Arbitrage Return Calculator
The formula
What the arbitrage return tells you
Exactly what arbitrage return earned: total return, the annualised CAGR that makes it comparable, and the split between price gain and income.
Calculation: Total return = (sell + income − buy) ÷ buy; CAGR = ((sell + income) ÷ buy)^(1/years) − 1. Enter your inputs and every substitution is shown below the result.
Reading the result
Compare with the boring alternative over the same window — the verdict bands anchor to long-run market returns; income-heavy gains are usually steadier than price-only ones.
Rules of thumb: Long-run real equity return sits near 6–7 % nominal CAGR plus inflation; bonds run 2–4 points lower.
Limitations and best practice
Ignoring the timing of income (reinvested vs spent) can overstate a CAGR by a few tenths; dividends spent as cash belong outside the ending value.
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
Why does CAGR differ from average yearly return?
Are taxes included?
Source & methodology
Time-weighted return arithmetic per CFA Institute conventions.
Arbitrage Return: what this tool answers
Capital decisions deserve better than a gut feeling — this page gives you the arithmetic to defend one. Searchers land on an Arbitrage Return page for three reasons — to plan, to compare options, and to check that somebody else’s arithmetic is honest. This tool serves all three, and everything after the calculator explains the model instead of hiding it.
Every investing metric in Investing & Markets is a bet about the future priced in today’s language. Arbitrage Return translates that bet: Total return = (sell + income − buy) ÷ buy; CAGR = ((sell + income) ÷ buy)^(1/years) − 1. The translation is mechanical and reliable; the judgement is deciding whether the inputs you feed it are honest forecasts or wishful numbers.
There is a habit that separates people who get useful answers from Alternative Investments numbers: they decide what question the figure answers before they compute it. Arbitrage Return answers “Total return?” — and nothing else, which is precisely why the result is trustworthy.
What makes a calculation page trustworthy is that its copy is derived from its own arithmetic: here total return = 21.93%, recomputed every time a field changes, and the sensitivity section ranks the inputs that move the result — Buy price / invested first, at ≈61.8 % of the headline for a ten-percent error either way in that input — which is the thread the rest of this guide pulls on.
Inside the Arbitrage Return calculation: formula and every input
One formula, published in full: Total return = (sell + income − buy) ÷ buy; CAGR = ((sell + income) ÷ buy)^(1/years) − 1. Anything you can read, you can reproduce in a spreadsheet, and that reproducibility is the whole point of printing it rather than hiding it behind a button.
Buy price / invested ($) (example value 15,250) is a measured number in the unit named by the label; the formula does not convert for you. Use the figure exactly as the source document states it, not a rounded memory of it — an omitted line is the classic silent error.
Sell price / value now ($) (example value 17,750) is a plain measured quantity — the unit shown in the label is the unit the formula expects. If your source quotes a figure before and after some deduction, decide which one the formula wants and be consistent for every field.
Holding period (years) (example value 6) is a measured number in the unit named by the label; the formula does not convert for you. Use the value as of today, not as of the last time you looked — time fields drift silently.
Income received over the hold ($) (example value 845) is a measured number in the unit named by the label; the formula does not convert for you. Use the figure exactly as the source document states it, not a rounded memory of it — an omitted line is the classic silent error.
A fully worked Arbitrage Return example
Abstract formulas are hard to trust, so here is the complete substitution using the default inputs, written the way an examiner would want it. Starting figures: Buy price / invested ($), Sell price / value now ($), Holding period (years), Income received over the hold ($). The endpoint of that chain is 21.93% of total return, sitting in the “Modest gain — check it after inflation and costs” band.
- Ending value incl. income = $17,750.00 + $845.00 = $18,595.00
- Total return = (18,595.00 − 15,250.00) ÷ 15,250.00 = 21.93 %
- CAGR = (18,595.00 ÷ 15,250.00)^(1/6.0) − 1 = 3.36 % a year
Annualised (CAGR) — 3.36%. Compare it against the main result of 21.93% before drawing conclusions.
Net profit — $3,345.00. Read next to the headline, this is the figure that shows the shape of the trade-off.
Value multiple — 1.22 ×. Compare it against the main result of 21.93% before drawing conclusions.
Income share of gain — 25.3%. If your inputs change, this is usually the first companion figure to move.
Keep this worked example open while you enter your own figures: matching the shape of the substitution is the fastest way to spot a unit or convention mistake.
