CFA Level I Exam · Portfolio Risk and Return: Part II

Capital Market Line and the Market Portfolio Explained

Updated 7 October 2026 · Fact-checked

The capital market line (CML) is the capital allocation line that runs from the risk-free rate through the market portfolio, the tangency portfolio. Its equation is E(Rp) = Rf + [(E(Rm) − Rf) ÷ σm] × σp. Find the portfolio's weight in the market portfolio, then read off its return and risk.

Understand Capital Market Line and the Market Portfolio

Start with one risky portfolio and the risk-free asset. Mixing them gives a straight line called the capital allocation line (CAL). Its slope is the Sharpe ratio of the risky portfolio. A steeper line means more extra return per unit of risk.

Now look at all risky portfolios on the efficient frontier. Draw a line from the risk-free rate to touch the frontier. The steepest line just touches it at one point. That point is the tangency portfolio. It has the highest Sharpe ratio of all risky portfolios.

Capital market theory adds assumptions: investors share the same expectations (homogeneous), can borrow and lend at the risk-free rate, and markets have no taxes or transaction costs. Then every investor finds the same tangency portfolio. Since everyone holds it, it must contain every risky asset in proportion to its market value. That is the market portfolio. In this theory, the tangency portfolio and the market portfolio are the same.

The CAL drawn through the market portfolio is the capital market line (CML). Points between Rf and the market portfolio mean lending (weight in the market portfolio between 0 and 1). Points beyond the market portfolio mean borrowing at Rf to buy more of it (weight above 1).

The separation theorem says the investment decision has two separate parts. First, find the optimal risky portfolio. It is the same for everyone. Second, decide how much to put in it versus the risk-free asset. That depends on the investor's risk aversion. A cautious investor and an aggressive investor hold the same risky mix, just in different amounts.

The CML uses total risk (σ) on the x-axis and applies to efficient portfolios only. The security market line (SML) uses beta (systematic risk) and applies to any security or portfolio.

Key formulas to remember

CML equation: E(Rp) = Rf + [(E(Rm) − Rf) ÷ σm] × σp; Applies to efficient portfolios made of the risk-free asset and the market portfolio. The slope is the market Sharpe ratio.
Slope of the CML: Slope = (E(Rm) − Rf) ÷ σm; Extra return per unit of total risk. It is the Sharpe ratio of the market portfolio.
Portfolio return with weight w in the market: E(Rp) = w × E(Rm) + (1 − w) × Rf; w > 1 means borrowing at Rf. w < 1 means lending.
Portfolio risk with the risk-free asset: σp = w × σm; The risk-free asset has zero standard deviation and zero covariance with the market, so risk scales with w.
SML (for contrast): E(Ri) = Rf + βi × (E(Rm) − Rf); Uses beta, not σ. Applies to any asset, efficient or not.

How to solve Capital Market Line and the Market Portfolio questions

Use this method for any CML or market portfolio question.

1Identify what is given: Rf, E(Rm), σm, and either a target risk, a target return, or a weight.
2Check that the portfolio is a mix of Rf and the market portfolio. If it is a single stock or inefficient portfolio, the CML does not apply; think SML.
3Compute the CML slope: (E(Rm) − Rf) ÷ σm.
4If you are given σp, use E(Rp) = Rf + slope × σp. Or find w = σp ÷ σm.
5If you are given a target return, solve for σp, then w.
6Check the weight. Above 1 means borrowing; below 1 means lending. Make sure the answer fits that.
7For conceptual items, ask: does the question need total risk (CML) or beta (SML)? Does it involve choosing the risky mix (same for all) or the amount (varies)?

Quickest way: Weight shortcut

When to use it: When a question gives Rf, market return and σm and asks for return or risk of a mix.

Find w first: w = σp ÷ σm, or from the return target.
Return = Rf + w × (E(Rm) − Rf). Only the market premium is scaled by w.
Sanity check: if w > 1, return should exceed E(Rm).
Eliminate options: a return below Rf or above what w allows is wrong at once.

