Calculate the Weighted Duration of the Portfolio

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Portfolio Weighted Duration Calculator

Accurately measure your bond portfolio's sensitivity to interest rate changes.

Enter the Market Value and Duration for up to 5 individual assets to calculate the weighted duration of the portfolio.
Current value of holding
Please enter a positive value.
Effective or Macaulay duration
Must be positive.
Current value of holding
Please enter a positive value.
Effective or Macaulay duration
Must be positive.
Current value of holding
Please enter a positive value.
Effective or Macaulay duration
Must be positive.
Current value of holding
Please enter a positive value.
Effective or Macaulay duration
Must be positive.
Current value of holding
Please enter a positive value.
Effective or Macaulay duration
Must be positive.
Weighted Portfolio Duration
0.00 Years

This means for every 1% change in interest rates, the portfolio value is expected to change by approximately 0.00%.

Total Market Value
$0.00
Total Assets
0
Avg. Weighted Duration
0.00 Yrs
Asset Value ($) Weight (%) Duration (Yrs) Contrib. to Duration

Note: Contribution = Weight × Duration. The sum of contributions equals the Portfolio Duration.

Chart: Contribution of each asset to total portfolio duration (Years)

What is Calculate the Weighted Duration of the Portfolio?

When investors aim to calculate the weighted duration of the portfolio, they are essentially measuring the aggregated interest rate sensitivity of a collection of fixed-income assets. Unlike equity portfolios where beta measures risk, bond portfolios rely on duration to estimate how price will fluctuate in response to interest rate changes.

The weighted duration is not simply the average duration of the bonds. Instead, it weights each bond's duration by its proportion of the total portfolio value. This metric is critical for portfolio managers, risk analysts, and individual investors who need to match liabilities or manage interest rate risk exposure. If you fail to calculate the weighted duration of the portfolio accurately, you may expose your capital to unexpected volatility when central banks adjust rates.

Common misconceptions include assuming that a portfolio with half long-term bonds and half cash has the same duration as a medium-term bond portfolio. While mathematically the durations might average out, the specific weighted calculation is required to understand the precise price impact.

{primary_keyword} Formula and Mathematical Explanation

To calculate the weighted duration of the portfolio, we use a linear combination formula. The principle relies on the fact that the duration of a portfolio is equal to the weighted average of the durations of the individual components.

The Formula:

Durationportfolio = Σ ( wi × Di )

Where wi is the weight of asset i (Market Value of i / Total Portfolio Value) and Di is the duration of asset i.

Variable Meaning Unit Typical Range
Vtotal Total Market Value of Portfolio Currency ($) > 0
Vi Market Value of Individual Asset Currency ($) > 0
wi Weight of Asset (Vi / Vtotal) Decimal/Percent 0% to 100%
Di Duration of Individual Asset Years 0 to 30+ Years

Practical Examples (Real-World Use Cases)

Example 1: The Barbell Strategy

An investor holds a "barbell" portfolio to manage liquidity and yield. They have $100,000 in short-term bills (Duration = 0.5 years) and $100,000 in long-term treasury bonds (Duration = 15 years).

  • Total Value = $200,000
  • Weight of Bills = 50%, Weight of Bonds = 50%
  • Calculation: (0.50 × 0.5) + (0.50 × 15) = 0.25 + 7.5 = 7.75 Years

Even though half the portfolio is very safe, the weighted duration is high (7.75 years), meaning a 1% rise in rates could drop the portfolio value by roughly 7.75%.

Example 2: Diversified Corporate Bond Fund

A manager wants to calculate the weighted duration of the portfolio consisting of three bonds:
1. Bond A: $2M Value, 4.0 Duration
2. Bond B: $5M Value, 6.0 Duration
3. Bond C: $3M Value, 9.0 Duration

Total Value = $10M.
Weights: A (20%), B (50%), C (30%).
Calculation: (0.2 × 4.0) + (0.5 × 6.0) + (0.3 × 9.0) = 0.8 + 3.0 + 2.7 = 6.5 Years.

How to Use This {primary_keyword} Calculator

  1. Gather Data: Collect the current Market Value and the Duration (typically Modified or Effective Duration) for each holding in your portfolio.
  2. Input Assets: Enter the Name (optional), Market Value, and Duration into the rows provided. The calculator supports up to 5 distinct assets or asset classes.
  3. Review Weights: As you type, the tool will automatically calculate the weight of each asset relative to the total portfolio.
  4. Analyze Results: Look at the "Weighted Portfolio Duration". This single number summarizes your interest rate risk.
  5. Check Contribution: Use the chart and breakdown table to identify which specific assets are contributing the most to your risk. A high-value asset with low duration might contribute less risk than a low-value asset with extremely high duration.

