The Heterogeneity of Investors Based on Multi-fractal Features with Ultra-High Frequency Data

Abstract

In the financial markets, the heterogeneity of investors is mostly focusing on very different underlying assets. However, there is one specific heterogeneity need to be discussed, that is the heterogeneity represented by investors who are investing in very similar underlying assets. In another word, whether there is a method to quantitatively describe the heterogeneity when investors have the same expectation in the future. In order to detect this kind of heterogeneity we introduced multi-fractal feature values and select SSE (Shanghai Security Exchange) 50 Index and its derivatives, SSE 50 Index ETF (Exchanged Tradable Fund) and SSE 50 Index Future to research on this topic, since these three underlying assets presented very similar fluctuation during the same period. With the static scenario analysis and dynamic analysis we successfully find that the multi-fractal feature values are not only able to detect this heterogeneity but also be able to describe it quantitatively. The false nearest point test had shown that the multi-fractal values are necessary and rational in this process. The other advantage by introducing multi-fractal values is that they are quantitative numbers which could be applied to models directly.

Keywords

• multi-fractal analysis
• R+realized volatility
• scenario analysis
• ultra-high frequency data