Formula: Σ (Time × Principal Repaid) / Total Principal
Principal Paydown Projection
Chart displays the remaining principal balance over time, accounting for scheduled amortization and prepayments (CPR).
Annual Amortization & WAL Schedule
Year
Principal Repaid
Interest Paid
Ending Balance
WAL Contribution
Table showing yearly summary of cash flows used for calculating weighted average life.
What is Calculating Weighted Average Life?
Calculating weighted average life (WAL) is a critical financial process used to determine the expected time that a dollar of principal remains outstanding in a loan, bond, or mortgage-backed security (MBS). Unlike the simple maturity date, which tells you when the final payment is due, calculating weighted average life provides a more realistic measure of how long funds are tied up, especially when principal is repaid over time through amortization or prepayments.
Investors, portfolio managers, and lenders rely on calculating weighted average life to assess interest rate risk and liquidity. A shorter WAL implies that principal is returned faster, reducing exposure to long-term rate fluctuations, while a longer WAL indicates extended capital commitment. This metric is the standard convention for pricing amortizing securities.
Calculating Weighted Average Life Formula and Mathematical Explanation
The mathematical foundation for calculating weighted average life involves weighting each principal repayment by the time at which it is received. The sum of these time-weighted payments is then divided by the total original principal.
The formula is expressed as:
WAL = [ Σ ( P_t × t ) ] / Total Principal
Where P_t is the principal repaid at time t (typically expressed in years), and the summation runs from the first payment to the final maturity.
Variable
Meaning
Unit
Typical Range
P_t
Principal Repayment Amount at time t
Currency ($)
0 to Loan Amount
t
Time elapsed since origination
Years
0 to 30+ Years
Total Principal
Original Face Value or Loan Balance
Currency ($)
Any
WAL
Weighted Average Life
Years
Less than Maturity
Practical Examples of Calculating Weighted Average Life
Example 1: A Bullet Bond
Consider a $100,000 corporate bond that pays interest only for 5 years and repays the full principal at the end (a "bullet" structure).
Principal Repaid Years 1-4: $0
Principal Repaid Year 5: $100,000
Calculation: ($100,000 × 5) / $100,000 = 5 Years
In this simple case, calculating weighted average life yields the same result as the maturity.
Example 2: Amortizing Mortgage with Prepayments
Consider a $100,000 mortgage at 5% interest for 30 years. Without prepayments, the principal is paid back slowly at first, then accelerates.
Scheduled WAL: Approximately 19-20 years for a 30-year loan due to the amortization curve.
With 6% CPR (Prepayment): The borrower pays extra principal or refinances. This shifts principal repayment to earlier periods.
Result: Calculating weighted average life with 6% CPR might reduce the WAL to approximately 10-12 years. This drastic reduction is why understanding WAL is vital for MBS investors.
How to Use This Calculator for Calculating Weighted Average Life
Our tool simplifies the complex math of amortization schedules and prepayment assumptions. Follow these steps:
Enter Principal: Input the total starting balance of the loan or bond.
Set Interest Rate: Enter the annual coupon or note rate.
Define Term: Input the total number of months (e.g., 360 for a standard mortgage).
Adjust CPR: Enter a Constant Prepayment Rate (CPR). If you expect no early payments, set this to 0. A typical baseline for mortgages is often 6-10%.
Review Results: The "Weighted Average Life" will display prominently in years. Use the dynamic chart to visualize how quickly the balance drops.
Key Factors That Affect Calculating Weighted Average Life
Several economic and mechanical factors influence the outcome when calculating weighted average life. Understanding these helps in predicting cash flow behavior.
Amortization Schedule: Loans that pay principal monthly (like mortgages) have a WAL significantly shorter than their stated maturity, whereas interest-only loans have a WAL equal to their maturity.
Interest Rate: Higher interest rates on fixed-payment loans lead to slower initial principal repayment (since more of the payment goes to interest), slightly increasing the WAL.
Prepayment Speed (CPR): This is the most volatile factor. High prepayment rates (due to refinancing incentives) drastically shorten WAL.
Seasoning: Older loans have already moved past the initial slow-pay phase of the amortization curve, resulting in a naturally shorter remaining WAL.
Market Rates: When market rates fall below the loan's coupon, refinancing increases (CPR rises), and WAL decreases.
Default Rates: In distressed scenarios, defaults can act like involuntary prepayments (via liquidation proceeds), altering the expected WAL.
Frequently Asked Questions (FAQ)
Is Weighted Average Life the same as Duration?
No. Calculating weighted average life measures the time to receive principal repayment. Duration measures the sensitivity of the bond's price to interest rate changes and includes coupon payments in its calculation.
Why is WAL important for Mortgage-Backed Securities?
MBS investors face "prepayment risk." Calculating weighted average life helps them estimate how long their capital will actually be deployed versus the stated 30-year term of the underlying loans.
Does WAL include interest payments?
No. The formula for calculating weighted average life focuses strictly on the return of principal. Interest payments are excluded from the weighting.
What is a "Short" vs. "Long" WAL?
