Expected Return Calculator — Probability-Weighted Return
Estimate an investment's average likely return by weighting each scenario by its probability. Enter bull, base, and bear returns with their likelihoods (summing to 100%) to get the expected return, standard deviation, and a distribution view.
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Probability-weighted average of all scenario returns
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Bull scenario contribution
25% × 20% = 5 % - 2
Base scenario contribution
50% × 8% = 4 % - 3
Bear scenario contribution
25% × -10% = -2.5 % - 4
Expected Return
5 + 4 + -2.5 = 6.50 %Probability-weighted average of all three scenario returns.
How does this calculator work?
E[R] = Σ(probability × return). Enter bull, base, and bear scenario probabilities and returns — they must total 100% — to get the probability-weighted mean return plus standard deviation σ as a measure of how wide the uncertainty around that central estimate is.
Formula
How this is calculated
The expected return is the probability-weighted average of all discrete outcomes. Multiplying each scenario's return by its probability and summing gives the single number that, over many independent repetitions of the same bet, the investment would average. For three scenarios it is: E[R] = p_bull × r_bull + p_base × r_base + p_bear × r_bear.
The standard deviation σ = √(Σ pᵢ(rᵢ − E[R])²) measures dispersion — how spread the outcomes are around the expected value. A higher σ means greater uncertainty. The Sharpe-like ratio E[R]/σ is a rough risk-adjusted score (higher is better), though it only equals the true Sharpe ratio when the risk-free rate is zero and does not account for skewness or tail risk.
This three-scenario model treats the outcomes as mutually exclusive and collectively exhaustive (probabilities must sum to exactly 100%). Real return distributions are continuous and often fat-tailed; treat results as a useful first approximation rather than a precise forecast.
Frequently asked questions
The three scenarios are assumed to cover all possible outcomes with no overlap. Probabilities summing to any other value would violate the axioms of probability and produce a meaningless expected value — one scenario must happen.
A larger σ indicates returns vary more widely around the expected value. Two investments with the same E[R] but different σ values differ substantially in risk: the higher-σ one could return much more or much less than expected in any single period.
They are conceptually related but not identical. Expected return is a forward-looking, probability-weighted calculation over your stated scenarios. Historical average return is a backward-looking arithmetic mean of realised outcomes. The two converge over many periods if your probability estimates are correct.
TG we-Calculate Editorial Team. (2026). Expected Return Calculator — Probability-Weighted Return [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/expected-return-calculator
TG we-Calculate Editorial Team. "Expected Return Calculator — Probability-Weighted Return." TG we-Calculate. 2026. https://we-calculate.com/calculator/expected-return-calculator.
TG we-Calculate Editorial Team, "Expected Return Calculator — Probability-Weighted Return," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/expected-return-calculator
@misc{wecalculate_expected_return_calculator, title = {Expected Return Calculator — Probability-Weighted Return}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/expected-return-calculator}}, year = {2026}, note = {TG we-Calculate} }
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