Portfolios Optimization under Constraints

This article selects 10 companies in the financial sector, energy sector and consumption as well SPX500 index. paper uses two models, not only Markowitz model but also index model, to calculate correlation coefficient matrix, minimum variance, maximum Sharpe ratio, capital allocation line so on analyze return rate volatility of specific companies. Four limitations were calculated for Index respectively models compared under same constraints. Because common constraints industries are rarely noticed reality, results this reflect following three aspects: First, order strike a balance between risk return, SPX is an investment worth considering due its high coefficient; second that certain investors with added constraints, performs relatively poorly, does variance boundary. Thirdly, because stock's covariance while beta alpha stocks components construct portfolio, show conditions, inferior pursuing conditions.