Time Weighted Return Calculation Formula Calculator | Professional Finance Tools
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Cumulative Time-Weighted Return (TWR)
0.00%
This percentage represents the compound growth rate of $1 invested at the start, independent of your cash deposits or withdrawals.
Figure 1: Comparison of Portfolio Value (Absolute $) vs. TWR Growth Index (Start=100)
Calculation Breakdown by Sub-Period
| Period |
Start Value |
End (Pre-CF) |
Cash Flow |
Sub-Period Return |
What is Time Weighted Return Calculation Formula?
The time weighted return calculation formula (TWR) is the gold standard method used by investment professionals to measure the performance of a portfolio over a specific period. Unlike simple returns or money-weighted returns, the TWR eliminates the distorting effects of cash inflows (deposits) and outflows (withdrawals).
If you deposit a large sum of money into your account and the market subsequently rises, a simple return calculation might artificially inflate your performance metrics simply because you had more capital exposed to the gain. The time weighted return calculation formula neutralizes this by breaking the overall timeframe into distinct sub-periods based on when cash flows occur.
This metric is essential for fund managers, financial advisors, and individual investors who want to evaluate the quality of their investment decisions separate from their savings or spending behavior. It answers the critical question: "How well did the underlying assets perform?"
Practical Examples (Real-World Use Cases)
Example 1: The Lucky Deposit
Investor Alice starts with $10,000. In Period 1, her portfolio drops to $9,000. She then deposits $11,000 (total value $20,000). In Period 2, the portfolio grows to $22,000.
- Sub-period 1: ($9,000 – $10,000) / $10,000 = -10%
- New Basis: $9,000 + $11,000 = $20,000
- Sub-period 2: ($22,000 – $20,000) / $20,000 = +10%
- TWR Calculation: (0.90 × 1.10) – 1 = 0.99 – 1 = -1.0%
Even though she ended with $22,000 (more than her total contributions of $21,000), the TWR correctly shows a loss of 1% because the underlying assets lost value initially and only recovered partially.
Example 2: The Withdrawal Drag
Bob starts with $50,000. It grows to $60,000 (20% gain). He withdraws $30,000. The remaining $30,000 drops to $27,000 (10% loss).
- Sub-period 1: +20% (1.20 factor)
- Sub-period 2: -10% (0.90 factor)
- TWR Calculation: (1.20 × 0.90) – 1 = 1.08 – 1 = +8.0%
The time weighted return calculation formula highlights that the investment decisions generated an 8% positive return, regardless of Bob's withdrawal timing.
How to Use This Calculator
- Enter Initial Value: Input the starting balance of your portfolio at the beginning of the analysis timeframe.
- Define Sub-Periods: For each period where a significant cash flow occurred:
- Enter the Ending Value just before the cash flow happened.
- Enter the Cash Flow Amount (positive for money added, negative for money removed).
- Enter Final Value: Input the portfolio balance at the very end of the period.
- Review Results: The calculator will automatically display the cumulative TWR percentage and breakdown periodic returns.
- Analyze the Chart: Use the chart to compare absolute portfolio growth against the theoretical TWR index.
Key Factors That Affect TWR Results
Understanding the variables in the time weighted return calculation formula helps in better financial decision-making.
- Market Volatility: High volatility in sub-periods can compound significantly. A 50% loss requires a 100% gain just to break even, heavily impacting the final TWR.
- Timing of Valuation: TWR requires accurate valuations exactly when cash flows occur. If valuations are delayed, the return attribution between periods may be skewed.
- Fees and Expenses: If fees are deducted from the portfolio (cash outflow), they should be treated carefully. Usually, management fees are not treated as external withdrawals for net-of-fee TWR calculations.
- Dividend Reinvestment: Dividends are internal cash flows. If they are reinvested, they do not affect the TWR calculation logic as external flows do, but they contribute to the ending value of the sub-period.
- Inflation: TWR is typically a nominal figure. To understand real purchasing power, you must adjust the final TWR result by the inflation rate over the same period.
- Currency Fluctuations: For international portfolios, changes in exchange rates between the reporting currency and asset currency will directly impact the Beginning and Ending Values of each sub-period.
Frequently Asked Questions (FAQ)
What is the difference between TWR and IRR?
TWR (Time-Weighted Return) eliminates the effect of cash flows to measure manager performance. IRR (Internal Rate of Return) or Money-Weighted Return includes the timing and size of cash flows, measuring the actual wealth generation for the investor.
Why is my TWR negative when I made money?
This happens if you had a small balance during a period of high losses, and a large balance during a period of small gains. The formula weighs time periods equally, not dollars.
