Introduction

Understanding forward rates is crucial in the world of finance. Forward rates provide insights into the expected future interest rates, and they play a pivotal role in pricing financial instruments, especially in the fixed-income market. In this chapter, we will explore what forward rates are, how to interpret them, and how to calculate forward rates given spot rates. By the end of this chapter, you will have a solid grasp of forward rates and their significance in financial decision-making.

Interpretation of Forward Rates

A forward rate is the interest rate for a future period that can be locked in today. It represents the expected interest rate for a specific future time frame. To interpret forward rates, consider the following:

• Spot Rate vs Forward Rate: The spot rate is the current interest rate for a specific maturity date, while the forward rate is the expected rate for a future date. If the forward rate is higher than the spot rate, it implies an expectation of rising interest rates.

• Market Expectations: Forward rates reflect market expectations. A rising forward rate curve suggests expectations of increasing interest rates in the future, while a falling curve implies expectations of decreasing rates.

Calculating Forward Rates from Spot Rates

Forward rates can be calculated using spot rates and the formula for compounding. The formula for calculating the forward rate for a future period ‘$n$’ years from today is:

$$F_n=\frac{\left(1+S_n\right)^n}{\left(1+S_{n-1}\right)^{n-1}}-1$$

Where:

• $F_n=$ Forward rate for ‘$n$’ years from today
• $S_n=$ Spot rate for ‘$n$’ years from today
• $S_{n-1}=$ Spot rate for ‘$n-1$’ years from today

Example: Let’s say the current spot rates for 1-year and 2-year periods are 3% and 4%, respectively. You want to calculate the 1-year forward rate for the period from year 1 to year 2. Using the formula:

$$\begin{aligned} & F_{1,2}=\frac{(1+0.04)^2}{(1+0.03)^1}-1 \\ & F_{1,2}=\frac{1.0816}{1.03}-1 \\ & F_{1,2} \approx 4.96 \end{aligned}$$

So, the 1-year forward rate for the period from year 1 to year 2 is approximately 4.96%.