What Is CML vs SML?

Comparing the Capital Market Line (CML) and the Security Market Line (SML) to understand their roles in finance, particularly in the context of portfolio management and individual asset expected returns.

In the realm of finance, the concepts of the Capital Market Line (CML) and the Security Market Line (SML) are fundamental, particularly in the areas of portfolio theory and capital asset pricing. While both lines are foundational in modern portfolio theory, they serve different purposes and convey unique relationships between risk and return.

Capital Market Line (CML)

The CML represents the risk-return profile of efficient portfolios, which are portfolios that optimally balance risk and return. It is derived from the Capital Asset Pricing Model (CAPM) and reflects the trade-off between risk (as measured by standard deviation) and expected return.

Definition

The Capital Market Line (CML) is the line in the mean-variance portfolio performance space that extends from the risk-free rate through the market portfolio. The equation of the CML can be given by:

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

where:

• \( \text{E}(R_p) \) is the expected return on the portfolio
• \( R_f \) is the risk-free rate
• \( \text{E}(R_m) \) is the expected return on the market portfolio
• \( \sigma_p \) is the standard deviation of the portfolio
• \( \sigma_m \) is the standard deviation of the market portfolio

Key Characteristics

• Efficiency: Only efficient portfolios lie on the CML.
• Std. Deviation: The risk measure used is the standard deviation of portfolio returns.
• Slope: The slope of the CML represents the Sharpe Ratio of the market portfolio.

Example

Assume the risk-free rate \( R_f \) is 3%, the expected market return \( \text{E}(R_m) \) is 10%, and the standard deviation of the market portfolio \( \sigma_m \) is 15%. For a portfolio with a standard deviation \( \sigma_p \) of 10%, the expected return \( \text{E}(R_p) \) would be calculated as:

$$ \text{E}(R_p) = 3\% + \left(\frac{10\% - 3\%}{15\%}\right) \times 10\% = 7.67\% $$

Security Market Line (SML)

The SML represents the expected return of individual assets as a function of their beta. Unlike CML, which pertains to efficient portfolios, the SML is crucial for understanding the risk of individual securities in relation to the overall market.

Definition

The Security Market Line (SML) illustrates the relationship between the expected return of a security and its systemic, non-diversifiable risk, measured by beta \( \beta \). The equation of the SML is:

$$ \text{E}(R_i) = R_f + \beta_i \times [\text{E}(R_m) - R_f] $$

where:

• \( \text{E}(R_i) \) is the expected return on security i
• \( \beta_i \) is the beta of security i
• \( R_f \) is the risk-free rate
• \( \text{E}(R_m) \) is the expected return on the market portfolio

Key Characteristics

• Individual Securities: The SML applies to individual assets.
• Beta: The risk measure used is beta, indicating the security’s sensitivity to market movements.
• Application: Helps in determining if an asset is under or overvalued based on its risk.

Example

Assume the risk-free rate \( R_f \) is 3%, the expected market return \( \text{E}(R_m) \) is 10%, and the beta of a security \( \beta_i \) is 1.2. The expected return \( \text{E}(R_i) \) for the security would be:

$$ \text{E}(R_i) = 3\% + 1.2 \times (10\% - 3\%) = 11.4\% $$

Comparison: CML vs SML

Conceptual Differences

• Focus: The CML focuses on efficient portfolios, whereas the SML focuses on individual securities.
• Risk Measure: CML uses standard deviation, while the SML uses beta.

Practical Implications

• Portfolio Selection: CML is used for selecting the optimal portfolio.
• Asset Pricing: SML helps in pricing individual securities and assessing their expected returns.

FAQs

What is the primary difference between CML and SML?

The CML pertains to efficient portfolios and uses standard deviation as the risk measure, while the SML pertains to individual securities and uses beta as the risk measure.

How do CML and SML relate to CAPM?

Both CML and SML are derived from the Capital Asset Pricing Model (CAPM). The CML represents efficient portfolios, whereas the SML represents the expected return of securities given their beta.

Can a non-efficient portfolio lie on the CML?

No, only efficient portfolios that provide the highest expected return for a given level of risk will lie on the CML.

References

1. Sharpe, W. F. (1964). “Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk”. Journal of Finance.
2. Markowitz, H. (1952). “Portfolio Selection”. Journal of Finance.

Summary

Understanding both the Capital Market Line (CML) and the Security Market Line (SML) is crucial for portfolio management and asset pricing. While the CML deals with efficient portfolios and the overall risk-return trade-off, the SML focuses on individual asset returns based on their beta. Both tools are derived from the Capital Asset Pricing Model (CAPM) but serve different, complementary purposes in financial theory and practice.