Regularized Index-Tracking Optimal Portfolio Selection

Abstract

The aim of index-tracking approaches in portfolio optimization is to create a mimicking portfolio which tracks a specific market index. However, without regularization, this mimicking behavior of the index-tracking model is susceptible to the volatility in the market index and has negative effects on the tracking portfolio. We recast the index-tracking optimization problem by applying a form of regularization using the convex combination of 1 and squared 2 norm constraints on the portfolio weights. The proposed optimization model enables us to control the tracking performance and the sparsity structure of the portfolio simultaneously. A sample of assets from Borsa Istanbul (BIST) is used to demonstrate the performance of the regularized portfolios with various levels of regularization. Results indicated that the regularized portfolios obtained using this approach had better tracking performances with a desired sparsity structure compared to the standard index-tracking portfolio where no regularization is applied.

An enhanced GRASP approach for the index tracking problem

“…Finally, future work could analyze the performance of GRASP approaches for broader indexes, such as the Russell 1000 (Sant'Anna et al., 2020). In this research direction, it would be possible to evaluate the pros and cons of the mathematical programming models solved by GRASP against sparse regression approaches, where the latter has been providing competitive solutions when considering broader indexes (Benidis et al., 2018; Tas and Turkan, 2018; Sant'Anna et al., 2020).…”

“…Index tracking research is scattered in many different research areas, with a diverse set of solution approaches being proposed. Recently, the construction of tracking portfolios based on statistical techniques, such as cointegration (Sant'Anna et al., 2017a, 2019, 2020) and sparse regression (Benidis et al., 2018; Tas and Turkan, 2018; Sant'Anna et al., 2020), have been studied. Some researchers are also introducing machine learning techniques such as deep learning (Ouyang et al., 2019; Kwak et al., 2021) and clustering (Hong et al., 2021), and thus providing a new perspective on index tracking solution approaches, which is still evolving.…”