Study On Portfolio Optimization Of Foreign Exchange Based On Vine Copula And CVaR

The rapid development of economic integration and financial liberalization, not only promote economic and trade exchanges among countries, but also enhance the international capital flowing in the national markets. Thus stimulate a growth in the demand for foreign exchange, and promote the rapid development of foreign exchange markets. At the same time, with the rapid development of financial markets and financial instruments, foreign exchange investment has become a hot spot for investment of the investor, which makes investors and risk managers focusing on how to build an effective foreign exchange portfolio to guard against foreign exchange risk, and on how to achieve risk aversion or passed on, in order to increase the value of assets. Thus is becoming a problem that people pay close attention to.Markowitz's portfolio theory has provided a framework for us to analysis on how to build an effective portfolio. The theory is based on determined earnings seeking to minimize risk or seeking to maximize income in certain risk. Therefore, the accuracy of the risk measurement plays an important role on portfolio optimization. Currently, VaR(Value-at-Risk, VaR) technology can be easily and clearly showing the risk of financial assets which attracts scholars to use it in their researches. This makes it become the common measure method of financial risk, and also be widely used in practice. Although VaR technology has excellent performance in the characterization of single assets, but because of its not having subadditivity, leading to their portfolio risk calculation is not accurate. At the same time, VaR does not have a convexity, thus making the risk indicators as portfolio optimization objective function in measuring the minimum risk, there may be more than one optimal solution. This is to say that using VaR as objective function of portfolio optimization to get the optimal weights, the optimal solution may be a partial one, rather than the global optimum solution. Focus on the defects of VaR, the paper selects CVaR(Conditional Value-at-Risk) to replace VaR as combinatorial optimization objective function, which has subadditivity and convexity compared to the value at risk, for the sake of carrying out foreign exchange portfolio optimization strategy. And thus makes portfolios to be optimized.It should be pointed out that neither the use of VaR technology or CVaR, which is based on VaR risk measure, the market is generally assumed that there is no friction. Thus the investors can trade a large number of positions easily at any time at the assured transaction price, but will not change assets' prices. However, a large number of empirical studies have demonstrated that not only there are market frictions in financial markets, and liquidity risk by the market friction, in extreme cases, can lead to market liquidity black hole, which then may induce financial crisis. If we do not to modify this defect of VaR model, ignoring such an important liquidity risk, it is bound to underestimate the risks faced by investors, which probably led to risk measurement inaccurate. Therefore, in order to overcome this deficiency of CVaR, we will incorporate the liquidity risk of foreign exchange into the portfolio optimization. Given the technology CVaR in the process of risk measure does not consider the dependence structure among the assets, while the dependence structure of assets has a major impact on an accurate measure of risk. So the paper also apply vine Copula to capture the dependencies between the foreign investment portfolios in order to accurately measure foreign investment portfolios risk, and then to optimize the investment of foreign exchange assets.Therefore, the paper selects the RMB against the dollar, the RMB against the euro and the RMB against the British pound as the research objects, and selects market risk factors as well as liquidity risk factors, a total of six risk indicators. Given the existence of typical fact characterized of risk factors, this paper uses ARMA mean models and GARCH variance models, and also uses extreme value theory(EVT) which models for assets' tails distribution characterization. Focus on the defects of VaR technology that do not consider the asset dependency structure and do not have subadditivity and convexity, this paper uses of Vine Copula function to capture the dependences among those risk factors, and uses of CVaR risk measure indicators which has convexity and meets the consistency measure method in order to accurately measure the value of foreign exchange risk. Based on CVaR, using this indicator as portfolio optimization as foreign exchange objective function to minimum CVaR for the sake to get right optimal foreign investment portfolio weights. Through empirical analysis and get the following conclusions: 1) For the tails of the distribution of the assets using of EVT to model the tail are much better than using of normal and Student's t-distribution which can capture heavy tail of information to model and can extract more information of tails; 2) For capturing the dependent on the structure of foreign exchange assets, using t Copula function can be a good characterization of dependencies between assets, and the use of D-vine structure than using C-vine structure to capture the dependence structure among foreign exchange assets shows a stronger ability to capture dependence information; 3) The optimization model we constructed based on D vine Copula function and CVaR has better optimization capabilities and can not only effectively optimize the portfolio, but also has a strong robustness.