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Nowadays, the trend as capital securities and derivative financial products in the financial market, the increase of the share of the world's financial regulators, financial advisory and private consortium of assessment, supervision and control of financial market risk increasingly takes as management VaR model for risk control in the financial sector has been a wide range of applications, while CVaR VaR based on the model, also obtained in the practical application of the VaR model approximation consistent conclusions. VaR and CVaR applications in the control risk in the portfolio model, a lot of research at home and abroad, but also need to be further improved and perfected. This is the significance of the topic of this article. Comprehensive introduction to VaR and CVaR theory of based on this article, summarize their definitions, algorithm, application range and classic portfolio optimization model Introduction highlighted a CVaR-based portfolio optimization model it is the traditional mean - variance model to improve the introduction of VaR and CVaR model. improved model can not only better help investors make decisions, and take full account of the investor reality with different tolerance for risk factors, more in line with today's market investment securities portfolio status quo. computationally to facilitate the application of mathematical and statistical software to achieve specific model: the case of no friction, the revenue function (loss set the rate of return to make assumptions, the revenue function is negative), r (x, y) =-yTx = - (x1y1 x2y2 ... xnyn) scenario, yij = ln (pitj-1 Δt/pitj-1), j = 1 , 2, ..., M in the CVaR constraints, so that the combined loss of the minimal optimization problem can be expressed as: (?)-E [yi] xi first equation is the objective function, so that losses are minimized (expected revenue maximization ); restrictions CVaR constraint is not allowed to buy empty; xj ≥ 0. by solving linear programming problems, you can get the optimal vector x * corresponding VaR value equal to ξ * maximum expected revenue compared with Σi = 1n E [yi] xi the optimal solution under different risk constraints that can get income-CVaR efficient frontier. number of parameters needed in the model increases linearly, while the mean - the variance model parameters to input the number was increasing quadratic more so when considering the number of securities, this model will be more convenient and mean - variance model given yield variance - covariance estimates, but this model need only given the historical rate of return or simulated yield can be. article, the empirical analysis of this model, which is the core content of this article we selected from January 2010 to September stock's daily closing price as calculating the historical gains rate data. (data from Yahoo Finance Web site of the historical data download), randomly select the SSE ten stocks as the model calculation used, the following table: For an asset (stock) i, its j-th scenario gains rate is taken in this article data is obtained according to the method described above according to this formula, (yij) 10 × 10 are as follows: such substituted into the model, we use the Matlab software, direct call linear programming function linprog programming, optimal value can be derived, and optimal vector x * the first component is ξ *, i.e. VaR value so of α = 0.95 when calculating the optimal value of -0.083, i.e., the maximum yield was 0.083, the optimal vector x * = (1,0 , 0,0,0,0,0,0,0.0,) T, transformation of α values, but also to get to a different confidence level VaR value, as shown in the following table: results basically meet the higher confidence level corresponding The lower level of risk, VaR definition is also consistent with, and also to verify the rationality and effectiveness of the model results in the last article, we discussed the improved algorithm of this model, the very feasibility of the method.
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