Strategic Financial Management · Portfolio Performance Evaluation and Portfolio Revision

Jensen's Alpha and Risk-Adjusted Performance Measures

Updated 11 October 2026 · Fact-checked

Jensen's alpha is the portfolio's actual return minus the return CAPM says it should earn for its beta: α = Rp − [Rf + βp(Rm − Rf)]. A positive alpha suggests the manager added value. Fama splits that excess into net selectivity and diversification. M-squared and the information ratio compare managers on a common risk basis.

Understand Jensen's Alpha and Other Risk-Adjusted Measures

Raw return tells you little about a fund manager. A fund that earned 16% may simply have taken a lot of risk. Risk-adjusted measures ask a better question: did the manager earn more than the risk justified?

Jensen's alpha answers this using CAPM. CAPM gives the required return for the portfolio's beta. Alpha is the gap between the actual return and that required return. It is measured in percentage points. Positive alpha means the portfolio sits above the Security Market Line. Negative alpha means it sits below.

Fama's decomposition looks inside the excess return. It asks how much came from stock selection and how much from simply bearing risk. It also tests whether the manager's portfolio was fully diversified. A portfolio with a high total risk (σp) but a modest beta is under-diversified. CAPM alpha ignores this. Fama's net selectivity takes it into account by using the Capital Market Line (CML) at the portfolio's total risk.

M-squared (Modigliani) converts Sharpe-style thinking into a return figure. You lever or de-lever the portfolio with the risk-free asset until its standard deviation equals the market's. You then compare that adjusted return with the market return. The answer is in percentage points, so it is easy to explain.

Information ratio judges active management against a benchmark. It divides the average active return by the tracking error, which is the standard deviation of that active return. It tells you how much extra return the manager earned for each unit of active risk taken.

Jensen and Treynor both use beta. Jensen gives a difference in return. Treynor gives a ratio of excess return per unit of beta. Sharpe and M-squared use total risk (σ).

Key rules to remember

Jensen's alpha: α = Rp − [Rf + βp(Rm − Rf)]; Use average returns over the same period for Rp, Rm and Rf. Positive α means the portfolio beat its CAPM required return.
CAPM required return: Rβ = Rf + βp(Rm − Rf); This is the benchmark return in Jensen's measure. It is the point on the SML at the portfolio's beta.
Return on CML at portfolio's total risk: Rx = Rf + (σp ÷ σm)(Rm − Rf); Used in Fama's net selectivity. It is the return a passive mix of market and risk-free asset would earn at risk σp.
Fama net selectivity: Net selectivity = Rp − Rx = Rp − [Rf + (σp ÷ σm)(Rm − Rf)]; This is the return from the manager's skill after allowing for lack of diversification.
Fama diversification: Diversification = (σp ÷ σm − βp)(Rm − Rf); This is the extra return needed to compensate for incomplete diversification. It is zero or positive, since σp ÷ σm is at least βp.
Link between Jensen and Fama: Jensen's α = Net selectivity + Diversification; Use this to check your working.
M-squared: Rp* = Rf + (σm ÷ σp)(Rp − Rf); M² = Rp* − Rm; Rp* is the portfolio's return after adjusting its risk to equal the market's. Positive M² means it beat the market at equal risk.
Information ratio: IR = (Rp − Rb) ÷ Tracking error; Rb is the benchmark return. Tracking error is the standard deviation of (Rp − Rb) over the period, not σp.
Treynor and Sharpe (for comparison): Treynor = (Rp − Rf) ÷ βp; Sharpe = (Rp − Rf) ÷ σp; Treynor uses systematic risk. Sharpe uses total risk.

How to solve Jensen's Alpha and Other Risk-Adjusted Measures questions

Use this order for any numerical on Jensen's alpha, Fama, M-squared or information ratio. It keeps the units and the risk basis consistent.

1List the data: Rp, Rm, Rf, βp, σp, σm, and the benchmark return and tracking error if given. Convert everything to the same period, usually annual percentages.
2Decide the risk basis the question wants. Beta means Jensen or Treynor. Standard deviation means Sharpe, Fama net selectivity or M-squared. A benchmark with tracking error means the information ratio.
3Compute the CAPM required return Rf + β(Rm − Rf). Then find alpha as actual minus required.
4For Fama, compute σp ÷ σm and then Rx. Net selectivity is Rp − Rx. Diversification is (σp ÷ σm − β)(Rm − Rf).
5Check that net selectivity plus diversification equals Jensen's alpha. If not, recheck your arithmetic.
6For M-squared, scale the excess return by σm ÷ σp, add Rf, then subtract Rm.
7Rank or judge: positive means better than expected. When comparing funds, use the same measure for all. State one clear line of conclusion with the reason.

Quickest way: Required return first, then compare

When to use it: Use it when the MCQ or the first part of a long question asks only whether a fund beat its expected return, or which of two funds did better.

Write Rm − Rf first. It is reused in every formula.
Compute Rf + β × (Rm − Rf) and subtract it from Rp for alpha.
For M-squared, compute (σm ÷ σp) × (Rp − Rf) + Rf and subtract Rm. If σp is below σm, the ratio is above 1, so the portfolio is levered up.
If Jensen's alpha and M-squared are both asked, remember they can rank funds differently because one uses beta and the other total risk.
Scan the options and discard any answer with the wrong sign or one that adds Rf twice.

