FRM Exam Part II · Alpha (and the Low-Risk Anomaly)

Alpha, Beta and the CAPM Framework Explained

Updated 11 October 2026 · Fact-checked

Alpha is the return a portfolio earns above what its risk exposure justifies. Under CAPM, Jensen's alpha = Rp − [Rf + β × (Rm − Rf)]. Beta measures market exposure. Alpha is what is left after you strip out beta. Positive alpha means the manager beat the CAPM expectation.

Understand Alpha, Beta and the CAPM Framework

Start with the idea that a portfolio's return has two parts. One part comes from taking market risk. The other part comes from something else, such as skill, or a different risk you did not model. Alpha is the second part.

Beta measures how much a portfolio moves with the market. A beta of 1.2 means the portfolio tends to move 1.2% for each 1% move in the market. You can buy beta cheaply with an index fund. So a manager should not be paid as if beta were skill.

The CAPM says the expected return on an asset depends only on its beta. Expected return = risk-free rate + beta × market risk premium. This gives the return you should expect for the market risk you carry. It is the fair benchmark.

Jensen's alpha is the actual excess return minus the CAPM expected excess return. In regression form, you regress the portfolio's excess returns on the market's excess returns. The intercept is alpha. The slope is beta. The residual is the part driven by neither.

Two cautions matter for FRM. First, alpha depends on the benchmark or model you choose. Change the model and alpha changes. Return that CAPM calls alpha may be a factor premium, such as value or low volatility, that a multi-factor model would call beta. Second, the low-risk anomaly shows low-beta stocks have earned more than CAPM predicts. A low-beta portfolio can show positive CAPM alpha without any manager skill.

Key formulas to remember

CAPM expected return: E(Ri) = Rf + βi × [E(Rm) − Rf]; Beta is the only risk that earns a premium under CAPM. (Rm − Rf) is the market risk premium.
Jensen's alpha: α = Rp − [Rf + βp × (Rm − Rf)]; Use realised returns for Rp and Rm over the same period. Positive means outperformance versus CAPM.
Single-index regression: Rp − Rf = α + β × (Rm − Rf) + ε; The intercept is alpha. The slope is beta. ε is the residual with mean zero.
Beta: β = Cov(Rp, Rm) ÷ Var(Rm) = ρ × σp ÷ σm; ρ is the correlation between portfolio and market returns.
Benchmark-relative alpha: Active return = Rp − Rb; This is not Jensen's alpha unless the benchmark beta is 1 and the benchmark is the market. Adjust for beta first if betas differ.
Systematic variance share: β² × σm² ÷ σp² = ρ²; This is R² of the regression. The rest of variance is residual risk.

How to solve Alpha, Beta and the CAPM Framework questions

Use this order for any alpha, beta or CAPM question. It keeps you from mixing raw returns with excess returns.

1Identify what the question asks: alpha, beta, expected return or an interpretation.
2List the inputs: portfolio return, risk-free rate, market return, beta. Note the period and units, such as annual or monthly.
3If beta is not given, compute it from Cov ÷ Var or from ρ × σp ÷ σm.
4Compute the market risk premium: Rm − Rf.
5Compute the CAPM expected return: Rf + β × premium.
6Subtract the expected return from the actual return to get alpha.
7Interpret the sign and size. Ask whether the benchmark or model is adequate for this portfolio.
8Check the answer against the options. A low-beta portfolio that beats the market should still be tested for factor exposure.

Quickest way: Three-line alpha check

When to use it: Use this when a question gives you Rp, Rf, Rm and beta and asks for alpha.

Write the expected return: Rf + β × (Rm − Rf).
Subtract it from Rp.
Read the sign: positive means beat CAPM, negative means lagged.
Scan the options for the trap that skips beta and uses Rp − Rm.

