Understanding Forward Rates
A forward rate is an interest rate that is agreed upon today for a loan or investment that will begin at some future date. It's an implied rate derived from current spot rates (interest rates for immediate settlement).
The concept is based on the idea of no-arbitrage. If there were no differences between borrowing and lending at the spot rate for a longer period versus borrowing/lending at the spot rate for a shorter period and then entering into a forward contract for the remaining period, then the implied forward rate would be the only rational choice.
The formula used in this calculator is derived from the relationship between spot rates and forward rates:
(1 + r2 * t2) = (1 + r1 * t1) * (1 + f * (t2 - t1))
Where:
r1 is the spot interest rate for the first period.t1 is the duration of the first period in years.r2 is the spot interest rate for the second, longer period.t2 is the duration of the second period in years.f is the forward interest rate for the period from t1 to t2.
Rearranging the formula to solve for f (the forward rate):
f = [((1 + r2 * t2) / (1 + r1 * t1)) - 1] / (t2 - t1)
This calculator helps financial analysts, investors, and economists understand market expectations about future interest rate movements.
Example Calculation:
Let's say:
- The 1-year spot rate (r1) is 2% (0.02).
- The time period 1 (t1) is 1 year.
- The 2-year spot rate (r2) is 3% (0.03).
- The time period 2 (t2) is 2 years.
Using the formula:
f = [((1 + 0.03 * 2) / (1 + 0.02 * 1)) - 1] / (2 - 1)
f = [((1 + 0.06) / (1 + 0.02)) - 1] / 1
f = [(1.06 / 1.02) - 1] / 1
f = [1.039215686 - 1] / 1
f = 0.039215686
So, the implied forward rate for the period between year 1 and year 2 is approximately 3.92%.
function calculateForwardRate() {
var r1 = parseFloat(document.getElementById("spotRate1").value);
var t1 = parseFloat(document.getElementById("time1").value);
var r2 = parseFloat(document.getElementById("spotRate2").value);
var t2 = parseFloat(document.getElementById("time2").value);
var resultDiv = document.getElementById("result");
resultDiv.innerHTML = "; // Clear previous results
if (isNaN(r1) || isNaN(t1) || isNaN(r2) || isNaN(t2)) {
resultDiv.innerHTML = "Please enter valid numbers for all fields.";
return;
}
if (t1 <= 0 || t2 <= 0) {
resultDiv.innerHTML = "Time periods must be positive.";
return;
}
if (t2 <= t1) {
resultDiv.innerHTML = "Time period 2 (t2) must be greater than Time period 1 (t1).";
return;
}
var numerator = (1 + r2 * t2);
var denominator = (1 + r1 * t1);
if (denominator === 0) {
resultDiv.innerHTML = "Calculation error: Denominator is zero.";
return;
}
var forwardRate = ((numerator / denominator) – 1) / (t2 – t1);
if (isNaN(forwardRate)) {
resultDiv.innerHTML = "Calculation resulted in an invalid number. Please check your inputs.";
return;
}
resultDiv.innerHTML = "The implied forward rate (f) for the period from year " + t1 + " to year " + t2 + " is:
" + (forwardRate * 100).toFixed(4) + "%";
}
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