Introduction

In this chapter, we delve into the foundational concepts of the Capital Asset Pricing Model (CAPM), a cornerstone of modern finance. The CAPM provides a systematic framework for understanding the relationship between risk and expected returns of assets in a well-diversified portfolio. We will explore how the CAPM is derived and dissect its key components, which play a crucial role in assessing the risk and potential return of an investment.

The Capital Asset Pricing Model (CAPM) is a powerful tool that helps investors evaluate the expected return of an investment based on its risk characteristics. CAPM is grounded in the notion that investors require compensation for taking on risk. By understanding the components and derivation of CAPM, you gain insights into the factors that influence asset pricing in the financial markets.

Derivation of CAPM

The CAPM is derived from the following key concepts:

• Risk-Free Rate $(R_f)$: This is the return on a risk-free investment, typically represented by government bonds. It serves as a baseline for assessing the expected return of risky assets.

• Market Risk Premium $(R_m - R_f)$: The market risk premium represents the additional return that investors demand for holding a diversified portfolio of risky assets instead of risk-free assets. It captures the compensation for bearing systematic risk.

• Beta $(\beta)$: Beta measures the sensitivity of an asset’s returns to the overall market movements. A beta greater than 1 implies higher volatility compared to the market, while a beta less than 1 indicates lower volatility.

CAPM Formula

The CAPM formula combines these components to estimate the expected return of an asset: $$E(R_i)=R_f+\beta_i \times (R_m-R_f)$$

Where:

• $E(R_i)$ represents the expected return of asset $i$.
• $R_f$ is the risk-free rate.
• $R_m$ is the expected return of the market.
• $\beta_i$ is the beta of asset $i$, reflecting its sensitivity to market movements.
• $(R_m-R_f)$ is the market risk premium.

Components of CAPM

• Risk-Free Rate $(R_f)$: The risk-free rate reflects the return an investor can earn without taking on any risk. It serves as a baseline return that compensates for the time value of money.

• Market Risk Premium $(R_m - R_f)$: The market risk premium compensates investors for the extra risk they undertake by investing in the market rather than risk-free assets.

• Beta $(\beta)$: Beta measures an asset’s volatility relative to the overall market. A beta greater than 1 implies the asset is more volatile than the market, while a beta less than 1 signifies lower volatility.