不同借贷利率的投资组合的有效前沿

Efficient Frontier of Portfolio under Different Loan Interest Rates

研究在不同借贷利率下 ,投资组合的有效前沿 .运用一种几何方法 ,给出该有效前沿的方程 .把 Markowitz模型的有效前沿、不同借贷利率下的资本市场线 (CML) ,分别用投资组合的权重向量予以表示 .再由 CML的定义 ,就在 Markowitz模型的有效前沿上 ,分别求出不同借贷利率下资本市场线与 Markowitz模型有效前沿的切点 .由此 ,得到不同借贷利率下 CML的斜率 。

Efficient frontier of portfolio is studied under different loan interest rates and equation for this efficient frontier is given by using a geometric method. The details are described in 3 steps. Firstly, efficient frontier of Markowitz model is expressed by using weight vector of porlfolio, secondly, capital marketing lines (CML) under different loan interest rates are also expressed by using weight vector of portfolio. And finally, tangential points of CML under different loan interest rates with efficient frontier of Markowitz aresolved respectively, which are just solved on the efficient frontier of Markowitz model by the definition of CML; and moreover, the slopes of CML under different loan interest rates are also obtained. So the efficient frontier of portfolio under different loan interest rates is obtained.