This is the implied rate for the period between Year and Year .
function calculateForwardRate() {
// Get input values using var
var r1Input = document.getElementById('spotRate1').value;
var t1Input = document.getElementById('time1').value;
var r2Input = document.getElementById('spotRate2').value;
var t2Input = document.getElementById('time2').value;
var errorDiv = document.getElementById('errorDisplay');
var resultDiv = document.getElementById('resultDisplay');
// Clear previous results/errors
errorDiv.style.display = 'none';
resultDiv.style.display = 'none';
// Convert to floats
var r1 = parseFloat(r1Input);
var t1 = parseFloat(t1Input);
var r2 = parseFloat(r2Input);
var t2 = parseFloat(t2Input);
// Validation Logic
if (isNaN(r1) || isNaN(t1) || isNaN(r2) || isNaN(t2)) {
errorDiv.innerHTML = "Please enter valid numbers for all fields.";
errorDiv.style.display = 'block';
return;
}
if (t1 < 0 || t2 < 0 || r1 < 0 || r2 < 0) {
errorDiv.innerHTML = "Rates and time periods cannot be negative.";
errorDiv.style.display = 'block';
return;
}
if (t2 <= t1) {
errorDiv.innerHTML = "Time Period 2 must be greater than Time Period 1 to calculate a forward rate.";
errorDiv.style.display = 'block';
return;
}
// Calculation Logic: Forward Rate
// Formula: F = [ (1 + r2)^t2 / (1 + r1)^t1 ] ^ (1 / (t2 – t1)) – 1
// Convert percentage to decimal
var r1Decimal = r1 / 100;
var r2Decimal = r2 / 100;
// Calculate compounding factors
var numerator = Math.pow(1 + r2Decimal, t2);
var denominator = Math.pow(1 + r1Decimal, t1);
var timeDiff = t2 – t1;
// Calculate Forward Rate
var forwardRateDecimal = Math.pow(numerator / denominator, 1 / timeDiff) – 1;
var forwardRatePercent = forwardRateDecimal * 100;
// Update UI
document.getElementById('forwardRateResult').innerHTML = forwardRatePercent.toFixed(3) + "%";
document.getElementById('t1Display').innerHTML = t1;
document.getElementById('t2Display').innerHTML = t2;
resultDiv.style.display = 'block';
}
Forward Rate Calculation: Excel Formulas and Theory
The forward rate is a theoretical interest rate implied by the current spot rates of different maturities. It represents the interest rate that would be applicable to a future financial transaction, essentially "locking in" a rate today for a loan or investment that will occur later. This concept is fundamental in bond pricing, derivative valuation, and identifying arbitrage opportunities.
How to Calculate Forward Rate in Excel
While the calculator above provides an instant answer, financial analysts often need to perform forward rate calculation in Excel for entire yield curves. Below is the step-by-step logic to replicate these results in a spreadsheet.
The Forward Rate Formula
To calculate the annualized forward rate between time \( T_1 \) and \( T_2 \), based on spot rates \( R_1 \) and \( R_2 \), the formula is:
Note: If your inputs in Excel are whole numbers (e.g., 3 instead of 0.03), ensure you divide them by 100 or use the % symbol as shown above.
Why Calculate Forward Rates?
Understanding the forward rate is crucial for several financial strategies:
Hedging: Companies use forward rate agreements (FRAs) to protect against future interest rate volatility.
Expectations Hypothesis: Forward rates are often interpreted as the market's expectation of future spot rates. If the forward rate is significantly higher than the current spot rate, the market anticipates rising interest rates.
Arbitrage: Traders compare the calculated forward rate against actual quoted forward rates in the market. Discrepancies can signal profit opportunities.
Example Calculation
Let's verify the calculation manually to understand the underlying mechanics:
Metric
Value
1-Year Spot Rate (R1)
3.0%
2-Year Spot Rate (R2)
4.5%
Investment Horizon
2 Years
Scenario: You can invest for 2 years at 4.5% annually, or invest for 1 year at 3.0% and then reinvest for another year. To be indifferent between these two options, the rate at which you reinvest in the second year must be the Forward Rate.