Spot and Forward Interest Rates

10 Pages Posted: 21 Oct 2008

See all articles by Robert S. Harris

Robert S. Harris

University of Virginia - Darden School of Business

Robert M. Conroy

University of Virginia - Darden School of Business

Abstract

This note examines how spot and forward interest rates relate to bond prices and to each other. After defining spot and forward rates, the note shows how to estimate spot rates from data on either zero-coupon bonds or coupon bonds. It also shows how to express these stated rates for different compounding assumptions. The note pays particular attention to understanding how arbitrage forces in markets establish the links between forward and spot rates and how to infer one set of rates from the other. The note deepens understanding of bond pricing, assuming that the reader is already familiar with the basics of present-value techniques. It is a useful springboard for topics (e.g., swaps) that require familiarity with spot and forward rates.

Excerpt

UVA-F-1520

Spot and Forward Interest Rates

Every interest rate applies for a specific time period with a starting point and an end point. Rates that apply from today until some future date are referred to as spot rates. Rates agreed upon today but starting at some future date and covering a time period in the future are known as forward rates. For instance, suppose today you signed a contract to borrow \$ 1,000 at a 4% annual interest rate for one year. If the contract specifies that you get your \$ 1,000 today and have to pay back the interest and principal one year from today, the 4% is a one-year spot rate. In contrast, if your agreement says that you don't get your \$ 1,000 until one year from today and you pay back interest and principal two years from today, the 4% is a forward rate. The forward interest rate covers the period that starts one year from today and ends two years from today. Importantly, the forward rate is agreed upon today in a contract. After a year passes, market spot rates may be above or below the contracted forward rate, but the contract obligates you to honor the forward rate agreed upon today.

While spot interest rates are the ones we usually see, forward-rate contracts can be extremely valuable in a host of financial settings. Suppose, for example, you were the CFO of a large company that planned to borrow money to finance a major expenditure (e.g., building a plant, paying off an existing debt, acquiring a company) but did not need the money until some future date. Rather than wait and face uncertainty about what interest rates might be in the future, you might consider a forward contract to lock in your rate.

This note addresses how spot and forward interest rates relate to bond prices and to each other. We focus particularly on what happens in developed financial markets when well-informed investors buy and sell contracts quickly and at low transaction costs. In such markets, any potential arbitrage profits that temporarily appear are quickly eliminated as traders' actions realign market prices. This market activity enforces very specific mathematical relationships between spot and forward rates.

Spot Rates

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Keywords: valuation, bond pricing, interest rates, spot interest rates, forward interest rates, arbitrage, compounding, Black-Scholes option-pricing model

Suggested Citation

Harris, Robert S. and Conroy, Robert M., Spot and Forward Interest Rates. Darden Case No. UVA-F-1520, Available at SSRN: https://ssrn.com/abstract=1279956