Key Factors That Affect {primary_keyword} Results

Several factors influence the outcome when you calculate the weighted duration of the portfolio:

  • Coupon Rates: Bonds with higher coupon rates generally have lower durations because more cash flow is received earlier. This lowers the weighted duration of the portfolio.
  • Time to Maturity: Generally, longer maturity equals higher duration. A portfolio heavily weighted toward long-term debt will have a higher sensitivity score.
  • Yield to Maturity (YTM): There is an inverse relationship between yield and duration. As yields rise, duration tends to fall slightly, though this is a second-order effect (convexity).
  • Call Provisions: Callable bonds have lower durations because the issuer may repay the principal early if rates drop, limiting the price appreciation.
  • Asset Allocation Weights: Rebalancing a portfolio alters the weights ($w_i$). Selling long-term bonds to buy short-term notes is the most direct way to lower portfolio duration.
  • Floating Rate Notes: Assets with floating rates typically have durations near zero (or equal to the time until the next reset), significantly reducing the overall weighted average.

Frequently Asked Questions (FAQ)

What is the difference between Modified and Macaulay Duration?

Macaulay duration is the weighted average time to receive cash flows. Modified duration adjusts this figure for yield to estimate the percentage price change for a change in yield. For risk management, Modified Duration is the standard input.

Why should I calculate the weighted duration of the portfolio?

It acts as a proxy for risk. If you expect interest rates to rise, you should aim for a lower weighted duration to minimize capital losses. If rates are falling, a higher duration maximizes gains.

Can duration be negative?

Yes, certain derivatives like Interest Only (IO) strips or inverse floaters can exhibit negative duration, meaning their value rises when interest rates rise.

Does this calculator handle cash?

Yes. Enter cash as an asset with a Market Value and a Duration of 0. This will lower the overall weighted duration of the portfolio.

Is portfolio duration just the sum of individual durations?

No. It is the weighted average sum. Simply adding durations would result in a nonsensical number. You must weight them by market value.

How often should I recalculate?

You should recalculate whenever there is a significant change in market values (price drift) or after rebalancing trades, as the weights ($w_i$) change constantly.

What is "Immunization"?

Immunization is a strategy where you match the weighted duration of assets to the duration of liabilities to protect the portfolio's net worth from interest rate moves.

What if my portfolio has options?

For portfolios with embedded options (like mortgage-backed securities), "Effective Duration" is the most accurate input to use in this calculator.

Related Tools and Internal Resources

Expand your financial toolkit with these related calculators and articles:

© 2023 Financial Tools Inc. All rights reserved.
Disclaimer: This tool is for informational purposes only and does not constitute financial advice.

