Portfolio Risk Measurement Methods

Portfolios theory is one of the important research contents in Economics. It aims to attain the portfolios of the maximum of the investment's return with the given value of the risk of portfolios or of the minimum of investment's risk with the given level of the investment's return. VaR(value-at-risk) and CVaR(conditional value-at-risk), which are new risk measurement methods, are put forth recently. Because of its eminent properties, CVaR is given attentions by more and more researchers in particular, and becomes a latest research content in financial risk management.The generalized variance model was introduced at first, and the log-optimal portfolios models with the risk control of mean absolute deviationi were proposed. The properties of the existence and uniqueness of the optimal solution of the model were proved, and the Genetic Algorithms were designed, which were used to solve the model and gave the number imitations. Then, on the foundation of the definitions of VaR and CVaR, the sensitivity of CVaR with respect to portfolio allocation was analyzed, and the analytical expressions for the first and second derivatives of the CVaR were derived through which proved the convex property of CVaR further and estimated the CVaR efficient portfolio. Based on the introduction of the efficient boundary and two-fund separation theorem in Mean-Variance, the Mean-CVaR model under the assumption of normality of risk securities is studied, and the two-fund separation theorem in Mean-CVaR and the corresponding properties are proposed, and the comparison between the Mean-CVaR model and Mean-Variance model is provided. Finally, we introduced the coherent measures of risk and mentioned the directions of the further research.