NISM-Series-X-A: Investment Adviser (Level 1) · Introduction to Modern Portfolio Theory

Capital Allocation Line and Capital Market Line: CAL vs CML

Updated 11 October 2026 · Fact-checked

The Capital Allocation Line (CAL) shows the risk-return combinations you get by mixing a risk-free asset with any risky portfolio. The Capital Market Line (CML) is the special CAL that uses the tangency (market) portfolio. Its slope is the Sharpe ratio: (E(Rp) − Rf) ÷ σp. Expected return = Rf + slope × σ.

Understand Capital Allocation Line and Capital Market Line

Start with two assets. One is a risk-free asset, such as a Treasury bill, with return Rf and zero standard deviation. The other is a risky portfolio with expected return E(Rp) and standard deviation σp. You can split money between them. The mix you choose decides your risk and return.

If you put weight w in the risky portfolio and (1 − w) in the risk-free asset, your portfolio return is Rf + w × (E(Rp) − Rf). Your risk is w × σp. Both move in a straight line as w changes. That straight line, plotted with risk on the x-axis and expected return on the y-axis, is the Capital Allocation Line (CAL). Its intercept is Rf. Its slope is the extra return per unit of risk, which is the Sharpe ratio of the risky portfolio.

You can draw a CAL for any risky portfolio. A steeper CAL is better, because it gives more return for the same risk. So the investor wants the risky portfolio with the highest Sharpe ratio. On the efficient frontier of risky assets, that portfolio is the point where a line from Rf just touches the frontier. This point is the tangency portfolio.

The CAL drawn through the tangency portfolio is the Capital Market Line (CML). Under the theory's assumptions, all investors hold the same tangency portfolio, which is taken to be the market portfolio. They differ only in how much they put in the risk-free asset. This is the separation idea: first find the best risky portfolio, then decide the mix by risk appetite.

Points on the line to the left of the tangency portfolio mean lending at Rf (w below 1). Points to the right mean borrowing at Rf to invest more than 100% in the risky portfolio (w above 1). This assumes you can borrow at the same risk-free rate, which is a simplification.

In short: CAL is any risk-free plus risky mix. CML is the CAL with the tangency portfolio. Every CML is a CAL, but not every CAL is a CML.

Key formulas to remember

Portfolio expected return: E(Rc) = Rf + w × (E(Rp) − Rf); w is the weight in the risky portfolio. Equivalent to w × E(Rp) + (1 − w) × Rf.
Portfolio risk: σc = w × σp; The risk-free asset has zero standard deviation and zero covariance with the risky portfolio, so risk scales with w.
CAL equation: E(Rc) = Rf + [(E(Rp) − Rf) ÷ σp] × σc; Slope is the Sharpe ratio of the chosen risky portfolio.
CML equation: E(Rc) = Rf + [(E(Rm) − Rf) ÷ σm] × σc; Same as CAL but the risky portfolio is the market (tangency) portfolio m.
Slope of CML: (E(Rm) − Rf) ÷ σm; Called the market price of risk per unit of standard deviation.
Weight for target risk: w = σtarget ÷ σp; Use to find the risky weight that gives a desired total risk.

How to solve Capital Allocation Line and Capital Market Line questions

Most questions give Rf, the risky portfolio's return and risk, and ask for a return, risk, weight or slope. Use this order.

1Identify Rf, E(Rp) (or E(Rm)) and σp (or σm) from the question.
2Decide whether the risky portfolio is the tangency or market portfolio. If yes, the line is the CML. Otherwise it is a CAL.
3Compute the slope: (E(Rp) − Rf) ÷ σp.
4If the question gives a weight w, find risk as w × σp and return as Rf + w × (E(Rp) − Rf).
5If the question gives target risk, find w = σtarget ÷ σp, then compute the return.
6If w is above 1, the investor is borrowing at Rf. If w is below 1, the investor is lending. Check the sign of the risk-free weight (1 − w).
7Check that the answer lies on the line: the return must equal Rf plus slope times total risk.

Quickest way: Slope times risk plus Rf

When to use it: Use when the question gives a target risk or asks for return at a given standard deviation.

Calculate the slope once: (E(Rp) − Rf) ÷ σp.
Multiply the slope by the required standard deviation.
Add Rf. That is the expected return on the line.
For a weight question, scale the excess return (E(Rp) − Rf) by w and add Rf.

