How to Calculate Expected Rate of Return with Probability

Expected Rate of Return Calculator

Enter the probability and the estimated return for each potential market scenario. Ensure the total probability equals 100%.

Scenario Name

Probability (%)

Return Rate (%)

Total Probability Sum: %

Expected Rate of Return: %

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The expected rate of return is a fundamental concept in finance used to estimate the average outcome of an investment based on various possible scenarios. Unlike a fixed interest rate, the expected return accounts for uncertainty and risk by weighting each potential return by its likelihood of occurring.

The Mathematical Formula

To find the expected rate of return with probability, we use the weighted average formula:

            E(R) = (P₁ × R₁) + (P₂ × R₂) + … + (Pₙ × Rₙ)
        

Where:

E(R): Expected Rate of Return.
Pₙ: The probability of scenario n occurring (expressed as a decimal).
Rₙ: The return associated with scenario n.

Step-by-Step Calculation Example

Imagine you are evaluating a stock with three potential outcomes over the next year:

Bull Market (30% Chance): You expect a 20% return.
Normal Market (50% Chance): You expect an 8% return.
Bear Market (20% Chance): You expect a -10% return.

Applying the formula:

Bull Case: 0.30 × 20% = 6.0%
Normal Case: 0.50 × 8% = 4.0%
Bear Case: 0.20 × -10% = -2.0%
Total Expected Return: 6.0% + 4.0% – 2.0% = 8.0%

Why Use Probability-Weighted Returns?

Relying on a single "best guess" for an investment can be dangerous. By assigning probabilities to different economic environments, investors can:

Model Risk: Understand how a crash (even if unlikely) impacts the overall portfolio.
Compare Assets: Evaluate two different investments that might have the same average return but very different volatility profiles.
Make Data-Driven Decisions: Move away from emotional guessing toward statistical analysis.

Important Considerations

When using this calculator, remember that the sum of all probabilities must equal exactly 100%. If your scenarios do not account for all possibilities, your expected return calculation will be skewed and provide an inaccurate picture of your investment's potential performance.

Expected Rate of Return Calculator