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TPLVM: Portfolio Construction by Student's $t$-process Latent Variable Model

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  • Yusuke Uchiyama
  • Kei Nakagawa

Abstract

Optimal asset allocation is a key topic in modern finance theory. To realize the optimal asset allocation on investor's risk aversion, various portfolio construction methods have been proposed. Recently, the applications of machine learning are rapidly growing in the area of finance. In this article, we propose the Student's $t$-process latent variable model (TPLVM) to describe non-Gaussian fluctuations of financial timeseries by lower dimensional latent variables. Subsequently, we apply the TPLVM to minimum-variance portfolio as an alternative of existing nonlinear factor models. To test the performance of the proposed portfolio, we construct minimum-variance portfolios of global stock market indices based on the TPLVM or Gaussian process latent variable model. By comparing these portfolios, we confirm the proposed portfolio outperforms that of the existing Gaussian process latent variable model.

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  • Yusuke Uchiyama & Kei Nakagawa, 2020. "TPLVM: Portfolio Construction by Student's $t$-process Latent Variable Model," Papers 2002.06243, arXiv.org.
    • Handle: RePEc:arx:papers:2002.06243
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    References listed on IDEAS

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    1. Stephen A. Ross, 2013. "The Arbitrage Theory of Capital Asset Pricing," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 1, pages 11-30, World Scientific Publishing Co. Pte. Ltd..
    2. Olivier Ledoit & Michael Wolf, 2017. "Nonlinear Shrinkage of the Covariance Matrix for Portfolio Selection: Markowitz Meets Goldilocks," The Review of Financial Studies, Society for Financial Studies, vol. 30(12), pages 4349-4388.
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    6. Rajbir-Singh Nirwan & Nils Bertschinger, 2018. "Applications of Gaussian Process Latent Variable Models in Finance," Papers 1806.03294, arXiv.org, revised Apr 2019.
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    Cited by:

    1. Kei Nakagawa & Yusuke Uchiyama, 2020. "GO-GJRSK Model with Application to Higher Order Risk-Based Portfolio," Mathematics, MDPI, vol. 8(11), pages 1-12, November.
    2. Patrick Toman & Nalini Ravishanker & Nathan Lally & Sanguthevar Rajasekaran, 2023. "Latent Autoregressive Student- t Prior Process Models to Assess Impact of Interventions in Time Series," Future Internet, MDPI, vol. 16(1), pages 1-17, December.
    3. Julia Adamska & Łukasz Bielak & Joanna Janczura & Agnieszka Wyłomańska, 2022. "From Multi- to Univariate: A Product Random Variable with an Application to Electricity Market Transactions: Pareto and Student’s t -Distribution Case," Mathematics, MDPI, vol. 10(18), pages 1-29, September.
    4. Donghun Lee, 2022. "Knowledge Gradient: Capturing Value of Information in Iterative Decisions under Uncertainty," Mathematics, MDPI, vol. 10(23), pages 1-20, November.
    5. Yusuke Uchiyama & Kei Nakagawa, 2022. "Schr\"{o}dinger Risk Diversification Portfolio," Papers 2202.09939, arXiv.org.

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