function calculateReverseReturn() {
var lossInput = document.getElementById('drawdownPercentage').value;
var loss = parseFloat(lossInput);
var resultBox = document.getElementById('rr-result-box');
var output = document.getElementById('rr-output-value');
var explanation = document.getElementById('rr-explanation');
if (isNaN(loss) || loss = 100) {
output.innerText = "Infinity";
explanation.innerText = "A 100% loss means your capital is gone. No amount of gain can recover from zero.";
resultBox.style.display = "block";
resultBox.style.backgroundColor = "#fef2f2";
resultBox.style.borderColor = "#fecaca";
output.style.color = "#991b1b";
return;
}
// Reverse Rate Formula: (1 / (1 – Loss)) – 1
var lossDecimal = loss / 100;
var gainRequired = (1 / (1 – lossDecimal)) – 1;
var gainPercentage = (gainRequired * 100).toFixed(2);
output.innerText = gainPercentage + "%";
explanation.innerText = "To recover a " + loss + "% loss, you must achieve a " + gainPercentage + "% return on your remaining capital to break even.";
// Reset styles if previously changed by error
resultBox.style.display = "block";
resultBox.style.backgroundColor = "#f0fdf4";
resultBox.style.borderColor = "#bbf7d0";
output.style.color = "#15803d";
}
Understanding the Reverse Rate of Return
The Reverse Rate of Return (also known as the Break-Even Return) is a fundamental concept in mathematics and finance that illustrates the asymmetrical nature of investment losses and gains. Simply put, it calculates the percentage gain you need to recover a specific percentage loss.
Why Losses Hurt More Than Gains Help
Mathematical drawdown is not linear. When you lose a percentage of your capital, you have a smaller base of money left to work with. To get back to your original starting point, your remaining money must work harder than it did when it was lost.
Example: If you have $100 and lose 50%, you are left with $50. To return to $100, you need to gain $50. However, $50 is 100% of your current balance. Therefore, a 50% loss requires a 100% gain to break even.
Common Drawdown Recovery Table
| Loss Percentage |
Gain Required to Break Even |
| 10% |
11.1% |
| 20% |
25% |
| 30% |
42.9% |
| 50% |
100% |
| 75% |
300% |
| 90% |
900% |
The Math Behind the Calculation
The formula to calculate the reverse rate of return is:
Required Gain % = [ 1 / (1 – Loss %) ] – 1
Where "Loss %" is expressed as a decimal (e.g., 20% = 0.20). This formula helps investors understand the importance of risk management and capital preservation. As the loss increases, the gain required to recover grows exponentially, making large drawdowns extremely difficult to overcome.