Portfolio Optimization Model Based On Non-Historical Information

The portfolio selection is used for identifying the best allocation of a basket of stocks in order to reduce the investment risk.More than half century ago,Markowtiz propose the mean-variance?MV?portfolio selcection model which paved the foundation of the modern investment theory.In order to implement the MV portfolio opyimization model,it needs the input of the expected value and covariance matrix of the returns of the candidate securities.The estimation error may damage the efficiency of the MV model.To deal with the estimation error,Black and Litterman proposed a model to modify the equilibrium estimation of the expected return by integrating the investor's private information.The main contributions can be summarized as follows:1.The classic portfolio theory and performance metrics are introduced in this paper.Through the comparison between mean-variance model under different constraints,BL model with rolling optimization and BL model under different views,we conclude that BL model is superior to the traditional mean-variance model.2.Recognizing only the expected returns of the stocks are updated by investor's private information in traditional BL model,we extend such approach by integrating the information of the variance?volatility?of the stock from the correspondent options.By using the inverse optimization technique,it is possible to find the updated estimation of the expected return R_BL and covariance matrix?50?_BL solving one Semidefinite Programming problem?SDP?,which can be computed by cplex toolbox.3.Furthermore,we combine these improved estimations of the return statistics with the mean-CVaR based portfolio optimization model.4.Without assuming the prior distribution of the random return of the assets,we use the moment matching technique to generate the discrete scenarios,which is a key step in computing mean-CVaR portfolio.5.In the simulation based on real market data,we analyze the proposed model with different minimum rates of return and different scenarios.And we compare dynamic mean-CVaR model with traditional BL model.The results show that the proposed model is superior than the traditional BL model.