Does the time weighted return calculation formula include deposits?
No, it specifically excludes the impact of deposits on the performance percentage. It treats a deposit as a non-event for performance measurement purposes.
How often should I calculate TWR?
Ideally, TWR is calculated daily. However, for most individual investors, calculating it monthly or whenever a significant cash flow occurs is sufficient.
Is TWR better for personal finance?
Usually, no. TWR is better for judging a fund manager. For personal goals, Money-Weighted Return (MWR) often reflects your personal reality better because you control the cash flows.
Can TWR be annualized?
Yes. The result from our calculator is a cumulative total return. To annualize it: (1 + Total TWR)^(1/Years) – 1.
Does this formula account for taxes?
Generally, no. TWR is a pre-tax measure unless the Ending Values entered are specifically net-of-tax valuations.
What if there are no cash flows?
If there are no external deposits or withdrawals, the time weighted return calculation formula yields the exact same result as a simple percentage growth calculation.
// GLOBAL VARS ONLY
var ctx = document.getElementById('twrChart').getContext('2d');
var chartInstance = null;
// INITIALIZATION
window.onload = function() {
calculateTWR();
};
function getVal(id) {
var el = document.getElementById(id);
var val = parseFloat(el.value);
return isNaN(val) ? 0 : val;
}
function formatCurrency(num) {
return "$" + num.toFixed(2).replace(/\d(?=(\d{3})+\.)/g, '$&,');
}
function formatPercent(num) {
return (num * 100).toFixed(2) + "%";
}
function resetCalculator() {
document.getElementById('initialValue').value = "100000";
document.getElementById('endVal1').value = "105000";
document.getElementById('cashFlow1').value = "10000";
document.getElementById('endVal2').value = "118000";
document.getElementById('cashFlow2').value = "-5000";
document.getElementById('finalValue').value = "120000";
calculateTWR();
}
function calculateTWR() {
// Inputs
var startVal = getVal('initialValue');
var ev1 = getVal('endVal1');
var cf1 = getVal('cashFlow1');
var ev2 = getVal('endVal2');
var cf2 = getVal('cashFlow2');
var finalVal = getVal('finalValue');
// Validation: Prevent divide by zero or negative base
if (startVal 0) {
r2 = (ev2 – basis2) / basis2;
}
// New Basis for Period 3 (Final) = EV2 + CF2
var basis3 = ev2 + cf2;
// Period 3 (Final Stretch)
// r3 = (Final – Basis3) / Basis3
var r3 = 0;
if (basis3 > 0) {
r3 = (finalVal – basis3) / basis3;
}
// Total TWR
// (1+r1)*(1+r2)*(1+r3) – 1
var totalTWR = ((1 + r1) * (1 + r2) * (1 + r3)) – 1;
// — UPDATE UI —
document.getElementById('resultTWR').innerText = formatPercent(totalTWR);
// Intermediate cards
document.getElementById('resultR1').innerText = formatPercent(r1);
document.getElementById('resultR2').innerText = formatPercent(r2);
document.getElementById('resultR3').innerText = formatPercent(r3);
// Update Table
var tableHTML = "";
// Row 1
tableHTML += "
";
tableHTML += "| 1 | ";
tableHTML += "" + formatCurrency(startVal) + " | ";
tableHTML += "" + formatCurrency(ev1) + " | ";
tableHTML += "" + formatCurrency(cf1) + " | ";
tableHTML += "" + formatPercent(r1) + " | ";
tableHTML += "
";
// Row 2
tableHTML += "
";
tableHTML += "| 2 | ";
tableHTML += "" + formatCurrency(basis2) + " | ";
tableHTML += "" + formatCurrency(ev2) + " | ";
tableHTML += "" + formatCurrency(cf2) + " | ";
tableHTML += "" + formatPercent(r2) + " | ";
tableHTML += "
";
// Row 3
tableHTML += "
";
tableHTML += "| 3 (Final) | ";
tableHTML += "" + formatCurrency(basis3) + " | ";
tableHTML += "" + formatCurrency(finalVal) + " | ";
tableHTML += "$0.00 | ";
tableHTML += "" + formatPercent(r3) + " | ";
tableHTML += "
";
document.getElementById('breakdownTableBody').innerHTML = tableHTML;
// Draw Chart
drawChart([startVal, ev1, ev2, finalVal], [100, 100*(1+r1), 100*(1+r1)*(1+r2), 100*(1+totalTWR)]);
}
function drawChart(portfolioValues, indexValues) {
// Native Canvas Chart (No libraries)
var canvas = document.getElementById('twrChart');
var ctx = canvas.getContext('2d');
// Clear canvas
ctx.clearRect(0, 0, canvas.width, canvas.height);
// Setup Dimensions (Hardcoded for simplicity in single file, normally dynamic)
// Canvas coordinate system logic
var padding = 40;
var width = canvas.width;
var height = canvas.height;
var drawWidth = width – (padding * 2);
var drawHeight = height – (padding * 2);
// Find min/max for scaling
var allValues = portfolioValues.concat(indexValues);
// Normalized scaling is tricky because Portfolio is $100k+ and Index is ~100.
