Two Lines, Two Measures of Risk

The capital market line shows the expected return of efficient portfolios that combine a risk-free asset with the market portfolio, plotted against total risk measured by standard deviation. The security market line shows the expected return of any individual security or portfolio plotted against its beta, the measure of market risk used in the capital asset pricing model.

Both lines start at the risk-free rate and slope upwards, because investors expect higher returns for taking more risk. The difference is the risk measure on the horizontal axis and which investments belong on each line.

Only fully diversified, efficient portfolios lie on the capital market line, while every security, efficient or not, can be plotted against the security market line. For the full route from the exam to a career applying these ideas, our complete guide to how to become an investment adviser representative covers every step.

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Where Both Lines Come From

Both lines grow out of modern portfolio theory, developed by Harry Markowitz in the 1950s. Markowitz showed that combining assets whose returns do not move perfectly together reduces risk, and that there is a set of portfolios offering the highest expected return for each level of risk, known as the efficient frontier.

When a risk-free asset, such as a Treasury bill, is added, investors can do better than the efficient frontier alone. The best combination of risky assets is the market portfolio, and every efficient portfolio becomes a mix of the market portfolio and the risk-free asset.

That idea produces the capital market line. The capital asset pricing model, developed in the 1960s, then extended it to explain the expected return of individual securities, producing the security market line; the Series 65 Exam Preparation course at FRC covers both as part of its portfolio management material.

How the Capital Market Line Works

The capital market line runs from the risk-free rate on the vertical axis through the market portfolio. Its equation is: expected return equals the risk-free rate plus the portfolio’s standard deviation multiplied by the market’s excess return divided by the market’s standard deviation.

The slope of the line, the market’s excess return divided by its standard deviation, is the market portfolio’s Sharpe ratio. It shows how much extra return the market offers for each unit of total risk.

Points on the line to the left of the market portfolio represent mixes of the market and the risk-free asset, a lending portfolio. Points to the right represent borrowing at the risk-free rate to invest more than 100 percent in the market, a leveraged portfolio.

How the Security Market Line Works

The security market line is the capital asset pricing model drawn as a graph. Its equation is: expected return equals the risk-free rate plus beta multiplied by the market risk premium, the market return minus the risk-free rate.

The slope of the security market line is the market risk premium itself. A security with a beta of 1.0 sits at the market return, while securities with higher betas sit further up the line and those with lower betas sit closer to the risk-free rate.

The line shows the required return for each level of market risk. A security’s expected return can then be compared with the line to judge whether it is fairly priced.

Security Market Line and Capital Market Line Compared

Worked Example: Moving Along the Capital Market Line

The risk-free rate is 4 percent, the market portfolio is expected to return 10 percent and its standard deviation is 16 percent. The slope of the capital market line is 6 divided by 16, or 0.375.

Step one: a portfolio with a standard deviation of 8 percent, half in Treasury bills and half in the market, has an expected return of 4 percent plus 0.375 times 8, or 7 percent. Step two: a portfolio with a standard deviation of 24 percent, created by borrowing to invest 150 percent in the market, has an expected return of 4 percent plus 0.375 times 24, or 13 percent.

Step three: both portfolios are efficient, because they lie on the line. The choice between them depends only on how much total risk the investor is willing to take, which is why the line is useful when setting a client’s overall mix of risky and safe assets.

Worked Example: Using the Security Market Line to Spot Mispricing

Using the same risk-free rate of 4 percent and market return of 10 percent, the market risk premium is 6 percent. A stock has a beta of 1.3, so its required return on the security market line is 4 percent plus 1.3 times 6 percent, or 11.8 percent.

Step one: an analyst forecasts the stock will return 13 percent, which plots above the line. Step two: the stock offers 1.2 percentage points more than its risk requires, a positive alpha, so it appears undervalued.

