Expected Return Calculator
Compute the expected return as the probability-weighted average of up to five scenarios.
Input Data
Results
At a glance:Expected Return is the probability-weighted average of the returns of all possible scenarios: E(R) = Σ pᵢ × rᵢ, where pᵢ is each scenario's probability and rᵢ its return. The scenario probabilities should sum to 100%. It is the basis for evaluating investments, comparing assets and measuring risk (dispersion of returns).
Formula
Expected return E(R) = Σ pᵢ × rᵢ, i from 1 to each scenario.
pᵢ is the probability and rᵢ the return of scenario i.
Scenario probabilities should sum to 100%; this calculator also shows the total for checking.
$$$E(R) = \\sum_{i} p_i \\times r_i$$$$$$0.3(20\\%)+0.5(10\\%)+0.2(-5\\%)=10\\%$$$$$$\\sum_i p_i = 100\\%$$$How to Use
- Enter the probability and return for each scenario.
- Set unused scenarios' probability to 0.
- View the probability-weighted expected return and check the total probability is 100%.
Expected return across bull/neutral/bear scenarios
| Scenario | Probability | Return | Contribution (p×r) |
|---|---|---|---|
| Bull | 30% | +20% | +6.0% |
| Neutral | 50% | +10% | +5.0% |
| Bear | 20% | −5% | −1.0% |
| Total | 100% | — | +10.0% (E(R)) |
Case Studies
Case 1: Expected return across three scenarios
A stock: bull (30%) +20%, neutral (50%) +10%, bear (20%) −5%. Total probability = 30+50+20 = 100%.
E(R) = 0.30×20% + 0.50×10% + 0.20×(−5%) = 6% + 5% − 1% = 10%.
Interpretation: the probability-weighted average return is 10% — a long-run, repeated-average concept, not any single year's result. It gives a comparable 'centre value' for decisions under uncertainty.
Case 2: High expected return ≠ better investment
Compare two stocks. A: as above, E(R)=10%, returns clustered (worst −5%). B: bull (25%) +30%, neutral (50%) +8%, bear (25%) −20%, E(R)=0.25×30%+0.5×8%+0.25×(−20%)=7.5%+4%−5%=6.5%, but returns spread wider (worst −20%).
A's expected return (10%) exceeds B's (6.5%), and A's worst case (−5%) is far better than B's (−20%) — A wins on both return and risk.
Interpretation: expected return is only the average, not risk. With equal expected return, the less volatile is usually better; here A also has lower downside, clearly preferable. Judge with risk too — pair with standard deviation and Sharpe ratio. Scenarios/probabilities are subjective; set cautiously and do sensitivity analysis.
FAQ
Must the probabilities sum to 100%?
In theory all possible scenarios' probabilities should sum to 100%. If short or over, scenarios are incomplete or overlapping, and the expected return is biased — adjust to 100% first.
Is expected return the actual return?
No. Expected return is the probability-weighted average, a 'long-run average' concept; a single actual outcome is just one scenario's return, not necessarily the expectation.
Is a high expected return always worth it?
Not necessarily. Also weigh risk (dispersion of returns). With equal expected returns, the less volatile is usually better; pair with standard deviation and the Sharpe ratio.
How are expected return and risk (standard deviation) related?
Expected return and risk (standard deviation) are two sides of the same coin and must be read together: expected return E(R) is the probability-weighted average (the 'centre'); standard deviation σ measures how spread actual returns are around it — larger σ means more uncertain, higher risk. Example: two stocks both 10% expected return, but A ranges 5%–15% (small σ) while B ranges −20%–40% (large σ); though the average is equal, B is far riskier. Read both because expected return alone ignores the volatility to reach that average. Rational decisions trade off risk and return: (1) at equal expected return pick lower risk (diversification basis); (2) at equal risk pick higher expected return; (3) if higher expected return comes with higher risk, judge whether the extra return compensates the extra risk — that is what risk-adjusted measures like the Sharpe ratio (excess return ÷ σ) address. Standard deviation also relates to worst case: a 10% expected return with large σ can lose heavily in some years, which you may not afford if you need the money soon. So evaluate expected return (gain) with σ/downside (uncertainty, possible loss) together.
How to set scenarios and probabilities reasonably? Limits of the estimate?
Accuracy depends entirely on how reasonable your scenarios and probabilities are — and that is its biggest limit, because both are subjective, not facts. To set them well: (1) scenarios should be complete and mutually exclusive (bull/neutral/bear) so probabilities sum to 100%; short means missed scenarios, over means overlap or error — both distort the result; (2) probabilities need a basis — use history (past bull/bear frequency), market consensus, analyst forecasts or economic indicators, and stay cautious against over-optimism; (3) returns should be realistic, not wishful. Limits: subjectivity (different people, different results), history may not repeat (crashes, policy shocks), black swans (rare extreme events outside preset scenarios), and the average trap (a single outcome may differ wildly). Use it as a decision framework: set scenarios cautiously, do sensitivity analysis (shift probabilities and see the change), and always pair with risk metrics — not as a precise prediction.
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References
Content review: Calculatorism Finance Team. Results are for reference only; please refer to the relevant authorities for the official figures.