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Adaptive online portfolio strategy based on exponential gradient updates

Abstract

Based on the momentum principle and adaptive learning mechanism, we design online portfolio selection strategies, which are suitable for nonstationary financial market. Firstly, we propose a Moving-window-based Adaptive Exponential Gradient (MAEG) strategy, which updates the learning rate of the EG algorithm by maximizing the recent cumulative return using the price data in a fixed length moving window. Secondly, we consider a special case where all-historical price data is used to design another strategy named Adaptive Exponential Gradient (AEG). Finally, we conduct an extensive numerical analysis using real price data and the empirical results show that the performance of the proposed strategies is steadily superior to some online strategies. In addition, MAEG and AEG are able to withstand certain transaction costs, which further supports their practical applicability in trading applications.

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Notes

  1. 1.

    Comb. 1 contains the following stocks: Alcoa, GM, IBM, Kin Ark, Kodak; Comb. 2 contains the following stocks: Alcoa, American Brands, GM, IBM, Kin Ark, Kodak; Comb. 3 contains the following stocks: Dupont, Ford, GE, GM, IBM, Kin Ark; Comb. 4 contains the following stocks: AHP, Dupont, Ford, GE, GM, IBM, JNJ, Kin Ark, MMM, Sherman Williams; Comb. 5 contains the following stocks: 600757, 600171, 000060, 000830, 000750; Comb. 6 contains the following stocks: 600757, 600171, 000060, 000830, 000750, 000930; Comb. 7 contains the following stocks: 600757, 600171, 000060, 000830, 000750, 000930, 000062, 600060; Comb. 8 contains the following stocks: 000858, 000725, 600585, 600028, 600741, 000898, 600104, 600115, 600027, 600016, 000625, 000069, 600674, 600036, 600663, 000063, 000157, 600066, 000415, 000627, 600271, 600118, 600886, 000768, 600018, 600170, 600068, 600177, 002044.

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Acknowledgements

This research was supported by the National Natural Science Foundation of China (No. 71501049), the Humanities and Social Science Foundation of the Ministry of Education of China (No. 21YJA630117) and the Philosophy and Social Sciences Planning Project of Guangdong Province (GD19CGL06).

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Correspondence to Xingyu Yang.

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Zhang, Y., Lin, H., Zheng, L. et al. Adaptive online portfolio strategy based on exponential gradient updates. J Comb Optim (2021). https://doi.org/10.1007/s10878-021-00800-7

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Keywords

  • Online portfolio selection
  • Adaptive strategy
  • Exponential gradient
  • Learning rate
  • Quantitative finance

Mathematics Subject Classification

  • 91G10