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

Explanations for the Low-Risk Anomaly in FRM Part 2

Updated 11 October 2026 · Fact-checked

The low-risk anomaly is the finding that low-beta or low-volatility stocks earn higher risk-adjusted returns than the CAPM predicts. Explanations are behavioural and institutional: leverage constraints, lottery preferences, and benchmarking and agency issues all push investors toward high-risk stocks and overprice them. To answer exam questions, match the described behaviour to the mechanism.

Understand Explanations for the Low-Risk Anomaly

The CAPM says expected return rises with beta in a straight line, the security market line. In the data, the line is too flat. Low-beta stocks earn more than CAPM predicts, and high-beta stocks earn less. The result is positive alpha for low-risk stocks and negative alpha for high-risk stocks.

The explanations do not say investors are unaware of risk. They say that real investors face limits or hold preferences that the CAPM ignores. Each explanation creates extra demand for high-risk stocks. That demand raises their prices and lowers their future returns. Low-risk stocks are left cheaper than they should be.

Leverage constraints. Many investors cannot borrow, or will not borrow, to scale up a portfolio. Pension funds, mutual funds and many individuals fall in this group. An investor who wants a higher expected return cannot lever a low-beta portfolio. Instead, they buy high-beta stocks. This extra demand for high beta lowers its return. In the equilibrium, the market line is flatter than the CAPM line. The few investors who can lever (some hedge funds) could exploit this, but their capacity is limited.

Lottery preferences. Some investors like small chances of very large gains, as with a lottery ticket. Stocks with high volatility and positive skewness offer this. Demand for them pushes up their prices and lowers their expected returns. This is a behavioural explanation tied to preferences, not to a rule that stops investors from borrowing.

Benchmarking and agency issues. Many managers are judged against a benchmark and are paid for beating it. A manager with a low-beta tilt will lag in strong markets and risks being fired. A manager who holds high-beta stocks can beat the benchmark in rising markets. Tracking-error limits and career risk discourage low-beta bets, even when they offer good alpha. Delegated management therefore leaves low-risk stocks underheld. This is an institutional and agency explanation.

These explanations can work together, and none is proven to be the single cause. On the exam, you need to name each one, state its mechanism, and say which direction it pushes prices and returns.

Key formulas to remember

CAPM expected return: E(Ri) = Rf + βi × [E(Rm) − Rf]; The benchmark line. The anomaly says the actual line is flatter than this.
Jensen's alpha: αi = Ri − [Rf + βi × (Rm − Rf)]; Positive for low-beta stocks and negative for high-beta stocks under the anomaly.
Sharpe ratio: SR = (Rp − Rf) ÷ σp; Low-risk portfolios tend to show higher Sharpe ratios than high-risk ones.
Mechanism chain (rule): Constraint or preference → extra demand for high-risk stocks → higher price → lower expected return; Apply the same chain to leverage constraints, lottery preferences and benchmarking.

How to solve Explanations for the Low-Risk Anomaly questions

Most questions give a scenario and ask which explanation applies, or what its effect is. Use this method.

1Read the scenario and find the key behaviour or limit: a borrowing limit, a taste for skewed payoffs, or a benchmark-linked mandate.
2Map it to the explanation: borrowing limit means leverage constraint; taste for big-win stocks means lottery preference; benchmark or career risk means benchmarking and agency.
3State the mechanism: who is pushed to buy high-beta or high-volatility stocks, and why.
4Give the price effect: high-risk stocks are overpriced, so their future returns are lower.
5Give the result for the security market line: it is flatter than CAPM, so alpha is positive for low beta and negative for high beta.
6Check the options for traps, such as claims that the explanation relies on irrational ignorance of risk or that it makes the anomaly disappear.
7Choose the option that fits both the cause and the direction.

Quickest way: Three-cue matching

When to use it: Use this when you have about a minute and the question asks you to identify the explanation.