A short WAL (e.g., 2-3 years) implies high liquidity and lower rate risk. A long WAL (e.g., 10+ years) implies higher yield potential but greater exposure to rate hikes.
Can WAL be greater than the maturity date?
No. Since WAL is an average of time periods within the loan term, it cannot mathematically exceed the final maturity date.
How does CPR affect the calculation?
CPR (Constant Prepayment Rate) assumes a percentage of the principal is paid off early every year. Higher CPR moves cash flows to earlier periods, reducing the WAL.
Is WAL calculated in months or years?
While the underlying cash flows may be monthly, the final result for calculating weighted average life is almost always annualized for easier comparison with bond yields.
Does this apply to auto loans?
Yes. Any loan with principal amortization, including auto loans and student loans, can be analyzed using this metric.
Related Tools and Internal Resources
Enhance your financial analysis with our suite of related calculators and guides:
// Global variable for chart instance
var chartContext = null;
// Initialize on load
window.onload = function() {
calculateWAL();
};
function getVal(id) {
var el = document.getElementById(id);
return parseFloat(el.value);
}
function setHtml(id, val) {
document.getElementById(id).innerHTML = val;
}
function formatCurrency(num) {
return new Intl.NumberFormat('en-US', { style: 'currency', currency: 'USD', maximumFractionDigits: 0 }).format(num);
}
function formatNumber(num, decimals) {
return num.toLocaleString('en-US', { minimumFractionDigits: decimals, maximumFractionDigits: decimals });
}
function calculateWAL() {
// Get Inputs
var principal = getVal("principal");
var rate = getVal("rate");
var term = getVal("term");
var cpr = getVal("cpr");
// Validation
var isValid = true;
if (isNaN(principal) || principal <= 0) {
document.getElementById("err-principal").style.display = "block";
isValid = false;
} else {
document.getElementById("err-principal").style.display = "none";
}
if (isNaN(rate) || rate < 0) {
document.getElementById("err-rate").style.display = "block";
isValid = false;
} else {
document.getElementById("err-rate").style.display = "none";
}
if (isNaN(term) || term <= 0) {
document.getElementById("err-term").style.display = "block";
isValid = false;
} else {
document.getElementById("err-term").style.display = "none";
}
if (isNaN(cpr) || cpr 100) {
document.getElementById("err-cpr").style.display = "block";
isValid = false;
} else {
document.getElementById("err-cpr").style.display = "none";
}
if (!isValid) return;
// Calculations
// Monthly Rate
var r = rate / 100 / 12;
// Single Monthly Mortality (SMM) from CPR
// SMM = 1 – (1 – CPR)^1/12
var smm = 1 – Math.pow((1 – cpr / 100), 1/12);
var balance = principal;
var totalPrincipalRepaid = 0;
var totalInterestPaid = 0;
var walNumerator = 0;
var monthsPassed = 0;
// Data for Chart and Table
var chartDataBalance = [principal];
var chartLabels = [0];
var tableData = [];
// Standard Amortization PMT (assuming fixed term mortgage style for base schedule)
// If rate is 0, simple division
var pmt;
if (r === 0) {
pmt = principal / term;
} else {
pmt = principal * (r * Math.pow(1 + r, term)) / (Math.pow(1 + r, term) – 1);
}
var currentTerm = term;
for (var i = 1; i <= term + 120; i++) { // Allow some buffer, though prepayments shorten it
if (balance balance (end of loan), cap it
if (scheduledPrincipal > balance) {
scheduledPrincipal = balance;
}
// Prepayment Calculation
// Prepay is applied to balance AFTER scheduled principal
var balanceAfterSched = balance – scheduledPrincipal;
var prepayment = balanceAfterSched * smm;
var totalPrincipalThisMonth = scheduledPrincipal + prepayment;
// Hard cap check
if (totalPrincipalThisMonth > balance) {
totalPrincipalThisMonth = balance;
prepayment = balance – scheduledPrincipal; // adjustment
}
var endingBalance = balance – totalPrincipalThisMonth;
// WAL Accumulation: Time (in years) * Principal Repaid
// Time is i/12 years
walNumerator += totalPrincipalThisMonth * (i / 12);
totalPrincipalRepaid += totalPrincipalThisMonth;
totalInterestPaid += interest;
balance = endingBalance;
monthsPassed = i;
// Store data for chart (every 12 months or end)
if (i % 12 === 0 || balance <= 0.01) {
chartLabels.push(Math.ceil(i/12));
chartDataBalance.push(balance);
// Store yearly data for table
var yearIdx = Math.ceil(i/12);
if (!tableData[yearIdx]) {
tableData[yearIdx] = {
year: yearIdx,
principal: 0,
interest: 0,
endingBal: balance,
walContrib: 0
};
}
}
// Accumulate monthly data into yearly bucket
var currentYear = Math.ceil(i/12);
// Since we initialized above, we might need a different approach or just summing logic.
// Simpler: Just reconstruct tableData from accumulated monthly flows.
}
// Re-run simple loop for table grouping to be cleaner
// We need accurate yearly sums.
