Decomposition Of Portfolio Value At Risk And Standard Deviation And Its Application

After being proposed in 1993, Value at Risk (VaR) technique has become the standard for risk management industry. The theory and applications of that method have been studied by many scholars both in china and abroad, but those studies mainly focus on the calculation of Value at Risk, while little attention is paid to the variables of portfolio VaR.Firstly, this thesis introduces the traditional risk measure, the background and current status of VaR, and summarizes basic principle and frequently-used methods of VaR calculating methods.Secondly, we study the decomposition of portfolio VaR and its application. The exact solution of the marginal VaR, which is held under the hypothesis of multivariate normal distribution, is presented. Also, utilizing the rational function approximation, linear local approximation and asymmetric response model, the estimative methods of the marginal VaR, which is held with the hypotheses of non-normal distribution, is Presented. Decomposition of VaR help usto have a better understanding of the influence of each asset that constitutes the portfolio and the corresponding adjustment and variety of that on the whole risk of the portfolio and to identify the main source of the risk in the whole risk exposure of the portfolio.Thirdly, this section is divided into two parts. The first part is to give the decomposition of portfolio variance based on the method of VaR composition, and the concepts of marginal variance, component variance and incremental variance are presented; The second part is to give the triangular risk decomposition of volatility (standard deviation) based on the method of triangle decomposition, which provides a useful, geometric view of the relationship between the risk of a position and that of the portfolio, allowing risk managers to quickly understand the correlations between individual positions and the balance of the portfolio. And the correlation information is readily analyzed to obtain best hedge positions for each asset. Hence, the portfolio risk can be managed by manipulating the size of the positions.