CML vs SML: Capital & Security Market Lines

• Capital Market Line (CML) and Security Market Line (SML) are fundamental concepts in modern portfolio theory.
• They provide insights into the risk-return trade-off but differ significantly.

Definition and Purpose

• Capital Market Line (CML)
  • Represents the expected return of efficient portfolios.
  • Shows the risk-return trade-off for a portfolio of assets.
  • Identifies the optimal combination of the risk-free asset and the market portfolio to achieve maximum returns for a given level of total risk (standard deviation).
• Security Market Line (SML)
  • Depicts the relationship between the expected return of individual assets (or portfolios) and their systematic risk (beta).
  • Shows the risk-return trade-off for individual securities rather than entire portfolios.
  • Evaluates if a security is fairly priced, overvalued, or undervalued based on its beta.

Axes and Variables

• CML
  • X-Axis: Total Risk (Standard Deviation, σ), representing the overall risk (systematic + unsystematic) of the portfolio.
  • Y-Axis: Expected Return, E(Rp).
  • Applies only to efficient portfolios that combine the risk-free asset and the market portfolio.
• SML
  • X-Axis: Systematic Risk (Beta, β), representing only the non-diversifiable, or market-related, risk of individual securities or portfolios.
  • Y-Axis: Expected Return, E(Ri).
  • Applies to all assets or portfolios, regardless of diversification.
• The slope of the CML is the Sharpe Ratio of the market which represents the market price of risk per unit of total risk.
• The slope of the SML represents the market price of risk per unit of systematic risk (the risk premium)

Types of Risk Considered

• CML
  • Considers Total Risk (Standard Deviation), which includes both systematic and unsystematic risk.
  • Relevant only for fully diversified portfolios on the efficient frontier, where unsystematic risk has been diversified away.
• SML
  • Considers only Systematic Risk (Beta), which is the risk inherent to the entire market and cannot be diversified away.
  • Applicable to both individual securities and portfolios, regardless of their diversification level.

Applicability to Assets or Portfolios

• CML
  • Only applies to efficient portfolios that lie on the efficient frontier and are fully diversified.
  • Assumes portfolios are optimally diversified to eliminate unsystematic risk.
  • Represents a mix of the market portfolio and the risk-free asset.
• SML
  • Applies to individual securities, portfolios, or any combination thereof.
  • Helps determine whether a particular security or portfolio provides an adequate return for its level of systematic risk.
  • Any asset on the SML is considered fairly priced; assets above the line are undervalued, while those below are overvalued.

Use in Performance Evaluation

• CML
  • Measures portfolio performance based on total risk.
  • Sharpe Ratio (measuring excess return per unit of total risk) is often used alongside the CML for comparing diversified portfolios.
• SML
  • Evaluates the performance of individual securities based on their systematic risk.
  • Treynor Ratio (measuring excess return per unit of systematic risk) is often used alongside the SML for comparing securities or portfolios.

Example Interpretation

• CML Example

  • A portfolio with a standard deviation of 10% might lie on the CML if it’s well-diversified.
  • If the market return is 12% and risk-free rate is 4%, the CML can help find the expected return for a portfolio with that total risk level.

• SML Example

  • A stock with a beta of 1.2 would have a higher expected return than a stock with beta 0.8, assuming the market risk premium is positive.
  • The SML shows if these stocks are fairly priced relative to their systematic risk.

• CML focuses on diversified portfolios and total risk.

• SML is applicable to all securities, focusing solely on systematic risk.

• Both lines are essential tools in investment analysis but serve distinct purposes in portfolio management and security valuation.