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Capital Market Line (CML): Expected Return and Efficient Portfolio Risk

Understand the CML as the efficient risk-free and market-portfolio combination, derive its Sharpe-ratio slope, distinguish it from the CAL and SML, and test leverage assumptions.

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For educational purposes only; not investment advice. Investing may result in loss.

Direct answer

The Capital Market Line is the straight expected-return relationship for mean-variance-efficient portfolios formed by combining a risk-free asset with the CAPM market portfolio. Its vertical axis is expected return, its horizontal axis is total return standard deviation, its intercept is the risk-free rate, and its slope is the market portfolio’s expected excess return per unit of total volatility.

The CML is a special capital allocation line, not a line for every security. A capital allocation line can connect the risk-free asset to any chosen risky portfolio; it becomes the CML only when the risky portfolio is the market tangency portfolio under the model. The Security Market Line is different: it plots expected return against beta and, under CAPM, applies to individual assets as well as portfolios.

Formula and assumptions

For the usual efficient ray with a nonnegative weight in the market portfolio:

E(Rp) = Rf + [(E(Rm) - Rf) / σm] × σp

Here E(Rp) is expected portfolio return, Rf is the risk-free rate, E(Rm) is expected market return, σm is market-portfolio volatility, and σp is portfolio volatility. The slope is:

CML slope = [E(Rm) - Rf] / σm

This is the ex ante Sharpe ratio of the market portfolio when the risk-free rate and return horizon are consistent. If w is the weight in the market portfolio and the rest is in the risk-free asset:

E(Rp) = w × E(Rm) + (1 - w) × Rf

σp = w × σm

The volatility formula above assumes w ≥ 0; standard deviation is nonnegative, so a short-market portfolio needs sign-aware treatment and does not lie on the usual efficient CML ray. For 0 ≤ w ≤ 1, the investor lends at the risk-free rate. For w > 1, the model requires borrowing at that same rate and investing more than 100% in the market portfolio.

The result depends on strong assumptions: investors choose only by expected return and variance over a common horizon; expectations are homogeneous; assets are divisible and tradable; markets have no taxes or transaction costs; and investors can borrow and lend unlimited amounts at one risk-free rate. CAPM’s market portfolio includes all risky assets, not merely a convenient stock index. In practice, the true portfolio and expected inputs are unobservable, borrowing and lending rates differ, and constraints can bend or truncate the feasible line.

Worked example

Assume a horizon-consistent risk-free rate of 4%, expected market return of 10%, and market volatility of 15%. The expected market risk premium is 6%:

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

For target volatility of 9%, the market weight is:

w = 9% / 15% = 60%

The other 40% is held in the risk-free asset, so:

E(Rp) = 4% + 0.40 × 9% = 7.6%

E(Rp) = 60% × 10% + 40% × 4% = 7.6%

For target volatility of 18%, the theoretical market weight is 120% and the risk-free weight is -20%:

E(Rp) = 120% × 10% - 20% × 4% = 11.2%

That calculation assumes borrowing at 4%. If the actual borrowing rate is 6%, the simplified expected return becomes:

E(Rp) = 120% × 10% - 20% × 6% = 10.8%

The realized financing spread reduces the slope. Margin requirements, forced deleveraging, fees, taxes, and path-dependent losses can reduce results further; volatility also does not cap the possible loss.

Practical checklist

  • State whether the line is a generic capital allocation line or the CAPM Capital Market Line.
  • Define the return horizon, currency, compounding convention, and nominal or real basis consistently.
  • Choose a risk-free proxy whose maturity and currency match the analysis; a short Treasury bill is not risk-free for every horizon or investor.
  • Define the market proxy and disclose assets it omits, including nonpublic, foreign, real, or human-capital exposures where relevant.
  • Use expected returns in the formula; historical arithmetic or geometric averages are estimates, not expected returns themselves.
  • Estimate expected return, volatility, and correlation with ranges and sampling uncertainty rather than false precision.
  • Align gross or net returns across the risk-free asset and market proxy, including fund fees and index implementation costs.
  • Distinguish lending from borrowing rates and include spreads, margin interest, haircuts, collateral, and leverage limits.
  • Model taxes, transaction costs, rebalancing, turnover, liquidity, tracking error, and cash drag.
  • Check whether short selling, leverage, derivatives, or the chosen risk-free instrument are permitted for the investor.
  • Stress recessions, volatility spikes, correlation shifts, funding withdrawal, margin calls, and forced sales.
  • Treat standard deviation as symmetric dispersion, not maximum drawdown, default risk, liquidity risk, or a complete risk measure.
  • Compare the CML with the risky-asset efficient frontier and confirm the proposed market proxy is actually tangent under the chosen estimates.
  • Do not place an individual security on the CML to judge mispricing; use the SML for CAPM beta analysis or use a cash-flow valuation.
  • For an individual security, distinguish total volatility from beta and diversifiable from systematic risk.
  • Treat points below the estimated CML as inefficient only relative to the stated model, inputs, constraints, and opportunity set.
  • Do not call an observed point above an estimated CML impossible; estimation error, stale inputs, omitted assets, leverage, or realized noise can produce it.
  • Re-estimate inputs carefully rather than mechanically after market moves; procyclical estimates can induce buy-high and sell-low behavior.
  • Evaluate realized performance over multiple periods using returns, volatility, drawdowns, costs, exposures, and benchmark consistency.
  • Record which assumptions would invalidate the recommendation and how the portfolio would be rebalanced or deleveraged.

Common misconceptions

“Every asset should lie on the CML.” Only efficient combinations of the risk-free asset and market portfolio lie on the theoretical CML. The SML, which uses beta rather than total volatility, is the CAPM relation for individual assets.

“The CML slope is a guaranteed return per unit of risk.” It is an expected model ratio built from uncertain inputs. Realized returns, volatility, correlations, and the risk-free rate can differ materially.

“Moving right of the market portfolio preserves the same Sharpe ratio in practice.” The theoretical result assumes borrowing at the lending rate without frictions. Financing spreads, margin rules, fees, taxes, deleveraging, and nonlinear losses usually change the outcome.

“A low-volatility portfolio is automatically efficient.” Efficiency depends on expected return relative to total risk and the available opportunity set. A low-volatility portfolio can lie below the relevant capital allocation line.

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