Xu Wu

This study is the first to use the Bayesian Estimator of Abrupt Change, Seasonality, and Trend (BEAST) algorithm to detect trend change points in the nexuses between the green bond index (Green Bond) and WTI of crude oil, gasoline, as well as natural gas futures. The COVID-19 pandemic and the Russia–Ukraine war are identified as common significant trend change points, and the total sample is subsequently divided into three stages based on these points. Utilizing a skewed MF-DCCA method, this study analyzed the skewed multifractal characteristics between the Green Bond and the energy futures across these stages. The results revealed that both the multifractal characteristics and risk levels experienced significant changes across different periods, exhibiting skewed multifractality. Specifically, from the pre-pandemic period to the post-Russia–Ukraine conflict period, the multifractal features and risk of the Green Bond and WTI and Green Bond and Gasoline groups first declined and then increased, while the Green Bond and Natural Gas group displayed an opposite trend, showing an initial increase followed by a decline. A portfolio analysis further indicated that Green Bond provided effective hedging against all three types of energy futures, particularly during crisis periods. Notably, the portfolios constructed using the Mean-MF-DCCA model, which incorporated multifractal features, outperformed those constructed by traditional portfolio models. These findings offered new insights into the dynamic characteristics of the Green Bond and energy futures markets and provided important policy implications for portfolio optimization and risk management strategies.

Since the discovery of momentum effect, people have started the journey of using the momentum effect to construct momentum strategies. As a result of coupling cross-sectional and time-series momentum strategy, dual momentum strategy (DM strategy) has been widely used in practice and closely followed by academics. To address the shortcoming of the classical DM strategy that has not considered the multi-fractal characteristics of the stock market, we construct the fractal dual momentum strategy (FDM strategy) from the two aspects of optimizing the ranking index of the cross-sectional momentum strategy by using fractal statistical measures and improving the timing selection of the time-series momentum strategy by using the trend entropy dimension. The empirical results show that the FDM strategy outperforms the DM strategy. Both in terms of the size and stability of the strategy returns, the FDM strategy shows an optimization effect compared with the DM strategy, which is beneficial to provide investors with better decision-making references.

An effective portfolio selection model is constructed on the premise of measuring accurately the risk and return on assets. According to the reality that asset returns obey the asymmetric power-law distribution, this paper first builds two fractal statistical measures, fractal expectation and fractal variance to measure the asset returns and risks, inspired by the method of measuring the curve length in the fractal theory. Then, by incorporating the fractal statistical measure into the return–risk criterion, a portfolio selection model based on the fractal statistical measure is established, namely, the fractal portfolio selection model, and the closed-form solution of the model is given. Finally, through empirical analysis, it is found that under the constraints of typical factual characteristics that the asset returns obey the asymmetric power-law distribution, the fractal portfolio is better than the traditional portfolio as a whole, which not only can improve the investment performance but also has better robustness. The validity of the fractal investment portfolio is experimentally tested.

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.

In recent years, the extreme risk events occurred frequently in the financial market have not only brought huge losses to investors and inflicted heavy losses on the market, but also posed a severe challenge for the traditional effective market hypothesis. These extreme risk events are often accompanied by sudden plummeting of liquidity. Different from the efficient market hypothesis(EMT), firstly, this paper studies the nonlinear fluctuation characteristics and causes of contracts with different maturity periods in China stock index futures market under the framework of fractal market theory and using the multifractal detrended fluctuation model Secondly, under the framework of the fractal market theory, the existence of the liquidity spillover effect between the stock index futures and spot is tested, the direction, intensity, and contribution of spillover between stock index futures and spot are analyzed. Finally, there is a robustness test. The study finds that both stock index futures and stock index spot in China have obvious nonlinear fractal fluctuation characteristics, and stock index futures have higher degree of multifractal, the characteristics are related to correlated multifractal and distributed multifractal; the longer the maturity period of the stock index futures contract, the lower the multifractal degree; there are significant asymmetric liquidity spillover effects between the stock index futures and spot; the multifractal degree has an important influence on the intensity and contribution of the liquidity spillover effect, and the multifractal degree is inversely proportional to the intensity of liquidity spillover and the contribution of spot to futures fluctuations.

Under the realistic background that the capital market nowadays is a fractal market, this paper embeds the detrended cross-correlation analysis (DCCA) into the return-risk criterion to construct a Mean-DCCA portfolio model, and gives an analytical solution. Based on this, the validity of Mean-DCCA portfolio model is verified by empirical analysis. Compared to the mean-variance portfolio model, the Mean-DCCA portfolio model is more conducive for investors to build a sophisticated investment portfolio under multi-time-scale, improve the performance of portfolios, and overcome the defect that the mean-variance portfolio model has not considered the existence of fractal correlation characteristics between assets.