What is the Capital Market Line and how does it differ from the CAL?

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AcadiFi · Accepted Answer

The Capital Market Line (CML) is the specific Capital Allocation Line drawn from the risk-free rate through the market portfolio M — which under CAPM equilibrium assumptions equals the tangency portfolio with maximum Sharpe.

CML equation: E[R_p] = rf + [(E[R_M] − rf) / σ_M] × σ_p

The slope (E[R_M] − rf) / σ_M is the market's Sharpe ratio and the market price of risk.

Distinctions from CAL:

1. CAL applies to any risky portfolio P. CML applies only to the market portfolio.

2. CAL varies across portfolios — each portfolio has its own CAL. CML is unique — drawn to M specifically.

3. CML has the steepest possible slope among all CALs, because M has the maximum Sharpe ratio (by definition of tangency).

4. In CAPM equilibrium, all investors hold combinations of rf and M, so their complete portfolios lie on the CML. Portfolios not on CML are suboptimal.

Relationship to efficient frontier:

- Without risk-free asset: frontier is curved (hyperbola).
- With risk-free asset: frontier becomes CML — straight line tangent to old frontier at M.
- All efficient portfolios now lie on CML rather than curved frontier.

Example: rf = 3%, E[R_M] = 10%, σ_M = 18%. Market Sharpe = 7/18 = 0.389.

CML: E[R_p] = 3% + 0.389 × σ_p.

- 60/40 risky/rf: σ = 10.8%, E[R] = 3% + 0.389 × 10.8 = 7.2%.
- 120% risky (leveraged): σ = 21.6%, E[R] = 11.4%.

CML vs SML (Security Market Line):

- CML uses total risk (σ) — applies only to efficient portfolios.
- SML uses beta (systematic risk only) — applies to any asset, efficient or not.
- For efficient portfolios, σᵢ = βᵢ × σ_M, so both give the same expected return.
- For individual securities with idiosyncratic risk, SML gives the fair expected return but CML would overvalue them (because their total σ exceeds βσ_M).

Passive index investing is justified by CML logic: since the market portfolio is on the CML, no active manager should beat it after costs — buying the index is efficient.

What is the Capital Market Line and how does it differ from the CAL?

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