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

The Low-Risk Anomaly: Low Beta and Low Volatility Explained

Updated 11 October 2026 · Fact-checked

The low-risk anomaly is the empirical finding that low-beta and low-volatility stocks earn higher risk-adjusted returns than CAPM predicts, while high-beta stocks earn less. The security market line is flatter than theory says. To solve questions, compute the CAPM expected return, compare it with the actual return, and read the gap as alpha.

Understand The Low-Risk Anomaly

CAPM says expected return rises in a straight line with beta. The line is the security market line (SML). Its slope is the market risk premium, E(Rm) − Rf. A stock with beta 0.5 should earn half the premium. A stock with beta 1.5 should earn one and a half times it. Any gap between actual and CAPM return is alpha.

The low-risk anomaly says the data do not follow this line. Over long periods and in many markets, low-beta and low-volatility stocks earned returns close to, or above, what CAPM predicts. High-beta stocks earned less than CAPM predicts. So the empirical SML is flatter than the theoretical SML. Low-beta stocks plot above the line (positive alpha). High-beta stocks plot below it (negative alpha).

The result is that risk-adjusted returns fall as risk rises. Sharpe ratios and alphas are higher for low-risk stocks. This is a puzzle because CAPM says investors are paid only for bearing market risk. Here the lowest-risk stocks look like the better deal per unit of risk.

The anomaly shows up in two forms. The low-beta anomaly sorts stocks by beta. The low-volatility anomaly sorts them by total volatility, or sometimes by idiosyncratic volatility. These are related but not identical. Beta depends on correlation with the market as well as volatility.

The best-known way to capture it is betting against beta (BAB). You go long low-beta assets and short high-beta assets. You scale each leg so that both have a beta of 1, usually by leveraging the low-beta leg and de-leveraging the high-beta leg. The resulting portfolio is market neutral in beta terms and has earned a positive return historically. The common explanations, such as leverage constraints, are covered in their own topic. Here you need to know what the anomaly is and how to read it.

Key formulas to remember

CAPM expected return (security market line): E(Ri) = Rf + βi × [E(Rm) − Rf]; The theoretical benchmark. Slope of the SML is the market risk premium.
Alpha (Jensen's alpha): α = Ri − [Rf + βi × (Rm − Rf)]; Use realised or average returns. Positive alpha means the stock plots above the SML.
Sharpe ratio: Sharpe = (Ri − Rf) ÷ σi; Return per unit of total volatility. The anomaly says this falls as volatility rises.
Treynor ratio: Treynor = (Ri − Rf) ÷ βi; Return per unit of beta. Flat SML means low-beta stocks have a higher Treynor ratio.
Beta: β = ρ(i, m) × σi ÷ σm; Low beta can come from low volatility, low correlation, or both.
Beta-neutral BAB portfolio: BAB return = (1 ÷ βL) × (RL − Rf) − (1 ÷ βH) × (RH − Rf); Long the low-beta leg scaled up, short the high-beta leg scaled down. Both legs have beta of 1, so net beta is zero.

How to solve The Low-Risk Anomaly questions

Use this method for any question on the low-risk anomaly, whether it asks for alpha, a ranking, or an interpretation.

1Identify what is given: risk-free rate, market return, each portfolio's beta or volatility, and actual returns.
2Compute the CAPM required return for each portfolio using Rf + β × (Rm − Rf).
3Subtract to get alpha for each portfolio. Positive alpha plots above the SML, negative below.
4If asked about risk-adjusted performance, compute the Sharpe ratio (uses σ) or Treynor ratio (uses β) as the question specifies.
5Check the pattern. If alpha falls as beta rises, the empirical SML is flatter than the theoretical one. That is the anomaly.
6For a BAB question, scale each leg by 1 ÷ beta, then combine long minus short. Confirm net beta is zero.
7State the interpretation in one line: what the result says about CAPM and which side earns excess return.

Quickest way: Alpha-sign shortcut

When to use it: When an MCQ gives betas and returns and asks which portfolio plots above or below the SML, or whether the data show the anomaly.

Compute the premium: Rm − Rf.
For each portfolio, CAPM return = Rf + β × premium. Do it mentally.
Compare with the actual return. Higher actual means above the SML.
If low-beta portfolios are above and high-beta are below, the SML is flatter than CAPM. Pick that option.
Discard options that say CAPM holds, or that call the anomaly a higher return for higher risk.

