Expected Rate of Return Calculator
The expected rate of return is a forward-looking average: it weights every return an investment could produce by how likely that return is, so a strong outcome you only half believe counts for half. Add your scenarios below, each with a return and a probability that together cover 100%, and this calculator returns the probability-weighted expected return, the variance and standard deviation around it, and what each scenario contributes. A second tab handles the opposite case, one known growth path, and computes its compound annual growth rate (CAGR).
Quick Answer
With the pre-filled scenarios, +10% at 30% probability, -5% at 20% and +4% at 50%, the expected rate of return is +4.00%, with variance 27.00 and standard deviation 5.20%. On the CAGR tab, $10,000 growing to $20,000 over 10 years gives 7.18% per year. The first number averages an uncertain future; the second smooths one known path, and the two are not interchangeable.
Key takeaways
- Expected return is a weighted average, not a forecast of the outcome you will actually get. You will land on one scenario, never on the average.
- Probabilities must cover everything and add to 100%. A 30/30/30 split leaves 10% of reality unpriced, and this tool refuses to run it.
- Standard deviation is the price tag on the expectation. Two investments at +8% expected are not equal if one spreads at 3% and the other at 20%.
- Use scenarios for uncertain futures and the CAGR tab for a single known or projected path.
- Quick Answer
- How to use the expected rate of return calculator
- The expected return formula, and the risk formulas beside it
- Worked example: three scenarios, checked in the tool
- How expected return differs from the other rate-of-return pages
- Reading the spread: variance, standard deviation and the badge
- Where honest probabilities come from
- What competing calculators miss
- Limits worth stating plainly
- Frequently asked questions
- Add This Calculator to Your Website
- References
How to use the expected rate of return calculator
List the outcomes, attach a return and an honest probability to each one, then click Calculate. The results stay hidden until you do.
- Build the scenario list: start with the three pre-filled rows and edit them, or use Add scenario and Remove to shape the list. Each row needs a return in percent (negative for a loss) and a probability in percent.
- Check the total: the probabilities must add to exactly 100%, within a small rounding tolerance. If they add to 90% or 110%, the tool tells you the actual total instead of quietly rescaling it.
- Read all three outputs: the expected return, the variance and standard deviation, and the contribution printed beside each row after a successful run, which shows exactly which scenarios pull the average up or down.
- Switch to the CAGR tab only for a single path: an investment amount, a future value and a number of years, with no probabilities involved.
The expected return formula, and the risk formulas beside it
Expected return = Σ(Ri × Pi): multiply each scenario return by its probability and add the products.
Variance = Σ(Pi × (Ri - E[r])2)
Standard deviation = √Variance
CAGR = (Future value ÷ Investment)(1 ÷ Years) - 1
This is the discrete expected value from probability theory applied to returns, the same construction behind a general conditional expected value calculator when outcomes are grouped by condition. The variance formula uses the probabilities as weights rather than dividing by a sample count, because the scenario list is meant to be the full set of possible outcomes, not a sample drawn from a larger history. That distinction matters: a historical standard deviation from past monthly returns and a scenario standard deviation from your own forward-looking list answer related but different questions.
Worked example: three scenarios, checked in the tool
An investor models one year ahead with three outcomes: a good year at +10% with 30% probability, a bad year at -5% with 20% probability, and a flat-ish year at +4% with 50% probability.
| Check (scenarios) | Expected | Variance | SD |
|---|---|---|---|
| +20% at 50%, -5% at 50% | +7.50% | 156.25 | 12.50% |
| +8% at 100% (single outcome) | +8.00% | 0.00 | 0.00% |
| +15% at 25%, +10% at 50%, 0% at 25% | +8.75% | 29.69 | 5.45% |
| -10% at 30%, +5% at 70% | +0.50% | 47.25 | 6.87% |
Every row is a real run of this calculator. The second row is the instructive one: a single certain outcome has zero variance, which is the tool telling you the model contains no uncertainty, not that the investment is risk-free in the real world. On the CAGR tab, the matching checks are $5,000 to $5,000 over 5 years at 0.00%, $10,000 falling to $8,000 over 3 years at -7.17%, and $25,000 to $40,000 over 7 years at 6.94%.
