Expected Rate of Return Calculator
Enter the probability of different market scenarios and the anticipated return for each. Ensure Total Probability equals 100%.
Based on the probability-weighted sum of all scenarios.
What is Expected Rate of Return?
The Expected Rate of Return (ERR) is a key financial metric used to evaluate the potential profit or loss of an investment. Unlike a simple average, the ERR calculates a weighted average based on the probability of various outcomes occurring. This makes it an essential tool for risk assessment and portfolio management.
Investors use this calculation to decide whether an asset's potential rewards justify its risks. By assigning probabilities to different economic states (such as a recession, normal growth, or an economic boom), an investor can estimate what the investment will yield over the long term.
How to Calculate Expected Rate of Return
The formula for Expected Rate of Return involves multiplying the potential return of each scenario by the probability of that scenario happening, and then summing the results.
Where:
- E(R) = Expected Rate of Return
- P = Probability of the scenario (expressed as a decimal)
- R = Rate of return in that scenario
Real-World Example
Imagine you are analyzing a stock with three potential outcomes for the coming year:
- Bull Market (Optimistic): 30% chance of occurring, with a 20% return.
- Base Case (Neutral): 50% chance of occurring, with a 10% return.
- Bear Market (Pessimistic): 20% chance of occurring, with a -5% loss.
The calculation would look like this:
(0.30 × 20) + (0.50 × 10) + (0.20 × -5) = 6 + 5 – 1 = 10%
In this example, the Expected Rate of Return is 10%. Even though there is a risk of losing money, the probability-weighted average suggests a positive outcome.
Why Probabilities Must Sum to 100%
For the ERR calculation to be mathematically valid, the sum of all probabilities must equal 100% (or 1.0). If the probabilities do not cover all possible outcomes, the model is incomplete. This calculator checks your inputs to ensure they sum correctly, providing a reliable estimate for your financial planning.
Limitations of this Metric
While ERR is a powerful tool, it is based on estimates, not guarantees. Historical data and economic forecasts are used to determine probabilities, but actual market conditions can be unpredictable. Therefore, Expected Rate of Return should be used alongside other metrics like Standard Deviation (volatility) and Sharpe Ratio to get a full picture of an investment's risk profile.