Cue 'cannot borrow' or 'cannot lever': leverage constraints.
Cue 'skewness', 'jackpot' or 'gambling': lottery preference.
Cue 'benchmark', 'tracking error', 'mandate' or 'fired': benchmarking and agency.
Then check the direction: always extra demand for high risk, lower returns there.

Common mistakes in Explanations for the Low-Risk Anomaly

Saying leverage constraints make investors buy low-beta stocks.
Students link constraints with caution.
Fix: Constrained investors still want higher returns. They buy high-beta stocks instead of leveraging, which overprices high beta.
Treating lottery preference as an institutional constraint.
All explanations get lumped together as market frictions.
Fix: Lottery preference is a behavioural taste for skewed payoffs. Leverage limits and benchmarking are institutional.
Claiming the anomaly proves the CAPM is wrong about beta being unimportant.
The flat line is misread as zero beta pricing.
Fix: The line is flatter than predicted, not flat. The explanations are about why the slope is too small.
Thinking benchmarked managers hold high beta because they like risk.
The agency motive is confused with risk appetite.
Fix: They fear lagging the benchmark in rising markets. Career risk, not preference, drives the behaviour.
Assuming arbitrageurs will quickly remove the anomaly.
Efficient-market thinking.
Fix: Arbitrage capital is limited, and it faces leverage needs and tracking-error risk. This is why the effect can persist.

Worked examples

Example 1

A pension fund is barred from borrowing. Its trustees want a return above what its low-beta portfolio offers. The manager moves into high-beta stocks. Which explanation of the low-risk anomaly does this describe, and what is the effect on the pricing of high-beta stocks?

Show the solution

The key limit is the ban on borrowing, so the fund cannot lever up a low-beta portfolio.
This maps to leverage constraints.
To raise expected return, the fund buys high-beta stocks instead.
Many investors doing the same raises demand for high beta.
Higher demand lifts prices, which lowers expected returns on high-beta stocks.

Answer: Leverage constraints. High-beta stocks become overpriced and earn lower subsequent returns, so the security market line is flatter than the CAPM predicts.

Example 2

A portfolio manager is paid a bonus for beating a broad equity index and faces dismissal if she trails it for several years. She has found low-volatility stocks that appear cheap on a risk-adjusted basis but avoids them. Which explanation fits, and why does the anomaly persist?

Show the solution

The key facts are a benchmark, a bonus for beating it, and the threat of dismissal for lagging.
This maps to benchmarking and agency issues.
Low-volatility stocks lag in strong rising markets, which creates tracking-error and career risk.
Managers in the same position avoid low-beta stocks or hold high-beta stocks to beat the index.
Low-risk stocks stay underheld and cheap, so the alpha is not competed away.

Answer: Benchmarking and agency issues. Career and tracking-error risk discourage low-risk positions, so the anomaly persists.

Exam tips

Learn the three explanations as cause, mechanism and effect. Questions often change the wording but keep the structure.
Remember that leverage constraints and benchmarking are institutional, while lottery preference is behavioural.
Always state the direction: high-risk stocks are overpriced and earn lower returns, and low-risk stocks earn positive alpha.
Watch for options that say the anomaly is fully arbitraged away or needs irrational investors. Both overstate the explanations.
In case questions, link the explanation to who can exploit it, such as investors who can lever or are not benchmarked.

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

Explanations for 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 the CAPM predicts. High-risk stocks have earned less than predicted. The result is a security market line that is too flat.

How do leverage constraints explain the low-risk anomaly?

Investors who cannot borrow cannot scale up a safe portfolio to reach a higher return. They buy high-beta stocks instead. This extra demand overprices high beta and lowers its future return.

Why do lottery preferences matter for low-volatility stocks?

Some investors like stocks with a small chance of a very large gain. Volatile, positively skewed stocks offer this. Demand for them pushes prices up and expected returns down, which leaves low-volatility stocks relatively cheap.

How does benchmarking affect the low-risk anomaly?

Managers judged against a benchmark risk lagging it in rising markets if they hold low-beta stocks. Career risk makes them avoid such positions. Low-risk stocks therefore stay underheld.