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Portfolio Optimization with Sparse Multivariate Modelling

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  • Pier Francesco Procacci
  • Tomaso Aste

Abstract

Portfolio optimization approaches inevitably rely on multivariate modeling of markets and the economy. In this paper, we address three sources of error related to the modeling of these complex systems: 1. oversimplifying hypothesis; 2. uncertainties resulting from parameters' sampling error; 3. intrinsic non-stationarity of these systems. For what concerns point 1. we propose a L0-norm sparse elliptical modeling and show that sparsification is effective. The effects of points 2. and 3. are quantifified by studying the models' likelihood in- and out-of-sample for parameters estimated over train sets of different lengths. We show that models with larger off-sample likelihoods lead to better performing portfolios up to when two to three years of daily observations are included in the train set. For larger train sets, we found that portfolio performances deteriorate and detach from the models' likelihood, highlighting the role of non-stationarity. We further investigate this phenomenon by studying the out-of-sample likelihood of individual observations showing that the system changes significantly through time. Larger estimation windows lead to stable likelihood in the long run, but at the cost of lower likelihood in the short-term: the `optimal' fit in finance needs to be defined in terms of the holding period. Lastly, we show that sparse models outperform full-models in that they deliver higher out of sample likelihood, lower realized portfolio volatility and improved portfolios' stability, avoiding typical pitfalls of the Mean-Variance optimization.

Suggested Citation

  • Pier Francesco Procacci & Tomaso Aste, 2021. "Portfolio Optimization with Sparse Multivariate Modelling," Papers 2103.15232, arXiv.org.
  • Handle: RePEc:arx:papers:2103.15232
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    References listed on IDEAS

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    12. Pier Francesco Procacci & Tomaso Aste, 2018. "Forecasting market states," Papers 1807.05836, arXiv.org, revised May 2019.
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    Cited by:

    1. Wang, Yuanrong & Aste, Tomaso, 2023. "Dynamic portfolio optimization with inverse covariance clustering," LSE Research Online Documents on Economics 117701, London School of Economics and Political Science, LSE Library.
    2. Yuanrong Wang & Tomaso Aste, 2021. "Dynamic Portfolio Optimization with Inverse Covariance Clustering," Papers 2112.15499, arXiv.org, revised Jan 2022.
    3. Isobel Seabrook & Fabio Caccioli & Tomaso Aste, 2021. "An Information Filtering approach to stress testing: an application to FTSE markets," Papers 2106.08778, arXiv.org.
    4. Seabrook, Isobel & Caccioli, Fabio & Aste, Tomaso, 2022. "Quantifying impact and response in markets using information filtering networks," LSE Research Online Documents on Economics 115308, London School of Economics and Political Science, LSE Library.
    5. Antonio Briola & Tomaso Aste, 2022. "Dependency structures in cryptocurrency market from high to low frequency," Papers 2206.03386, arXiv.org, revised Dec 2022.
    6. Yuanrong Wang & Antonio Briola & Tomaso Aste, 2023. "Topological Portfolio Selection and Optimization," Papers 2310.14881, arXiv.org.

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