How expected return differs from the other rate-of-return pages
Expected return is the only member of the rate-of-return family that is built from probabilities about the future. The siblings each answer a different question, and swapping them produces confident nonsense:
| Measure | Question it answers | Inputs it needs |
|---|---|---|
| Expected rate of return (this page) | What return should I expect, on average, across the futures I can imagine? | Scenario returns with probabilities summing to 100% |
| Required rate of return | What return must this investment clear to be worth its risk? | A hurdle: risk-free rate, beta and market premium in the CAPM version |
| Personal rate of return | What did my account actually earn, given my deposits and withdrawals? | Real account history with dated cash flows |
| Net rate of return | What remains after fees, charges or taxes are taken out? | A gross return plus the costs to subtract |
| Insurance rate of return | What do premiums paid into a policy return, in policy terms? | Premiums, policy values and timing inside an insurance contract |
| Geometric rate of return | What constant compounded rate reproduces a realized multi-period record? | A series of actual period returns, compounded |
The practical test is tense. If the numbers have not happened yet and carry probabilities, you are in expected-return territory, and the natural comparison is expected return against required return: an investment whose expected return sits below the return its risk requires is a pass, however attractive the headline scenario looks. If the numbers already happened, you want a realized measure instead, and the CAGR tab here or a dedicated CAGR return calculator handles the single-path version.
Reading the spread: variance, standard deviation and the badge
Standard deviation is the spread of your scenarios around their own average, in the same percentage units as the returns. The badge under the result sorts it into bands:
| Standard deviation | Reading | What it usually means |
|---|---|---|
| Under 5% | Narrow spread | Scenarios cluster tightly. Either the asset is genuinely steady or the scenario list is too timid. |
| 5% to under 10% | Moderate spread | A normal range for a diversified holding modelled honestly. |
| 10% to under 20% | Wide spread | Outcomes diverge sharply. The expected return needs to be high to justify living with this range. |
| 20% and above | Very wide spread | Speculative territory. Check whether one extreme scenario is doing all the work in the average. |
Standard deviation treats upside and downside surprise symmetrically, which real investors do not. A scenario set with a small chance of a severe loss can share a standard deviation with a set whose spread is mostly upside. For the left tail specifically, a measure such as the one in the expected shortfall calculator focuses on average losses beyond a threshold rather than overall spread. Use both readings before treating a high expected return as a good deal.
Where honest probabilities come from
The arithmetic is exact and the probabilities are not, so the quality of the answer is set before you touch the calculator. Three habits keep the inputs honest. Start from base rates: long-run historical return distributions, such as the stock, bond and bill histories maintained in Damodaran's historical return data at NYU Stern, show how often years like your scenarios have actually occurred. Force a genuine loss scenario into every list, with a probability you would defend out loud; a list with no negative row is marketing, not modelling. Finally, make the scenarios cover distinct futures rather than three shades of the same future, because near-duplicate rows double-count one outcome and starve the rest.
For a portfolio, the same weighting runs holding by holding: each asset contributes its own expected return weighted by its share of the portfolio, which is the calculation a portfolio performance calculator approaches from the realized side. The U.S. Securities and Exchange Commission's investor education arm makes the underlying point plainly in its introduction to investing on Investor.gov: risk and return travel together, and any expected return that ignores the spread around it is half an analysis.
What competing calculators miss
The expectation itself is one line of arithmetic, and most tools stop there. The gaps that matter:
- Brave Calculator: computes the weighted average correctly and uses this page's exact three-scenario example, but shows no variance or standard deviation, so two bets with the same 4% expectation and wildly different risk look identical.
- Spreadsheet guides (Wall Street Prep, The Bricks, SoFi Learn): teach SUMPRODUCT and the scenario method well, with portfolio and CAPM context, but the reader has to build the sheet, wire the variance formula themselves, and gets no validation when probabilities fail to sum to 100%.
- FasterCapital: explains standard deviation for investment returns in depth, including portfolio correlation, but offers teaching rather than a scenario tool you can rerun.
