), GJR-GARCH(1,1) models, and a stationary block bootstrap model is used as a benchmark for comparison. A fixed historical covariance matrix and a multi-period estimation of DCC-GARCH(1,1) are also considered as inputs of the objective function. Forecasts are evaluated through their asymmetric dependencies as quantified by the transfer entropy measure. In general, we find very similar glide-paths so that the overall structure of the investment is maintained and does not rely on the particular forecasting model. However, the GARCH(1,1) under a fixed historical covariance matrix exhibits the highest Sharpe ratio and in this sense represents the best trade-off between wealth and risk. As expected, the initial stages of the obtained glide-paths are initially dominated by risky assets and gradually transition into bonds towards the end oof the trajectory. Overall, the methodology proposed here is computationally efficient and displays the desired properties of a TDF strategy in realistic settings.