Multifractal Analysis On Stock Index Futures Market Based On Fractal Market Hypothesis

The Efficient Market Hypothesis (EMH) was regarded as basis and premise in financial researches since it was put forward in1970s. But at the same time, more and more abnormal phenomenon that cannot be explained by EMH were discovered, such as self-correlation and peak thick tail of the assets’returns. More importantly, collapse incidents occurred frequently in the financial market which made people cast doubt on its reasonableness and effectiveness. As a result, objectors made great efforts to find methods that can provide more accurate analysis to the financial market. The most striking two methods are Behavioral Finance and Econophysics, both of which deny the ideas of rational investors and linear information transmission, analysis the market from a point of nonlinear and complexity, and gradually become hot and frontiers in financial analysis. In the field of Econophysics, grows Fractal Market Hypothesis (FMH) that distinct from EMH, it thinks that the distribution of assets returns has characteristics of non-normal with fat tails, long memory, scale invariance and so on, which are more in line with the real market. Multifractal analysis is one of the most widely used methods in Econophysics, and has been proved to be a powerful tool to depict the complex fluctuation of financial market by a large number of studies. Furthermore, multifractal analysis has shown its suitability in financial markets, such as stock market, bond market, foreign exchange market, futures market and so on. Some new methods about portfolio selection, risk management and derivatives pricing based on multifractal analysis are designed, which are superior to the classical models at some extent.Stock Index Futures is developed to hedge and to improve the market trading mechanism, which have been launched in major developed countries and developing countries from last century. However, the launch of Stock Index Futures is hindered in China, because our capital market starts late with inadequate laws and regulations. On April16th,2010, another short mechanism following margin was introduced in China’s capital market, that’s CSI300stock index futures contracts. Now, although the CSI300stock index futures is still the only trading product in China’s stock index futures market, it is very important in increasing market liquidity because of its fast development and large turnover, and has been attracting attention from all over the world. Therefore, research in-depth in this field and find out the complex feature and law during fluctuation is conducive to the market’s effectiveness and investors and regulators’decision making.There are two purposes in this paper, one is to explore the effectiveness of China’s stock index futures market. The analysis consists of assets returns’normal distribution, the market volatility’s long-term memory and scale invariance. From these analyzes we can know whether EMH or FMH is suitable to study China’s stock index futures market. The other purpose is to study our stock index futures market with multifractal method, discussing its application in index futures market and enriching research findings in multifractal area. As the FMH pays attention to the discontinuous few big changes rather than the continuous large amount of small changes in the market, the multifractal characteristics should be more obvious in substantially fluctuation process theoretically speaking. This paper selects the wide fluctuation period as a sample to analysis, trying to discover the abundant wave information implicit in those important parameters of multifractal spectrum, and to study the change laws of multifractal spectrum during substantial fluctuations.By empirical analysis we find that our stock index futures market is non-effective and line with FMH situation. First, the descriptive statistical analysis shows that in China’s stock index futures market, there exists significant non-normality feature with peak and fat tails in yield distribution. Second, the Hurts index is significantly greater than0.5, indicating long-term memory in market volatility, which become more obvious with time scale increases. Third, results by R/S analysis show that returns of China’s stock futures market obey the Stable Pareto distribution or called fractal distribution with well scale invariance.Multifractal analysis under FMH framework shows, there is significant multi-scale fractal characteristics in China’s stock index market, and is suitable to describe by multifractal language. In this paper, we select one of the basic multifractal language α-f(a) to analysis the significant fluctuation processes of CSI300index futures index, find out the important volatility information implicit in major parameters of multifractal spectrum Δα and Δf, and analysis the change laws of the multifractal spectrum during the whole process. Empirical analysis shows, that the multifractal spectrum often distribute singularly at the start and end of the fluctuation and its parameters tend to increase, and these characteristics disappear with the trend become clearer. Operation strategy according to the larger Δα and Δf at the start and end of the fluctuation is designed to prove the effectiveness of multifractal method. The result is that investors