Sparse Tracking of Stock Indices with Principal Component Analysis and LASSO
Sparse Tracking of Stock Indices with Principal Component Analysis and LASSO

Author(s): Mateusz Andrzejewski, Piotr Wójcik
Subject(s): Financial Markets
Published by: Wydawnictwa Uniwersytetu Warszawskiego
Keywords: Principal Component Analysis; LASSO; sparse portfolio; index tracking
Summary/Abstract: Index tracking is a passive investment strategy attempting to replicate the behaviour of a selected index. As indices are not traded instruments, fund managers need to construct portfolios mimicking the index by selecting appropriate assets. The simplest approach, namely buying all assets contained in the index, minimises the tracking error, but incurs significant trading costs. This paper applied Principal Component Analysis and LASSO regression to the task of creating replicating portfolios with small cardinality and good out-of-sample tracking performance. We conducted the analysis for a set of Polish and German indices and found that while PCA is quite successful at creating diversified, well-performing sparse portfolios, the tracking error of LASSO-based portfolios is much lower. Tracking performance of both methods is affected by market development and index capitalisation. The results indicate better outcomes for developed market and positive impact of capitalisation on sparse index performance.

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