The Capital Asset Pricing Model and the security market line

A lot of the financial literature devotes exclusive discussions to the Capital Asset Pricing Model (CAPM). In this section, we will explore key concepts that highlight the importance of linearity in finance.

In the famous CAPM, the relationship between risk and rates of return in a security is described as follows:

For a security, i, its returns are defined as R_i and its beta as β_i. The CAPM defines the return of the security as the sum of the risk-free rate, R_f, and the multiplication of its beta with the risk premium. The risk premium can be thought of as the market portfolio's excess returns exclusive of the risk-free rate. The following is a visual representation of the CAPM:

Beta is a measure of the systematic risk of a stock – a risk that cannot be diversified away. In essence, it describes...