can win a return of4.64%per annual, greater than the interest rate on bank deposit of the same period, which confirms the effectiveness of the strategy and the suitability of multifractal method in China’s stock index futures market.There are two innovations in this paper:First, multifractal method is introduced to analysis China’s stock index futures market. Tests about EMH and FMH in domestic literatures mainly concentrate on stock market, seldom on the stock index futures market. We have not yet found related researches about multifractal spectrum features during large fluctuation processes in stock index futures market. In view of the advantages of multifractal analysis to describe the complexity features in financial fluctuations, the introduction of this method can not only describe volatility characteristics of stock index futures market more accurately, examine the explanatory power of the multifractal method in actual market, but also increase empirical support in multifractal area.Second, the data is obtained from China’s stock index futures market directly. Now the stock index future is still an emerging thing in China’s, the too short transaction time to obtain enough data in study, study based on fewer data is questionable so that correlated studies are very few. Some literatures use proxy variables to study the effectiveness of Chinese stock index futures market. However, the accuracy and representativeness of the results are inferior to those based on data directly from this market. The data in this paper is the CSI300index futures monthly continuous index, including478day closing data and up to25812high frequency data of5min, to guarantee the accuracy and reliability of the conclusion.This thesis is divided into six chapters, main contents and conclusions of each chapter are as follows:Chapter1is introduction. In this chapter, theoretical and practical backgrounds are elaborated, research significance in theory and in practice is pointed out, the contents and structures of every chapter are arranged, and the innovations of this article are also summed up.Chapter2is literature review. In this chapter, we describe the existing researches home and abroad, including studies of complex market volatility, empirical studies of multifractal features in various types of financial markets and the improvements to classic methods based on multifractal analysis. Conclusions and shortcomings of the past researches are also summarized at the end of this chapter. From it we can know, multifractal features exist in both mature and emerging markets, exist in stock markets, bond markets, foreign exchange markets and other types of financial market. The risk management methods based on multifractal analysis are superior to those under EMH. However, compared with EMH, there are many disagreements on conclusions in the field of Econophysics especially in multifractal, for example, the sources of multifractal feature.Chapter3is theoretical basis, which is divided into two parts: market effectiveness theories and multifractal theories. The market efficiency theories include EMH and FMH, whose introduction, basic assumptions, features and types contained are described in detail. Detailed comparison of the two hypotheses is stated in aspect of the market environmental factors, the motion pattern and path of market price. In multifractal theory, local singular exponent and mulfractal spectrum are introduced.Chapter4and Chapter5are empirical and core parts in this paper. Chapter4analyzes the effectiveness of China’s stock index futures market, its launch process and present situation are introduced, and the monthly continuous index of CSI300stock index futures is taken as a sample, to study the fat-tail and non normality distribution of the asset’s returns. Method to obtain Hurst exponent through R/S analysis is introduced in detail, and the long-term memory and scale invariance of the market volatility are analyzed by comparing Hurst index under different time scales. The above analysis show that features are obvious in China’s stock index futures market, such as non-normal distribution, which followed with peak and fat tail, long-range correlation and scale invariance. Therefore, our stock index futures market is an inefficient market and in line with FMH situation rather than EMH.We do multifractal analysis in chapter5. Steps of calculating multifractal spectrum are introduced in detail, and take high frequency data of CSI300stock index futures monthly continues index as a sample, to analysis whether there exist multifractal features in China’s stock index futures market, and to further analysis the characteristics and laws of multifractal spectrum during the process of heavy gains and plummet. Based on the law obtained above, a simple operation strategy is designed to analysis the effectiveness and applicability of multifractal analysis by examine whether this strategy can bring excess return. The analysis of this chapter not only affirms the multifractal characteristics in China’s stock index futures market, but also supports the validity of the multifractal method and its conclusions.Chapter6is the summary and outlook of this paper. A summary of the works done in the whole paper and conclusions are stated, and then point out the problems that should be further researched in the future.