The fractal characteristics of the security market were considered in portfolio strategy optimization. First, the detrended cross-correlation analysis was adopted to measure the fractal correlation of different securities. Second, the fractal correlation was embedded into the mean-variance criterion of the modern portfolio theory. Third, the mean-detrended cross-correlation analysis portfolio strategy of multiple risk assets was constructed, and the analytic solution of the strategy was given. Finally, the evaluation results revealed that the constructed the mean-detrended cross-correlation analysis portfolio strategy clearly improved investment performance, thus achieving the goal of optimizing the multiple risk asset portfolio strategy.
BaptistaA M. 2012. “Portfolio selection with mental accounts and background risk[J].” Journal of Banking and Finance36, 4: 968‐980.
2.
ChunW DLiH SXuW. 2020. Portfolio Model Under Fractal Market Based on Mean-DCCA[J]. Fractals.
3.
ClementsAAScottASilvennoinen. 2019. “Volatility-dependent correlations: further evidence of when, where and how[J].” Empirical Economics57, 2: 505‐540.
4.
ContR. 2001. “Empirical properties of assets returns: stylized facts and statistical issues[J].” Quantitative Finance1, 2: 223‐236.
5.
FabozziF JFGuptaH MMarkowitz. 2002. “The Legacy of Modern Portfolio Theory[J].” The Journal of Investing11, 3: 7‐22.
6.
FerreiraPE A LPereiraM F DSilva, et al.2019. “Detrended correlation coefficients between oil and stock markets: The effect of the 2008 crisis[J].” Physica A: Statal Mechanics and Its Applications517: 86‐96.
7.
GiorgiE DTHensJMayer. 2011. “A note on reward-risk portfolio selection and two-fund separation[J].” Finance Research Letters8, 2: 52‐58.
8.
GoddardJEOnali. 2009. “Unifractality and multifractality in the Italian stock market[J].” International Review of Financial Analysis18, 4: 154‐163.
9.
GuoXR HChanW KWong, et al.2019. “Mean-variance, mean-VaR, and mean-CVaR models for portfolio selection with background risk[J].” Risk Management-An International Journal21, 2: 73‐98.
10.
HuangX.2017. “A review of uncertain portfolio selection[J].” Journal of Intelligent & Fuzzy Systems32, 6: 4453‐4465.
11.
HuyH TH NHuuL N TThuy. 2016. “Relationship between Financial Liberalization and Economic Growth in Emerging Economies: The Case of Vietnam[J].” Journal of Asian Business and Economic Studies23, 1: 25‐49.
12.
IkedaT. A detrended cross correlation analysis for stock markets of the United States, Japan, and the Europe[J]. 2017a, 484: 194-198.
13.
IkedaT. 2017b. “A fractal analysis of world stock markets[J].” Economics Bulletin37, 3: 1514‐1532.
14.
IqbalJK JLoneLHussain, et al.2020. “Detrended cross correlation analysis (DCCA) of radon, thoron, temperature and pressure time series data[J].” Physica Scripta95, 8: 085213.
15.
KalayciC BOErtenliceM AAkbay. 2019. “A comprehensive review of deterministic models and applications for M-V portfolio optimization[J].” Expert Systems with Applications125: 345‐368.
16.
KamaliRSMahmoodiM TJahandideh. 2019. “Optimization of multi-period portfolio model after fitting best distribution[J].” Finance Research Letters30: 44‐50.
17.
KarpAGVan Vuuren. 2019. “Investment Implications of The Fractal Market Hypothesis[J].” Annals of Financial Economics14, 1: 1950001.
18.
LiJXWuLZhang, et al.2020. “Research on the portfolio model based on Mean-MF-DCCA under multifractal feature constraint[J].” Journal of Computational and Applied Mathematics386, 2021: 113264.
19.
LiangCYWeiYZhang. 2020a. “Is implied volatility more informative for forecasting realized volatility: An international perspective[J].” Journal of Forecasting39, 8: 1253‐1276.
20.
LiangCLTangYLiYWei. 2020b. “Which sentiment index is more informative to forecast stock market volatility? Evidence from China[J].” International Review of Financial Analysis71: 101552.
21.
LiemN TT HSonH TNghia. 2016. “Factors Affecting Bank Risk-Taking: Evidence from Southeast Asian Countries[J].” Journal of Asian Business and Economic Studies23, 2: 120‐136.
22.
LinAPShangXZhao. 2011. “The cross-correlations of stock markets based on DCCA and time-delay DCCA[J].” Nonlinear Dynamics67, 1: 425‐435.
23.
MarkowitzH M. 1991. “Foundations of portfolio theory[J].” The Journal of Finance46, 2: 469‐477.
24.
MarkowitzH M. 1952. “Portfolio Selection[J].” The Journal of Finance7, 1: 77‐91.