Common mistakes in Capital Allocation Line and Capital Market Line

Treating CAL and CML as the same thing.
Both are straight lines starting at Rf, so they look alike.
Fix: Remember that CML is a CAL that passes through the tangency (market) portfolio. A CAL can use any risky portfolio.
Using E(Rp) instead of the excess return (E(Rp) − Rf) in the slope.
Students forget the line starts at Rf, not at zero.
Fix: Always subtract Rf before dividing by σ.
Weighting risk by (1 − w) or adding the risk-free asset's risk.
Students mix up return weights and risk weights.
Fix: Risk-free asset has zero risk and zero correlation, so total risk is w × σp only.
Confusing CML with the Security Market Line (SML).
Both involve Rf and the market return.
Fix: CML has standard deviation on the x-axis and applies to efficient portfolios. SML has beta on the x-axis and applies to individual securities.
Thinking a weight above 100% in the risky portfolio is impossible.
Students assume weights must be between 0 and 1.
Fix: A weight above 1 means borrowing at Rf. The risk-free weight (1 − w) is then negative.
Placing the tangency portfolio anywhere on the efficient frontier.
Students forget how it is chosen.
Fix: It is the single frontier point with the highest Sharpe ratio, where the line from Rf just touches the frontier.

Worked examples

Example 1

Rf = 6%. A risky portfolio has expected return 14% and standard deviation 16%. An investor puts 60% in the risky portfolio and 40% in the risk-free asset. Find the expected return and standard deviation of the combined portfolio.

Show the solution

Excess return of risky portfolio = 14% − 6% = 8%.
Expected return = 6% + 0.60 × 8% = 6% + 4.8% = 10.8%.
Check: 0.60 × 14% + 0.40 × 6% = 8.4% + 2.4% = 10.8%.
Standard deviation = 0.60 × 16% = 9.6%.

Answer: Expected return 10.8%, standard deviation 9.6%.

Example 2

Rf = 5%. The market portfolio has expected return 13% and standard deviation 20%. Using the Capital Market Line, what expected return should an efficient portfolio with a standard deviation of 30% offer, and how is it built?

Show the solution

Slope of CML = (13% − 5%) ÷ 20% = 0.40.
Expected return = 5% + 0.40 × 30% = 5% + 12% = 17%.
Weight in market portfolio = 30% ÷ 20% = 1.5.
Risk-free weight = 1 − 1.5 = −0.5, so the investor borrows 50% of own capital at Rf.
Check: 1.5 × 13% + (−0.5) × 5% = 19.5% − 2.5% = 17%.

Answer: Expected return is 17%. The investor puts 150% in the market portfolio by borrowing 50% at the risk-free rate.

Exam tips

Expect questions that ask what the slope of the CML or CAL represents. The answer is the Sharpe ratio of the risky portfolio, or reward per unit of total risk.
When asked what makes a portfolio the tangency portfolio, choose the option with the highest Sharpe ratio on the efficient frontier.
Check the x-axis. Standard deviation means CAL or CML. Beta means SML.
With negative marking of 25% of the marks for each wrong answer, do not guess blindly on 2-mark caselet questions. Work the slope and weight first; they are quick.
In caselets, one set of data may serve several questions. Compute the slope once and reuse it.

Practice questions from Introduction to Modern Portfolio Theory

Capital Allocation Line and Capital Market Line in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Capital Allocation Line and Capital Market Line: frequently asked questions

What is the difference between CAL and CML?

A CAL is the line of risk-return combinations from mixing the risk-free asset with any chosen risky portfolio. The CML is the CAL for the tangency or market portfolio, which has the highest Sharpe ratio. So the CML is the best possible CAL.

What is the tangency portfolio?

It is the risky portfolio on the efficient frontier where a line drawn from the risk-free rate just touches the frontier. It has the highest Sharpe ratio of all risky portfolios. In theory, all investors hold it and vary only the risk-free mix.

What does the slope of the Capital Market Line mean?

The slope is (E(Rm) − Rf) ÷ σm. It shows the extra expected return you earn for each additional unit of standard deviation. It is also the Sharpe ratio of the market portfolio.

Can an investor earn a return above the market portfolio on the CML?

Yes, by borrowing at the risk-free rate and investing more than 100% in the market portfolio. Return and risk both rise. Total risk is then above the market's standard deviation.