Calculate the implied one-year forward rate between two periods.
Years
%
Years
%
Error: Longer period must be greater than shorter period.
Implied Forward Rate
0.00%
function calculateForwardRate() {
// Get Input Values
var t1 = parseFloat(document.getElementById('shorterPeriod').value);
var r1 = parseFloat(document.getElementById('spotRate1').value);
var t2 = parseFloat(document.getElementById('longerPeriod').value);
var r2 = parseFloat(document.getElementById('spotRate2').value);
var errorDiv = document.getElementById('errorMsg');
var resultDiv = document.getElementById('frcResult');
// Reset Display
errorDiv.style.display = 'none';
resultDiv.style.display = 'none';
// Validation
if (isNaN(t1) || isNaN(r1) || isNaN(t2) || isNaN(r2)) {
errorDiv.innerText = "Please fill in all fields with valid numbers.";
errorDiv.style.display = 'block';
return;
}
if (t2 t1 check, but for safety)
if (denominator === 0) {
errorDiv.innerText = "Invalid spot rate configuration.";
errorDiv.style.display = 'block';
return;
}
var base = numerator / denominator;
var exponent = 1 / (t2 – t1);
var forwardRateDecimal = Math.pow(base, exponent) – 1;
var forwardRatePercent = forwardRateDecimal * 100;
// Display Results
document.getElementById('resultValue').innerText = forwardRatePercent.toFixed(3) + "%";
var duration = t2 – t1;
var durationText = duration === 1 ? "one-year" : duration + "-year";
document.getElementById('resultExplanation').innerHTML =
"This is the implied annualized rate for a " + durationText + " period starting " + t1 + " years from now.";
resultDiv.style.display = 'block';
}
Understanding the One Year Forward Rate
The forward rate is a theoretical interest rate implied by the current spot rates of the yield curve. It represents the interest rate for a future period that is "locked in" today. Specifically, the "one year forward rate" usually refers to the interest rate for a one-year period starting one year from now (denoted as 1f1).
Investors and analysts use this calculation to identify market expectations for future interest rates and to identify arbitrage opportunities between investing in long-term bonds versus rolling over short-term bonds.
The Forward Rate Formula
To calculate the forward rate between two time periods, we utilize the "No-Arbitrage" principle. The return on a longer-term investment should equal the return on a sequence of shorter-term investments, assuming no arbitrage opportunities exist.
Let's assume the current 1-year Treasury spot rate is 4.5% and the 2-year Treasury spot rate is 5.0%. An investor wants to know the implied interest rate for the second year (the one-year forward rate starting one year from today).
Using the logic that investing for 2 years should yield the same as investing for 1 year and then reinvesting for another year at the forward rate:
(1.05)2 = (1.045)1 × (1 + f)
1.1025 = 1.045 × (1 + f)
(1 + f) = 1.1025 / 1.045
(1 + f) ≈ 1.05502
f ≈ 5.502%
Therefore, the market is pricing in a 5.502% interest rate for the year following the current one.
Why Calculate Forward Rates?
1. Hedging Interest Rate Risk: Companies expecting to borrow money in the future can use forward rate agreements (FRAs) to lock in costs based on these calculations.
2. Investment Strategy: If an investor believes the actual future rate will be lower than the calculated forward rate, they might lock in the long-term rate (buy the 2-year bond) rather than rolling over 1-year bonds.
3. Yield Curve Analysis: Forward rates help decompose the yield curve. If forward rates are significantly higher than spot rates, it suggests an upward-sloping yield curve, often indicating economic expansion or rising inflation expectations.