Portfolio Based On EMD Denoising Algorithms For Stock Market

Constructing an effective portfolio to diversify investments can not only help investors minimize the risks they face in stock market,but also potentially increase the expected returns.However,due to the existence of incomplete and asymmetric information,etc,financial time series are usually noisy.An easily ignored fact is that portfolio allocation is sensitive to noise in practice,If ignoring the existence of noise,the empirical results undoubtedly carry the distortion risks,Besides,it’s difficult for investors to obtain an effective and robust portfolio allocation strategy.With the increase of investment risk in current market,how to reduce noise interference on portfolio investment becomes an issue requiring urgent attention.At present,scholars have tried to introduce popular denoising algorithms,such as wavelet denoising,into portfolio management to solve the noise interference.Compared with popular denoising algorithms such as wavelet denoising,EMDbased denoising has the advantages of adaptivity,low operational difficulty,and wide applicability.However,the study of analyzing portfolios based on EMD denoising is still in the initial stage,more researches need to be carried out.Based on EMD denoising,the in-depth research on the application of denoising for portfolio management can not only help to improve the EMD denoising algorithm,but also has significance to the development of portfolio theory.The study has strong practical relevance when securities portfolio is becoming an important component of economic and social life.Considering these facts,we start the research from elucidating the impact of noise on portfolios.The ultimate goal is to construct efficient portfolio strategies.We argue the necessity of denoising,and select EMD denoising as a method to address the interference of noise.Finally,the overall framework that portfolio strategies based on EMD denoising is established.In total,the study contains three different perspectives:First,the bridge between noise and portfolio connection is established through theoretical and empirical analysis,which mainly explains the impact of noise on portfolio and compensates for the lack of theoretical support in previous studies.Second,a novel EMD denoising algorithm is constructed to address the deficiencies of previous EMD denoising algorithms,such as inadequate or excessive denoising in portfolios management.Third,a novel EMD denoising correlation-based network algorithm is constructed to address the deficiency that EMD denoising increases portfolio risk.The main work of this research is summarized as follows.Considering that the studies analyzing portfolios from a denoising perspective lack theoretical foundations,chapter 3 explains the impact of noise on portfolio through theoretical analysis and empirical studies.Specifically,the noisy prices are decomposed into non-noise components and noise.Then,under noisy and nonnoisy environments,the optimal portfolio weights for the minimum-variance,meanvariance,minimum-CVaR,and mean-CVaR models are derived.By comparing their differences,the facts that noise can cause the optimal portfolio to deviate from its true position and denoising is necessary are established.Based on theoretical analysis,we further validate the noise interference on portfolio,and compare the differences in the impact of noise on different portfolio models through empirical study.The empirical results show that instead of the mean-risk models;CVaR;semiparametric and nonparametric estimation methods,the minimum risk models;choosing variance to measure risk;parametric estimation methods are less affected by noise,naturally,their performance is more robust.On the other hand,contrary to the degree of noise interference,the mean-risk model,CVaR,semiparametric and nonparametric estimation methods can achieve higher portfolio returns and better risk-return equilibrium.In practice,it is more urgent to carry out denoising research for the portfolio models that are highly affected by noise,such as the mean-CVaR model,it can not only eliminate the noise interference,improve the robustness of the model,but also reap more portfolio returns.Considering that common denoising algorithms,especially EMD denoising algorithms,have some weaknesses in portfolio management such as inadequate or excessive denoising etc.Chapter 4 proposes a novel EMD denoising algorithm based on correlation coefficient test to improve portfolio performance.In detail,the EMD technique is used to decompose the original noisy price into a series of IMFs.Then,based on the difference that the correlation between noise and noisy price is extremely low,while the correlation between effective price and noisy price is very high,the hypothesis tests on the correlation coefficients between the decomposed IMFs and noisy price are performed to identify which IMFs are noises.Finally,the superiority of the proposed denoising algorithm is illustrated under the mean-CVaR framework.The empirical study shows that although the proposed EMD denoising algorithm increases portfolio risk to some extent,it significantly outperforms the common EMD denoising,EEMD denoising,and wavelet denoising in portfolio return,Sharpe ratio,information ratio,and tracking error ratio.The robustness test by simulation study,changing the confidence level,optimized objective and window width validate the above conclusions.Considering that the stock market can be conceived as a complex correlationbased network,and investing the peripheral components can effectively reduce portfolio risk.By incorporating these network features into EMD denoising,chapter 5 proposes a novel EMD denoising correlation-based network algorithm to address the weakness that EMD denoising increases portfolio risk.Specifically,the EMD denoising is first applied to denoise the noise from the original prices.Then,the complex correlation-based network is constructed by using the PMFG algorithm and correlation coefficient matrix for the denoised returns.The peripheral components are screened from the correlation-based network by using some centrality measures.Finally,the superiority of the proposed algorithm is illustrated based on three minimum-CVaR models,and the equally-weighted portfolio model.The empirical study shows that the portfolio based on the proposed EMD denoising correlation-based network algorithm outperforms that of EMD denoising in portfolio risk,and outperforms that of correlation-based network in portfolio returns.The robustness of findings is verified by changing the confidence level and empirical data.