## Dynamic Asset Allocation for Bivariate Enhanced Index Tracking using Sparse PLS

published: Aug. 21, 2009, recorded: July 2009, views: 568

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# Description

Index tracking is a popular portfolio management strategy which involves creating a portfolio whose returns track very closely those achieved by a benchmark index. There are two interconnected problems associated with index tracking: asset selection and asset allocation. Asset selection involves selecting a subset of p out of n available assets, whereas asset allocation involves investing a proportion of the total available capital in each one of the p assets with the objective of reproducing the performance of the index. The capital invested in asset i is in proportion i of the total capital so that Pp i=1 i = 1. These portfolio weights are generally estimated by minimzing the tracking error, that is the error between the index returns yt and the portfolio returns ˆy, given by T−1PT t=1(yt − ˆyt)2. Following this setting, the problem of asset allocation becomes a standard regression problem with the portfolio weights being the parameters to be estimated. In the literature, only a few attempts have been made to tackle both the asset selection and allocation problems at the same time; for instance, [8] use a quadratic programming approach and the method in [3] is based on genetic algorithms. Our interest lies in taking a unified approach which simultaneously selects a subset of assets in the available basket and minimizes the tracking error. We take a regularized regression approach. In a full index replication scenario, asset selection can be thought of as assigning certain assets a zero weight, so that those assets are not included in the portfolio, whereas the selected one should be able to reproduce the index. These ideas have recently been exploited in the context of minimum variance portfolios and L1-penalized least squares have been proved to be a promising method for creating robust portfolios [4]; see also the related work by [5]. We extend on these ideas in three main ways. Firstly, we consider a multivariate version of the index tracking problem, where the selected portfolio is expected to reproduce the performance of multiple indices. Secondly, we are interested in enhanced versions of the indices to be tracked so that the portfolio is also expected to overperform each index by a given annual percentage return (say, plus 15%). Thirdly, we propose a methodology that works well in real-time and is fully adaptive, in the sense that both the asset allocation and optimization solutions can be updated in a recursive manner, keeping the number of computations low, every time new data points are made available. This last feature makes the methodology more robust against non-stationarities presented in the data and yelds superior tracking results, before transaction costs.

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