- Trading expectancy tools (RealTradingRoom): a different expectancy, win rate times average win minus loss rate times average loss, built for trade journals. Useful in its niche; it does not take scenario probabilities for an investment.
- The gap this page fills: expectation, variance, standard deviation and per-scenario contributions in one validated run, with the 100% probability check enforced, plus the single-path CAGR one tab away instead of on a separate page.
Limits worth stating plainly
This tool averages the scenarios you give it; it cannot judge whether those scenarios are the right ones. It has no CAPM mode, no beta input and no market data feed, so it will not tell you what return an asset should offer for its risk, only what your own scenarios average to. The scenario standard deviation is a forward-looking modelling spread, not a historical volatility figure, and it says nothing about correlations between holdings. Treat the output as a disciplined way to argue with your own assumptions, ideally before money moves.
Frequently asked questions
Multiply each possible return by its probability and add the products: E[r] = sum of (Ri x Pi). In the worked example, 10% at 30%, -5% at 20% and 4% at 50% give 3 - 1 + 2 = 4.00%.
Yes. The scenarios must cover every possible outcome, or part of reality is left unpriced. This calculator refuses to run until the total is 100% and tells you the actual total when it is not.
They measure how far the scenarios spread around the expected return. Variance is the probability-weighted average of squared deviations, and standard deviation is its square root, in the same percentage units as the returns, which makes it the practical risk reading.
Yes, and at least one usually should be. Loss scenarios are exactly what expected-return math is for: a list with no negative outcome hides the downside the weighting is meant to price in.
Expected return is what your scenarios average to. Required return is the hurdle an investment must clear to compensate for its risk, often set with a model such as CAPM. Comparing the two is the decision: expected below required means the risk is not being paid for.
Expected return averages uncertain scenarios before the fact. CAGR is the single constant annual rate connecting two known values over time, with no probabilities involved. This page keeps CAGR on its own tab for exactly that reason.
Because it is an average across scenarios, and any single period lands on one scenario, not the average. A 7.50% expectation built from +20% and -5% at equal probability pays one of those two, never 7.50% itself.
Yes, in two ways: model the portfolio itself as scenarios, or run each holding separately and weight the expected returns by portfolio share. What the scenario list cannot capture is correlation between holdings, which is part of true portfolio risk.
From base rates and history where you can get them: how often similar years, deals or markets have produced outcomes like each scenario. Probabilities chosen to make the average look good produce a precise number that means nothing.
No. It is an educational model of uncertainty that organizes your own assumptions. It does not know your goals, taxes or time horizon, and it is not a recommendation to buy or avoid any investment.
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References
- U.S. Securities and Exchange Commission, Investor.gov. Introduction to Investing. Accessed October 21, 2026.
- U.S. Securities and Exchange Commission, Investor.gov. Compound Interest Calculator. Accessed October 21, 2026.
- Damodaran, Aswath (NYU Stern School of Business). Historical Returns on Stocks, Bonds and Bills: 1928 to Present. Accessed October 21, 2026.
- Damodaran, Aswath (NYU Stern School of Business). Country Default Spreads and Risk Premiums. Accessed October 21, 2026.
- Nasdaq. S&P 500 Index Data. Accessed October 21, 2026.
- Board of Governors of the Federal Reserve System. Statistical Release H.15, Selected Interest Rates. Accessed October 21, 2026.
- Financial Industry Regulatory Authority (FINRA). Know Your Risk Tolerance. Accessed October 21, 2026.
- CFA Institute. CFA Program Curriculum, Portfolio Management and Quantitative Methods. Accessed October 21, 2026.
- Ross, Westerfield and Jordan. Fundamentals of Corporate Finance, Risk and Return Chapters. Accessed October 21, 2026.
- U.S. Securities and Exchange Commission, Investor.gov. Investor Alert: 5 Ways Fraudsters May Lure Victims Into Scams Involving Crypto Asset Securities. Accessed October 21, 2026.
- Bodie, Kane and Marcus. Investments, Risk and Return and Portfolio Theory Chapters. Accessed October 21, 2026.