Mean Variance Complex-Based Portfolio Optimization
Keywords:
Mean Variance (MV), Mean Variance Complex-Based, Hilbert Transform, Portfolio Construction
Abstract
Mean-Variance (MV) is a method that collects several assets using appropriate weight intending to maximize profits and to reduce risk. Stock market conditions are very volatile, mean variance method does not reach stock market fluctuation well because MV method is only limited to one time period. This study proposes a mean variance complex-based approach that transforms real returns into complex returns by using Hilbert transform to construct an optimal mean-variance portfolio based on complex returns and then find its dynamic asset allocation. The results show that with the same risk tolerance, the mean variance complex-based approach outperforms MV method in profits, losses, and portfolio performance tests. Keywords Mean Variance (MV), Mean Variance Complex-Based, Hilbert Transform, Portfolio ConstructionReferences
1. Fisher, K. L., & Statman, M. The mean–variance-optimization puzzle: Security portfolios and food portfolios. Financial Analysts Journal, 53(4), 41-50, 1997.
2. Gunning, Wade dan Vuuren, Gary Van. Optimal Omega-Ratio Portfolio Performance Constrained by Tracking Error, Investment Management and Financial Innovations, 2020, Vol. 17, Issue 3, 2020.
3. Guo, X., Jiang, X., Wong, W.-K. Stochastic Dominance and Omega Ratio: Measures to Examine Market Efficiency, Arbitrage Opportunity, and Anomaly. Economies, 5, 38. https://doi.org/10.3390/economies5040038, 2017.
4. Gusliana, S. A., & Salih, Y. Mean-Variance Investment Portfolio Optimization Model Without Risk-Free Assets in Jii70 Shar, Operations Research: International Conference Series, Vol. 3, No. 3, 101-106, 2022.
5. Kandel S, Stambaugh RF., A mean–variance framework for tests of asset pricing models, The Review of Financial Studies, Vol. 2 No.2, 125–56, 1989.
6. Kapsos, M., Christofides, N. & Rustem, B., Worst-case robust Omega ratio. European Journal of Operational Research, vol. 234(2), pages 499-507, 2014.
7. Keating, C. & Shadwick, W. F, A Universal Performance Measure. Journal of Performance Measurement, Vol. 6, 59-84, 2002.
8. Kurbatsky, V.G., Sidorov, D.N., Spiryaev, V.A. et al., Forecasting nonstationary time series based on Hilbert-Huang transform and machine learning, Automat Remote Control 75, 922–934, 2014
9. Li, H., Bai, Z., Wong, W., & McAleer, M., Spectrally-Corrected Estimation for High-Dimensional Markowitz Mean-Variance Optimization, Econometrics and Statistics, Volume 24, 133-150, 2022.
10. Ma, S., Ma, X., Xia, L., An optimistic value iteration for mean–variance optimization in discounted Markov decision processes, Results in Control and Optimization, Volume 8, 100165, 2022.
11. Malhotra, D.K., Mooney, T., Poteau, R., Russel, P., Assessing the Performance and Risk-Adjusted Returns of Financial Mutual Funds, Int. J. Financial Study, Volume 11, 136. https://doi.org/10.3390/ijfs11040136, 2023.
12. Markowitz, H., Portfolio Selection. Journal of Finance, 77-91, 1952.
13. Mba, J.C. Ababio, K.A. Agyei, S.K., Markowitz Mean-Variance Portfolio Selection and Optimization under a Behavioral Spectacle: New Empirical Evidence, Int. J. Financial Stud., 10, 28. https://doi.org/10.3390/ijfs10020028, 2022.
14. Robbani, M. G., & Jain, A., Is the S&P100 Index a Mean-Variance Efficient Portfolio?, International Journal of Financial Research, Vol. 7, No. 5, 2016.
15. Rosadi, D., Setiawan, E. P., Tempi, M., & Filzmoser, P.,Robust Covariance Estimators for Mean-Variance Portfolio Optimization with Transaction Lots, Operation Research Perspectives, 100154, 2020.
16. Soeryana, E., Fadhlina, N., Rusyaman, E., & Supian, S., Mean-variance portfolio optimization by using time series approaches based on logarithmic utility function. IOP Conference Series: Materials Science and Engineering, Vol. 166, No. 1, p. 012003, 2017.
17. Sugitomo, S., & Maeta, K., Quaternion Valued Risk Diversification. Entropy, 22, 390, 2020.
18. Tobin, J., Liquidity Preference as Behavior Towards Risks, The Review Economic Studies, Vol. 25 No. 2, 65-86, 1958.
19. Uchiyama, Y., Kadoya, T., & Nakagawa, K., Complex Valued Risk Diversification. Entropy, 21, 119, 2019.
20. Yu, Jin Rung, et al., Omega portfolio models with floating return threshold, International Review of Economics & Finance, Vol. 82, pages 743-758, ISSN 1059-0560, 2022.
