Jensen's Alpha Calculator
The formula
What the jensen's alpha tells you
Michael Jensen's 1968 test of whether managers truly beat the market after adjusting for the risk they took: the excess of realized return over the CAPM-required return. Positive alpha means the portfolio delivered more than its beta owed it.
Calculation: α = Rp − [Rf + β × (Rm − Rf)]. Enter your inputs and every substitution is shown below the result.
Reading the result
Alpha is only as good as the benchmark and beta behind it. A market-neutral fund compared to the S&P can look like a genius or a disaster depending on nothing real — pick a benchmark whose risk factors you actually wanted to avoid.
Rules of thumb: α ≈ 0 is normal for passive; +1 to +3% annualized net of fees is a realistic ceiling for genuine skill; bigger claims usually hide factor exposures
Limitations and best practice
Single-factor CAPM attributes to skill what may just be exposure to size, value or momentum. Statistical significance matters: a 2% annual alpha over an 18-month sample is noise, not skill.
This calculator gives an estimate based on standard formulas; it is not professional financial, medical, legal or engineering advice. Verify anything you plan to act on with a qualified professional and your own records.
Frequently asked questions
Is alpha the same as beating the market?
Who was Michael Jensen?
Can alpha be manufactured?
Source & methodology
Jensen, M. C. (1968) "The Performance of Mutual Funds in the Period 1945–1964", Journal of Finance.
Jensen's Alpha: what this tool answers
You are here because you need a specific number, and you want to see how it was produced before you rely on it. Jensen's Alpha is the kind of number people argue about from memory. This page ends that argument with arithmetic you can watch happen: enter your figures, get Jensen's alpha in real time, and see every substitution printed below.
Like most useful measures, Jensen's Alpha is a summary, and summaries hide as much as they reveal. The companion outputs and the input table are here to reopen what the headline compressed.
A calculation like this one is worth roughly as much as a careful sentence: it forces several vague considerations into one comparable quantity. Once Jensen's Alpha is on the table, the argument can stop being about impressions.
What makes a calculation page trustworthy is that its copy is derived from its own arithmetic: here jensen's alpha = 5.60 %, recomputed every time a field changes, and the sensitivity section ranks the inputs that move the result — Portfolio return first, at ≈25.0 % of the headline for a ten-percent error either way in that input — which is the thread the rest of this guide pulls on.
The Jensen's Alpha formula, explained
Here is the complete model this tool runs — α = Rp − [Rf + β × (Rm − Rf)] — with each input explained below. If a competitor’s page gives you a different answer from the same inputs, this is the text that settles which of you is right.
Portfolio return (%) (example value 14) is a plain measured quantity — the unit shown in the label is the unit the formula expects. Enter it exactly as your document states it — quoted annual, monthly and effective rates are three different numbers.
Risk-free rate (%) (example value 4) is a quantity rather than a category — precision here is cheap and worth having. Enter it exactly as your document states it — quoted annual, monthly and effective rates are three different numbers.
Market return (%) (example value 8) is a numeric input whose unit is fixed by the label; a wrong unit is a wrong answer wearing a plausible disguise. Rates are the most mis-transcribed input on any page like this; copy it from the document rather than retyping from memory.
Portfolio beta (example value 1) is a numeric input whose unit is fixed by the label; a wrong unit is a wrong answer wearing a plausible disguise. Replace the example with the figure from your own records — the tool recomputes instantly and the printed steps follow your numbers.
A fully worked Jensen's Alpha example
Rather than describe the calculation, here it is end to end — every substitution in order, starting from the inputs above. Starting figures: Portfolio return (%), Risk-free rate (%), Market return (%), Portfolio beta. The endpoint of that chain is 5.60 % of jensen's alpha, sitting in the “Beat CAPM requirement by 5.60%” band.
- CAPM requirement = 4% + 1.1 × (8% − 4%) = 8.40%
- α = 14% − 8.40% = 5.60%
CAPM required return — 8.40 %. If your inputs change, this is usually the first companion figure to move.