Step three: a second stock with a beta of 0.9 has a required return of 9.4 percent, but its forecast return is only 8 percent. It plots below the line, offering less than its risk requires, so it appears overvalued; our article on alpha vs beta explains how that gap is measured as alpha.

Study Portfolio Theory With FRC

Portfolio theory questions often show a graph or a set of numbers and ask which line applies, which portfolio is efficient or whether a security is fairly priced. Our Series 65 course explains each concept step by step, with worked calculations that prepare you for these questions.

Consider studying with FRC for every exam on your route. Explore our USA exam courses, from the SIE through the Series 7, Series 63 and Series 65.

To take advantage of the membership, explore FRC Professional Membership, which gives you a verified Digital Profile that shows employers your real-time course progress, together with the Video Resume. Current offers are on our membership deals page.

The Efficient Frontier and the Power of Diversification

The efficient frontier exists because combining assets that do not move perfectly together lowers risk without necessarily lowering return. The lower the correlation between two assets, the greater the reduction in risk when they are combined.

Worked example: two stocks each have an expected return of 9 percent and a standard deviation of 20 percent, and the correlation between them is 0.2. Step one: a portfolio split equally between them still has an expected return of 9 percent. Step two: its variance is 0.25 times 400, plus 0.25 times 400, plus 2 times 0.25 times 0.2 times 400, or 240, giving a standard deviation of about 15.5 percent.

Step three: the investor has cut risk from 20 percent to about 15.5 percent with no loss of expected return. Adding more assets with low correlations pushes the portfolio closer to the efficient frontier, and the market portfolio, which holds everything, sits at the point where that diversification is complete.

Why the Risk Measures Differ

The capital market line uses standard deviation because it describes efficient portfolios, which are fully diversified. For those portfolios, all remaining risk is market risk, so total risk and systematic risk are effectively the same.

Individual securities carry company-specific risk as well as market risk. Because that specific risk can be diversified away, the market does not reward investors for bearing it, so expected returns depend only on beta, the measure used by the security market line.

This is why an individual stock can sit well below the capital market line, because its standard deviation is high relative to its return, while still sitting exactly on the security market line. The two lines answer different questions about risk.

How the Lines Shift

Both lines move when market conditions change. If the risk-free rate rises, both lines shift upwards, raising the required return on every investment.

If investors become more fearful and demand a larger market risk premium, the security market line becomes steeper, and riskier securities must offer higher returns to attract buyers. Prices of high-beta securities tend to fall until their expected returns rise to match.

Changes in the market’s volatility affect the capital market line’s slope. A more volatile market with the same expected excess return produces a flatter line, offering less reward per unit of total risk.

Assumptions and Limitations

Both lines rest on simplifying assumptions: investors can borrow and lend at the risk-free rate, share the same expectations, face no taxes or transaction costs, and care only about expected return and standard deviation. None of these hold perfectly in real markets.

Beta is estimated from past data and can change, and the true market portfolio, which in theory includes every risky asset, cannot be observed directly; in practice, a broad stock index stands in for it. Empirical studies have found that low-beta stocks have often earned more, and high-beta stocks less, than the security market line predicts.

Despite these limits, the two lines remain the foundation of how professionals think about risk and return. They also explain why low-cost diversified portfolios are so central to sound investment advice.

Using the Lines in Client Advice

The capital market line supports a simple and powerful idea: the most efficient way to adjust risk is to change the mix between a diversified market portfolio and safe assets. A conservative client might hold 40 percent in the market and 60 percent in short-term Treasuries, while an aggressive client holds all, or more than all, in the market.

The security market line helps with selection. When reviewing a fund or stock, advisers can compare its expected return with what its beta requires, and question whether a high-beta holding is likely to compensate the client for the extra market risk.

Both lines remind advisers that risk should be judged in context. A single volatile holding may add little risk to a well-diversified portfolio, while the same holding could dominate the risk of a concentrated one.

The Memory Aid

Remember “CML counts total, SML sees systematic”: the capital market line uses standard deviation, the security market line uses beta.

