The role of momentum factor on an investment portfolio formation

The fundamental issue of an investor is to find the best possible portfolio given her/his constraints. In order for an investor to build such portfolio, she/he has to predict the risk and the return of the its assets. The work on risk measurement is generally associated to the portfolio optimization techniques over the covariance matrix.
The question of prediction derives from the early work that tests the efficient market hypothesis [1-2] and the finding that some variables have forecasting ability. In order to reconcile these findings, behavioral finance became prominent and tries to link abnormal returns to psychological bias. Behavioral finance has attempted to explain why some strategies are able to be systematically profitable and at the same time this line of research has generated an enormous list of what has been termed stock factors [3]. The identification of such factors has been put to practical use as risk factors in order to help covariance matrix estimation and optimization and today it is a large industry.
Here we propose an alternative method to those based on the correlation ma-trix. Recently, it was found that risk adjusted performance of a time series momen-tum strategy appears to present two phases [4]. The first phase is mainly driven by autocorrelation while the second phase is driven by the drift. By following [4] we ex-tend the work from one stocks to a portfolio and we show how understand the mo-mentum strategy performance in terms of autocorrelation, drift and cross time lag cor-relation.
First we use as a benchmark the patterns we get from artificial data generated from random matrices [5]. After that we use real data and we compare both to present our findings. One interesting aspect here is that in present approach the random matrix can be asymmetric, which admit complex eigenvalues. Portfolio also may involve different market sector which lead to a network formation where nodes are stocks and the links are associated to the strength of the cross correlation connecting those assets.
Finally, to apply this methodology or technique we study data set before and after marked crashes. Here we focused on the momentum factor. The methodology presented here may be extended to analyze other factors or to study nonlinear momentum factor model.