Based on the jumping test and variance decomposition method of non-parametric frequency data, the stock index returns and volatility are both decomposed into successive and jumping ingredients with positive and negative directions, and the relation between the risk and the return of Shanghai index during 2003—2012 was tested. The analysis results show that the jumping days of Shanghai Composite Index take 11.99% of the total number of days between 2003—2012, that the average jumping intensity is 1.1 times, that there is asymmetrical feature between positive and negative jumps, that the contribution of downward jumps to jump variance is bigger than that of forward jumps, that the realized variance can not explain the return in different times ranges, that each decomposed risk factor can play better forecast role in earnings in the medium term （in one week）, that the tradeoff relation between the risk and the return in different compositions is different, that each of upside risks has negative risk premium while each of the downside risks has positive risk premium. There is significant leverage effect in China’s stock market, and the asymmetrical effect of the return on volatility mainly results from the contribution of consecutive return but not from jumping return.