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A Monte Carlo Simulation of Portfolio Dynamic Risk and Its Application

Zhidong Liu, Song Bin, Xu Miao

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Abstract

It is of great importance for portfolio risk measurement to grasp the actual distribution and dependence of financial asset returns. There are some drawbacks in Markowitz's portfolio theory, which reflects the risk and the dependence of financial assets returns by means of variance and Pearson's linear correlation. Basely on the virtues of copula in reflecting the dependence of random variables, and connected with the fat tail, no-asymmetry characters of the distribution of the financial assets returns, and the time-varying mean and variance, the paper constructed a dynamic measure of portfolio risk based on Copula-Garch-Evt, which selected value at risk or conditional value at risk as the indexes of computation. Finally, according to the data from China security market, the paper did empirical research with the constructed models.

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What this paper is about

It is of great importance for portfolio risk measurement to grasp the actual distribution and dependence of financial asset returns. There are some drawbacks in Markowitz's portfolio theory, which reflects the risk and the dependence of financial assets returns by means of variance and Pearson's linear correlation. Basely on the virtues of copula in reflecting the dependence of random variables, and connected with the fat tail, no-asymmetry characters of the distribution of the financial assets returns, and the time-varying mean and variance, the paper constructed a dynamic measure of portfolio risk based on Copula-Garch-Evt, which selected value at risk or conditional value at risk as the indexes of computation. Finally, according to the data from China security market, the paper did empirical research with the constructed models.

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Available abstract

It is of great importance for portfolio risk measurement to grasp the actual distribution and dependence of financial asset returns. There are some drawbacks in Markowitz's portfolio theory, which reflects the risk and the dependence of financial assets returns by means of variance and Pearson's linear correlation. Basely on the virtues of copula in reflecting the dependence of random variables, and connected with the fat tail, no-asymmetry characters of the distribution of the financial assets returns, and the time-varying mean and variance, the paper constructed a dynamic measure of portfolio risk based on Copula-Garch-Evt, which selected value at risk or conditional value at risk as the indexes of computation. Finally, according to the data from China security market, the paper did empirical research with the constructed models.

Key concepts: Copula (linguistics), Value at risk, Econometrics, Portfolio, Expected shortfall, Autoregressive conditional heteroskedasticity, Portfolio optimization, Monte Carlo method

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