The Capital Asset Pricing Model answers one deceptively simple question: what return should you expect from a risky asset? Every valuation, every cost-of-capital calculation, every judgement about whether a stock is cheap runs through it. A financial economics tutor spends more time on this one model than on almost any other, because it is where risk, return and equilibrium finally fit together. This page builds the CAPM from the ground up and shows you how to read its central picture — the security market line.
1 · Risk that pays and risk that does not
Start with a fact that surprises most students. Not all risk earns a return.
Split the risk of any single asset into two parts. Idiosyncratic risk is specific to the firm — a failed product, a lawsuit, a factory fire. Systematic risk is common to the whole market — recessions, rate changes, oil shocks. The difference matters because you can diversify one away and not the other.
Hold enough assets and the idiosyncratic shocks cancel. One firm’s lawsuit is offset by another’s lucky quarter, so in a large portfolio only the common, market-wide movements survive. Diversification is close to free, so the market does not reward you for bearing risk you could have removed at no cost. Only systematic risk is priced. That single idea is the whole foundation of the CAPM.
So you need a measure of systematic risk alone. That measure is beta.
2 · Beta — measuring systematic risk
Beta answers: when the market moves by 1%, how much does this asset move? Formally, for asset i,
β_i = Cov(R_i, R_m) / Var(R_m)
where R_i is the asset’s return and R_m is the market’s. It is the covariance of the asset with the market, scaled by the market’s own variance.
Read beta as a sensitivity. A stock with β = 1 moves one-for-one with the market. A defensive utility with β = 0.5 moves half as much — it is half as exposed to the business cycle. A high-growth technology stock with β = 1.5 amplifies market swings by half again. The market portfolio, by construction, has β = 1, and a risk-free asset has β = 0.
Examiners like to test the intuition alongside the formula. A high beta does not mean a bad asset. It means an asset whose bad days tend to land on the market’s bad days — exactly when losses hurt most — so investors demand more return to hold it.
3 · The CAPM equation and the security market line
The CAPM turns beta into a required return. For any asset i,
E(R_i) = R_f + β_i [E(R_m) − R_f]
The expected return equals the risk-free rate R_f plus a risk premium. That premium is beta multiplied by the market risk premium, E(R_m) − R_f: the extra return the market as a whole offers over the safe asset.
Plot this equation with beta on the horizontal axis and expected return on the vertical, and you get a straight line: the security market line (SML). Its intercept is the risk-free rate. Its slope is the market risk premium. Every asset that is correctly priced sits exactly on it.
The SML is the CAPM made visible. Two assets with different betas are compared not by their raw return but by their position relative to this line. That comparison is where the model earns its keep.
4 · The SML is not the CML
Here is the distinction most likely to cost you marks. The security market line and the capital market line look similar and mean different things.
The capital market line (CML) plots expected return against total risk — the standard deviation σ — and it describes only efficient portfolios, combinations of the risk-free asset and the market portfolio. Inefficient assets do not lie on it.
The security market line (SML) plots expected return against systematic risk — beta — and it applies to every asset and portfolio, efficient or not. An individual stock carries diversifiable risk, so it sits below the CML, but if it is fairly priced it still sits on the SML. The move from σ to β is the move from total risk to priced risk, and it is the reason the SML can price a single stock while the CML cannot.
5 · Alpha — reading mispricing off the line
The SML gives the return an asset should earn for its beta. Compare that with the return you actually expect, and the gap is alpha:
α_i = E(R_i) − {R_f + β_i [E(R_m) − R_f]}
Alpha is the vertical distance from the asset to the line.
- An asset above the SML has a return higher than its beta requires. Positive alpha. It is underpriced — you get more return than the risk deserves, so you buy.
- An asset below the SML earns less than its beta requires. Negative alpha. It is overpriced — you sell, or short.
- An asset on the SML has zero alpha and is fairly priced.
In equilibrium, alpha is competed away. Buyers bid up the underpriced asset until its expected return falls back to the line; sellers push down the overpriced one until it rises to the line. The SML is where the market comes to rest. Active managers, in effect, are hunting for assets that have temporarily strayed off it.
Worked example — pricing a utility and a tech stock
Take a market with a risk-free rate of R_f = 3% and an expected market return of E(R_m) = 9%. Two stocks are on your desk: a regulated utility (call it asset A) and a high-growth technology firm (asset B).
Step 1 — Write the CAPM for this market. The market risk premium is E(R_m) − R_f = 9% − 3% = 6%. So the required return on any asset is
E(R_i) = 3% + β_i × 6%
This is the security market line: intercept 3%, slope 6%.
Step 2 — Price asset A (the utility). The utility has β = 0.5. Its required return is 3% + 0.5 × 6% = 6%. You forecast the utility will actually return 8%.
Step 3 — Judge asset A. Actual 8% exceeds required 6%, so its alpha is +2%. The utility plots above the SML. Positive alpha means it is underpriced — a buy.
