Forward Rates Calculator

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Forward Rates Calculator

Understanding Forward Rates

In finance, a forward rate is the predetermined interest rate for a future transaction. It's the rate agreed upon today for a loan or investment that will begin at some point in the future. Forward rates are crucial for hedging against interest rate risk and for making informed investment decisions about future cash flows.

The concept is derived from the principle of no-arbitrage. If you can invest for a certain period today and also lock in a rate for a future period, the returns from both strategies should be consistent when extrapolated to the same future point. This consistency allows us to calculate the implied forward rate.

The formula to calculate a forward rate, denoted as $_n r_m$ (the forward rate for the period from time $n$ to time $m$), based on two spot rates, $_0 r_n$ (spot rate from time 0 to $n$) and $_0 r_m$ (spot rate from time 0 to $m$, where $m > n$), is as follows:

$(1 + _0 r_m)^m = (1 + _0 r_n)^n \times (1 + _n r_m)^{m-n}$

Rearranging this formula to solve for the forward rate $_n r_m$:

$_n r_m = \left( \frac{(1 + _0 r_m)^m}{(1 + _0 r_n)^n} \right)^{\frac{1}{m-n}} – 1$

In our calculator, we simplify this by considering two spot rates for different periods. Let the first spot rate be for period $P_1$ and the second spot rate be for period $P_2$, where $P_2 > P_1$. The forward rate from $P_1$ to $P_2$ is calculated as:

Forward Rate = $\left( \frac{(1 + \text{Spot Rate}_2)^{P_2}}{(1 + \text{Spot Rate}_1)^{P_1}} \right)^{\frac{1}{P_2-P_1}} – 1$

This calculator helps you determine the implied interest rate for a future investment period, given the current spot rates for shorter and longer durations.

Example:

Suppose the current spot rate for a 1-year investment is 2.5% (0.025) and the current spot rate for a 2-year investment is 3.0% (0.030). We want to find the forward rate for the second year (i.e., the rate from year 1 to year 2).

  • Spot Rate (Year 1): 0.025
  • Period 1: 1 year
  • Spot Rate (Year 2): 0.030
  • Period 2: 2 years

Using the formula:

Forward Rate = $\left( \frac{(1 + 0.030)^2}{(1 + 0.025)^1} \right)^{\frac{1}{2-1}} – 1$

Forward Rate = $\left( \frac{(1.030)^2}{1.025} \right)^{1} – 1$

Forward Rate = $\left( \frac{1.0609}{1.025} \right) – 1$

Forward Rate = $1.03502439 – 1$

Forward Rate = $0.03502439$, or approximately 3.50%

This means that the market currently implies an interest rate of approximately 3.50% for an investment that starts one year from now and lasts for one year.

function calculateForwardRate() { var spotRate1 = parseFloat(document.getElementById("spotRate1").value); var spotRate2 = parseFloat(document.getElementById("spotRate2").value); var period1 = parseInt(document.getElementById("period1").value); var period2 = parseInt(document.getElementById("period2").value); var resultElement = document.getElementById("result"); if (isNaN(spotRate1) || isNaN(spotRate2) || isNaN(period1) || isNaN(period2)) { resultElement.innerHTML = "Please enter valid numbers for all fields."; return; } if (period1 <= 0 || period2 <= 0) { resultElement.innerHTML = "Periods must be positive values."; return; } if (period2 <= period1) { resultElement.innerHTML = "Period 2 must be greater than Period 1."; return; } if (spotRate1 < -1 || spotRate2 < -1) { resultElement.innerHTML = "Spot rates cannot be less than -100%."; return; } var term1 = Math.pow(1 + spotRate1, period1); var term2 = Math.pow(1 + spotRate2, period2); var exponent = 1 / (period2 – period1); if (term1 === 0) { resultElement.innerHTML = "Cannot divide by zero. Check Spot Rate 1 and Period 1."; return; } var forwardRate = Math.pow(term2 / term1, exponent) – 1; resultElement.innerHTML = "

Result:

"; resultElement.innerHTML += "The implied forward rate from year " + period1 + " to year " + period2 + " is: " + (forwardRate * 100).toFixed(4) + "%"; }

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