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Optimization study of momentum investment strategies under asymmetric power-law distribution of return rate

  • Xu Wu , Kun Wang EMAIL logo , Linlin Zhang and Chong Peng
Published/Copyright: November 11, 2022
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Studies in Nonlinear Dynamics & Econometrics
From the journal Studies in Nonlinear Dynamics & Econometrics Volume 27 Issue 5

Abstract

In the context that the tails of security returns obey an asymmetric power-law distribution, this paper constructs two fractal statistical measures based on fractal theory: fractal expectation and fractal variance. Subsequently, a new momentum strategy is constructed by introducing the fractal measures into the momentum strategy as measures of returns and risks to optimize the selection criterion. Finally, the empirical results show that the new momentum strategy outperforms the traditional momentum strategy and the risk-adjusted momentum strategy, confirming the effectiveness of fractal expectation and fractal variance.

Keywords: asymmetric power-law distribution; fractal expectation; fractal variance; momentum strategy; risk-adjusted momentum strategy
Corresponding author: Kun Wang, School of Business, Chengdu University of Technology, Chengdu, China, E-mail:

Funding source: National Natural Science Foundation of China

Award Identifier / Grant number: 71903017

Funding source: National Social Science Foundation of China

Award Identifier / Grant number: 17BJY188

  1. Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: National Natural Science Foundation of China, Funder ID: https://doi.org/10.13039/501100001809 (Grant Number: 71,903,017); National Social Science Fund of China, Funder ID: https://doi.org/10.13039/501100012456 (Grant Number: 17BJY188).

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

References

Asness, C. S., T. J. Moskowitz, and L. H. Pedersen, 2013. “Value and Momentum Everywhere.” The Journal of Finance 68 (3): 929–85. https://doi.org/10.1111/jofi.12021.Search in Google Scholar

Cakici, N., F. J. Fabozzi, and S. Tan. 2013. “Size, Value, and Momentum in Emerging Market Stock Returns.” Emerging Markets Review 16: 46–65. https://doi.org/10.1016/j.ememar.2013.03.001.Search in Google Scholar

Choi, J., Y. S. Kim, and I. Mitov. 2015. “Reward-risk Momentum Strategies Using Classical Tempered Stable Distribution.” Journal of Banking and Finance 58: 194–213. https://doi.org/10.1016/j.jbankfin.2015.05.002.Search in Google Scholar

Cont, R. 2001. “Empirical Properties of Asset Returns: Stylized Facts and Statistical Issues.” Quantitative Finance 1 (2): 223–36. https://doi.org/10.1080/713665670.Search in Google Scholar

Dong, T. N., N. D. Yang, and Y. G. Shao. 2008. “Analysis of Chinese Open-End Fund Investment Styles.” Management Review 20 (7): 3–9.Search in Google Scholar

Fama, E. F. 1965. “The Behavior of Stock Market Prices.” Journal of Business 38 (1): 34–105. https://doi.org/10.1086/294743.Search in Google Scholar

Fama, E. F. 1991. “Efficient Capital Market: II.” The Journal of Finance 46 (5): 1575–617. https://doi.org/10.1111/j.1540-6261.1991.tb04636.x.Search in Google Scholar

Jegadeesh, N., and S. Titman. 1993. “Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency.” The Journal of Finance 48 (1): 65–91. https://doi.org/10.1111/j.1540-6261.1993.tb04702.x.Search in Google Scholar

Kantelhardt, J. W., S. A. Zschiegner, E. Koscielny-Bunde, S. Havlin, A. Bunde, and H. E. Stanley. 2002. “Multifractal Detrended Fluctuation Analysis of Nonstationary Time Series.” Physica A: Statistical Mechanics and its Applications 316 (1): 87–114, https://doi.org/10.1016/s0378-4371(02)01383-3.Search in Google Scholar

Lim, G., S. Y. Kim, H. Lee, K. Kim, and D. Lee. 2007. “Multifractal Detrended Fluctuation Analysis of Derivative and Spot Markets.” Physica A: Statistical Mechanics and its Applications 286 (1): 259–66, https://doi.org/10.1016/j.physa.2007.07.055.Search in Google Scholar

Lim, B. Y., J. G. Wang, and Y. Q. Yao. 2018. “Time-series Momentum in Nearly 100 Years of Stock Returns.” Journal of Banking & Finance 97: 283–96. https://doi.org/10.1016/j.jbankfin.2018.10.010.Search in Google Scholar

Ku, S., C. Lee, W. Chang, and J. W. Song. 2020. “Fractal Structure in the S&P500: A Correlation-Based Threshold Network Approach.” Chaos, Solitons and Fractals 137: 109848, https://doi.org/10.1016/j.chaos.2020.109848.Search in Google Scholar

Mandelbrot, B. B. 1963. “The Variation of Certain Speculative Prices.” Journal of Business 36 (4): 394–419. https://doi.org/10.1086/294632.Search in Google Scholar

Menkhoff, L., L. Sarno, M. Schmeling, and A. Schrimpf. 2012. “Currency Momentum Strategies.” Journal of Financial Economics 106 (3): 660–84, https://doi.org/10.1016/j.jfineco.2012.06.009.Search in Google Scholar