For which investments belong, remember “CML for the efficient few, SML for everyone”: only efficient portfolios lie on the capital market line, but any security can be plotted against the security market line.

For mispricing, remember “above the line, a buy sign”: a security plotting above the security market line appears undervalued.

Exam Traps to Avoid

The first trap is putting beta on the capital market line. The capital market line uses standard deviation; beta belongs to the security market line.

The second trap is assuming every stock should lie on the capital market line. Only efficient, fully diversified portfolios do.

The third trap is reading a security above the security market line as overvalued. It offers more return than its risk requires, so it appears undervalued. The fourth trap is forgetting that the slope of the security market line is the market risk premium, while the slope of the capital market line is the market’s Sharpe ratio.

A Client Scenario

A client holds a single high-volatility technology stock alongside cash and asks whether the stock is a good investment. The stock has a beta of 1.4 and a standard deviation of 45 percent, the risk-free rate is 4 percent and the market is expected to return 10 percent with a standard deviation of 16 percent.

The adviser explains that on the security market line the stock’s required return is 4 percent plus 1.4 times 6, or 12.4 percent, and the analyst consensus expects about 12 percent, so it looks roughly fairly priced. On the capital market line, however, a portfolio with 45 percent volatility should expect about 20.9 percent, so holding the stock alone exposes the client to far more total risk than the return justifies.

The adviser recommends building a diversified portfolio around the stock, which keeps its market exposure but removes much of its company-specific risk. The recommendation is documented with the client’s goals, time horizon and the reasons for reducing concentration.

The Dictionary as a Video Library

The FRC dictionary is a study tool, not just a glossary. Every entry pairs a written explanation with deep-dive video, on-page quizzes and interactive flash cards, so you can read a concept, watch it explained and test yourself in one place.

Rules are covered in the same depth: open a rule and you will find the full explanation alongside video walk-throughs of how it applies in practice. Open the security market line and CAPM entries to see the formulas worked through on video and test yourself with the quizzes.

Practice Questions to Test Yourself

Question one: Which line uses beta as its measure of risk? The security market line.

Question two: The risk-free rate is 3 percent and the market risk premium is 7 percent. What is the required return for a stock with a beta of 0.8? 8.6 percent, because 3 plus 0.8 times 7 equals 8.6.

Question three: A stock’s forecast return plots below the security market line. What does that suggest? It appears overvalued, offering less return than its market risk requires.

Question four: The market returns 11 percent with a standard deviation of 20 percent, and the risk-free rate is 3 percent. What is the slope of the capital market line? 0.4, the market’s excess return of 8 percent divided by 20 percent.

Question five: Which portfolios lie on the capital market line? Efficient portfolios combining the risk-free asset and the market portfolio.

Turn Analytical Skill Into Career Evidence

Portfolio theory sits behind every asset allocation decision, and advisers who can explain it simply earn client trust. FRC’s Digital Profile shows employers the courses you are actively studying and the progress you have earned through assessed learning, verified by FRC, and a QR code on your resume takes them straight to it.

The FRC Video Resume lets a hiring manager hear you before the interview. Explaining clearly why a volatile stock can be fairly priced yet still too risky to hold alone shows the analytical depth investment firms look for.

Related Questions

The same principle, that investors demand a higher expected return for taking more risk, applies in the bond market too. Our comparison of investment grade vs high yield bonds shows how credit risk is priced through higher yields.

Key Points to Retain

The capital market line plots expected return against standard deviation for efficient portfolios that mix the risk-free asset with the market portfolio, and its slope is the market’s Sharpe ratio. The security market line plots expected return against beta for any security or portfolio, using the CAPM, and its slope is the market risk premium.

A security above the security market line appears undervalued, with positive alpha, and one below it appears overvalued. Both lines rest on simplifying assumptions, but together they explain why diversification matters and how risk should be priced.

For the role the exam leads to, read our guide to what an investment advisor representative is.