Capital Market Line and Security Market Line¶
Capital Market Line (CML)¶
The Capital Market Line (CML) is a graphical representation used in the Capital Asset Pricing Model (CAPM) to illustrate the rates of return for efficient portfolios depending on their level of risk (standard deviation). The CML is a straight line starting from the risk-free rate on the y-axis and extending upward, showing the best possible level of return for a given level of risk.
Overview¶
- Components: The CML includes all portfolios that optimally combine risk (as measured by standard deviation) and return, using a mix of the market portfolio and the risk-free asset.
- Interpretation: The slope of the CML represents the market's price of risk, which is the return per unit of risk. Portfolios that lie on the CML offer the best possible expected return for a given amount of risk.
Formula¶
The equation for the CML is:
\(E(R_p) = R_f + \frac{E(R_m) - R_f}{\sigma_m} \sigma_p\)
Where:
- \(E(R_p)\) is the expected return on the portfolio,
- \(R_f\) is the risk-free rate,
- \(E(R_m)\) is the expected return of the market,
- \(sigma_m\) is the standard deviation of the market,
- \(sigma_p\) is the standard deviation of the portfolio.
Key Points¶
- Risk and Return: Investors can see the trade-off between risk and return and choose a portfolio along the CML based on their risk tolerance.
- Efficiency: Only portfolios that include a combination of the market portfolio and risk-free assets lie on the CML, emphasizing optimal investment choices.
Security Market Line (SML)¶
The Security Market Line (SML) is also a key concept in the Capital Asset Pricing Model (CAPM) and represents the expected return of investments as a function of their systematic, or non-diversifiable, risk (represented by beta).
Overview¶
- Components: The SML plots risk versus return of the market and individual securities. It serves as a tool for evaluating whether an investment offers a favorable expected return against its risk level.
- Interpretation: The slope of the SML indicates the reward per unit of risk (beta). Securities plotted above the SML are considered undervalued, while those below are seen as overvalued.
Formula¶
The equation for the SML is:
\(E(R_i) = R_f + \beta_i (E(R_m) - R_f)\)
Where:
- \(E(R_i)\) is the expected return of investment
i, - \(R_f\) is the risk-free rate,
- \(beta_i\) is the beta of the investment,
- \(E(R_m)\) is the expected market return,
- \((E(R_m) - R_f)\) is the market risk premium.
Key Points¶
- Beta: Beta measures how much risk an investment will add to a portfolio that replicates the market.
- Market Risk Premium: The SML reflects the compensation investors require for taking on additional risk beyond the risk-free rate.
Conclusion¶
Both the CML and SML are foundational concepts in finance that help investors understand and manage the relationship between risk and return. While the CML focuses on the optimal portfolios that can be formed with the market portfolio and risk-free assets, the SML deals with the risk-return profiles of individual securities relative to market risk.
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