Capital Market Line (CML): Risk, Return, and Efficient Portfolios

For educational purposes only; not investment advice.

Direct answer

The Capital Market Line (CML) describes the expected return and total risk of efficient portfolios made from a risk-free asset and the market portfolio. Its vertical axis is expected return. Its horizontal axis is portfolio standard deviation. Its slope is the market portfolio’s Sharpe ratio.

The CML is an asset allocation concept. It applies to efficient portfolios, not to individual stocks. A single stock can have high expected return and still sit below the CML because it contains diversifiable risk.

Formula

The common CML formula is:

E(Rp) = Rf + [(E(Rm) - Rf) / σm] × σp

Rf is the risk-free rate, E(Rm) is expected market return, σm is market portfolio volatility, and σp is the target portfolio volatility.

The slope is:

(E(Rm) - Rf) / σm

That is the reward per unit of total volatility for the market portfolio. Portfolios between the risk-free asset and the market portfolio hold some of each. Points to the right of the market portfolio require borrowing or leverage in the theoretical model.

Worked example

Assume the risk-free rate is 4%, expected market return is 10%, and market volatility is 15%.

CML slope = (10% - 4%) / 15% = 0.40

For a target volatility of 9%:

E(Rp) = 4% + 0.40 × 9% = 7.6%

This is equivalent to roughly 60% market portfolio and 40% risk-free asset:

0.60 × 10% + 0.40 × 4% = 7.6%

If the target volatility is 18%, the model implies 120% market portfolio and -20% risk-free asset. In real life, borrowing costs, margin rules, taxes, and drawdowns make that extension less clean.

Practical checks

Choose a realistic risk-free proxy for the investment horizon.
Remember that no investor can literally hold the full global market portfolio.
Estimate expected return and volatility with ranges, not single-point certainty.
Include fund fees, taxes, financing costs, and rebalancing.
Treat volatility as a risk measure, not a maximum loss.
Do not use the CML to value individual stocks; use beta-based models or cash-flow analysis for that.

Common misconceptions

The CML is not a guarantee of return. It is a model relationship under strong assumptions.

Low-volatility assets are not automatically efficient. They can have low return per unit of risk.

Leverage does not preserve the same slope in practice because borrowing costs and margin constraints differ from the risk-free rate.

CML and SML are different: CML uses total volatility for efficient portfolios; SML uses beta for individual assets and portfolios.

Sources

Sharpe, “Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk.”
Sharpe, “Mutual Fund Performance.”
Investor.gov, “Risk and Return.”