Common mistakes in Capital Market Line and the Market Portfolio

Using beta on the CML x-axis
CML and SML look alike and both use the market premium.
Fix: CML: σ on the x-axis, efficient portfolios only. SML: β on the x-axis, any asset.
Thinking riskier investors hold a different risky portfolio
People forget the separation theorem.
Fix: Everyone holds the same risky portfolio. Only the mix between it and Rf changes.
Treating borrowing as a weight below 1
Confusion about leverage.
Fix: Borrowing at Rf means w > 1, for example 130% in the market and −30% in Rf.
Applying the CML to a single stock
Students plot any asset on the CML.
Fix: A single stock has diversifiable risk, so it plots below the CML. Only efficient portfolios sit on it.
Multiplying Rf by w as well as the premium wrongly, or forgetting Rf
Rushing the formula.
Fix: Use E(Rp) = Rf + w × (E(Rm) − Rf). It avoids slips with (1 − w).
Confusing the tangency portfolio with the minimum-variance portfolio
Both sit on the efficient frontier.
Fix: The tangency portfolio has the highest Sharpe ratio. The minimum-variance portfolio has the lowest risk.

Worked examples

Example 1

The risk-free rate is 3%, the expected market return is 9% and the market standard deviation is 15%. What is the expected return of an efficient portfolio with a standard deviation of 20%? (A) 8% (B) 11% (C) 14%

Show the solution

Slope = (9% − 3%) ÷ 15% = 0.40.
E(Rp) = 3% + 0.40 × 20% = 3% + 8% = 11%.
Check: w = 20 ÷ 15 = 1.333, so the investor borrows. Return = 3% + 1.333 × 6% = 11%. Consistent.

Answer: B (11%)

Example 2

Rf is 2%, E(Rm) is 10% and σm is 16%. An investor wants an expected return of 6%. What is the weight in the market portfolio and the portfolio standard deviation? (A) w = 0.50, σ = 8% (B) w = 0.75, σ = 12% (C) w = 1.25, σ = 20%

Show the solution

Required premium over Rf = 6% − 2% = 4%.
Market premium = 10% − 2% = 8%.
w = 4% ÷ 8% = 0.50, so half is in the market and half is lent at Rf.
σp = 0.50 × 16% = 8%.

Answer: A (w = 0.50, σ = 8%)

Exam tips

If the question mentions total risk or standard deviation with efficient portfolios, use the CML. If it mentions beta, use the SML.
Remember the separation theorem as: one risky portfolio for all, the amount depends on risk aversion.
Weights above 1 signal borrowing. Use that to rule out options fast.
Conceptual items often test the assumptions: homogeneous expectations, a common risk-free rate for borrowing and lending, and no frictions.
You have about 90 seconds a question. Compute the slope once and reuse it.

Practice questions from Portfolio Risk and Return: Part II

Capital Market Line and the Market Portfolio in other exams

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

Capital Market Line and the Market Portfolio: frequently asked questions

What is the difference between the CML and the SML?

The CML plots expected return against total risk (σ) and applies only to efficient portfolios of the risk-free asset and the market portfolio. The SML plots expected return against beta and applies to any security or portfolio. A single stock can sit on the SML but below the CML.

Is the tangency portfolio the same as the market portfolio?

In capital market theory, yes. With homogeneous expectations, all investors find the same tangency portfolio. For markets to clear, it must hold every risky asset in proportion to market value, which is the market portfolio.

What does the separation theorem say?

It says investing splits into two steps. First, find the optimal risky portfolio, which is the same for every investor. Second, choose the mix of that portfolio and the risk-free asset based on your risk tolerance.

What does a point above the market portfolio on the CML mean?

It means the investor borrows at the risk-free rate and invests more than 100% of their own money in the market portfolio. This raises both expected return and risk.