# Expected Return Calculator

URL: https://speedycalculator.com/calculators/finance/expected-return/
Last updated: 2026-10-25

> The expected return calculator works out the probability-weighted expected return of up to two stocks across up to four economic scenarios, with each stock's variance and standard deviation (risk).

## Inputs

- Scenario 1 (boom) – probability (%)
- Stock A return in scenario 1 (%)
- Stock B return in scenario 1 (%)
- Scenario 2 (normal) – probability (%)
- Stock A return in scenario 2 (%)
- Stock B return in scenario 2 (%)
- Scenario 3 (recession) – probability (%)
- Stock A return in scenario 3 (%)
- Stock B return in scenario 3 (%)
- Scenario 4 – probability (%)
- Stock A return in scenario 4 (%)
- Stock B return in scenario 4 (%)

## Results

- Total probability
- Stock A – expected return
- Stock A – standard deviation
- Stock B – expected return
- Stock B – standard deviation
- Stock A – variance

## Formula

```
E(R) = Σ pᵢ × Rᵢ
Variance = Σ pᵢ × (Rᵢ − E(R))²; standard deviation = √variance
```

## Explanation

Expected return summarises what you can expect on average, and the standard deviation measures how far actual returns may stray from it. Comparing both helps judge whether a riskier stock offers enough extra return.

### How to use the Expected Return Calculator

- **Scenario 1 (boom) – probability**
- **Stock A return in scenario 1**
- **Stock B return in scenario 1**
- **Scenario 2 (normal) – probability**
- **Stock A return in scenario 2**
- **Stock B return in scenario 2**
- **Scenario 3 (recession) – probability**
- **Stock A return in scenario 3**
- **Stock B return in scenario 3**
- **Scenario 4 – probability**
- **Stock A return in scenario 4**
- **Stock B return in scenario 4**

Results update as you type, and every field accepts the units shown in its menu.

### How it works

Enter the probability of each scenario (they should add up to 100%) and each stock's return in that scenario.

### Tips

- Use the nominal annual rate and pick the compounding frequency your bank or broker states.
- Small differences in return or fees compound into large differences over decades.
- Run the calculation with a cautious, a central and an optimistic return to see the range of outcomes.
- Past returns do not guarantee future returns – nothing here is investment advice.

### Common mistakes to avoid

- Comparing an APR with an APY or effective rate.
- Ignoring inflation, taxes and fees when judging a real return.
- Entering a percentage as a decimal (5 instead of 0.05 is correct here).

### Inputs explained

FieldWhat to enterScenario 1 (boom) – probabilityIn %Stock A return in scenario 1In %Stock B return in scenario 1In %Scenario 2 (normal) – probabilityIn %Stock A return in scenario 2In %Stock B return in scenario 2In %Scenario 3 (recession) – probabilityIn %Stock A return in scenario 3In %Stock B return in scenario 3In %Scenario 4 – probabilityIn %Stock A return in scenario 4In %Stock B return in scenario 4In %

### What each result means

- **Total probability** = [Scenario 1 (boom) – probability] + [Scenario 2 (normal) – probability] + [Scenario 3 (recession) – probability] + [Scenario 4 – probability]
- **Stock A – expected return** = ([Scenario 1 (boom) – probability]×[Stock A return in scenario 1] + [Scenario 2 (normal) – probability]×[Stock A return in scenario 2] + [Scenario 3 (recession) – probability]×[Stock A return in scenario 3] + [Scenario 4 – probability]×[Stock A return in scenario 4])÷100
- **Stock A – standard deviation** = sqrt(([Scenario 1 (boom) – probability]×([Stock A return in scenario 1] - [Stock A – expected return])^2 + [Scenario 2 (normal) – probability]×([Stock A return in scenario 2] - [Stock A – expected return])^2 + [Scenario 3 (recession) – probability]×([Stock A return in scenario 3] - [Stock A – expected return])^2 + [Scenario 4 – probability]×([Stock A return in scenario 4] - [Stock A – expected return])^2)÷100)
- **Stock B – expected return** = ([Scenario 1 (boom) – probability]×[Stock B return in scenario 1] + [Scenario 2 (normal) – probability]×[Stock B return in scenario 2] + [Scenario 3 (recession) – probability]×[Stock B return in scenario 3] + [Scenario 4 – probability]×[Stock B return in scenario 4])÷100
- **Stock B – standard deviation** = sqrt(([Scenario 1 (boom) – probability]×([Stock B return in scenario 1] - [Stock B – expected return])^2 + [Scenario 2 (normal) – probability]×([Stock B return in scenario 2] - [Stock B – expected return])^2 + [Scenario 3 (recession) – probability]×([Stock B return in scenario 3] - [Stock B – expected return])^2 + [Scenario 4 – probability]×([Stock B return in scenario 4] - [Stock B – expected return])^2)÷100)
- **Stock A – variance** = [Stock A – standard deviation]^2

### Example values

How the main result changes when **Scenario 1** changes and everything else stays at the example values above:

Scenario 1 (boom) – probability (%)Stock A – expected return (%)12.56.2518.757.5258.7531.251037.511.255013.75

## Worked example

Inputs — Scenario 1 (boom) – probability: 25 %; Stock A return in scenario 1: 20 %; Stock B return in scenario 1: 30 %; Scenario 2 (normal) – probability: 50 %; Stock A return in scenario 2: 10 %; Stock B return in scenario 2: 12 %; Scenario 3 (recession) – probability: 25 %; Stock A return in scenario 3: -5 %; Stock B return in scenario 3: -15 %; Scenario 4 – probability: 0 %; Stock A return in scenario 4: 0 %; Stock B return in scenario 4: 0 %.

Results — Total probability = 100 %; **Stock A – expected return = 8.75 %**; Stock A – standard deviation = 8.93 %; Stock B – expected return = 9.75 %; Stock B – standard deviation = 16.07 %; Stock A – variance = 79.69.

## FAQ

**What is expected return?**
The average return weighted by the probability of each outcome.

**What does standard deviation tell me?**
How spread out the possible returns are – a measure of risk.

**Must probabilities add up to 100%?**
Yes, the scenarios should cover all outcomes.

**What formula does the Expected Return Calculator use?**
E(R) = Σ pᵢ × Rᵢ.