论文标题
通用距离与单纯距离和用于投资组合优化的新几何方法
Generalized distance to a simplex and a new geometrical method for portfolio optimization
论文作者
论文摘要
在发展投资组合的过程中，风险规避在投资者的决策中起着重要而核心的作用。在此投资组合优化的框架中，我们确定了使用新的几何方法具有最小风险的投资组合。为此，我们详细阐述了一种算法，该算法使我们能够计算任何通用的欧几里得距离与标准单纯形。通过这种新方法，我们能够处理投资组合优化的情况，而无需全部销售，并且还以几何术语恢复了投资组合优化的众所周知的结果，并允许短暂销售。然后，我们应用结果以确定CAC 40股票的哪种凸组合的风险最低：与指数相比，我们不仅获得了非常低的风险，而且还获得了回报率几乎是指数的三倍。
Risk aversion plays a significant and central role in investors' decisions in the process of developing a portfolio. In this framework of portfolio optimization we determine the portfolio that possesses the minimal risk by using a new geometrical method. For this purpose, we elaborate an algorithm that enables us to compute any generalized Euclidean distance to a standard simplex. With this new approach, we are able to treat the case of portfolio optimization without short-selling in its entirety, and we also recover in geometrical terms the well-known results on portfolio optimization with allowed short-selling. Then, we apply our results in order to determine which convex combination of the CAC 40 stocks possesses the lowest risk: not only we get a very low risk compared to the index, but we also get a return rate that is almost three times better than the one of the index.