Common mistakes in Jensen's Alpha and Other Risk-Adjusted Measures

Using the market return Rm instead of the market risk premium (Rm − Rf) in the CAPM term.
Students recall the formula as β × Rm and forget the risk-free adjustment.
Fix: Always write Rf + β(Rm − Rf) in full. Compute (Rm − Rf) as a separate line first.
Treating a positive alpha as proof of skill.
The sign is read as a verdict, ignoring the diversification issue and luck.
Fix: Say that alpha is positive and then add the qualification. A high σp with a low β can create alpha that is just a diversification component. Fama's net selectivity separates the two.
Using σp where tracking error is needed in the information ratio.
Both are standard deviations, and the Sharpe ratio is fresh in mind.
Fix: The denominator is the standard deviation of (Rp − Rb). Use the figure labelled tracking error or active risk.
Forgetting to subtract Rm at the end of M-squared, or subtracting Rf instead.
Students stop at the risk-adjusted return Rp*.
Fix: M² is Rp* − Rm. Rp* alone is only the adjusted return. Compare it with the market return.
Getting the sign of the diversification component wrong in Fama's split.
The formula is memorised without the logic.
Fix: Write diversification as (σp ÷ σm − β)(Rm − Rf). Then check that net selectivity plus diversification equals Jensen's alpha.
Mixing monthly figures with annual figures.
Return data in a case may be given for different periods.
Fix: Convert all inputs to the same period before substituting. State the period in your working.

Worked examples

Example 1

Fund Meridian earned an average return of 16% with a beta of 1.2 and a standard deviation of 18%. The market returned 13% with a standard deviation of 12%. The risk-free rate is 7%. (a) Compute Jensen's alpha. (b) Decompose it using Fama's approach. (c) Compute M-squared and comment.

Show the solution

Market risk premium: Rm − Rf = 13 − 7 = 6%.
(a) Required return = 7 + 1.2 × 6 = 7 + 7.2 = 14.2%. Jensen's alpha = 16 − 14.2 = +1.8%.
(b) σp ÷ σm = 18 ÷ 12 = 1.5. Rx = 7 + 1.5 × 6 = 16%.
Net selectivity = Rp − Rx = 16 − 16 = 0%.
Diversification = (1.5 − 1.2) × 6 = 0.3 × 6 = 1.8%.
Check: 0 + 1.8 = 1.8%, which equals Jensen's alpha.
(c) Rp* = 7 + (12 ÷ 18) × (16 − 7) = 7 + 0.6667 × 9 = 7 + 6 = 13%. M² = 13 − 13 = 0%.
Comment: the positive alpha comes entirely from the diversification component. Net selectivity and M-squared are both zero. The manager gave no skill-based return beyond what a mix of the market and the risk-free asset would give at the same total risk.

Answer: Jensen's alpha = +1.8%. Net selectivity = 0% and diversification = 1.8%. M² = 0%. The positive alpha is only compensation for under-diversification, not evidence of selection skill.

Example 2

Two equity funds are reviewed against the same market. Risk-free rate is 6%. Market return is 11% with a standard deviation of 12%. Fund A returned 14% with a standard deviation of 20%. Fund B returned 12% with a standard deviation of 10%. (a) Compute M-squared for each fund and rank them. (b) Fund A's benchmark return was 11% and its tracking error was 5%. Compute its information ratio.

Show the solution

(a) Fund A: Rp* = 6 + (12 ÷ 20) × (14 − 6) = 6 + 0.6 × 8 = 6 + 4.8 = 10.8%.
M² for A = 10.8 − 11 = −0.2%.
Fund B: Rp* = 6 + (12 ÷ 10) × (12 − 6) = 6 + 1.2 × 6 = 6 + 7.2 = 13.2%.
M² for B = 13.2 − 11 = +2.2%.
Ranking: B is first as it beats the market at equal risk. A trails the market after risk adjustment even though its raw return is higher.
(b) Active return of A = 14 − 11 = 3%. Information ratio = 3 ÷ 5 = 0.6.

Answer: M² of Fund A = −0.2% and Fund B = +2.2%, so B ranks higher. Fund A's information ratio = 0.6.

Exam tips

In MCQs, the sign and the unit of the answer usually separate the options. Check whether the answer should be a percentage difference (alpha, M²) or a ratio (Treynor, Sharpe, IR).
If a question gives both beta and standard deviation, the verb tells you the measure. Required return or SML points to Jensen. Total risk or CML points to Sharpe, M-squared or Fama.
In a descriptive answer, end with a recommendation. State which fund or manager is preferred, on which measure, and why.
Write the formula before substituting. Show the market risk premium as a separate line. Method marks are easy to protect this way.
Be ready to explain in two lines why Jensen and Treynor can agree on a single fund against the market but can rank several funds differently.

Practice questions from Portfolio Performance Evaluation and Portfolio Revision

Jensen's Alpha and Other Risk-Adjusted Measures in other exams

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

CA FinalPerformance Evaluation and Risk-Adjusted Measures

Jensen's Alpha and Other Risk-Adjusted Measures: frequently asked questions

How do I calculate Jensen's alpha?

Find the CAPM required return as Rf + β(Rm − Rf). Subtract it from the portfolio's actual return. The result is alpha in percentage points. Use average returns over the same period.

What is the difference between the Jensen and Treynor measures?

Jensen's measure is a difference in return from the CAPM benchmark, in percentage points. Treynor is excess return per unit of beta, so it is a ratio. Both use systematic risk. Jensen tells you how much the manager added. Treynor allows ranking of portfolios on a per-unit-of-beta basis.

What is Fama's net selectivity?

It is the portfolio return minus the return on the CML at the portfolio's total risk: Rp − [Rf + (σp ÷ σm)(Rm − Rf)]. It shows the manager's skill after allowing for any shortfall in diversification. Jensen's alpha equals net selectivity plus the diversification component.

How is M-squared explained simply?

M-squared adjusts the portfolio to the market's level of risk by mixing it with the risk-free asset. You then compare its return with the market's. A positive result means the portfolio beat the market at the same total risk.