讨论了资本资产定价模型(CAPM)中两类资产组合有效前沿边界的相切关系,介绍了一些著作和教科书中对它的处理方式,事实上他们均未给出严格意义上的证明.本文对两类资产组合有效前沿边界的相切关系给出了三种较严格的证明. This paper discusses the tangential relationship between the effective frontiers of the two types of asset portfolios in the Capital Asset Pricing Model (CAPM), introduces some of the ways in which they are dealt with in some books and textbooks, and in fact none of them gives a strict sense of proof. The tangential relationship between the effective frontier boundaries of the two asset classes gives three more rigorous proofs.