How far Arbitrage Return can reasonably move
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 Arbitrage Return, not an interpolation.
| Buy price / invested setting | Total return |
|---|---|
| 80 % of the example value | 52.42% |
| 90 % of the example value | 35.48% |
| example inputs | 21.93% |
| 110 % of the example value | 10.85% |
| 120 % of the example value | 1.61% |
That spread — 1.61% at the low end, 52.42% at the high — is what a careful read of Arbitrage Return looks like: a band you can state out loud, with the reason for each edge. Reproduce it in the form above by editing Buy price / invested alone; the substitution steps will follow your figures exactly.
Where Arbitrage Return 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 total return was recalculated from scratch. It is the fastest honest answer to “what matters most in Arbitrage Return?” — and it is specific to these defaults, because sensitivity moves with the starting point.
- Buy price / invested +10 % → Arbitrage Return = 10.85% · −10 % → 35.48% (the total return shifts ≈61.8 %)
- Sell price / value now: ten percent up gives 33.57%, ten percent down gives 10.30% — ≈53.1 % of the total return either way
- Income received over the hold +10 % → Arbitrage Return = 22.49% · −10 % → 21.38% (the total return shifts ≈2.5 %)
Buy price / invested is the dominant lever here: ten percent either way moves the result by about 61.8 %, from 10.85% to 35.48%. Measure that input from a document rather than from memory, and treat Sell price / value now as the second priority (≈53.1 % per ten percent). The rest of the inputs earn only a rounding-error of attention, and that asymmetry is the practical payoff of measuring rather than asserting.
Interpreting the Arbitrage Return verdict
A number on its own is trivia; a number against a range is intelligence. The verdict attached to the default calculation — “Modest gain — check it after inflation and costs” — is one band on a ladder your own figure may sit somewhere else on. Before treating the band as fact, note its width: ten percent either way on Buy price / invested already spans 10.85% to 35.48%. The practical reading rules: read the band as a starting hypothesis, then test it: change the two dominant inputs by ten percent and see whether the verdict survives. Verdicts that survive stress are the ones worth acting on.
Where Arbitrage Return sits next to similar measures: this tool answers “how much is the Arbitrage Return”, 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.
Common mistakes with Arbitrage Return (and the fix)
Ignoring the timing of income (reinvested vs spent) can overstate a CAGR by a few tenths; dividends spent as cash belong outside the ending value. 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 Buy price / invested dominating — a careful figure there beats false precision everywhere else.
Another is comparing across contexts: an Arbitrage Return 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 Arbitrage Return: a short checklist
- State, in one sentence, which convention each rate, unit or period in the form is using.
- Compare the result with one independent method or published benchmark.
- Re-verify Buy price / invested against a source document — ten percent of error there moves the headline by ≈61.8 %.
- Record the date and the inputs alongside the number so future-you knows what was assumed.
- Re-run the calculation with a ±10 % stress on the two most sensitive inputs.
- Repeat the ±10 % test on the inputs that matter and see whether the decision — not just the number — still holds.
A routine for decision-grade Arbitrage Return
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 (buy price / invested ($), sell price / value now ($), holding period (years), income received over the hold ($)). 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. Suspiciously tidy answers deserve the same scrutiny as untidy ones.
Step 2 — enter the conservative case first. Resist the flattering scenario. Type the inputs you would defend in front of a sceptical reader, read the Total return (21.93% for the example values), and note the verdict band. The input you reach for first is usually the one you measured longest ago.
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. A figure nobody can reproduce is a figure nobody will act on twice.
Step 4 — run the scenario trio. Expected, pessimistic, optimistic. The gap between pessimistic and expected is the number to plan against; the optimistic result is useful only as a ceiling. Numbers are cheap to produce and expensive to retract; the extra minute is the cheapest insurance available.
Step 5 — save the story with the figure. A number without its inputs and its date is unusable within a quarter. Record 21.93%, the assumptions behind it, and today’s date; your future self will be auditing a stranger’s arithmetic. Precision is a promise you make about your data; make sure your inputs can keep it.
The real-world conversations Arbitrage Return settles
Most Alternative Investments disagreements are arithmetic disagreements in disguise. When Total return of 21.93% sits on the table with its working shown, the conversation stops being about who sounds more confident and starts being about which input is wrong. Comparisons are cheap: run the identical calculation for the alternative and look at the gap.
Professionals in Alternative Investments use this style of calculation as a screening filter before spending real money or effort: a quick Arbitrage Return check eliminates weak options in minutes, and the survivors earn the deeper, slower analysis. A figure with a date beside it becomes evidence; without one it stays an anecdote.
