A Study On Price Fluctuation And Risk Measurement Of Cross-border ETF Based On Fractal Theory

With the gradual opening up of China's capital market and the rapid rise of China's economy,international investors are paying more and more attention to China's securities market.However,limited by the size of the investment,the investment path and the investors' ability to control the risk,not all foreign investors choose to allocate assets in the Chinese securities market directly.As a special ETF that is listed on the securities market of one country and tracks the index of other countries' securities market,cross-border ETF provides an effective and relatively low-risk way for investors to allocate overseas assets.It is important for investors to analyze the price volatility characteristics and measure the risks of cross-border ETFs.Under the fractal market theory,we select several representative cross-border ETFs that are listed overseas and track China's securities market index as the research object to explore the complexity of its' price fluctuation by using Multifractal detrending analysis.The empirical results show that cross-border ETFs have obvious multi-fractal characteristics,and effective market theory is not suitable for its' s analysis.In order to analyze the causes of multifractal features,we random the order and phase of the return series to eliminate its' thick tail features and long memory,then we comparison the multifractal features of original and processed sequences.Result shows that the multifractal characteristics of the processed sequences were significantly weaker than the original ones,which indicats that thick tail characteristics and long memory are the main reasons for the multifractal characteristics of cross-border ETFs.By fitting the return sequence and testing the fitting results,we found that the fractal distribution can fit the return sequence cross-border ETF income and fractal distribution fit better.At last,we establish a VaR risk measurement model based on fractal distribution,and perform backtesting test on the estimated results of the model.At various confidence levels,the VaR risk measurement model based on fractal distribution has passed the test,and the estimated results are close to the actual ones.Comparing the the multifractal features of these cross-border ETFs and the risk values measured by the VaR risk measurement model based on fractal distribution,it is not difficult to see that the greater the multi-fractal degree of the cross-border ETF,the greater the risk value calculated by the VaR risk measurement model based on fractal distribution.The results are mutually evidenting,which indicats that multifractal features exist in cross-border ETFs,and the VaR risk measurement model based on fractal distribution can well fit return sequence of them and estimate their risks accurately.