// Global chart variable var durationChartInstance = null; // Helper to format currency function formatCurrency(num) { return '$' + num.toFixed(2).replace(/\d(?=(\d{3})+\.)/g, '$&,'); } // Input Validation function validateInput(input) { var val = parseFloat(input.value); var errorDiv = input.parentElement.querySelector('.error-msg'); if (isNaN(val) || val < 0) { if (input.value !== "") { errorDiv.style.display = 'block'; input.style.borderColor = '#dc3545'; } } else { errorDiv.style.display = 'none'; input.style.borderColor = '#ced4da'; } } // Main Calculation Logic function calculateDuration() { var totalValue = 0; var totalWeightedDuration = 0; var activeAssetCount = 0; var breakdownData = []; // Loop through 5 fixed rows for (var i = 1; i <= 5; i++) { var nameInput = document.getElementById('name_' + i); var valInput = document.getElementById('val_' + i); var durInput = document.getElementById('dur_' + i); var name = nameInput.value || 'Asset ' + i; var val = parseFloat(valInput.value); var dur = parseFloat(durInput.value); // Handle empty or invalid inputs gracefully (treat as 0) if (isNaN(val) || val < 0) val = 0; if (isNaN(dur) || dur 0) { totalValue += val; activeAssetCount++; } breakdownData.push({ id: i, name: name, value: val, duration: dur }); } // Calculate Weights and Contributions var portfolioDuration = 0; var tableHTML = "; var chartLabels = []; var chartData = []; for (var j = 0; j 0) { weight = item.value / totalValue; contribution = weight * item.duration; } portfolioDuration += contribution; // Only add to table/chart if it has value if (item.value > 0) { tableHTML += ''; tableHTML += '' + item.name + ''; tableHTML += '' + formatCurrency(item.value) + ''; tableHTML += '' + (weight * 100).toFixed(2) + '%'; tableHTML += '' + item.duration.toFixed(2) + ''; tableHTML += '' + contribution.toFixed(4) + ' Yrs'; tableHTML += ''; chartLabels.push(item.name); chartData.push(contribution); } } if (totalValue === 0 && breakdownData.some(function(d){ return d.duration > 0; })) { // Edge case: Durations entered but no value document.getElementById('resultDuration').innerText = "0.00 Years"; } else { document.getElementById('resultDuration').innerText = portfolioDuration.toFixed(2) + " Years"; } document.getElementById('pctChangeDisplay').innerText = portfolioDuration.toFixed(2) + "%"; document.getElementById('totalValue').innerText = formatCurrency(totalValue); document.getElementById('totalAssets').innerText = activeAssetCount; document.getElementById('avgDuration').innerText = portfolioDuration.toFixed(2) + " Yrs"; var tbody = document.getElementById('breakdownBody'); if (tableHTML === ") { tbody.innerHTML = 'Enter asset values to see breakdown'; } else { tbody.innerHTML = tableHTML; } drawChart(chartLabels, chartData); } // Reset Function function resetCalculator() { // Restore defaults for first 3 rows, clear others document.getElementById('name_1').value = "Bond A"; document.getElementById('val_1').value = "100000"; document.getElementById('dur_1').value = "5.5"; document.getElementById('name_2').value = "Bond B"; document.getElementById('val_2').value = "50000"; document.getElementById('dur_2').value = "2.1"; document.getElementById('name_3').value = "Bond C"; document.getElementById('val_3').value = "75000"; document.getElementById('dur_3').value = "8.4"; for (var k = 4; k <= 5; k++) { document.getElementById('name_' + k).value = ""; document.getElementById('val_' + k).value = ""; document.getElementById('dur_' + k).value = ""; } // Clear errors var errors = document.querySelectorAll('.error-msg'); for (var i = 0; i < errors.length; i++) { errors[i].style.display = 'none'; } var inputs = document.querySelectorAll('input'); for (var j = 0; j < inputs.length; j++) { inputs[j].style.borderColor = '#ced4da'; } calculateDuration(); } // Copy Results Function function copyResults() { var resText = "Portfolio Duration Calculation Results:\n"; resText += "Weighted Portfolio Duration: " + document.getElementById('resultDuration').innerText + "\n"; resText += "Total Market Value: " + document.getElementById('totalValue').innerText + "\n"; resText += "Assets Analyzed: " + document.getElementById('totalAssets').innerText + "\n"; var tempTextArea = document.createElement("textarea"); tempTextArea.value = resText; document.body.appendChild(tempTextArea); tempTextArea.select(); document.execCommand("copy"); document.body.removeChild(tempTextArea); var btn = document.querySelector('.btn-success'); var originalText = btn.innerText; btn.innerText = "Copied!"; setTimeout(function() { btn.innerText = originalText; }, 2000); } // Chart Drawing Logic (Native Canvas, NO Libraries) function drawChart(labels, data) { var canvas = document.getElementById('durationChart'); var ctx = canvas.getContext('2d'); // Handle High DPI var dpr = window.devicePixelRatio || 1; var rect = canvas.getBoundingClientRect(); canvas.width = rect.width * dpr; canvas.height = rect.height * dpr; ctx.scale(dpr, dpr); var width = rect.width; var height = rect.height; var padding = 40; var chartHeight = height – padding * 2; var chartWidth = width – padding * 2; ctx.clearRect(0, 0, width, height); if (data.length === 0) { ctx.font = "14px Arial"; ctx.fillStyle = "#666"; ctx.textAlign = "center"; ctx.fillText("Enter data to view chart", width / 2, height / 2); return; } // Determine max value for scaling var maxVal = 0; for (var i = 0; i maxVal) maxVal = data[i]; } if (maxVal === 0) maxVal = 1; maxVal = maxVal * 1.1; // Add headroom // Draw Axes ctx.beginPath(); ctx.moveTo(padding, padding); ctx.lineTo(padding, height – padding); ctx.lineTo(width – padding, height – padding); ctx.strokeStyle = "#ccc"; ctx.stroke(); // Draw Bars var barCount = data.length; var barSpacing = 20; var totalBarSpace = chartWidth – (barSpacing * (barCount + 1)); var barWidth = totalBarSpace / barCount; // Cap bar width visually if (barWidth > 80) { barWidth = 80; // Center chart if few bars var totalUsedWidth = (barWidth * barCount) + (barSpacing * (barCount + 1)); var offset = (chartWidth – totalUsedWidth) / 2; padding += offset; } for (var j = 0; j 8) label = label.substring(0, 8) + '…'; ctx.fillText(label, x + barWidth/2, height – padding + 15); // Value Label (on top of bar) ctx.fillStyle = "#000"; ctx.fillText(val.toFixed(2), x + barWidth/2, y – 5); } // Y-Axis Labels ctx.textAlign = "right"; ctx.fillStyle = "#666"; ctx.font = "10px Arial"; ctx.fillText(maxVal.toFixed(1), padding – 5, padding); ctx.fillText("0", padding – 5, height – padding); // Y-Axis Title ctx.save(); ctx.translate(15, height/2); ctx.rotate(-Math.PI/2); ctx.textAlign = "center"; ctx.fillText("Duration Contribution (Yrs)", 0, 0); ctx.restore(); } // Initialize on load window.onload = function() { calculateDuration(); // Add resize listener for chart window.addEventListener('resize', function() { calculateDuration(); }); };

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