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

Sources of Alpha and Alpha Measurement

Updated 11 October 2026 · Fact-checked

Alpha is the return a portfolio earns beyond what its exposure to risk factors explains. It comes from skill, better information or genuine mispricing, not from risk premia. You measure it as the intercept of a factor regression, and judge it with the information ratio: alpha ÷ tracking error.

Understand Sources of Alpha and Alpha Measurement

Start with a simple idea. A portfolio return has two parts. One part is payment for bearing systematic risk, such as market, value or momentum exposure. The other part is what is left over. That left-over part is alpha.

Where can real alpha come from? There are three common answers. Skill: the manager forecasts better than others, for example by picking securities or timing markets. Information: the manager has analysis or data that is not yet in prices. Structural or behavioural edges: the manager is paid for providing liquidity or for taking the other side of investors who must trade for non-return reasons. Note that a risk premium is not alpha. If a return is compensation for factor risk, it is beta, even if it was once sold as alpha.

This is why the benchmark matters. Against the market only, a value tilt looks like alpha. Against a model that includes a value factor, it is beta. The same fund can show positive alpha in one model and zero in another. Smart beta products capture known factor premia cheaply and systematically. Alpha is the part no known factor explains and that needs skill or information.

To measure alpha, regress the portfolio's excess return on factor returns: Rp − Rf = α + β1F1 + ... + βkFk + ε. The intercept α is the estimated alpha. Check its t-statistic. With noisy returns and short histories, a positive alpha is often not statistically significant.

To judge how efficiently a manager earns alpha, use the information ratio: active return divided by tracking error. Tracking error is the standard deviation of active return. A higher ratio means more active return per unit of active risk.

Key formulas to remember

Single-factor (CAPM) alpha: α = (Rp − Rf) − β × (Rm − Rf); Also called Jensen's alpha. Use average returns over the same period for all terms.
Multi-factor regression: Rp − Rf = α + β1F1 + β2F2 + ... + βkFk + ε; α is the intercept. Factors can be market, size, value, momentum and others.
Active return: Active return = Rp − Rb; Rb is the benchmark return. Simple but depends entirely on the benchmark chosen.
Tracking error: TE = standard deviation of (Rp − Rb); Annualise by multiplying a monthly figure by √12.
Information ratio: IR = α ÷ ω, or (Rp − Rb) ÷ TE; ω is residual (active) risk. Compare the same horizon and annualisation for both numerator and denominator.
t-statistic of alpha: t = α̂ ÷ standard error of α̂; Roughly, |t| above about 2 suggests alpha is significant at the 5% level.

How to solve Sources of Alpha and Alpha Measurement questions

Use this sequence for any alpha or information ratio question.

1Identify the benchmark or factor model the question uses. Alpha only exists relative to it.
2List the inputs: portfolio return, risk-free rate, factor returns, betas, tracking error.
3If asked for alpha, subtract the factor-implied return (risk-free plus betas times factor returns) from the portfolio return.
4If asked for the information ratio, take alpha or active return and divide by tracking error or residual risk.
5Check units and horizon. Convert monthly to annual before dividing if needed.
6Interpret: is alpha significant (t-statistic), and is it skill, a hidden factor tilt or luck?
7Match the answer to the options, watching for use of total volatility instead of tracking error.

Quickest way: Three-line alpha check

When to use it: When you have a few numbers and about a minute per question.

Write expected return = Rf + β(Rm − Rf), adding any other factor terms.
Alpha = actual return − expected return.
IR = alpha ÷ tracking error; ignore total volatility unless the question asks for Sharpe.

Common mistakes in Sources of Alpha and Alpha Measurement

Treating a factor premium as alpha
The model in the question has fewer factors than the strategy actually uses.
Fix: Ask whether the return is compensation for a known factor. If the model includes that factor, it is beta, not alpha.
Dividing by total volatility to get the information ratio
It is confused with the Sharpe ratio.
Fix: Information ratio uses tracking error or residual risk. Sharpe uses excess return over the risk-free rate and total volatility.
Forgetting to subtract β × market premium
Students compare the portfolio return only with the market or the risk-free rate.
Fix: Compute the CAPM-expected return first, then subtract it.
Mixing monthly and annual figures
Alpha is given annually and tracking error monthly.
Fix: Convert first. Annualise monthly tracking error by multiplying by √12.
Calling any positive alpha skill
The t-statistic and sample length are ignored.
Fix: Check significance. A small alpha with a t-statistic below about 2 can easily be luck.

Worked examples

Example 1

A fund returned 12% over the year. The risk-free rate was 3%, the market returned 10%, and the fund's beta is 1.2. Compute Jensen's alpha.

Show the solution

Market excess return = 10% − 3% = 7%.
Expected excess return = 1.2 × 7% = 8.4%.
Expected return = 3% + 8.4% = 11.4%.
Alpha = 12% − 11.4% = 0.6%.

Answer: Alpha = 0.6% per year.

Example 2

A manager has annual alpha of 2.4% against a factor model. The residual (tracking) risk is 4.0% per year. What is the information ratio, and how do you interpret it?

Show the solution

IR = alpha ÷ residual risk.
IR = 2.4% ÷ 4.0% = 0.6.
Interpretation: 0.6 units of alpha per unit of active risk.
Check whether alpha is significant before treating it as skill.

Answer: IR = 0.6. Moderately good, but confirm significance and that no omitted factor explains the alpha.

Exam tips

Always read which model defines alpha. The answer often changes when a factor is added.
Information ratio questions nearly always use tracking error or residual risk in the denominator, not total volatility.
Watch for options that confuse alpha with active return. Active return ignores beta.
For conceptual questions, remember risk premia are compensation for risk, so a smart beta return is not alpha.
Know that a short sample or low t-statistic means alpha may be luck.

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

Sources of Alpha and Alpha Measurement: frequently asked questions

What are the main sources of alpha?

Skill in selection or timing, superior information, and structural or behavioural edges such as supplying liquidity. Compensation for known risk factors is not alpha. It is a risk premium.

How do you measure alpha with a factor model?

Regress the portfolio's excess returns on factor returns. The intercept is the alpha. Check its t-statistic, since a positive but insignificant alpha is weak evidence of skill.

What is the difference between alpha and smart beta?

Smart beta is a rules-based way to capture known factor premia such as value or low volatility. It is beta to those factors. Alpha is return beyond what all such factors explain.

What is a good information ratio?

A higher ratio is better because it shows more active return per unit of active risk. There is no fixed pass level. Treat any rule of thumb as a rough guide, and compare managers on the same benchmark and horizon.