// Reset and do logic properly for aggregation
balance = principal;
var yearlyPrincipal = 0;
var yearlyInterest = 0;
var yearlyWalContrib = 0;
var tableRows = "";
for (var m = 1; m balance) schedP = balance;
var remBal = balance – schedP;
var prepay = remBal * smm;
var totP = schedP + prepay;
if (totP > balance) totP = balance;
balance -= totP;
yearlyPrincipal += totP;
yearlyInterest += int;
yearlyWalContrib += totP * (m/12);
if (m % 12 === 0 || balance <= 0.01) {
var yr = Math.ceil(m/12);
// Add row to table string
// Limit table to first 10 years + every 5th year + final year to save space if needed
// For this requirement, let's show all years but max 30 rows is fine.
tableRows += "
" +
"
" + yr + "
" +
"
" + formatCurrency(yearlyPrincipal) + "
" +
"
" + formatCurrency(yearlyInterest) + "
" +
"
" + formatCurrency(balance) + "
" +
"
" + formatNumber(yearlyWalContrib / principal * 100, 2) + "%
" +
"
";
yearlyPrincipal = 0;
yearlyInterest = 0;
yearlyWalContrib = 0;
}
if (balance <= 0.01 && m % 12 !== 0) {
// Final partial year
var yr = Math.ceil(m/12);
tableRows += "
" +
"
" + yr + "
" +
"
" + formatCurrency(yearlyPrincipal) + "
" +
"
" + formatCurrency(yearlyInterest) + "
" +
"
" + formatCurrency(balance) + "
" +
"
" + formatNumber(yearlyWalContrib / principal * 100, 2) + "%
" +
"
";
}
}
// Final Result
var wal = walNumerator / principal;
setHtml("walResult", formatNumber(wal, 2) + " Years");
setHtml("totalPrincipalRes", formatCurrency(totalPrincipalRepaid));
setHtml("totalInterestRes", formatCurrency(totalInterestPaid));
setHtml("durationRes", monthsPassed + " Mos");
document.querySelector("#scheduleTable tbody").innerHTML = tableRows;
drawChart(chartLabels, chartDataBalance, principal);
}
function drawChart(labels, data, maxVal) {
var canvas = document.getElementById('walChart');
var ctx = canvas.getContext('2d');
// Clear canvas
ctx.clearRect(0, 0, canvas.width, canvas.height);
// Dimensions (assuming CSS sets size, we need internal resolution)
// Fix resolution for sharpness
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 graphWidth = width – 2 * padding;
var graphHeight = height – 2 * padding;
// Axes
ctx.beginPath();
ctx.moveTo(padding, padding);
ctx.lineTo(padding, height – padding);
ctx.lineTo(width – padding, height – padding);
ctx.strokeStyle = '#333';
ctx.lineWidth = 1;
ctx.stroke();
// Labels
ctx.fillStyle = '#666′;
ctx.font = '12px Arial';
ctx.textAlign = 'center';
ctx.fillText("Years", width / 2, height – 10);
ctx.save();
ctx.translate(15, height / 2);
ctx.rotate(-Math.PI / 2);
ctx.textAlign = 'center';
ctx.fillText("Balance ($)", 0, 0);
ctx.restore();
// Plot Data
ctx.beginPath();
ctx.strokeStyle = '#004a99'; // Primary color
ctx.lineWidth = 3;
var maxDataVal = maxVal;
var xStep = graphWidth / (labels.length – 1);
for (var i = 0; i < labels.length; i++) {
var x = padding + i * xStep;
var y = height – padding – (data[i] / maxDataVal * graphHeight);
if (i === 0) ctx.moveTo(x, y);
else ctx.lineTo(x, y);
}
ctx.stroke();
// Fill Area
ctx.lineTo(padding + (labels.length – 1) * xStep, height – padding);
ctx.lineTo(padding, height – padding);
ctx.fillStyle = 'rgba(0, 74, 153, 0.1)';
ctx.fill();
// Add Title inside chart if needed or legend
ctx.fillStyle = '#004a99';
ctx.font = 'bold 12px Arial';
ctx.fillText("Balance Profile", width – 80, padding + 10);
}
function resetCalculator() {
document.getElementById("principal").value = 100000;
document.getElementById("rate").value = 5.0;
document.getElementById("term").value = 360;
document.getElementById("cpr").value = 6.0;
calculateWAL();
}
function copyResults() {
var wal = document.getElementById("walResult").innerText;
var prin = document.getElementById("totalPrincipalRes").innerText;
var text = "Weighted Average Life Calculation:\n" +
"WAL: " + wal + "\n" +
"Total Principal: " + prin + "\n" +
"Calculated using standard amortization + CPR model.";
var tempInput = document.createElement("textarea");
tempInput.value = text;
document.body.appendChild(tempInput);
tempInput.select();
document.execCommand("copy");
document.body.removeChild(tempInput);
var btn = document.querySelector(".btn-copy");
var originalText = btn.innerText;
btn.innerText = "Copied!";
setTimeout(function() {
btn.innerText = originalText;
}, 2000);
}
// Handle Resize for Chart
window.onresize = function() {
calculateWAL();
};