ABSTRACT
Team performance of the Mexican Football League (Liga MX), measured as the percentage of the total points obtained during each short tournament, is analyzed using Dynamic Factor Models (DFMs). The estimation of the common components is carried out with Principal Components and the stochastic nature of the DFM is studied through Panel Analysis of Non-stationarity in Idiosyncratic and Common Components. The results reveal that there are two common factors, one being possibly non-stationary. These factors show an interesting dynamic behavior in the league and allow to split the teams into two groups, namely, top competitors and emerging or relegated teams. Some discussion is given in this direction.
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.