High-Dimensional Portfolio VaR Measurement Based On DF-GARCH Model

In recent years, VaR of the portfolio of financial assets in high-dimensional metric has got more and more attention. On the one hand, as the global financial development, as well as the continuous development of China’s financial markets and perfect. Massive financial assets generated financial products and their derivatives are more and more, even some fund is formed by hundreds of financial assets portfolio, such as ETF180, ETF280, ETF300. They appear not only enrich the product market in the financial market, such large-scale high-dimensional portfolio of financial assets can be more effective, fully integrated to the type of information in the financial markets. Research and risk assessment for such a high-dimensional portfolio of financial assets, the risk factors of a more comprehensive grasp of the financial markets and thus its risk management and control. Academic VaR of high-dimensional portfolio of financial assets has become a trend. On the other hand, high-dimensional portfolio of financial assets because of their covers information and more comprehensive. Plus to prevent systemic crisis in the market of high-dimensional portfolio of financial assets since the systemic crises such as the global financial crisis in2008has also become a new idea. In this context, the accurate measure of a portfolio of financial assets in high-dimensional VaR value applied to modern financial markets, risk management, risk monitoring and portfolio investment has a very profound theoretical and practical significance.The domestic existing literature for the study of the above problems are basically the following three issues:(1) usually VaR measure of a single variable (such as a market index, a single financial asset). VaR measure for a single variable and do not reflect the market modern financial markets, mutual contact and mutual influence among the various assets. Therefore, the study of such methods even if the market index class. It is also on the market information loss, or slightly interrelated and influence mechanism between assets.(2) in the theoretical study, the multi-dimensional financial assets. Using multivariate GARCH model theoretically or exponential moving average model seems to be able to effectively solve the problem of single variable study. However, the form of multivariate GARCH financial practice no matter what form of this article can not be studied high-dimensional portfolio of financial assets, the effective parameter estimation. This is a the Multivariate GARCH class model often complex vector and matrix form. When the increase in the number of variable dimension, the parameters to be estimated exponential growth into the plight of the "curse of dimensionality". Exponentially moving average such models take into account the time-varying characteristics of financial time series, but by a simple sliding index to characterize this variability of course, certain inaccuracies. Thus, such methods prevalent theoretically feasible but difficult to implement in practice. Through dimensionality reduction of high-dimensional asset class (3) drop Invensys want to extract important market factor to characterize interrelated and influence each asset in the portfolio of financial assets. Factor GARCH model is usually used in most empirical molecule. Factor GARCH model, however, exist in the process of dimension reduction loss of information, and the determination of the number of extracted factors and there is no uniform standard. Therefore, such methods can be effective on massive volatility of a portfolio of financial assets portray. But the information part of the loss can not be ignored.For the deficiencies of the existing literature, this article by the dynamic factor GARCH model to characterize the high-dimensional volatility of the portfolio of financial assets. The effective combination of model through a dynamic factor model with GARCH class model to measure the volatility of the high-dimensional financial assets. The dynamic factor model high-dimensional portfolio of financial assets are broken down into market segments (or part of the system) as well as independent qualities part of financial assets (or heterogeneity part) by market factors. The dimension of market segments in the factor model is far less than the dimension of the large-scale financial assets. Therefore, market parts and qualities part to establish reasonable multivariate GARCH univariate GARCH model will be able to more accurate portrayal of the volatility of the portfolio of financial assets without loss of information in the case. Then apply dynamic factor GARCH model portrayed volatility to the VaR measure can solve the problem of high-dimensional financial portfolio VaR measure.In this paper, the analysis of the literature, and summarized on the basis of empirical analysis.218stocks selected based on the CSI300Index constituent stocks on January1,2010to2012as a research object to the closing price of the sample interval. Of the financial assets portfolio VaR measure depth theoretical analysis and empirical research.The main content of this paper includes the background and significance of the topic, and expounded this research ideas, methods, content arrangement, as well as innovation. In this paper, the existing literature of the sort, summarize. For its shortcomings, the method has the advantage of this study and innovation. The object of this study is the high-dimensional return series of financial assets by the dynamic factor model. Series decomposition of the yield can be observed by the dynamic factor driving public part of the portfolio of financial assets, the characteristics of each sequence part. Factor model, the public part (the part of the system) and the characteristics of part (heterogeneous part) do not overlap. The public part is driven by the potential unobservable dynamic factor; qualities part by a portfolio of financial assets within each individual yield sequence qualities factors arising. Factor model are broken down by a small number of dynamic factors such changes can have an impact on the public portion of the entire portfolio (systemic effects). Thus portrayed on the public part of the volatility can be selected according to the number of factors get appropriate multivariate GARCH model fitting. Such systematic fluctuations in high-dimensional portfolio of financial assets on the adoption of a very small number of common factors fluctuations characterize out (to play a very important role of dimensionality reduction). Then the trait part characteristics to establish its own rate of return sequence presented the univariate GARCH to portray its fluctuations. So that both the volatility of the portfolio of financial assets by of systemic volatility trait fluctuations, but also avoid the loss of traditional factor GARCH model. While ignoring the fluctuations of the qualities part because the latter often only extract the static factor multivariate GARCH model. Dynamic factor GARCH model is good to make up for it. Through theoretical analysis and empirical research for this article, has been about the conclusions:(1) built for China’s CSI300Index constituent stocks selected based218stock portfolio. Generated by the market impact of the volatility of individual stocks can be driven by three dynamic factor. These three dynamic factors and not by the existing theory to a reasonable explanation or named another dynamic correlation coefficients between the three dynamic factors that exist between them weakly correlated. To characterize the high-dimensional portfolio volatility,(2) dynamic factor GARCH estimated in a portfolio of high-dimensional building in the domestic stock market volatility has a certain effect, that the dynamic factor GARCH model provides a high-dimensional portfolio volatility Characterization and prediction methods.95%with99%confidence, on the application of dynamic factor GARCH model to calculate the VaR value index sliding average model to calculate the VaR value comparison, slightly smaller dynamic factor GARCH model to calculate the VaR value. The exponential moving average model to calculate the VaR value slightly larger relative. Backtesting test showed VaR values calculated dynamic factor GARCH model with exponential moving average model by95%with99%confidence. Under the95%confidence level, the the dynamic factor GARCH model with exponential moving average model results are better.99%confidence, the effect of dynamic factor GARCH model than the exponential moving average model, exponential moving average model is more conservative VaR metric. Therefore, financial institutions, financial supervision and risk control section can be considered a dynamic factor model portfolio of high-dimensional metric, supervision and management of the risk.The innovation of this paper is mainly reflected in the following three aspects:(1) for the first time in the country of the variance-covariance matrix of over200Japanese financial assets yield estimates, and for VaR metric. The results show that dynamic the factor GARCH applies VaR metrics in high-dimensional financial assets.(2) the characteristics of the218stocks yield data TGARCH (GJR-GARCH) and GARCH model is a reasonable estimate idiosyncratic volatility is partly Compared with the conventional factor GARCH model, to avoid the loss of the characteristics of part of the information.(3) using the method of rolling forecasts218stock portfolio VaR measure, and results with the index sliding average (EWMA) VaR metric comparison. The results show that the VaR measure dynamic factor GARCH model is better than under the exponential moving average VaR measure.The direction of further research of this article:(1) the application of dynamic factor GARCH model to more areas of the market, these applications in order to better verify the applicability of the dynamic factor GARCH model.(2) of this article only volatility estimation results of the dynamic factor GARCH model can also be applied to the VaR metric. The results of the model can also be applied to more areas, such as portfolio decisions.