Many financial literatures devote exclusive discussions to the capital asset pricing model (CAPM). In this section, we will explore the key concepts that highlight the importance of linearity in finance.

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

For a security , its returns is defined as and its beta as . The CAPM defines the return of the security as the sum of the risk-free rate 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 figure 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 the sensitivity of stock returns with respect to movements in the market. For example, a stock with a beta of zero produces no excess returns regardless...