// We need Dual Axis logic or simple normalization.
// Let's normalize both to % change from start for visualization purposes.
var pStart = portfolioValues[0];
var iStart = indexValues[0];
var pNorm = [];
var iNorm = [];
var minVal = 0;
var maxVal = 0;
for(var i=0; i maxVal) maxVal = p;
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}
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var range = maxVal – minVal;
if(range === 0) range = 10;
maxVal += range * 0.1;
minVal -= range * 0.1;
// Draw Axes
ctx.beginPath();
ctx.strokeStyle = '#ccc';
ctx.lineWidth = 1;
// Y Axis
ctx.moveTo(padding, padding);
ctx.lineTo(padding, height – padding);
// X Axis
ctx.lineTo(width – padding, height – padding);
ctx.stroke();
// Draw Zero Line if visible
var zeroY = height – padding – ((0 – minVal) / (maxVal – minVal)) * drawHeight;
if (zeroY > padding && zeroY < height – padding) {
ctx.beginPath();
ctx.strokeStyle = '#999';
ctx.setLineDash([5, 5]);
ctx.moveTo(padding, zeroY);
ctx.lineTo(width – padding, zeroY);
ctx.stroke();
ctx.setLineDash([]);
}
// Function to map X, Y
function getX(index) {
return padding + (index * (drawWidth / 3)); // 3 segments for 4 points
}
function getY(val) {
var rel = (val – minVal) / (maxVal – minVal);
return (height – padding) – (rel * drawHeight);
}
// Draw Portfolio Line (Blue)
ctx.beginPath();
ctx.strokeStyle = '#004a99';
ctx.lineWidth = 3;
for(var i=0; i<pNorm.length; i++) {
var x = getX(i);
var y = getY(pNorm[i]);
if(i===0) ctx.moveTo(x, y);
else ctx.lineTo(x, y);
}
ctx.stroke();
// Draw TWR Line (Green)
ctx.beginPath();
ctx.strokeStyle = '#28a745';
ctx.lineWidth = 3;
for(var i=0; i<iNorm.length; i++) {
var x = getX(i);
var y = getY(iNorm[i]);
if(i===0) ctx.moveTo(x, y);
else ctx.lineTo(x, y);
}
ctx.stroke();
// Draw Points & Labels
ctx.fillStyle = '#333';
ctx.font = '12px Arial';
ctx.textAlign = 'center';
var labels = ["Start", "Period 1", "Period 2", "Final"];
for(var i=0; i<4; i++) {
var x = getX(i);
ctx.fillText(labels[i], x, height – 10);
// Dots
ctx.fillStyle = '#004a99';
ctx.beginPath();
ctx.arc(x, getY(pNorm[i]), 5, 0, Math.PI*2);
ctx.fill();
ctx.fillStyle = '#28a745';
ctx.beginPath();
ctx.arc(x, getY(iNorm[i]), 5, 0, Math.PI*2);
ctx.fill();
}
// Legend
ctx.textAlign = 'left';
ctx.fillStyle = '#004a99';
ctx.fillText("● Portfolio Value Growth %", padding + 10, padding + 10);
ctx.fillStyle = '#28a745';
ctx.fillText("● TWR Index Growth %", padding + 10, padding + 30);
}
function copyResults() {
var txt = "Time Weighted Return Calculation Results:\n";
txt += "Total TWR: " + document.getElementById('resultTWR').innerText + "\n";
txt += "Period 1: " + document.getElementById('resultR1').innerText + "\n";
txt += "Period 2: " + document.getElementById('resultR2').innerText + "\n";
txt += "Period 3: " + document.getElementById('resultR3').innerText + "\n";
var dummy = document.createElement("textarea");
document.body.appendChild(dummy);
dummy.value = txt;
dummy.select();
document.execCommand("copy");
document.body.removeChild(dummy);
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var originalText = btn.innerText;
btn.innerText = "Copied!";
setTimeout(function() { btn.innerText = originalText; }, 2000);
}