Research On Multifractal Portfolio Optimization Based On Denoising Method

The financial market is changing rapidly,and it is significant to establish and improve effective investment decision-making methods to improve asset risk management capabilities.This paper is based on the overall optimisation perspective of the model and the local optimisation perspective of the portfolio in a non-linear framework.The overall optimisation effect of denoising on the multiple fractal portfolio model is analysed from a macro perspective,and the multi-time investment value of various portfolios under different magnitude of volatility constraints is analysed from a local optimisation perspective.The Chinese-US stock market portfolios are selected to represent traditional financial markets and cryptocurrency portfolios to represent emerging financial markets,capturing the non-linear dependence structure between different markets and providing targeted investment recommendations.The empirical results show that(1)In terms of portfolio model optimisation,the non-linear multifractal portfolio model(Mean-MF-DCCA)is superior to the mean-variance portfolio model(M-V)for both traditional Chinese-US stock market portfolios and cryptocurrency portfolios;the multifractal portfolio model with variable modal decomposition denoising(VMD-Mean-MF-DCCA)outperforms the multifractal portfolio model.(2)Analyzing the impact of denoising on the effectiveness of multifractal portfolio strategies from a macro perspective,it is found that overlaying multifractal portfolio models with variational modal decomposition can optimize portfolio investment strategies for most time scales under volatility constraints of various magnitudes,compared with empirical modal decomposition and integrated empirical modal decomposition,which are less effective in denoising.For ChineseUS stock market portfolios,overlaying the variational modal decomposition method can reduce the risk due to the change of investment cycle and provide a more robust investment strategy for risk-averse investors.For cryptocurrency portfolios,overlaying the variational modal decomposition method can improve the investment efficiency and provide a more effective investment strategy for risk-averse investors.(3)The local characteristics of different portfolios under the non-linear framework suggest that when making portfolio investments in the ChineseUS stock markets,the non-linear dependency structure between variables in small fluctuations needs to be fully considered.when making portfolio investments in cryptocurrencies,investors need to be aware of the factors that cause large fluctuations in cryptocurrency prices,especially the impact of extreme events on cryptocurrency portfolios,and that short-term investments in cryptocurrency portfolios are inefficient and should be taken more advantage of Long-term investment value.(4)A cross-market portfolio of equities and cryptocurrencies does not yield better investment returns.