Actual minus required — 5.60 %. If your inputs change, this is usually the first companion figure to move.
Return needed for α = 1% — 9.40 %. If your inputs change, this is usually the first companion figure to move.
Alpha if beta were 1 — 6.00 %. Compare it against the main result of 5.60 % before drawing conclusions.
Re-running with your own figures is instant; re-running by hand once is the best way to know the tool is telling you the truth.
Scenario table: Jensen's Alpha at ±10 % and ±20 % of the key input
Single-point answers invite false confidence, so the same engine was run across a band around the input that matters most here. Each row is a full recalculation of Jensen's Alpha, not an interpolation.
| Portfolio return setting | Jensen's alpha |
|---|---|
| 80 % of the example value | 2.80 % |
| 90 % of the example value | 4.20 % |
| example inputs | 5.60 % |
| 110 % of the example value | 7.00 % |
| 120 % of the example value | 8.40 % |
The corridor runs from 2.80 % to 8.40 % across that band — which is the range worth planning inside rather than the single 5.60 % point estimate. Reproduce it in the form above by editing Portfolio return alone; the substitution steps will follow your figures exactly.
Where Jensen's Alpha is fragile — and where it is not
This list was computed for this specific engine just now: each numeric input was nudged ±10 % while every other field held its example value, and the jensen's alpha was recalculated from scratch. Read it as a map of where Jensen's Alpha is fragile — drawn for the example inputs, which is the map you want when deciding what to measure carefully.
- Nudge Portfolio return by ±10 % and Jensen's Alpha lands between 4.20 % and 7.00 % (sensitivity ≈25.0 %)
- Nudge Market return by ±10 % and Jensen's Alpha lands between 4.72 % and 6.48 % (sensitivity ≈15.7 %)
- Portfolio beta +10 % → Jensen's Alpha = 5.16 % · −10 % → 6.04 % (the jensen's alpha shifts ≈7.9 %)
- Nudge Risk-free rate by ±10 % and Jensen's Alpha lands between 5.56 % and 5.64 % (sensitivity ≈0.7 %)
Portfolio return is the dominant lever here: ten percent either way moves the result by about 25.0 %, from 4.20 % to 7.00 %. Spend your verification effort there first, and treat Market return as the second priority (≈15.7 % per ten percent). Everything below that can stay approximate, which is a licence to stop chasing data that would not change the decision.
What a Jensen's Alpha of 5.60 % means in practice
Nobody acts on a bare figure — they act on a figure with a comparison attached. The verdict attached to the default calculation — “Beat CAPM requirement by 5.60%” — is one band on a ladder your own figure may sit somewhere else on. The sensitivity list shows how far a modest input error moves you along that ladder: for Portfolio return, ±10 % covers 4.20 % to 7.00 %. The practical reading rules: compare against your own history before comparing against other people; treat band boundaries as zones, not walls — one point on the wrong side of a threshold rarely changes a real outcome; and when a companion output contradicts the headline, believe the pair.
Where Jensen's Alpha sits next to similar measures: this tool answers “how much is the Jensen's Alpha”, while the related calculators answer “what do I do about it”. Reading the result alone tends to over-weight a single snapshot; pairing it with the companion tools above turns the number into a decision.
Why Jensen's Alpha results go wrong — and how to prevent it
Single-factor CAPM attributes to skill what may just be exposure to size, value or momentum. Statistical significance matters: a 2% annual alpha over an 18-month sample is noise, not skill. This calculator gives an estimate based on standard formulas; it is not professional financial, medical, legal or engineering advice. Verify anything you plan to act on with a qualified professional and your own records.
Feeding best-case scenarios and calling them plans. Run the number at least at expected and at pessimistic inputs; the gap between them is the actual risk you are accepting.
One mistake is specific to this engine: assuming every input matters equally. The computation above shows Portfolio return dominating — a careful figure there beats false precision everywhere else.