Step 4 — Price asset B (the tech stock). The tech firm has β = 1.5. Its required return is 3% + 1.5 × 6% = 12%. You forecast it will return 10%.
Step 5 — Judge asset B. Actual 10% falls short of the required 12%, so its alpha is −2%. The tech stock plots below the SML. Negative alpha means it is overpriced — a sell.
Step 6 — Locate the market itself. The market portfolio has β = 1, so its required return is 3% + 1 × 6% = 9% — exactly E(R_m), with zero alpha. It sits on the line, as it must. Notice the lesson: the higher-beta stock has the higher required return (12% versus 6%), yet it is the worse buy here, because required return and forecast return are different things. The SML compares the two, and the utility wins.
Confusing the security market line with the capital market line? That single distinction is one of the most common exam traps in financial economics, and it is exactly the kind of thing a one-on-one financial economics tutor untangles with you in a session. Book a trial session.
Practice
Q1. A stock’s return has a covariance with the market of 0.036, and the market’s variance of returns is 0.03. The risk-free rate is 3% and the expected market return is 9%. Find the stock’s beta and its CAPM-required return.
Q2. In the same market (R_f = 3%, E(R_m) = 9%), a stock has β = 0.8 and you forecast its return at 9%. Compute its alpha. Is it underpriced or overpriced?
Q3. A different market has a risk-free rate of 2% and an expected market return of 10%. A stock has β = 1.25 and a forecast return of 11%. Compute its alpha, and state whether you buy or sell.
Answers: Q1: β = Cov/Var = 0.036 / 0.03 = 1.2, so required return = 3% + 1.2 × 6% = 10.2%. Q2: required return = 3% + 0.8 × 6% = 7.8%, so α = 9% − 7.8% = +1.2%. Positive alpha, above the SML — underpriced, a buy. Q3: market risk premium = 10% − 2% = 8%, so required return = 2% + 1.25 × 8% = 12%. α = 11% − 12% = −1%. Negative alpha, below the SML — overpriced, a sell.
Key takeaways
- Diversification removes idiosyncratic risk for free, so only systematic risk earns a return. Beta measures that systematic risk.
- The CAPM gives an asset’s required return: E(R_i) = R_f + β_i [E(R_m) − R_f]. Drawn against beta, it is the security market line.
- The SML uses beta and prices every asset; the CML uses total risk σ and describes only efficient portfolios. Do not swap them.
- Alpha is the vertical gap from an asset to the SML. Above the line means underpriced (buy); below means overpriced (sell); on the line means fairly priced.
- In equilibrium every asset lies on the SML — mispricings are arbitraged away, which is precisely what active investors try to exploit before that happens.
Why New York and London students choose our financial economics tutoring
- Two-market fluency: our tutors teach the CAPM as it appears in both US and UK curricula, from the notation your lecturer uses to the conventions your marking scheme expects.
- Genuine specialists: sessions are led by tutors who have taught asset pricing at degree level, so the SML, the CML and multi-factor extensions are core ground, not something skimmed.
- Exam-first method: we work past papers with the mark scheme open, because the marks in financial economics are won on the distinctions — priced versus diversifiable risk, SML versus CML, required versus expected return.
FAQ
Q: What is the security market line?
A: It is the graph of the CAPM: expected return on the vertical axis, beta on the horizontal. Its intercept is the risk-free rate and its slope is the market risk premium. Every fairly priced asset lies on it.
Q: What is the difference between the security market line and the capital market line?
A: The SML plots return against systematic risk (beta) and applies to all assets. The CML plots return against total risk (standard deviation) and applies only to efficient portfolios. Individual stocks lie on the SML but below the CML.
Q: What does beta actually measure?
A: Beta measures how much an asset moves with the overall market — its systematic, non-diversifiable risk. It is the covariance of the asset with the market divided by the market’s variance. A beta of 1 moves with the market; above 1 amplifies it; below 1 dampens it.
Q: What does a positive alpha mean?
A: Positive alpha means an asset’s expected return is higher than the CAPM requires for its beta, so it plots above the security market line and is underpriced. A negative alpha means the opposite — overpriced.
Q: What are the main assumptions of the CAPM?
A: Investors are rational and hold diversified portfolios, they can borrow and lend at the risk-free rate, there are no taxes or transaction costs, and everyone shares the same expectations. These are strong, which is why empirical work (such as the Fama–French factors) extends the model — but the CAPM remains the standard starting point.
Q: Is the CAPM hard to learn if my maths is rusty?
A: The core equation is straightforward algebra. The difficulty is conceptual — knowing why only systematic risk is priced and how to read the SML — and that is exactly what a tutor can make click quickly. Tell us your background when booking and we match the pace to it.
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The CAPM is one line and one equation, but the ideas behind it — priced risk, alpha, equilibrium — run through the whole of asset pricing and corporate finance. A one-on-one session turns the security market line from a diagram you memorise into a tool you can reason with. Tell us your university and module, and we will match you with the right tutor this week.
