Research Of Portfolio Selection Under The Constraint Of Downside Risk

Institutional investor and individual investor all began to rethink their investment philosophy since bull market in 2007 and bear market in 2008. They found that they would lost extra risk premium in bull market and also suffer losses in bear market if they only depend on MV theory to diversify. So they turn to depend to technical analysis of the Stock market and band operation. Basing on it, this paper tries to focus on the value of investment diversification and assets allocation, and study on them under the constraint of downside risk. It is different to MV theory. Portfolio theory under the constraint of downside risk aims at ensuring assets safe firstly.The paper cover a framework and two fields:portfolio selection under the constraint of downside risk, portfolio theory and downside risk measure theory. Portfolio selection under the constraint of downside risk is also a part of modern portfolio theory, and it replaces the standard deviation with VaR, So it improves the MV theory. The paper mainly studies the Mean-VaR model and CHKmodel by theory and demonstration analysis, and the study focused on the CHK model. Another key issue is the downside risk measure. Because it is portfolio theory model's key parameter, accurately measuring the downside risk decide the applied value of model in investment diversification and assets allocation.The paper also tried to discover potential and power applying dynamic financial econometric methods to risk management. The paper measured the market risk with DCC-MV-GARCH modle in search of the best model which fitted the volatility, and expected to accurately forecast the portfolio downside risk. The innovation lies in the methods estimating the VaR and CVaR that combine multiple financial econometric technique, such as DCC-GARCH method, bootstrap method, and history simulation. In a word, the paper primely synthesized and unified the methods and theories of measuring downside risk, and applied them to the empirical anlysis of portfolio selection in actual risk-return circumstances. At the last core section of paper, the paper analyzed the CHK model in theory and extend its application from static circumstances to dynamic circumstances. At actual risk-return circumstances, the paper gived dynamic portfolio selection recommends with the CHK model, and further adjusted actual assets allocation of portfolio based the investment recommends. The empirical results shows that the adjusted portfolio depended on CHK model's recommends have earned higher yield. In the process of portfolio selection decision study with CHK model, the paper also shows that the portfolio selection solution CHK model gived could be use as the actual assets allocation crierion of portfolio under the principal purpose of protecting the safety of assets, and the cash amount decision CHK model gived also shows the direction and degree of the change of downside risk. For the investor and risk manager, the cash amount can be used as risk indicator and risk control variable. They can buy or sell maximizing portfolio CHK model decided equal to the cash amount to cause the portfolio actual VaR return to its constrait value.In short, the paper used advanced financial econometric technique measuring the downside risk, applied CHK model at actual risk-return circumstances, revealed the potential and value of portfolio selection model under the constraint of downside risk, boosted the application of CHK model. The paper also synthesized and unified the downside risk measure and portfolio selection system in view of statistics and econometrics, demonstrated the model risk during the portfolio selection under the constraint of downside risk. The research can also be easily extended to a large investment portfolio.