Introduction

In the world of investment and portfolio management, understanding the concepts of the Capital Market Line (CML) and the Security Market Line (SML) is pivotal. These two lines play a crucial role in depicting the relationship between risk and return for individual assets and portfolios. In this chapter, we delve into the interpretation and comparison of the CML and SML, exploring their distinct characteristics and implications for investors.

The Capital Market Line (CML)

The Capital Market Line represents the efficient portfolios achievable by combining the riskfree asset and the market portfolio. The CML shows the optimal risk-return trade-off for a given level of risk. It is a tangent line drawn from the risk-free rate to the efficient frontier of risky assets. Mathematically, the equation of the CML is:

$$E(R_p)=R_f+\frac{E(R_m)-R_f}{\sigma_m} \times \sigma_p$$

Where:

• $E(R_p)$ is the expected return of the portfolio.
• $R_f$ is the risk-free rate.
• $E(R_m)$ is the expected return of the market portfolio.
• $\sigma_m$ is the standard deviation of the market portfolio’s returns.
• $\sigma_p$ is the standard deviation of the portfolio’s returns.

The CML illustrates that the higher the risk (standard deviation), the greater the expected return.

The Security Market Line (SML)

The Security Market Line represents the relationship between risk and expected return for individual assets. It’s derived from the Capital Asset Pricing Model (CAPM). The equation of the SML is:

$$E(R_i)=R_f+\beta_i \times (E(R_m)-R_f)$$

Where:

• $E(R_i)$ is the expected return of asset $i$.
• $R_f$ is the risk-free rate.
• $\beta_i$ is the beta of asset $i$.
• $E(R_m)$ is the expected return of the market portfolio.

The SML shows that the expected return of an asset increases linearly with its beta, indicating the asset’s systematic risk. Assets above the SML are considered underpriced, while those below are overpriced.

Interpreting and Comparing CML and SML

Both the CML and SML provide insights into risk and return relationships. However, the CML focuses on portfolios, while the SML is concerned with individual assets. The CML allows investors to determine the optimal portfolio by considering the risk-free asset and the market portfolio. On the other hand, the SML helps investors assess the expected return an asset should offer based on its systematic risk (beta).