Capital Market Line

Capital Market Line

The Capital Market Line (CML) describes the risk-return trade-off for efficient portfolios formed by combining the tangency portfolio T with the risk-free asset.

Any point on the CML is a blend of the risk-free asset (σ = 0, return = r_f) and the tangency portfolio (σ = σ_T, return = μ_T).

The equation of the CML is:

$\mu(\sigma) = r_f + \frac{\mu_T - r_f}{\sigma_T} \cdot \sigma$

The slope (μ_T − r_f) / σ_T is the Sharpe ratio of the tangency portfolio — also called the price of risk or market price of risk.

Interpretation

• At σ = 0: you hold only the risk-free asset, earning r_f
• At σ = σ_T: you hold only the tangency portfolio, earning μ_T
• At σ > σ_T: you borrow at r_f to leverage into the tangency portfolio

Your Task

Implement cml_return(mu_t, s_t, rf, sigma) that returns the expected return on the CML at a given level of risk σ.