Abstract
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.
Highlights
At present, population aging poses substantial economic challenges to most of the governments of the world
This implies that the worker’s resources stay in the same fund, the long-term investment strategy of which is adjusted with respect to risk exposure and the age of the employee
The model was successfully applied to stock markets in [27, 31, 32], to daily average prices of energy products in [33], and to predict crypto and wold currencies in [34]. While all these models may be appropriate for modelling certain forms of the leverage effect in volatility, they offer no distinct advantage over the f-GARCH asymmetric models for our modelling purposes
Summary
Population aging poses substantial economic challenges to most of the governments of the world. In TDF, the investment portfolio is restructured reducing its share of risky assets as the worker approaches the retirement date This implies that the worker’s resources stay in the same fund (unlike the DC system in which funds were transferred from one SIEFORE to another), the long-term investment strategy of which is adjusted with respect to risk exposure and the age of the employee. We attempt to solve the TDF problem for the case of Mexico To this end, we implement a function that obtains an optimal asset allocation strategy and simultaneously allows maximizing a generation’s target wealth under the investment limits established by the new regulation.
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