Common mistakes in The Low-Risk Anomaly

Saying low-beta stocks earn higher raw returns than high-beta stocks.
The word 'outperform' is read as absolute return.
Fix: The claim is about risk-adjusted return and alpha. High-beta stocks may still earn more in raw terms, just not enough for their risk.
Describing the flat SML as having a negative slope.
Flat and inverted get mixed up.
Fix: Flatter means a smaller slope than the market risk premium. The slope is still usually positive.
Treating low-beta and low-volatility anomalies as the same thing.
Both are called low risk.
Fix: Beta sorts on market sensitivity, volatility sorts on total risk. A stock can have low volatility but a high beta, or the reverse.
Building a BAB portfolio with equal dollar amounts long and short.
Equal weights feel market neutral.
Fix: Scale each leg by 1 ÷ its beta. Equal dollars leave a net negative beta, since the long leg has the lower beta.
Calling the anomaly proof that CAPM is wrong in theory.
The finding is strong, so it is overstated.
Fix: It is an empirical result that CAPM fails to explain. It does not hold in every period or market, so describe it as historical evidence.
Using total volatility in a Treynor ratio or beta in a Sharpe ratio.
The two ratios look alike.
Fix: Sharpe divides by σ, Treynor divides by β.

Worked examples

Example 1

The risk-free rate is 3% and the expected market return is 9%. Portfolio L has beta 0.6 and an average return of 7.2%. Portfolio H has beta 1.4 and an average return of 10.0%. Compute each alpha and say what the pattern shows.

Show the solution

Market premium = 9% − 3% = 6%.
Portfolio L CAPM return = 3% + 0.6 × 6% = 6.6%. Alpha = 7.2% − 6.6% = +0.6%.
Portfolio H CAPM return = 3% + 1.4 × 6% = 11.4%. Alpha = 10.0% − 11.4% = −1.4%.
Low-beta portfolio plots above the SML and high-beta portfolio plots below it.
Alpha falls as beta rises, so the empirical SML is flatter than CAPM's.

Answer: Alpha of L is +0.6% and alpha of H is −1.4%. This is consistent with the low-risk anomaly and a flat security market line.

Example 2

A low-beta portfolio has beta 0.5 and excess return over the risk-free rate of 4%. A high-beta portfolio has beta 1.5 and excess return of 6%. Build a beta-neutral BAB portfolio and find its expected excess return.

Show the solution

Scale the long leg: 1 ÷ 0.5 = 2. Long 2 units of the low-beta portfolio, financed by borrowing.
Scale the short leg: 1 ÷ 1.5 = 0.6667. Short 0.6667 units of the high-beta portfolio.
Check beta: 2 × 0.5 − 0.6667 × 1.5 = 1.0 − 1.0 = 0.
Long leg excess return = 2 × 4% = 8%.
Short leg excess return = 0.6667 × 6% = 4%.
BAB excess return = 8% − 4% = 4%.

Answer: The BAB portfolio has zero beta and an expected excess return of 4%.

Exam tips

Expect applied questions: given betas and returns, compute alpha, then name the pattern. Practise the CAPM line until it takes seconds.
Read the verb carefully. 'Risk-adjusted' means Sharpe, Treynor or alpha, not raw return.
In BAB questions, always check that net beta equals zero before computing the return.
Eliminate options that claim the anomaly is a free lunch with no risk. The strategy relies on leverage and has its own risks, such as drawdowns when high-beta stocks rally.
Link this topic to its explanations and implementation topics. Questions may ask why the anomaly persists, not only what it is.

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

The Low-Risk Anomaly: frequently asked questions

What is the low-risk anomaly in simple terms?

Low-beta and low-volatility stocks have earned better risk-adjusted returns than CAPM predicts. High-beta stocks have earned worse. Risk has not been rewarded in the way the theory says.

What does a flat security market line mean?

The line relating return to beta has a smaller slope in the data than CAPM's market risk premium implies. Low-beta stocks sit above the theoretical line and high-beta stocks sit below it.

What is betting against beta?

It is a strategy that goes long low-beta assets and short high-beta assets. Each leg is scaled to a beta of 1, so the portfolio has zero market beta. Its historical positive return is the evidence for the anomaly.

How is the low-risk anomaly different from CAPM?

CAPM is the theory that expected return rises linearly with beta. The anomaly is the empirical evidence that the relationship is flatter than CAPM predicts. It shows up as positive alpha for low-beta stocks and negative alpha for high-beta stocks.