Capital Market Line (CML)

The Capital Market Line (CML) shows the set of optimal portfolios that combine a risk-free asset with a diversified market portfolio of risky assets. In the Capital Asset Pricing Model (CAPM) framework, portfolios on the CML achieve the highest expected return for a given level of total risk (standard deviation).

Key points

• The CML represents efficient risk–return trade-offs achievable by mixing a risk-free asset with the market (tangency) portfolio.
• Its slope equals the market portfolio’s Sharpe ratio.
• The tangency point where the CML meets the efficient frontier is the optimal risky portfolio (market portfolio).
• CML measures risk with total volatility (standard deviation); the Security Market Line (SML) measures risk with systematic risk (beta).
• Under CAPM assumptions, investors choose a position on the CML by lending (holding risk-free) or borrowing (levering the market portfolio) according to risk tolerance.

Formula and variables

Rp = rf + ((RT − rf) / σT) × σp

Where:
* Rp = expected return of the portfolio
* rf = risk-free rate
* RT = expected return of the market (tangency) portfolio
* σT = standard deviation of the market portfolio
* σp = standard deviation of the portfolio

The slope ( (RT − rf) / σT ) is the Sharpe ratio of the market portfolio. Moving along the CML increases both expected return and total risk.

Interpretation and investor implications

• Portfolios on the CML are mean–variance efficient when a risk-free asset is available.
• Investors select a point on the CML according to their risk aversion:
• More risk-averse investors hold more of the risk-free asset (closer to rf).
• Less risk-averse investors borrow at rf to invest more than 100% in the market portfolio (levering up).
• The tangency portfolio (market portfolio) is the optimal risky mix; combining it with the risk-free asset yields the entire CML (Tobin’s separation theorem: finding the market portfolio and deciding the allocation to it are separate decisions).

CML vs. related concepts

• CML vs. Capital Allocation Line (CAL): The CAL is the line from rf to any risky portfolio; the CML is the CAL specifically when the risky portfolio is the market (tangency) portfolio.
• CML vs. Efficient Frontier: The efficient frontier shows the best risky-only portfolios for each risk level. The CML includes the risk-free asset; its tangency to the efficient frontier identifies the optimal risky portfolio.
• CML vs. Security Market Line (SML):
• CML plots expected return against total risk (standard deviation) for efficient portfolios.
• SML plots expected return against systematic risk (beta) for individual securities and portfolios.
• Individual assets are evaluated using the SML; well-priced assets lie on the SML. Excesses or shortfalls relative to the SML indicate under- or overpricing given beta.

Practical use and limitations

Use the CML to:
* Evaluate whether a portfolio achieves an efficient trade-off of total risk and return.
* Assess allocation choices between a risk-free asset and the market portfolio.
* Understand how leveraging or de-leveraging affects expected return and volatility.

Limitations:
* The CML relies on CAPM assumptions (single-period horizon, homogeneous expectations, frictionless markets, and the ability to borrow/lend at rf). Real markets deviate from these assumptions, so the CML is a theoretical benchmark rather than a precise predictor.

Takeaway

The CML is a foundational concept in modern portfolio theory that describes the optimal combinations of a risk-free asset and the market portfolio, summarizing the best attainable risk–return trade-offs under CAPM assumptions. Use it as a theoretical guide for portfolio efficiency and for understanding the role of leverage and diversification.