25.
MedoMC HYeungY CZhang. 2009. “How to quantify the influence of correlations on investment diversification[J].” International Review of Financial Analysis18, 1–2: 34‐39.
26.
MertonR C.1972. “An analytical derivation of the efficient portfolio frontier[J].” Journal of Financial and Quantitative Analysis7, 4: 1851‐1872.
27.
NesazH HMJasemiLMonplaisir. 2019. “A New methodology for Multi-period Portfolio Selection based on the Risk Survey of Lower Partial Moments[J].” Expert Systems with Applications144: 113032.
28.
OmidMEAkbarSAbbas. 2019. “Collective mental accounting: an integrated behavioural portfolio selection model for multiple mental accounts[J].” Quantitative Finance19, 2: 265‐275.
29.
PantaleoE. 2011. “When do improved covariance matrix estimators enhance portfolio optimization? An empirical comparative study of nine estimators[J].” Quantitative Finance11, 7: 1067‐1080.
30.
PautRRSabatierMTchamitchian. 2019. “Reducing risk through crop diversification: An application ofportfolio theory to diversified horticultural systems[J].” Agricultural Systems168: 123‐130.
31.
PengC KSHavlinH EStanley, et al.1995. “Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series[J]. Chaos.” An Interdisciplinary Journal of Nonlinear Science5, 1: 82‐87.
PodobnikBH EStanley. 2008. “Detrended Cross-Correlation Analysis: A New Method for Analyzing Two Non-stationary Time Series[J].” Physical Review Letters100, 8: 084102.
34.
PuertoJMRodriguez-MadrenaAScozzari. 2020. “Clustering and portfolio selection problems: A unified framework[J].” Computers & Operations Research117: 104891.
35.
QuangT T. 2014. “Factors Affecting Liquidity Risk in the System of Vietnamese Commercial Banks[J].” Journal of Asian Business and Economic Studies219: 34‐48.
36.
QuekGCAtkinson. 2017. “Portfolio selection in discrete time with transaction costs and power utility function: a perturbation analysis[J].” Applied Mathematical Finance24, 2: 77‐111.
37.
SotiropoulosD PJRutterford. 2019. “Financial diversification strategies before World War I: Buy-and-hold versus naïve portfolio selection[J].” Business History61, 7: 1175‐1198.
38.
SupanantaroekSRLensinkNHansen. 2017. “The Impact of Social and Financial Education on Savings Attitudes and Behavior Among Primary School Children in Uganda[J].” Evaluation Review41, 6: 511‐541.
39.
TangYP FZhu. 2018. “Portfolio Strategies of Shanghai & Hong Kong Stock Markets from the Perspective of Fractal Theory[J].” Systems Engineering—Theory & Practice38, 09: 2188‐2201.
40.
VanD NH NTrongK NSon. 2017. “Economic growth: The role of knowledge economy in the context of selected Asian countries[J].” Journal of Asian Business and Economic Studies24, 1: 04‐31.
41.
WaltersCRPreston. 2018. “Net income risk, crop insurance and hedging[J].” Agricultural Finance Review78, 1: 135‐151.
42.
WangTZJinJWei. 2020. “M-V portfolio Selection under a Non-Markovian Regime-Switching Model: Time-Consistent Solutions[J].” SIAM Journal on Control and Optimization57, 5: 3249‐3271.
43.
WuXW DChunYLinY ZLi. 2018. “Identification of momentum life cycle stage of stock price[J].” Nonlinear Dynamics94, 1: 249‐260.
44.
WuXLZhangJLi, et al.2021. “Fractal statistical measure and portfolio model optimization under power-law distribution[J].” The North American Journal of Economics and Finance58, 2: 101496.
45.
XuQYZhouCJiang, et al.2016. “A large CVaR-based portfolio selection model with weight constraints[J].” Economic Modelling59: 436‐447.
46.
XuW JXDengJLi. 2015. “A new fuzzy portfolio model based on background risk using MCFOA[J].” International Journal of Fuzzy Systems17, 2: 246‐255.
47.
ZhangYFMaYWang. 2019. “Forecasting crude oil prices with a large set of predictors: Can LASSO select powerful predictors?[J].” Journal of Empirical Finance54: 97‐117.
48.
ZhangW GY JLiuW JXu. 2012. “A possibilistic mean-semivariance-entropy model for multi-period portfolio selection with transaction costs[J].” European Journal of Operational Research222, 2: 341‐349.
49.
ZhaoXPShangJHuang. 2017. “Several fundamental properties of DCCA cross-correlation coefficient[J].” Fractals25, 2: 1750017.
50.
ZhouW X.2008. “Multifractal detrended cross-correlation analysis for two nonstationary signals[J].” Physical Review E77, 6: 066211.