Nothing here is stored or transmitted, so the habit of checking is free: open the page, re-enter current figures, compare with the number you saved last time. Comparisons are cheap: run the identical calculation for the alternative and look at the gap.
The questions that come up most about Arbitrage Return
What affects Arbitrage Return the most?
The short answer: Buy price / invested. The longer answer is the sensitivity table on this page, where every numeric input was probed by ten percent and the total return recalculated — Buy price / invested moved it furthest, by roughly 61.8 % (10.85% to 35.48%).
Which matters more: sell price / value now or buy price / invested?
Buy price / invested, by a factor of about 1.2. Concretely: ten percent on Buy price / invested is worth ≈61.8 % of Arbitrage Return, the same nudge on Sell price / value now only ≈53.1 %. That ranking is re-computed for each page from that page’s own defaults.
What is a typical Arbitrage Return?
With the example inputs on this page the result is 21.93%, labelled “Modest gain — check it after inflation and costs”. “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 Arbitrage Return by hand?
Total return = (sell + income − buy) ÷ buy; CAGR = ((sell + income) ÷ buy)^(1/years) − 1 is the entire method. Work the inputs in that order — Ending value incl. income = $17,750.00 + $845.00 = $18,595.00 — and you will reach 21.93% on the default figures, the same number this tool prints.
What happens to Arbitrage Return if buy price / invested changes by 10 %?
Try it in the form above and the printed substitution will follow you; the pre-computed answer for the defaults is 10.85% to 35.48% across the ten-percent probe, i.e. ≈61.8 % sensitivity on the total return.
Is the Arbitrage Return result of 21.93% good or bad?
Neither, on its own — the label “Modest gain — check it after inflation and costs” is the band this figure falls in for the example inputs, and your own inputs will place you elsewhere on the same ladder. Judge the number against your history and your alternatives, and remember that a ten-percent error in Buy price / invested alone moves it by ≈61.8 %.
How do I calculate Arbitrage Return manually?
Write down the inputs, then follow the printed steps in order — Total return = (sell + income − buy) ÷ buy; CAGR = ((sell + income) ÷ buy)^(1/years) − 1. A spreadsheet replicates it with two or three cells. The manual route is worth doing once to build intuition; after that the calculator saves time and eliminates transcription slips.
Can Arbitrage Return be negative or empty?
Yes, and that is informative rather than broken: a negative Arbitrage Return usually means the inputs encode an outflow or a shortfall, and the verdict band above labels exactly that situation instead of hiding it.
Why does CAGR differ from average yearly return?
CAGR compounds — it is the single steady rate that turns the start into the end, while arithmetic averages flatter volatile paths.
Are taxes included?
No, this is the pre-tax picture; subtract tax drag on gains and income before comparing with a tax-sheltered alternative.
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.
Glossary for Arbitrage Return
- Annualised (CAGR)
- 3.36% in the default Arbitrage Return calculation — one of the secondary figures an experienced reader checks before trusting the primary number.
- Net profit
- $3,345.00 on the example inputs — a companion figure printed beside the headline of Arbitrage Return so that no result is read in isolation.
- Value multiple
- 1.22 × in the default Arbitrage Return calculation — one of the secondary figures an experienced reader checks before trusting the primary number.
- Total return
- The primary output of this tool: 21.93% for the default inputs, computed exactly from Total return = (sell + income − buy) ÷ buy; CAGR = ((sell + income) ÷ buy)^(1/years) − 1.
- Worked example
- The step-by-step substitution printed above, so the arithmetic can be re-derived by hand or in a spreadsheet.
- Verdict band
- A named zone on the range of plausible results; the example inputs land in “Modest gain — check it after inflation and costs”, and your inputs may not.
- Sensitivity (±10 %)
- How far the Arbitrage Return moves when a single input is nudged ten percent either way; the ranked list on this page is computed live from this engine.
Methodology, sources and limits
The model is published arithmetic implemented exactly as written: Total return = (sell + income − buy) ÷ buy; CAGR = ((sell + income) ÷ buy)^(1/years) − 1. Source of record: Time-weighted return arithmetic per CFA Institute conventions. 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.
Treat the output as a precise answer to the question you typed: exact arithmetic, transparent formula, published source, no hidden rounding. The promise to the reader is narrow and testable: same inputs, same output, no silent rounding, and no figure presented without the formula that produced it.
After the number: what to do with it
Run the pessimistic case before the optimistic one; an opportunity that survives the pessimistic inputs is the only kind worth pursuing.
Whoever you are (investors and founders comparing opportunities on equal terms), 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.