Another is comparing across contexts: a Jensen's Alpha computed with one set of conventions should never be lined up against a figure computed with another. Check the inputs behind both before ranking them.
Before you trust your Jensen's Alpha: a short checklist
- Record the date and the inputs alongside the number so future-you knows what was assumed.
- Compare the output against one published benchmark or a colleague’s independent estimate.
- Put Portfolio return under a magnifier; the sensitivity table above is the reason why.
- Recompute once with the dominant input deliberately set low, and see whether the decision changes.
- Check that every field the formula needs actually arrived from a document, not from recollection.
- Repeat the ±10 % test on the inputs that matter and see whether the decision — not just the number — still holds.
How to use the Jensen's Alpha tool properly
The tool does the arithmetic; the routine below is what makes the arithmetic trustworthy. Five steps, a minute total — and afterwards you will know not just what the number is, but which assumption produced it.
Step 1 — collect, then type. Everything this tool asks for is listed above (portfolio return (%), risk-free rate (%), market return (%), portfolio beta). Pull each figure from something you can point at — paperwork, a dashboard, a label — before touching a field. Guesswork at the input stage cannot be repaired at the interpretation stage. The input you reach for first is usually the one you measured longest ago.
Step 2 — start from the case you can defend. Enter pessimistic-but-honest figures first; the optimistic run is a ceiling, not a plan. A conclusion that holds on conservative inputs holds everywhere. A calculation you cannot explain to somebody else is a calculation you cannot defend.
Step 3 — isolate your variables. Change one field, observe, revert. The live sensitivity list does the ranking for the default inputs; verify it against your own, because dominance shifts when the starting point shifts. Estimates improve most when the worst case is written down in ink.
Step 4 — ask what would have to be true. Take the result you want and work backwards through the inputs until you find the assumption that produces it; then decide honestly whether that assumption is defensible. A calculation you cannot explain to somebody else is a calculation you cannot defend.
Step 5 — write the one-line memo. “Jensen's alpha = 5.60 % on this date, from these inputs.” That line is the entire deliverable; everything else on this page is how you earned the right to write it. When in doubt, prefer the boring input: the interesting one is usually the one you misread.
Where Jensen's Alpha matters in practice
In Portfolio Management the figure computed here is usually the first one somebody asks to see. Having it — with the formula behind it — changes your position in the conversation from participant to reference. The inputs are the part of the work that nobody else can do for you.
The companion outputs — CAPM required return and Actual minus required — exist for the second stage of that screen: the headline sizes the prize, while the companions describe the trade-off you are accepting to get it. A figure with a date beside it becomes evidence; without one it stays an anecdote.
Re-running this page costs nothing and catches the slow drifts that never announce themselves. In Investing & Markets the expensive mistakes are rarely sudden; they are small changes in Portfolio return (%) that nobody recalculated for a year. If the verdict changes with a ten-percent nudge, report the nudge alongside the number.
Quick answers: what searchers ask about Jensen's Alpha
What affects Jensen's Alpha the most?
The short answer: Portfolio return. The longer answer is the sensitivity table on this page, where every numeric input was probed by ten percent and the jensen's alpha recalculated — Portfolio return moved it furthest, by roughly 25.0 % (4.20 % to 7.00 %).
Which matters more: market return or portfolio return?
By the numbers, Portfolio return: a ten-percent change in it moves the result ≈25.0 %, versus ≈15.7 % for Market return. Spend your measuring effort in that order — precision on the weaker lever buys almost nothing.
What is a typical Jensen's Alpha?
With the example inputs on this page the result is 5.60 %, labelled “Beat CAPM requirement by 5.60%”. “Typical” varies with situation, which is why every result here ships with its verdict band and its sensitivity list: they turn one figure into a range you can locate yourself inside.
How do I calculate Jensen's Alpha by hand?
