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The Research for the Measurement of Portfolio Risk Based on Copula Functions

Author: LiXueShi
Tutor: LiZhanLei
School: Hebei University of Engineering
Course: Management Science and Engineering
Keywords: Portfolio Risk Measurement Copula function VaR
CLC: F224
Type: Master's thesis
Year: 2011
Downloads: 93
Quote: 0
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Abstract


Modern portfolio theory suggests that a combination of different asset constructed in a way can be dispersed single asset idiosyncratic risk, the portfolio can be dispersed in the part of non-systematic risk. Each asset in the portfolio may not be completely negative correlation, the structure of the portfolio can not completely eliminate non-systematic risk and portfolio also bear the systemic risk. Modern Portfolio Theory and models for portfolio risk measurement tool based on β coefficient and VaR as the representatives of these risk measurement tools exist for the distribution of portfolio risk and thick tail spikes characteristic measure is insufficient and they are built on portfolio income under the normal distribution assumption, therefore, the peak of portfolio risk characteristics and thick tail risk measurement methods of portfolio risk became a trend in the field. Copula function is the joint distribution of multidimensional random variables with one-dimensional marginal distribution function connected, its advantage is the joint distribution of the portfolio can function analysis combined assets yield dependency structure, and is capable of marginal distributions and their associated structures studied separately. This article is based on Copula function has the characteristics of a fat tail risk analysis capabilities, select the portfolio to better describe the tail characteristics Archimedean-Copula function family of Gumbel Copula functions and Clayton Copula function tail nonlinear correlation coefficient, instead of the traditional asset VaR of the portfolio metrics to measure the linear correlation coefficient risk, in order to better characterize the joint distribution of different asset risk the loss of status, to provide theoretical guidance for investment decisions. Papers in defining the modern portfolio theory, mean - variance portfolio model, the capital asset pricing model based on the application conditions, portfolio risk analysis and VaR metrics β coefficient of the applicability of the use of metrics Copula function has a fat tail distribution characteristics financial feasibility and portfolio risk conditions described. To verify Copula function measure the effectiveness of portfolio risk to the Copula VaR tail instead of a linear correlation coefficient correlation coefficient to measure the risk of the stock market on January 4, 2005 to 2010 January 4 day's benchmark Shanghai Composite Index and the Shenzhen Component Index on the daily number of panel data yields an empirical test. The empirical results show that using the tail instead of the linear correlation coefficient correlation coefficient to measure portfolio risk closer to a real risk of the portfolio distribution.

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CLC: > Economic > Economic planning and management > Economic calculation, economic and mathematical methods > Economic and mathematical methods
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