What it means
Portfolio choice involves both expected reward and uncertainty, so a CAL places expected return on the vertical axis and standard deviation of returns on the horizontal axis. One end is a modelled risk-free holding, and moving along the line adds exposure to a chosen risky portfolio.
The diagram makes a tradeoff visible rather than deciding a suitable allocation for every investor. In the simple model, the risk-free asset is assigned zero volatility and zero correlation concerns.
If a fraction w goes into the risky portfolio, the rest goes into the risk-free asset, so expected return is a weighted average of the two returns, while modelled volatility is w times the risky portfolio's volatility when w is nonnegative and within ordinary unleveraged bounds. Suppose the risk-free return is 3%, a risky portfolio's expected return is 9% and its standard deviation is 15%: at a 50% risky weight, expected return is 6% and modelled standard deviation is 7.5%, and at a 100% risky weight those become 9% and 15%.
The line's slope in this example is (9% minus 3%) divided by 15%, or 0.40, which shows expected excess return per unit of modelled standard deviation. A steeper line offers more expected return for the same modelled volatility under the assumptions, but comparing lines requires consistent return periods, risk estimates and a relevant risk-free benchmark.
These are scenario inputs, not forecasts verified by future markets. The CFA Institute distinguishes the CAL from the capital market line, which is a special case that uses a market portfolio in a particular model.
A general CAL can use any specified risky portfolio, and calling every CAL a capital market line silently substitutes a stronger assumption about the portfolio and the market. A weight above 100% implies borrowing at the risk-free rate in the idealised picture and putting more than total wealth into the risky portfolio, but in reality borrowing rates are usually above lending rates and margin rules create nonlinear risks, so the simple straight line may not extend unchanged into leveraged portfolios.
The choice of risk-free proxy matters. A short government bill in one currency may have low nominal default risk for a matching investor, but inflation and exchange rates still affect purchasing power for others, and a portfolio with a payment due in another currency needs a benchmark aligned with that liability.
For managers, the CAL can compare alternative diversified portfolios on a common basis, and it should sit beside drawdown analysis, liquidity, liability matching and sensitivity tests. Its value is a clear model of a particular assumption set, not an exact map of how a portfolio will behave tomorrow.
In practice
Real-world examples.
Example
A foundation compares a 40% and a 60% risky-portfolio weight. It plots expected return and modelled volatility for each, then checks cash needs before selecting either.
Example
An analyst redraws a CAL when the assumed risk-free return changes from 3% to 4%. The new intercept and slope show why old allocation charts should not be reused without updating inputs.
Example
An investor whose liabilities are in another currency rejects a foreign bill as automatically risk-free in home-currency terms, despite its low nominal credit risk.
Formula
Calculation
For an unleveraged mix: E(Rp) = Rf + w x [E(Rr) - Rf], and sigma(p) = w x sigma(r), assuming the risk-free component has zero volatility. CAL slope = [E(Rr) - Rf] / sigma(r).
Worked example. The risk-free return Rf is 3%, the risky portfolio's expected return E(Rr) is 9% and its volatility sigma(r) is 15%.
- At w = 0.5, expected return = 3% + 0.5 x (9% - 3%) = 3% + 3% = 6%.
- Modelled standard deviation = 0.5 x 15% = 7.5%.
- At w = 0.25, expected return = 3% + 0.25 x 6% = 4.5% and standard deviation = 3.75%; at w = 0.75, they are 7.5% and 11.25%.
- Slope = (9% - 3%) / 15% = 0.40.
- On a $100,000 fund at w = 0.5, $50,000 sits in the risky portfolio and $50,000 in the risk-free asset, giving an expected annual gain of $6,000 under these inputs.
Outside the model, borrowing and other risks can change the relation.Case study
Seen in the real world.
Fictional example: Investment analyst Sara prepared an allocation review for a scholarship fund. Her first chart combined a 3% short-bill return with a diversified risky portfolio modelled at 9% expected return and 15% volatility. It showed 25%, 50%, and 75% risky weights along one line.
The trustees initially chose the highest expected return shown. Sara added the fund's two-year scholarship commitments, possible drawdowns, and the uncertainty of the 9% assumption. The board retained a liquid reserve and selected a lower risky weight consistent with its spending obligations.
Watch out
Common mistakes.
- Treating the plotted expected return as certain or standard deviation as a complete measure of downside and liquidity risk.
- Calling any capital allocation line the capital market line without verifying the special market-portfolio assumption.
- Extending the straight line to borrowed investments while ignoring higher funding rates, collateral rules, and leveraged losses.
Questions
People also ask.
What are the axes?
Expected portfolio return is usually on the vertical axis and modelled risk, often standard deviation, on the horizontal axis.
Is the slope a guaranteed return for risk?
No. It compares estimated excess return with estimated volatility under stated inputs; realised outcomes can differ.
How does it differ from the capital market line?
The capital market line is a particular model case using the market portfolio, while a general CAL can use another risky portfolio.
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