The Application of Discrete Hilbert transform in Measuring Asset Return Risk in Investment Portfolios

https://doi.org/10.35912/jakman.v6i2.3803
Published: Mar 11, 2025

Abstract:

Abstract
Purpose: This study aims to explore the application of the discrete Hilbert transform (DHT) in measuring asset return risk within a portfolio, emphasizing its potential for enhancing risk evaluation in the field of financial mathematics.
Methodology/approach: The research utilized a quantitative approach with data sourced from publicly available historical stock prices. Analysis was conducted using software MATLAB to implement the discrete Hilbert transform, which transforms time-series data into phase and amplitude components. The portfolio risk was calculated based on the transformed data, and the results were compared against traditional risk metrics such as variance and Value at Risk (VaR).
Results/findings: The findings indicate that the discrete Hilbert transform provides additional insights into portfolio risk by capturing frequency-domain characteristics of asset returns. It complements traditional measures, offering a novel perspective on risk analysis. Specifically, the discrete Hilbert transform was effective in identifying subtle changes in risk patterns that were not apparent in time-domain analyses alone.
Conclusion: This study investigates the application of the discrete Hilbert transform (DHT) in measuring the risk of asset returns within investment portfolios, specifically focusing on Indonesian stocks. The
Limitations: This study is limited by its focus on a small sample of stocks within a single financial market, which may restrict the generalizability of the findings. Additionally, the research does not account for macroeconomic factors that could influence asset returns.
Contribution: This study contributes to the field of financial risk management by introducing the discrete Hilbert transform as a supplementary tool for risk analysis. It offers practical implications for portfolio managers, actuaries, and financial analysts seeking innovative methods to enhance risk assessment and decision-making processes.

Keywords:
1. Asset Return Risk
2. Discrete Hilbert Transform
3. Investment Portfolio
Authors:
1 . Wahyuni Ekasasmita
2 . Khaera Tunnisa
https://orcid.org/0000-0002-8193-4133
3 . Muh. Tri Aditya
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How to Cite
Ekasasmita, W., Tunnisa, K., & Aditya, M. T. . (2025). The Application of Discrete Hilbert transform in Measuring Asset Return Risk in Investment Portfolios. Jurnal Akuntansi, Keuangan, Dan Manajemen, 6(2), 399–408. https://doi.org/10.35912/jakman.v6i2.3803
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Issue & Section
Vol. 6 No. 2 (2025): Maret
Articles
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  2. Aliev, R., & S?m?dova, L. (2023). Boundedness of the discrete Hilbert transform in discrete Hölder spaces. Baku Mathematical Journal, 2, 47–56. https://doi.org/10.32010/j.bmj.2023.04.
  3. Allen, S. (2012). Financial Risk Management: A Practitioner’s Guide to Managing Market and Credit Risk (2nd edition). Wiley.
  4. Angelovska, J. (2013). Managing market risk with VaR (Value at Risk). Journal of Contemporary Management Issues, 18(2), 81-96.
  5. Antonius, R., & Tampubolon, L. D. (2019). Analisis penghindaran pajak, beban pajak tangguhan, dan koneksi politik terhadap manajemen laba. Jurnal Akuntansi, Keuangan dan Manajemen, 1(1), 39-52.
  6. Brown, A. (2015). Financial Risk Management For Dummies (1st ed). For Dummies.
  7. Ekasasmita, W., Tunnisa, K., & Aditya, M. T. (2024). Forecasting Nonstationary Time Series Based on Dicrete Hilbert Transform. Statistics, Optimization & Information Computing. http://www.iapress.org/index.php/soic/article/view/2060.
  8. Erickson, K. H. (2015). Financial Risk Management: A Simple Introduction.
  9. Majidah, I., Rahim, A., & Bahri, M. (2024). Mean Variance Complex-Based Portfolio Optimization. Statistics, Optimization & Information Computing, 12(5), 1382–1396. https://doi.org/10.19139/soic-2310-5070-2023.
  10. Karlina, B., & Sanoyo, A. M. (2021). Pengaruh Cluster Emiten terhadap Return Saham JSX Berbasis Parameter Rasio Analisa Fundamental. Jurnal Akuntansi, Keuangan dan Manajemen, 2(4), 279-291.
  11. Kolari, J., Liu, W., & Pynnonen, S. (2024). Net Long Portfolio Risk Analyses. Springer Nature. (169–189). https://doi.org/10.1007/978-3-031-48169-7_9.
  12. Li, B., Zhou, R., He, Q., & Li, H. (2024). A generation expansion planning method considering conditional value-at-risk. Journal of Physics: Conference Series, 2782, 012055. https://doi.org/10.1088/1742-6596/2782/1/012055.
  13. Li, Y., & Yuan, Q. (2019). Phaseless inverse discrete Hilbert transform and determination of signals in shift?invariant space. Mathematical Methods in the Applied Sciences, 42(12), 4511-4527. https://doi.org/10.1002/mma.5631.
  14. Manganelli, S., & Engle, R. (2001). Value at Risk Models in Finance. SSRN Electronic Journal. https://doi.org/10.2139/ssrn.356220.
  15. Matei, V., & Buz, A. (2023). Behavioural finance perspective in theory of international portfolio investment. Economics. Finances. Law, 4(1), 85–89. https://doi.org/10.37634/efp.2023.4.19.
  16. Miller, M. B. (2018). Quantitative Financial Risk Management (1st edition). Wiley.
  17. Qian, R. (2023). Management of Personal Finances and Investment Decisions. Advances in Economics, Management and Political Sciences, 64, 202–212. https://doi.org/10.54254/2754-1169/64/20231532.
  18. Seyedbarhagh, S., Laaksonen, H., & Karimi, M. (2024). Assessing Economic Performance of an Energy Microgrid: A Conditional Value-at-Risk Optimization Approach (pp. 227–233). https://doi.org/10.1007/978-3-031-59005-4_25.
  19. Sugitomo, S., & Maeta, K. (2020). Quaternion Valued Risk Diversification. Entropy, 22(4), 390. https://doi.org/10.3390/e22040390.
  20. Uchiyama, Y., Kadoya, T., & Nakagawa, K. (2019). Complex Valued Risk Diversification. Entropy, 21(2), 119. https://doi.org/10.3390/e21020119.