Muga, L., and R. Santamaria. 2009. “The Momentum Effect in the Mexican Stock Exchange.” Trimestre Economico 76 (302): 433–63.10.20430/ete.v76i302.533Search in Google Scholar

Nnadi, M., and S. Tanna. 2019. “Accounting Analyses of Momentum and Contrarian Strategies in Emerging Markets.” Asia-Pacific Journal of Accounting and Economics 26 (4): 457–77. https://doi.org/10.1080/16081625.2017.1284596.Search in Google Scholar

Pirie, S., and R. K. T. Chan. 2018. “A Two-Stage Study of Momentum Investing in Asia: A Case of Cognitive Dissonance?” Research in International Business and Finance 44: 340–9. https://doi.org/10.1016/j.ribaf.2017.07.102.Search in Google Scholar

Rachev, S., T. Jašić, S. Stoyanov, and F. Fabozzi. 2007. “Momentum Strategies Based on Reward–Risk Stock Selection Criteria.” Journal of Banking & Finance 31 (8): 2325–46, https://doi.org/10.1016/j.jbankfin.2007.02.006.Search in Google Scholar

Rouwenhorst, K. G. 1998. “International Momentum Strategies.” The Journal of Finance 1 (18): 267–84. https://doi.org/10.1111/0022-1082.95722.Search in Google Scholar

Shi, H. L., and W. X. Zhuo. 2017. “Time Series Momentum and Contrarian Effects in the Chinese Stock Market.” Physica A: Statistical Mechanics and its Applications 483: 309–18. https://doi.org/10.1016/j.physa.2017.04.139.Search in Google Scholar

Tang, W. M., Y. X. Tang, and H. Y. Yang. 2020. “The Research of Equity Premium Puzzle under Investors’ Heterogeneity.” Journal of Statistics and Information 35 (8): 64–72.Search in Google Scholar

Tilfani, O., P. Ferreira, and M. Y. Boukfaoui. 2019. “Building Multi-Scale Portfolios and Efficient Market Frontiers Using Fractal Regressions.” Physica A: Statistical Mechanics and its Applications 532: 121758. https://doi.org/10.1016/j.physa.2019.121758.Search in Google Scholar

Wang, Y., L. Li, and R. Gu. 2009. “Analysis of Efficiency for Shenzhen Stock Market Based on Multifractal Detrended Fluctuation Analysis.” International Review of Financial Analysis 18 (5): 271–6. https://doi.org/10.1016/j.irfa.2009.09.005.Search in Google Scholar

Warusawitharana, M. 2018. “Time-varying Volatility and the Power Law Distribution of Stock Returns.” Journal of Empirical Finance 49: 123–41. https://doi.org/10.1016/j.jempfin.2018.09.004.Search in Google Scholar

Wu, X., G. Song, Y. Deng, and L. Xu. 2015. “Study on Conversion between Momentum and Contrarian Based on Fractal Game.” Fractals - Complex Geometry, Patterns, and Scaling in Nature and Society 23 (3): 1550025, https://doi.org/10.1142/s0218348x15500255.Search in Google Scholar

Yao, C., C. Liu, and W. Ju. 2020. “Multifractal Analysis of the WTI Crude Oil Market, US Stock Market and EPU.” Physica A: Statistical Mechanics and its Applications 550: 124096. https://doi.org/10.1016/j.physa.2019.124096.Search in Google Scholar

Yuan, Y., X. T. Zhuang, and X. Jin. 2009. “Measuring Multifractality of Stock Price Fluctuation Using Multifractal Detrended Fluctuation Analysis.” Physica A: Statistical Mechanics and its Applications 388 (11): 2189–97. https://doi.org/10.1016/j.physa.2009.02.026.Search in Google Scholar

Supplementary Material

The online version of this article offers supplementary material (https://doi.org/10.1515/snde-2022-0020).

Received: 2022-03-01
Accepted: 2022-10-18
Published Online: 2022-11-11

© 2022 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Research Article
  3. Analysis of heterogeneous duopoly game with information asymmetry based on extrapolative mechanism
  4. Review
  5. Modelling volatility dependence with score copula models
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https://doi.org/10.1515/snde-2022-0020
Keywords for this article
asymmetric power-law distribution; fractal expectation; fractal variance; momentum strategy; risk-adjusted momentum strategy

Articles in the same Issue

  1. Frontmatter
  2. Research Article
  3. Analysis of heterogeneous duopoly game with information asymmetry based on extrapolative mechanism
  4. Review
  5. Modelling volatility dependence with score copula models
  6. Research Articles
  7. A new test for non-linear hypotheses under distributional and local parametric misspecification
  8. Optimization study of momentum investment strategies under asymmetric power-law distribution of return rate
  9. Comparison of Score-Driven Equity-Gold Portfolios During the COVID-19 Pandemic Using Model Confidence Sets
  10. Integrated variance of irregularly spaced high-frequency data: A state space approach based on pre-averaging
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