Common mistakes in Alpha, Beta and the CAPM Framework

Computing alpha as Rp − Rm.
It feels like outperformance versus the market, and it ignores that the portfolio may carry a beta different from 1.
Fix: Always adjust for beta. Use Rp − [Rf + β(Rm − Rf)]. Rp − Rm is only an active return.
Forgetting to subtract the risk-free rate inside the beta term.
Candidates multiply beta by Rm instead of by the premium.
Fix: Multiply beta by (Rm − Rf), then add Rf.
Treating all alpha as manager skill.
CAPM is a one-factor model, so any return from other factors lands in alpha.
Fix: Ask whether value, size, momentum or low-volatility exposure explains it. Under a multi-factor model it would be beta to those factors.
Confusing beta with total risk.
Both are called risk measures.
Fix: Beta captures only market covariance. Standard deviation includes residual risk. Two portfolios with equal beta can have very different volatility.
Assuming a high-beta portfolio earns higher return than CAPM implies.
It sounds natural that more risk gives more reward.
Fix: CAPM sets the fair return for beta. The low-risk anomaly says low-beta assets have historically beaten that line and high-beta assets fell short of it.
Mixing monthly returns with annual rates.
Inputs come in different units in case questions.
Fix: Convert everything to one period before computing.

Worked examples

Example 1

A fund returned 11.0% over the year. The risk-free rate is 3.0%, the market returned 9.0%, and the fund's beta is 1.20. Compute Jensen's alpha.

Show the solution

Market risk premium = 9.0% − 3.0% = 6.0%.
CAPM expected return = 3.0% + 1.20 × 6.0% = 3.0% + 7.2% = 10.2%.
Alpha = 11.0% − 10.2% = 0.8%.

Answer: Jensen's alpha is +0.8%. The fund beat its CAPM expectation. Note Rp − Rm would have given 2.0%, which overstates skill.

Example 2

A portfolio has volatility of 15%, the market has volatility of 20%, and the correlation between them is 0.80. The risk-free rate is 2.0% and the market return is 8.0%. The portfolio returned 6.0%. Find beta and alpha.

Show the solution

Beta = ρ × σp ÷ σm = 0.80 × 15% ÷ 20% = 0.60.
Market risk premium = 8.0% − 2.0% = 6.0%.
CAPM expected return = 2.0% + 0.60 × 6.0% = 2.0% + 3.6% = 5.6%.
Alpha = 6.0% − 5.6% = 0.4%.

Answer: Beta is 0.60 and Jensen's alpha is +0.4%. Because beta is low, check whether low-risk factor exposure, not skill, explains this alpha.

Exam tips

Write the CAPM line first, then subtract. Most wrong options come from skipping beta.
If a question mentions a low-beta or low-volatility portfolio with positive alpha, think about the low-risk anomaly and factor exposure.
Check whether returns given are total or excess. If excess, do not subtract Rf again.
Questions on interpretation often test that alpha depends on the chosen model or benchmark.
Know that the regression intercept is alpha and the slope is beta.

Practice questions from Alpha (and the Low-Risk Anomaly)

Alpha, Beta and the CAPM Framework in other exams

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

Alpha, Beta and the CAPM Framework: frequently asked questions

What is alpha in CAPM?

Alpha is the difference between a portfolio's actual return and the return CAPM predicts for its beta. It is the intercept when you regress the portfolio's excess returns on the market's excess returns. Positive alpha means it beat the CAPM expectation.

What is the difference between alpha and beta?

Beta is exposure to market movements. Alpha is return not explained by that exposure. You can obtain beta cheaply through an index, while alpha needs skill or a source of return that CAPM does not capture.

How do I calculate Jensen's alpha?

Compute the CAPM expected return as Rf + β × (Rm − Rf). Then subtract it from the portfolio's actual return. Use the same period and consistent units for all inputs.

Is positive alpha always proof of skill?

No. Alpha depends on the model. If the portfolio is tilted to a rewarded factor such as low volatility or value, CAPM labels that return alpha, while a multi-factor model would call it factor beta. Luck over a short sample can also produce positive alpha.