Capital Market Line Based on Efficient Frontier of Portfolio with Borrowing and Lending Rate

Abstract

Capital Asset Pricing Model (CAPM) is a general equilibrium model. It not only allows improved understanding of market behavior, but also practical benefits. However, there exists a risk-free asset in the assumption of the CAPM. Investors are able to borrow and lend freely at the rate may not be a valid representation of the working of the marketplace. Therefore, in this paper, it studies that the efficient frontier of portfolio in different borrowing and lending rate. This paper solves the highly difficult problem by matrix operation method. It first denotes the efficient frontier of Markowitz model with the matrix expression of portfolio. Then it denotes the capital market line (CML) with the matrix expression too. It is easy to calculate by using Excel function. The aim of this study is to develop the mean- variance analysis theory with regard to market portfolio and provide algorithmic tools for calculating the efficient market portfolio. Then explain that the portfolio frontier is hyperbola in mean-standard deviation space. It constructs CML in order to get more returns than that of efficient frontier if risk-free securities are included in the portfolio. A proposed step for CML on efficient frontier of portfolio with borrowing and lending rate is presented. Under these tools, it is easy calculation SML and CML by using Excel function. An example show that proposed method is correct and effective, and can improve the capability of the mean-variance portfolio efficiency frontier model.