Expected Rate of Return Calculator
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Expected Rate of Return Calculator
Calculate the probability-weighted expected return of an investment portfolio or asset based on multiple economic scenarios.
Calculation Results
Total Probability:
0%
Expected Rate of Return:
0.00%
function checkTotalProb() {
var p1 = parseFloat(document.getElementById('prob1').value) || 0;
var p2 = parseFloat(document.getElementById('prob2').value) || 0;
var p3 = parseFloat(document.getElementById('prob3').value) || 0;
var p4 = parseFloat(document.getElementById('prob4').value) || 0;
var total = p1 + p2 + p3 + p4;
var warningDiv = document.getElementById('probWarning');
document.getElementById('currentTotal').innerText = total.toFixed(1);
// Allow a small margin of error for floating point math
if (Math.abs(total – 100) > 0.1 && total > 0) {
warningDiv.style.display = 'block';
} else {
warningDiv.style.display = 'none';
}
}
function calculateExpectedRate() {
// Get Inputs
var p1 = parseFloat(document.getElementById('prob1').value);
var r1 = parseFloat(document.getElementById('rate1').value);
var p2 = parseFloat(document.getElementById('prob2').value);
var r2 = parseFloat(document.getElementById('rate2').value);
var p3 = parseFloat(document.getElementById('prob3').value);
var r3 = parseFloat(document.getElementById('rate3').value);
var p4 = parseFloat(document.getElementById('prob4').value);
var r4 = parseFloat(document.getElementById('rate4').value);
// Handle empty inputs by treating them as 0 for calculation
if (isNaN(p1)) p1 = 0; if (isNaN(r1)) r1 = 0;
if (isNaN(p2)) p2 = 0; if (isNaN(r2)) r2 = 0;
if (isNaN(p3)) p3 = 0; if (isNaN(r3)) r3 = 0;
if (isNaN(p4)) p4 = 0; if (isNaN(r4)) r4 = 0;
// Validation: At least one scenario must be valid
if (p1 === 0 && p2 === 0 && p3 === 0 && p4 === 0) {
alert("Please enter at least one probability value greater than 0.");
return;
}
// Calculate Weighted Returns
// Formula: (Prob1 * Rate1) + (Prob2 * Rate2)…
// Note: Inputs are in percentages (e.g. 50 for 50%), so we divide by 100 at the end or per item
var weighted1 = (p1 / 100) * r1;
var weighted2 = (p2 / 100) * r2;
var weighted3 = (p3 / 100) * r3;
var weighted4 = (p4 / 100) * r4;
var expectedRate = weighted1 + weighted2 + weighted3 + weighted4;
var totalProb = p1 + p2 + p3 + p4;
// Display Results
var resultDiv = document.getElementById('results');
resultDiv.style.display = 'block';
document.getElementById('resTotalProb').innerText = totalProb.toFixed(2) + "%";
document.getElementById('resExpectedRate').innerText = expectedRate.toFixed(2) + "%";
// Visual feedback for probability warning
checkTotalProb();
// Scroll to results
resultDiv.scrollIntoView({behavior: "smooth"});
}
Understanding Expected Rate of Return
The Expected Rate of Return is a key financial metric used by investors to anticipate the profit or loss of an investment based on the probability of various outcomes. Unlike a guaranteed interest rate on a savings account, investment returns fluctuate based on market conditions. This calculator helps you quantify that uncertainty by using a probability-weighted average.
How to Use This Calculator
This tool uses scenario analysis. You will need to estimate different potential future states (Scenarios) for your investment.
- Probability of Occurrence (%): The likelihood of a specific scenario happening. For example, you might estimate a 20% chance of a market boom.
- Anticipated Return (%): The percentage return the asset would generate in that specific scenario.
Ensure that the sum of your probabilities equals 100% for the most accurate mathematical result.
The Formula
The mathematical formula for calculating the Expected Rate of Return, denoted as E(R), is the sum of the products of potential returns and their probabilities:
E(R) = (P₁ × R₁) + (P₂ × R₂) + … + (Pₙ × Rₙ)
Where:
- P: The probability of a specific scenario (expressed as a decimal, e.g., 0.50 for 50%).
- R: The return rate in that scenario.
Example Calculation
Imagine you are analyzing a stock with three potential outcomes for the coming year:
- Bull Market: 30% chance (0.30) of gaining 20% return.
- Flat Market: 50% chance (0.50) of gaining 5% return.
- Bear Market: 20% chance (0.20) of losing 10% return (-10%).
The calculation would look like this:
(0.30 × 20) + (0.50 × 5) + (0.20 × -10) = 6 + 2.5 – 2 = 6.5%
In this example, the Expected Rate of Return is 6.5%.
Limitations
It is important to remember that the "Expected Rate" is a long-term statistical average, not a guarantee of what will happen in a single year. The actual return will likely match one of the specific scenarios (e.g., +20% or -10%) rather than the weighted average of 6.5%. This metric is best used for comparing different investment options or building diversified portfolios.