21. Zhou, C., Yang, L., Liu, Y., & Yang, Z., A novel method for computing the Hilbert transform with Haar Multiresolution Approximation, Journal of Computational and Applied Mathematics, 585-597, 2009.
22. Zhuo W, Shao L, Yang H., Mean–variance analysis of option contracts in a two-echelon supply chain, European Journal of Operational Research. Volume 271, Issue 2, 535-547, 2018.
2. Gunning, Wade dan Vuuren, Gary Van. Optimal Omega-Ratio Portfolio Performance Constrained by Tracking Error, Investment Management and Financial Innovations, 2020, Vol. 17, Issue 3, 2020.
3. Guo, X., Jiang, X., Wong, W.-K. Stochastic Dominance and Omega Ratio: Measures to Examine Market Efficiency, Arbitrage Opportunity, and Anomaly. Economies, 5, 38. https://doi.org/10.3390/economies5040038, 2017.
4. Gusliana, S. A., & Salih, Y. Mean-Variance Investment Portfolio Optimization Model Without Risk-Free Assets in Jii70 Shar, Operations Research: International Conference Series, Vol. 3, No. 3, 101-106, 2022.
5. Kandel S, Stambaugh RF., A mean–variance framework for tests of asset pricing models, The Review of Financial Studies, Vol. 2 No.2, 125–56, 1989.
6. Kapsos, M., Christofides, N. & Rustem, B., Worst-case robust Omega ratio. European Journal of Operational Research, vol. 234(2), pages 499-507, 2014.
7. Keating, C. & Shadwick, W. F, A Universal Performance Measure. Journal of Performance Measurement, Vol. 6, 59-84, 2002.
8. Kurbatsky, V.G., Sidorov, D.N., Spiryaev, V.A. et al., Forecasting nonstationary time series based on Hilbert-Huang transform and machine learning, Automat Remote Control 75, 922–934, 2014
9. Li, H., Bai, Z., Wong, W., & McAleer, M., Spectrally-Corrected Estimation for High-Dimensional Markowitz Mean-Variance Optimization, Econometrics and Statistics, Volume 24, 133-150, 2022.
10. Ma, S., Ma, X., Xia, L., An optimistic value iteration for mean–variance optimization in discounted Markov decision processes, Results in Control and Optimization, Volume 8, 100165, 2022.
11. Malhotra, D.K., Mooney, T., Poteau, R., Russel, P., Assessing the Performance and Risk-Adjusted Returns of Financial Mutual Funds, Int. J. Financial Study, Volume 11, 136. https://doi.org/10.3390/ijfs11040136, 2023.
12. Markowitz, H., Portfolio Selection. Journal of Finance, 77-91, 1952.
13. Mba, J.C. Ababio, K.A. Agyei, S.K., Markowitz Mean-Variance Portfolio Selection and Optimization under a Behavioral Spectacle: New Empirical Evidence, Int. J. Financial Stud., 10, 28. https://doi.org/10.3390/ijfs10020028, 2022.
14. Robbani, M. G., & Jain, A., Is the S&P100 Index a Mean-Variance Efficient Portfolio?, International Journal of Financial Research, Vol. 7, No. 5, 2016.
15. Rosadi, D., Setiawan, E. P., Tempi, M., & Filzmoser, P.,Robust Covariance Estimators for Mean-Variance Portfolio Optimization with Transaction Lots, Operation Research Perspectives, 100154, 2020.
16. Soeryana, E., Fadhlina, N., Rusyaman, E., & Supian, S., Mean-variance portfolio optimization by using time series approaches based on logarithmic utility function. IOP Conference Series: Materials Science and Engineering, Vol. 166, No. 1, p. 012003, 2017.
17. Sugitomo, S., & Maeta, K., Quaternion Valued Risk Diversification. Entropy, 22, 390, 2020.
18. Tobin, J., Liquidity Preference as Behavior Towards Risks, The Review Economic Studies, Vol. 25 No. 2, 65-86, 1958.
19. Uchiyama, Y., Kadoya, T., & Nakagawa, K., Complex Valued Risk Diversification. Entropy, 21, 119, 2019.
20. Yu, Jin Rung, et al., Omega portfolio models with floating return threshold, International Review of Economics & Finance, Vol. 82, pages 743-758, ISSN 1059-0560, 2022.
21. Zhou, C., Yang, L., Liu, Y., & Yang, Z., A novel method for computing the Hilbert transform with Haar Multiresolution Approximation, Journal of Computational and Applied Mathematics, 585-597, 2009.
22. Zhuo W, Shao L, Yang H., Mean–variance analysis of option contracts in a two-echelon supply chain, European Journal of Operational Research. Volume 271, Issue 2, 535-547, 2018.
Published
2024-06-06
How to Cite
Izza Anis Majidah, Rahim, A., & Bahri, M. (2024). Mean Variance Complex-Based Portfolio Optimization. Statistics, Optimization & Information Computing. Retrieved from http://iapress.org/index.php/soic/article/view/2023
Issue
Section
Research Articles
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