- Sources of Return from Investing in a Bond
- How to Calculate Current Yield
- How to Calculate Yield to Maturity
- Bond Equivalent Yield Convention
- Yield to Maturity (YTM) Approximation Formula
- YTM and Reinvestment Risk
- Factors Affecting Reinvestment Risk
- Calculate Bond-Equivalent Yield of Annual-Pay Bonds
- How to Calculate Yield to Call of a Bond
- Cash Flow Yield
- Bootstrapping Spot Rate Curve (Zero Curve)
- How to Price a Bond Using Spot Rates (Zero Curve)
- Nominal Spread
- Z-Spread: Definition and Calculation
- Option-adjusted Spreads (OAS)
- What are Forward Rates?
- How to Calculate Forward Rates from Spot Rates?
- How to Value a Bond Using Forward Rates

# What are Forward Rates?

Till now we have looked at the spot rates and we also learned about how to construct spot rate curve. Essentially a spot rate is the borrowing or lending interest rate today for a specified period of time. For example, *s _{1}* refers to the one-year spot rate, i.e., the interest rate you will realize in one year.

*s*represents the annualized two-year spot rate, i.e., the rate you will realize if you invest/lend/borrow for two years.

_{2}A forward rate, on the other hand, is the interest rate for the future. For example, you may want to know what will be the one-year interest rate one year from now. Similarly, you can find out what will be the 2-year forward rate one year from now. Just like spot rates, forward rates can also plotted on a graph to arrive at the forward rate curve.

Forward rates are represented with specific terminology, and once you know it, it will be very easy for you to read any forward rate. The forward rate itself is represented by an *f*, and there are two subscripts, one before *f* and the other after *f*, such as * _{1}f_{2}*.

The first subscript represents the time period for which the rate applies, for example, 1-year forward rate. The second subscript represents when the forward rate begins, for example, one year from now or two years from now.

Let’s take a few examples:

* _{1}f_{1}* represents 1-year forward rate 1 year from now.

* _{1}f_{2}* represents 1-year forward rate 2 year from now.

* _{1}f_{3}* represents 1-year forward rate 3 year from now.

* _{2}f_{1}* represents 2-year forward rate 1 year from now.

* _{2}f_{2}* represents 2-year forward rate 2 year from now.

Note that the above notations assume that each period is for one year. In some cases, you can assume one period equal to 6-months also. In that case * _{1}f_{2}* represents 6-month forward rate 1 year from now. Some other resources may have totally different notations, but this is the standard way of reading forward rates.

We can derive forward rates from the spot rate curve, which we will learn in our next article.

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