Expected return comparison
Stock B +1.90 pp
Stock B has the higher expected return.
Expected Return Calculator
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Description
Expected Return Calculator
Compare two investments across probability-weighted scenarios, including expected return, variance, standard deviation, and scenario-level contributions.
Probability total 100.00%
Complete scenarios 3
Higher expected return Stock B
Lower volatility Stock A
Scenario assumptions
Enter a probability and the return for each stock. Probabilities must total 100%.
Live results
Returns are probability-weighted. Risk is measured from the same scenario distribution.
Stock A expected return
8.50%
Probability-weighted average
Stock B expected return
10.40%
Probability-weighted average
Stock A standard deviation
10.50%
Variance: 0.0110
Stock B standard deviation
16.67%
Variance: 0.0278
Stock A return range
30.00 pp
-5.00% to 25.00%
Stock B return range
47.00 pp
-12.00% to 35.00%
Stock B leads expected return by 1.90 percentage points; Stock A has lower volatility.
Return and volatility comparison
The chart compares each stock’s expected return with its standard deviation using the current scenario assumptions.
Enter complete scenarios totaling 100% to draw the comparison chart.
| Investment | Expected return | Standard deviation | Variance |
|---|
Expected return describes the weighted average outcome; standard deviation indicates how widely scenario returns vary around that average.
Scenario contribution detail
Each contribution equals probability multiplied by the scenario return.
| Scenario | Probability | Stock A return | Stock A contribution | Stock B return | Stock B contribution |
|---|
The contribution columns cross-foot to each stock’s expected return. Variance and standard deviation use the same probabilities but measure squared deviations from the expected return.
How to use and interpret the expected return model
What this calculator estimates
Expected return is the probability-weighted average of several possible returns. It is not a forecast of one guaranteed outcome. Instead, it condenses a scenario distribution into a single average that can help compare investments on a consistent basis. This calculator evaluates two stocks or strategies side by side and also measures variance and standard deviation, which describe how dispersed the possible returns are around the expected return.
The model is useful for structured scenario analysis: a downside case, a base case, an upside case, and any additional outcomes you consider material. For general investor education about uncertainty, review the U.S. Securities and Exchange Commission’s explanation of investment risk.
Expected return: E(r) = Σ pᵢ × rᵢ
Here, pᵢ is the probability of scenario i expressed as a decimal, and rᵢ is the return in that scenario. Probabilities must cover the full outcome set and therefore total 100%.
How to enter each scenario
Probability is the estimated likelihood of the scenario. Enter it as a percentage from 0% to 100%. This field is required for every completed row, and the completed probabilities must total exactly 100% within normal rounding tolerance. Higher probability gives that scenario more influence over expected return and risk. A common mistake is entering decimal form such as 0.30 when 30% is intended.
Stock A return and Stock B return are the gains or losses expected if that scenario occurs. Enter positive percentages for gains and negative percentages for losses. These fields are required in every completed row. There is no need to force both stocks to have the same sign; one investment may gain while the other loses in the same market environment.
Use the Add scenario button for another outcome. A new blank row also appears automatically after the final row is completed. Remove rows that no longer belong in the distribution. Reset clears the current scenario set to a neutral blank row rather than reloading the example.
How the risk calculations work
Variance measures the weighted average squared distance between each scenario return and the expected return. Squaring prevents positive and negative deviations from cancelling each other. The calculator expresses variance in decimal-return units, so it may look small even when the percentage swings are meaningful.
Variance: Var(r) = Σ pᵢ × (rᵢ − E(r))²
Standard deviation: SD(r) = √Var(r)
Standard deviation: SD(r) = √Var(r)
Standard deviation converts variance back into return units, making it easier to compare with expected return. A higher standard deviation means the modeled outcomes are more spread out. It does not identify whether the uncertainty comes primarily from downside or upside scenarios, and it does not capture risks omitted from the scenario set. FINRA provides additional context on the relationship between risk and return.
How to read every result
Expected return is the weighted average for each stock. A higher value may be attractive, but it should be considered together with risk. A zero value means gains and losses offset on a weighted basis; a negative value means the modeled distribution has an expected loss.
Standard deviation shows dispersion around expected return. Lower is more stable under the entered scenarios, while higher indicates a wider range of possible outcomes. Variance is the squared form used to compute standard deviation. Return range is the difference between the highest and lowest entered return; it is intuitive but ignores probability, so it should not replace standard deviation.
The comparison headline reports the expected-return gap in percentage points. The chart puts expected return and standard deviation on the same percentage scale. The detail table shows each scenario’s direct contribution, allowing you to verify which outcomes drive the weighted average.
How assumption changes affect the output
Increasing the probability of a high-return scenario raises expected return, while increasing the probability of a low-return scenario lowers it. Volatility may rise or fall depending on how far the reweighted scenario is from the new average. Moving an extreme outcome farther from the center usually increases variance even if its probability is modest.
Scenario analysis is most informative when probabilities are mutually exclusive and collectively exhaustive. Avoid overlapping cases, mixing time horizons, or combining nominal and real returns in the same distribution. Use the same measurement period for both investments. For example, compare annual returns with annual returns rather than annual returns for one stock and monthly returns for the other.
Changing many assumptions simultaneously can obscure the driver of the result. A disciplined approach is to change one probability or return at a time, observe the effect, then test a coherent alternate scenario set.
Benefits, limits, and common mistakes
The main benefit is transparency: every result can be traced to explicit outcomes and probabilities. The main limitation is model risk. Expected return depends entirely on the completeness and quality of those assumptions, and historical patterns may not repeat. Standard deviation also treats upside and downside dispersion symmetrically.
- Do not interpret expected return as a promised future return.
- Do not omit plausible adverse scenarios merely to improve the average.
- Do not compare distributions built for different time periods.
- Do not assume the higher-return stock is automatically preferable.
- Do not rely on range alone when probabilities differ materially.
Diversification can change portfolio-level risk because investments may not move together. The SEC’s overview of diversification explains why evaluating assets individually is only one part of portfolio analysis. This calculator is educational and does not provide personalized investment advice.