Expected Rate of Return Calculator
.err-calculator-container {
font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif;
max-width: 800px;
margin: 0 auto;
padding: 20px;
background: #ffffff;
border: 1px solid #e0e0e0;
border-radius: 8px;
box-shadow: 0 4px 6px rgba(0,0,0,0.05);
}
.err-header {
text-align: center;
margin-bottom: 30px;
border-bottom: 2px solid #f0f0f0;
padding-bottom: 15px;
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.err-header h2 {
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margin: 0;
font-size: 24px;
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.err-input-section {
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grid-template-columns: 1fr 1fr;
gap: 20px;
margin-bottom: 25px;
}
.err-scenario-group {
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padding: 15px;
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.err-scenario-title {
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font-size: 13px;
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margin-bottom: 4px;
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.form-group input {
width: 100%;
padding: 8px 10px;
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border-radius: 4px;
font-size: 14px;
box-sizing: border-box;
}
.form-group input:focus {
outline: none;
border-color: #4dabf7;
box-shadow: 0 0 0 2px rgba(77,171,247,0.2);
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.investment-section {
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border-radius: 6px;
cursor: pointer;
transition: background-color 0.2s;
width: 100%;
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.calculate-btn:hover {
background-color: #1c7ed6;
}
.results-section {
margin-top: 30px;
background: #f1f3f5;
padding: 20px;
border-radius: 8px;
display: none;
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display: flex;
justify-content: space-between;
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.result-row:last-child {
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.result-label {
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.result-value {
font-weight: 700;
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font-size: 18px;
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.prob-warning {
grid-column: 1 / -1;
color: #e03131;
font-size: 13px;
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padding-bottom: 8px;
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.article-content li {
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@media (max-width: 600px) {
.err-input-section {
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}
Expected Rate of Return (ERR):
0.00%
Projected Profit/Loss:
$0.00
Total Expected Portfolio Value:
$0.00
Understanding the Expected Rate of Return
The Expected Rate of Return (ERR) is a key financial metric used by investors to estimate the profit or loss of an investment over time. Unlike a guaranteed interest rate, the ERR is calculated by weighing multiple potential outcomes (scenarios) by their probability of occurring. This tool is essential for portfolio management, capital budgeting, and risk assessment.
The Formula
The calculation involves multiplying the projected return of each scenario by its probability, and then summing these weighted returns. The mathematical formula is:
E(R) = (P₁ × R₁) + (P₂ × R₂) + … + (Pₙ × Rₙ)
- E(R): Expected Rate of Return
- P: Probability of the scenario (expressed as a decimal, e.g., 20% = 0.20)
- R: Return in that specific scenario (percentage)
How to Use This Calculator
- Enter Initial Investment: Input the dollar amount you plan to invest. This helps calculate the absolute monetary expected value.
- Define Scenarios: Financial markets are unpredictable. Define 2 to 4 market conditions (e.g., Recession, Normal Growth, High Growth).
- Assign Probabilities: Estimate the likelihood of each scenario happening. Ensure the total equals 100% for a complete statistical model.
- Assign Returns: Enter the anticipated percentage gain or loss for each specific scenario.
Example Calculation
Imagine you are analyzing a stock with three potential outcomes:
- Scenario A (Recession): 20% probability of losing 10%.
- Scenario B (Normal): 50% probability of gaining 8%.
- Scenario C (Boom): 30% probability of gaining 20%.
Calculation:
(0.20 × -10) + (0.50 × 8) + (0.30 × 20)
= -2 + 4 + 6
= 8% Expected Return
While the "Expected Return" is 8%, realize that in reality, you will likely earn either -10%, 8%, or 20%. The "Expected" value is simply the long-term weighted average.
function calculateExpectedReturn() {
// 1. Retrieve Input Values
var investAmount = parseFloat(document.getElementById('initialInvestment').value);
// Scenario 1
var p1 = parseFloat(document.getElementById('prob1').value);
var r1 = parseFloat(document.getElementById('ret1').value);
// Scenario 2
var p2 = parseFloat(document.getElementById('prob2').value);
var r2 = parseFloat(document.getElementById('ret2').value);
// Scenario 3
var p3 = parseFloat(document.getElementById('prob3').value);
var r3 = parseFloat(document.getElementById('ret3').value);
// Scenario 4
var p4 = parseFloat(document.getElementById('prob4').value);
var r4 = parseFloat(document.getElementById('ret4').value);
// 2. Normalize inputs (Handle NaN / Empty fields as 0)
if (isNaN(investAmount)) investAmount = 0;
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;
// 3. Check Probability Sum
var totalProb = p1 + p2 + p3 + p4;
var warningBox = document.getElementById('probWarning');
var sumSpan = document.getElementById('probSumVal');
sumSpan.innerText = totalProb.toFixed(1);
if (Math.abs(totalProb – 100) > 0.1 && totalProb !== 0) {
warningBox.style.display = 'block';
} else {
warningBox.style.display = 'none';
}
// 4. Calculate Expected Rate of Return (ERR)
// Formula: Sum(Probability * Return)
// Since inputs are in whole percentages (e.g. 50 for 50%), we divide by 100 later or keep as %
var contribution1 = (p1 / 100) * r1;
var contribution2 = (p2 / 100) * r2;
var contribution3 = (p3 / 100) * r3;
var contribution4 = (p4 / 100) * r4;
var errPercent = contribution1 + contribution2 + contribution3 + contribution4;
// 5. Calculate Monetary Values
// Profit = Investment * (ERR / 100)
var expectedProfit = investAmount * (errPercent / 100);
var expectedTotalValue = investAmount + expectedProfit;
// 6. Update DOM Results
document.getElementById('displayErrPercent').innerText = errPercent.toFixed(2) + "%";
// Formatting currency
var formatter = new Intl.NumberFormat('en-US', {
style: 'currency',
currency: 'USD',
});
document.getElementById('displayProfit').innerText = formatter.format(expectedProfit);
document.getElementById('displayTotalValue').innerText = formatter.format(expectedTotalValue);
// Color coding result
var errElement = document.getElementById('displayErrPercent');
if(errPercent < 0) {
errElement.style.color = "#e03131";
} else {
errElement.style.color = "#099268";
}
// Show results section
document.getElementById('resultsSection').style.display = 'block';
}