α = Rp − [Rf + β × (Rm − Rf)] is the entire method. Work the inputs in that order — CAPM requirement = 4% + 1.1 × (8% − 4%) = 8.40% — and you will reach 5.60 % on the default figures, the same number this tool prints.
What happens to Jensen's Alpha if portfolio return changes by 10 %?
On these inputs a ±10 % change in portfolio return takes Jensen's Alpha to 7.00 % against the 5.60 % example — around 25.0 % of the headline. The same test on every other field is in the sensitivity section.
Is the Jensen's Alpha result of 5.60 % good or bad?
The tool answers “what”, not “whether”: 5.60 % carries the verdict “Beat CAPM requirement by 5.60%” for the default case, which is a starting interpretation rather than a verdict on your situation. Re-run with your own figures and compare the bands.
What is a good Jensen's Alpha?
Markets give away free benchmarks: anything that beats the relevant index after costs earns the label "good", and this tool’s verdict band translates Jensen's Alpha against experience ranges. Before that, check that the inputs are realistic — a great Jensen's Alpha built on optimistic inputs is just a nicer-looking error.
How often should I check Jensen's Alpha?
Whenever an input changes by more than a few percent, and otherwise on the rhythm of your decisions — before a purchase, a review, a renewal. Jensen's Alpha is a snapshot, not a subscription; stale snapshots are the most common silent error in Investing & Markets planning.
Is alpha the same as beating the market?
No — alpha is beating the return your beta entitled you to. In a month where the index drops 10%, losing only 8% with a beta of 1.2 means negative alpha despite "outperforming".
Who was Michael Jensen?
The University of Rochester / Harvard economist whose 1968 mutual fund study launched modern performance evaluation and found the average fund could not beat the market after costs.
Is my data private on this page?
Yes — computation happens locally in your browser, with no account, no tracking of your inputs and nothing sent to a server. The printed formula is the whole story of what happens to your figures.
Key terms on this page
- CAPM required return
- 8.40 % for the Jensen's Alpha worked case; it sits next to the main result because it carries context the headline leaves out.
- Actual minus required
- 5.60 % for the Jensen's Alpha worked case; it sits next to the main result because it carries context the headline leaves out.
- Return needed for α = 1%
- 9.40 % in the default Jensen's Alpha calculation — one of the secondary figures an experienced reader checks before trusting the primary number.
- Jensen's alpha
- The primary output of this tool: 5.60 % for the default inputs, computed exactly from α = Rp − [Rf + β × (Rm − Rf)].
- Worked example
- The step-by-step substitution printed above, so the arithmetic can be re-derived by hand or in a spreadsheet.
- Verdict band
- The plain-language label — here “Beat CAPM requirement by 5.60%” — mapping the computed figure onto experience-based ranges for Investing & Markets.
- Sensitivity (±10 %)
- How far the Jensen's Alpha moves when a single input is nudged ten percent either way; the ranked list on this page is computed live from this engine.
The provenance of this Jensen's Alpha calculation
The model is published arithmetic implemented exactly as written: α = Rp − [Rf + β × (Rm − Rf)]. Source of record: Jensen, M. C. (1968) "The Performance of Mutual Funds in the Period 1945–1964", Journal of Finance. Where a professional version of this calculation differs, it differs in inputs and jurisdiction-specific coefficients, not in the algebra — which is why re-checking your inputs beats hunting for a second calculator.
Nothing here replaces a qualified professional, and nothing here is approximate either — the arithmetic is exact, and the honesty is in the inputs you supply. Nothing is smoothed, weighted or adjusted behind the scenes; where judgement enters, this page says so and names the input responsible.
Next steps after the calculation
Re-run the calculation with your own figures, stress the two most sensitive inputs by ±10 %, and only then act on the result.
Whoever you are (people who need one trustworthy number before their next decision), the next step is the same: replace the example inputs with your own, note the date, and re-run whenever a figure moves. In Investing & Markets, a dated figure is a trend, and an undated one is a rumour.