CAPM Formula Explained: 6 Traps That Cost CFA Candidates Easy Marks

The Capital Asset Pricing Model is one of a handful of expressions you can be near-certain of meeting on exam day. It is also short enough that candidates assume they know it and stop practising — which is precisely why examiners can build genuinely difficult questions around three variables.

Most CAPM marks are lost not to the model but to reading. This guide covers the formula properly, then works through the six errors that account for most of those losses.

The formula and its terms

E(R_i) = R_f + β_i × (E(R_m) − R_f)

In words: the expected return on an asset equals the risk-free rate plus a risk premium, where the premium is the market's excess return scaled by the asset's sensitivity to market movements.

• R_f — the risk-free rate. Usually proxied by a short-dated government security. Note that it appears twice, which is the origin of a surprising number of errors.
• β_i — beta. The asset's systematic risk relative to the market. Beta of 1 moves with the market; above 1 amplifies it; below 1 dampens it; negative beta moves against it.
• E(R_m) − R_f — the market risk premium. Compensation for holding market risk rather than the risk-free asset. This is a premium, not a return — a distinction that carries a trap all of its own.

Where beta comes from

β_i = Cov(R_i, R_m) / Var(R_m)

Equivalently:

β_i = ρ_i,m × (σ_i / σ_m)

Memorise the second form as well as the first. Questions frequently supply correlation and two standard deviations rather than a covariance, and a candidate who only knows the covariance version hits a dead end on data they were fully given.

The second form also carries useful intuition. Beta is correlation scaled by relative volatility. A stock can be twice as volatile as the market and still have a beta below 1 if its correlation with the market is weak — which is exactly why total risk and systematic risk are different quantities.

Adjusted beta

Historical regression betas tend to revert toward 1 over time, so practitioners often apply an adjustment. The common form is:

Adjusted beta = (2/3 × historical beta) + (1/3 × 1.0)

A historical beta of 1.6 becomes (0.667 × 1.6) + 0.333 = 1.40. Questions that mention forward-looking estimates or mean reversion are signalling this. The adjustment always pulls toward 1, so an adjusted beta above the raw beta tells you the raw beta was below 1.

SML versus CML — the distinction that gets tested

Candidates conflate these constantly. The difference is one line each.

• Security Market Line: expected return plotted against beta. Applies to any individual security or portfolio, efficient or not. CAPM is the equation of the SML.
• Capital Market Line: expected return plotted against total risk (standard deviation). Applies only to efficient portfolios combining the risk-free asset with the market portfolio.

The exam consequence follows directly. An asset plotting above the SML offers more return than its systematic risk warrants, so it is undervalued. An asset below the SML is overvalued. Questions asking you to identify a mispriced security are testing this, and answering requires comparing the CAPM required return against the expected return supplied in the vignette.

A useful memory hook: SML has a beta axis and applies to individual securities. CML has a standard deviation axis and applies only to efficient portfolios. If a question mentions a single stock and a line, it is the SML.

The six traps

1. Being given the premium and subtracting Rf anyway

This is the most productive trap on the exam. If a question states the market risk premium is 6% and the risk-free rate is 3%, then for a beta of 1.2:

Correct: 3% + (1.2 × 6%) = 10.2%

Wrong: 3% + 1.2 × (6% − 3%) = 6.6%

Subtracting the risk-free rate from a figure that is already a premium produces a plausible number that will be waiting in the answer choices. Before computing anything, decide whether you have been handed E(R_m) or the premium itself.

2. Confusing required return with expected return

CAPM produces the required return — what the market should demand given the asset's systematic risk. An analyst's forecast is the expected return. These are different quantities, and the gap between them is alpha.

Questions asking "what return should the investor require" want the CAPM output. Questions asking "is this security fairly valued" want you to compute the CAPM output and compare it against a forecast given elsewhere in the vignette. Answering the second question with only the first calculation loses the mark despite correct arithmetic.

3. Mishandling negative or sub-1 betas

A negative beta produces a required return below the risk-free rate, which looks wrong and is not. An asset that reliably moves against the market is valuable as a hedge, so investors accept a lower expected return to hold it. Candidates who assume they have made an arithmetic error and re-work the sum lose time and sometimes the mark.

4. Applying the wrong risk-free rate

Where a question supplies both a short-term treasury bill rate and a long-term government bond yield, the bill rate is generally the risk-free proxy. Where it supplies a nominal and a real rate, match the rate to the cash flows — nominal with nominal, real with real.

5. Averaging betas incorrectly at portfolio level

Portfolio beta is the weighted average of component betas, using market value weights. This is one of the few places where a simple weighted average is correct — unlike portfolio standard deviation, which is not. Candidates who have internalised "you cannot just average risk measures" sometimes overcomplicate a question that wanted exactly that.

6. Treating CAPM alpha as evidence of skill

CAPM is a single-factor model. It prices systematic market risk and nothing else. Any return arising from size, value, momentum or liquidity exposure shows up as alpha because the model has no term for it. A manager with a positive CAPM alpha may simply be tilted toward small-cap value stocks. Conceptual questions test whether you know this.

A worked example

A stock has a beta of 0.8. The risk-free rate is 4%, the expected market return is 10%, and an analyst forecasts the stock will return 9% next year. Is it correctly priced?

Required return = 4% + 0.8 × (10% − 4%) = 4% + 4.8% = 8.8%

The forecast of 9% exceeds the required 8.8%, so the stock plots above the SML and is undervalued. The 0.2 percentage point gap is the expected alpha.

Now change one thing: suppose the question had said "the market risk premium is 10%". Required return becomes 4% + 0.8 × 10% = 12%, the forecast of 9% falls short, and the stock is overvalued. Same numbers, opposite conclusion, and the only difference is one word in the question.

The assumptions, and why they are tested

CAPM rests on assumptions the exam expects you to recognise: investors are risk-averse utility maximisers operating over a single period; markets are frictionless with no taxes or transaction costs; investors hold homogeneous expectations; all investors can borrow and lend freely at the risk-free rate; and all assets are marketable and divisible.

These are testable in their own right, but they also explain the model's limitations. The single-period assumption sits awkwardly with long-horizon investing. Homogeneous expectations describe no real market. Unlimited risk-free borrowing is available to nobody. And the true market portfolio — which should contain every risky asset in existence, including property, human capital and private businesses — is unobservable, so every empirical beta is measured against a proxy. This last point is known as Roll's critique, and it is why CAPM tests are formally inconclusive.

Why unsystematic risk earns nothing

The deepest idea in CAPM is not in the formula — it is the reason beta is the only risk term.

Unsystematic risk can be diversified away at essentially no cost. In a market of rational investors, nobody will pay a premium to compensate someone for bearing a risk they could have eliminated for free. Only risk that cannot be diversified away commands compensation.

This principle recurs throughout the programme: in the Level 1 portfolio management material, in the choice between the Sharpe and Treynor ratios, and again at Level 3 in asset allocation. If a question asks why two portfolios with identical total risk carry different expected returns, this is the answer.

Exam checklist

• Were you given E(R_m) or the market risk premium? Decide before calculating
• Does the question want required return, or a valuation comparison?
• Do you have covariance, or correlation and standard deviations? Know both beta formulas
• SML uses beta; CML uses standard deviation
• Above the SML means undervalued; below means overvalued
• Portfolio beta is a weighted average; portfolio standard deviation is not
• A negative beta legitimately produces a required return below R_f