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Stochastic Portfolio Theory: A Machine Learning Perspective

Author

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  • Yves-Laurent Kom Samo
  • Alexander Vervuurt
Abstract
In this paper we propose a novel application of Gaussian processes (GPs) to financial asset allocation. Our approach is deeply rooted in Stochastic Portfolio Theory (SPT), a stochastic analysis framework introduced by Robert Fernholz that aims at flexibly analysing the performance of certain investment strategies in stock markets relative to benchmark indices. In particular, SPT has exhibited some investment strategies based on company sizes that, under realistic assumptions, outperform benchmark indices with probability 1 over certain time horizons. Galvanised by this result, we consider the inverse problem that consists of learning (from historical data) an optimal investment strategy based on any given set of trading characteristics, and using a user-specified optimality criterion that may go beyond outperforming a benchmark index. Although this inverse problem is of the utmost interest to investment management practitioners, it can hardly be tackled using the SPT framework. We show that our machine learning approach learns investment strategies that considerably outperform existing SPT strategies in the US stock market.

Suggested Citation

  • Yves-Laurent Kom Samo & Alexander Vervuurt, 2016. "Stochastic Portfolio Theory: A Machine Learning Perspective," Papers 1605.02654, arXiv.org.
    • Handle: RePEc:arx:papers:1605.02654
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    File URL: http://arxiv.org/pdf/1605.02654
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    References listed on IDEAS

    as
    1. Adrian Banner & Daniel Fernholz, 2008. "Short-term relative arbitrage in volatility-stabilized markets," Annals of Finance, Springer, vol. 4(4), pages 445-454, October.
    2. Winslow Strong, 2012. "Generalizations of Functionally Generated Portfolios with Applications to Statistical Arbitrage," Papers 1212.1877, arXiv.org, revised Oct 2013.
    3. Ioannis Karatzas & Johannes Ruf, 2016. "Trading Strategies Generated by Lyapunov Functions," Papers 1603.08245, arXiv.org.
    4. Alexander Vervuurt & Ioannis Karatzas, 2015. "Diversity-weighted portfolios with negative parameter," Annals of Finance, Springer, vol. 11(3), pages 411-432, November.
    5. L C G Rogers & Pawel Zaczkowski, 2013. "Monte Carlo approximation to optimal investment," Papers 1305.3433, arXiv.org.
    6. Alexander Vervuurt & Ioannis Karatzas, 2015. "Diversity-Weighted Portfolios with Negative Parameter," Papers 1504.01026, arXiv.org, revised Jul 2015.
    7. Ting-Kam Wong, 2015. "Optimization of relative arbitrage," Annals of Finance, Springer, vol. 11(3), pages 345-382, November.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Ali Al-Aradi & Sebastian Jaimungal, 2018. "Outperformance and Tracking: Dynamic Asset Allocation for Active and Passive Portfolio Management," Papers 1803.05819, arXiv.org, revised Jul 2018.
    2. Chendi Ni & Yuying Li & Peter Forsyth & Ray Carroll, 2020. "Optimal Asset Allocation For Outperforming A Stochastic Benchmark Target," Papers 2006.15384, arXiv.org.
    3. 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.
    4. Christa Cuchiero & Wahid Khosrawi & Josef Teichmann, 2020. "A generative adversarial network approach to calibration of local stochastic volatility models," Papers 2005.02505, arXiv.org, revised Sep 2020.
    5. Steven Campbell & Qien Song & Ting-Kam Leonard Wong, 2024. "Macroscopic properties of equity markets: stylized facts and portfolio performance," Papers 2409.10859, arXiv.org, revised Oct 2024.
    6. Yuanrong Wang & Tomaso Aste, 2021. "Dynamic Portfolio Optimization with Inverse Covariance Clustering," Papers 2112.15499, arXiv.org, revised Jan 2022.
    7. Zihao Zhang & Stefan Zohren & Stephen Roberts, 2020. "Deep Learning for Portfolio Optimization," Papers 2005.13665, arXiv.org, revised Jan 2021.
    8. Ali Al-Aradi & Sebastian Jaimungal, 2018. "Outperformance and Tracking: Dynamic Asset Allocation for Active and Passive Portfolio Management," Applied Mathematical Finance, Taylor & Francis Journals, vol. 25(3), pages 268-294, May.
    9. Ali Al-Aradi & Sebastian Jaimungal, 2019. "Active and Passive Portfolio Management with Latent Factors," Papers 1903.06928, arXiv.org.
    10. Chao Zhang & Zihao Zhang & Mihai Cucuringu & Stefan Zohren, 2021. "A Universal End-to-End Approach to Portfolio Optimization via Deep Learning," Papers 2111.09170, arXiv.org.

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