Application Of Robust Optimization Model In Portfolio Management

In1952, Markowitz introduced the famous Mean-Variance(MV) model, sug-gested that investors should consider risk and return together, and represent it under the framework of Quadratic Program(QP). The Mean-Variance model pro-vided the basis of the modern portfolio theory and opened an era for the quanti-tative financial analysis.Estimations of the return and risk must be made before they are used as the inputs of the model. But the Mean-Variance Model is very sensitive to changes in the inputs(expected returns and asset covariance). While it can be difficult to make accurate estimates of these inputs, estimation errors in the forecast sig-nificantly impact the resulting portfolio weights. Some approaches are used to control the estimation error, such as shrinkage estimators and robust statistics. Robust optimization is the latest attempt to address estimation error directly in the portfolio construction process.In this paper, we studied the empirical performance of robust optimization model based on the Monte Carlo simulation and the Chinese stock market data, and compared the model with the benchmark of traditional Mean-Variance model and the robust/shrinkage estimation model. The conclusion is that, in most cases, the optimal portfolios obtained by robust optimization have better out-of-sample performance than the traditional optimization techniques, and have improved sta-bility and low turnover rate. But the performance depends on the choice of model parameters.The thesis is organized as follows:In Chapter1, we introduce the background of our study and review the literature. In Chapter2, we introduced the traditional Mean-Variance Model, the estimation error problem and the traditional robust estimation approach. In Chapter3, we present a robust portfolio optimization model based on the uncertainty of the expected return. In Chapter4, we compare the performance of the robust optimization model with some benchmarks. Out-of-sample experiment is carried out using simulated data and real data. Finally, we summarized the main result and suggest some future research direction in Chapter5.