A Research On Volatility Of Shanghai Stock Exchange Treasury-Bond Index Based On R/S Analysis

Generally speaking, the volatility of security (portfolio) represents the uncertainty of return which is a kind of measurement of risk. Then, the standard error of return is regarded as the index of volatility in Modern Portfolio Theory (MPT). However, in Fractal Market Hypothesis (FMH), the fractal dimension is brought up to be a better index of volatility than the standard error because the most of time series in real world often contain persistent memory which can not be distinguished by the standard error. Based on the empirical research on Shanghai Stock Exchange (SSE) Treasury-Bond (T-Bond) Index, this paper adopts the rescaled range (R/S) analysis to compare the standard error with the fractal dimension. The volatility of SSE T-Bond Index is also researched on various time scales in this paper.The research result shows: (1) the fractal dimension is the characteristic of the irregularity of a time series so it is a better index of volatility than the standard error; (2) the time series of SSE T-Bond Index is a fractal random process which companied with persistence, instead of a random walk; (3) The volatility of SSE T-Bond Index is less than the one of SSE Composite Index. (4) An average cycle which is about 20 days was discovered in the time series of SSE T-Bond Index.