An Empirical Study Of Index Investment Based On S&P500 Volatility Roughness

In the long-term financial and economic research,how to better describe and predict the market volatility is an important task of the financial market,which has attracted the attention of numerous scholars and industry people in the past 20 years.If in a fully effective capital market,the stock price can fully reflect the value of information,but in terms of the controllability of risk,the volatility of the yield can not be predicted by the past yield.In the most classical and widely used BS option pricing formula in the industry,we always think that the stock price is subject to Brownian motion.In recent years,some foreign scholars have found that the volatility of stock price is actually "rough",because the evolution process of volatility is more irregular than the path of ordinary Brownian motion,and put forward the rough volatility model(rfsv),and put forward the concept of volatility roughness for the first time.As the "barometer" of financial markets in the United States and even in the world,the research on the volatility of S&P500 index plays an important role in the research of index investment strategy and risk management,and the relevant research on S & P500 index has never stopped.This paper first introduces the calculation method of volatility roughness and the background of rough volatility model,and applies this method to S&P500 index market to study the economic connotation of volatility roughness of S&P500 index and its investment value in index market.Based on descriptive analysis and time series analysis,we find that the volatility roughness of S&P500 index has Mean Reversion Effect and cluster effect.It fluctuates between 0-0.5 most of the time.During 1996-2017,the volatility roughness surges or plummets rarely in a single time.It often appears many times in a relatively short time.Generally,during the economic downturn,the volatility roughness will reach The lower valley value indicates the risk of market reversal in a certain period.Then we divided the whole time zone and the down time zone to carry on the Pearson correlation test and the stepwise regression equation analysis,we found that the S&P500 index volatility roughness and SPX index have a more significant positive relationship,but with the VIX Index and Amihud non liquidity index has a negative relationship.This means that the lower volatility roughness indicates the greater market volatility and the worse liquidity environment.Volatility roughness can be used as an indicator to measure market risk,but in the extreme environment of economic downturn,such correlation will be weakened.Then we further use VECM model to study its internal dynamic conduction relationship,and find that the volatility roughness of S&P500 index The price of SPX index has a long lasting positive impact,while it has a short negative impact on VIX Index.It has a cointegration relationship with VIX Index and SPX index and a significant price spillover effect.The volatility roughness is the Granger cause of the change of VIX Index,SPX index and Amihud index.Based on the above correlation analysis conclusion,we further study the investment timing ability of volatility roughness in SPX and VIX Index markets,and add volatility roughness h and its lag term and difference item into CAPM,Fama three factor and five factor models to make time series regression analysis of its significance.It is found that the volatility roughness of S&P500 index has a strong significance for the interpretation of SPX return.The higher the volatility roughness indicates the lower the SPX return,and the interpretation effect still exists within the second-order lag of the volatility roughness,indicating that the volatility roughness also has a certain predictive ability for the SPX return.The first-order difference sub item of volatility roughness has a certain negative relationship with the VIX Index Return,which shows that the change degree of volatility roughness affects the VIX Index Return to a certain extent.Then we build a dcc-mgarch model to analyze the dynamic volatility transmission relationship among SPX index,VIX Index and volatility roughness,and find that there is a significant positive volatility spillover effect between volatility roughness and SPX index,but in the case of extreme market downturn,this phenomenon will weaken or even reverse cycle.Then we build three time series models(pure time series model,time series model with residual and time series model with volatility equation)to predict the return of SPX index.It is found that the time series model with volatility roughness information is more effective in predicting the return of SPX index,which shows that volatility roughness is an effective index of SPX index timing.This paper also finds that there are differences in the roughness of index volatility in ten different industries of S&P500.We put forward the strategy of buying rough and selling slippery.We divide the ten industry indexes into five equal parts according to their roughness.We buy the roughest industry index every month and sell the smoothest industry index.Set 5 years as the rolling window,use the method of multi factor regression to get the average monthly excess return of each quintile portfolio,then use Fama macheth regression to add control variables to test whether the current volatility roughness has certain prediction ability for the next month's index crosssection return.The results show that the volatility roughness has a significant negative relationship with the return of SPX,and after adding other control variables,the volatility roughness coefficient and the significance are enhanced.Such an investment strategy can get 6.24% or higher annual excess return,and the durability of the strategy can be more than 60%.Volatility roughness can be used as a risk management index of market volatility risk,and also as an investment index reference of timing stock selection.