A 25/50/25 split across +20%, +8% and −10% averages to something none of them equals
Expected return multiplies each outcome by its probability and adds: 0.25 × 20 + 0.50 × 8 + 0.25 × (−10) = 5 + 4 − 2.5 = 6.5%. It is the long-run average if the same bet were repeated many times under the same odds, not a prediction of any single year.
E[R] = sum of (probability x return) across scenarios
That distinction matters because 6.5% will never actually happen here. The possible outcomes are 20%, 8% and −10%. Treating an expected value as a forecast is a common error, and it is why the best and worst cases are shown alongside — the spread between them is the part the average deliberately discards.
Weights that do not add up silently scale the whole answer
The total probability figure exists as a guard. If the scenarios sum to 80%, the expected return is computed across incomplete outcomes and is understated by a fifth — arithmetically consistent, and wrong. If they sum to 120%, it is overstated. Neither error announces itself in the headline number.
The requirement is not arbitrary. Probabilities over a complete set of mutually exclusive outcomes must sum to one, and if your scenarios do not cover every possibility, the missing probability mass belongs somewhere. Adding an explicit "everything else" scenario with a realistic return is more honest than leaving the total short.
The arithmetic is trivial; the inputs are guesses
This calculation is only as good as the scenario probabilities, and those are almost always subjective. Analysts routinely assign round numbers — 25/50/25 — that reflect a narrative rather than any measured frequency, and the output inherits that entirely.
Two biases recur. Scenarios are usually too narrow: the worst case is rarely bad enough, because genuinely extreme outcomes are hard to imagine and uncomfortable to write down. And probabilities cluster on the middle scenario, because a central estimate feels defensible. Running the calculation with a deliberately worse tail is usually more informative than refining the central case.
Risk, and the fact that you only live once
Two investments can share an expected return of 6.5% while one ranges from 5% to 8% and the other from −40% to +60%. The expected value is identical and the investments are not remotely comparable. Variance across the scenarios is the missing half, and the Sharpe ratio is one standard way of combining them.
There is also a sequencing point the average cannot capture. An outcome that wipes out the capital ends the sequence, so a bet with a positive expected value and a meaningful chance of total loss is not one to repeat. Expected value assumes many repetitions from an unchanged base, and real portfolios rarely satisfy that.
Frequently Asked Questions
Do the probabilities have to add up to 100%?
They should, because they are meant to cover all the outcomes you are weighing. The calculator shows the total so you can confirm it equals 100%; if it does not, the expected return will be off.
Can expected return be negative?
Yes. If the weighted losses outweigh the weighted gains, the expected return is negative. Returns in individual scenarios can also be negative, which the calculator accepts.
Is expected return the same as guaranteed return?
No. Expected return is a probability-weighted average across scenarios, not a promise. Any single outcome can be higher or lower, and none of the scenarios is guaranteed to occur.
What is the difference between expected return and average historical return?
Expected return is forward-looking and built from probabilities you assign to future scenarios. Average historical return simply summarizes what already happened. They can differ significantly.
How does expected return relate to risk?
Expected return measures the central tendency, while risk reflects how spread out the outcomes are. Two investments can share an expected return yet have very different ranges between their best and worst cases.
How many scenarios should I use?
Use enough to capture the outcomes that matter, typically a downside, a base case, and an upside. This calculator supports two to four, which is usually sufficient for a quick estimate.
Sources & References
Figures on this page are checked against primary, authoritative sources. Links open in a new tab.
Returns are assumptions, not guarantees. Actual results may vary because of market performance, taxes, fees, inflation, and timing. This is an educational projection, not investment advice.
Published the calculator with its formula, worked example, assumptions, limitations and a bespoke guide, and added an automated formula test suite covering it.
Verified that the expected value always lies between the best and worst scenarios, and that the probability total is reported so weights not summing to 100% are visible.
Frequently Asked Questions now show on the page: 6 answers, checked in a page-by-page audit.
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