Portfolio Optimization Based On Drawdown Constraint And Its Application

Portfolio management have been a persistent topic as the development of finance.Since Markowitz proposed the theory of mean-variance,describing risk with variance,the researchers have tried to measure risk from different perspectives.In particular,drawdown is one of the most important and well-known risk measurement.Therefore,researchers have studied a lot about it.However,most of them studied it from the prospect of the magnitude rather than the duration.Moreover,when studying the magnitude of drawdown,researchers rarely studied the robustness of the drawdown risk.Besides,though drawdown risk is an essential risk measurement,it is insufficient to consider only the drawdown risk.In particular,if we want to study the redemption risk that the portfolio managers concern a lot,we should take more risk measurements into account.The main contributions of this thesis are listed in the following three aspects:(1)Add the drawdown duration as the consideration to the portfolio optimization model of drawdown risk.We will build a strategy using the drawdown duration as the condition of filtering stocks while using portfolio optimization model to determine the weights of portfolio.Then an empirical study with Chinese stock market is conducted.We compare the performance of different groups sorted by the value of average historical drawdown duration in order to verify the condition of filtering stocks by using the drawdown duration.Finally,we compared the performance of strategy with the one not considering the drawdown duration.(2)Based on the portfolio optimization of drawdown risk,an indicator of worst-case drawdown risk is built,by considering the uncertainty of the sample paths.Referring to the method of constructing Worst-case Conditional Value-at-Risk(WCVaR),a portfolio model is constructed taking the Worst-case Conditional Drawdown-at-Risk(WCDaR)as a risk constraint into account.An assumption that there may be multiple scenarios of sample paths,and the probability of each scenario occurring is uncertain is made.With this condition,the worst-case earnings and drawdown risks are considered and the portfolio optimization problem is established to make the portfolio robust.Then the model can be transformed into a linear programming problem by the duality method.Finally,the Chinese stock market data is applied to compare the differences between the WCDaR model constructed in this paper and the existing CDaR model,and analyzed the advantages of considering worst-cast risk measurement.(3)Besides drawdown risk,other risk measurement in the portfolio selection model is tried to be added.The portfolio managers usually take into account various risk constraints in order to reduce the redemption of their fund products in reality.Therefore,in the paper,we consider the overall risk,relative risk and the drawdown risk as the redemption risk.Then we build the nonlinear programming with these multiple constraints and solve it with nonlinear algorithm.At last,we use the Chinese stock market data to verify the model and compare model built in this chapter with other existing models.Studying the portfolio with drawdown risk constraints,including the drawdown duration and the Worst-case Drawdown-at-Risk,contributes the theoretical system of drawdown risk measurement.In addition,considering other risk constraints besides drawdown risk can make the portfolio more practical.