The inverse relationship between the interest rate and the price of bonds is fundamental to understanding how monetary policy affects interest rates and why people in the financial world are always so worried about the future course of the interest rate. This inverse relationship is illustrated for the two main types of bonds—coupon bonds and discount bonds.

A coupon bond pays the owner of the bond a fixed interest payment each year until the bond matures when the face value (or par value) of the bond is paid. The name “coupon bond” comes from the fact that, until recently, the bond owner had to clip a coupon from the bottom of the bond each year to receive this fixed interest payment. Now these payments are made electronically.

Suppose you own a coupon bond that is due to mature in five years, with face value $1,000 and coupon $100. If the interest rate is 10 percent, the current price of this bond should be $1,000 because the $100 interest coupon payment is 10 percent of the price of the bond. Now suppose the interest rate rises to 12 percent. Seeing this increase, you decide to sell your bond and use the proceeds to buy a new bond that pays 12 percent. Unfortunately for you, however, nobody will be willing to pay $1,000 for your bond because everyone knows he or she can earn a 12 percent return elsewhere. To sell your bond you will have to lower its price, in this case to $833.33 because at this price the $100 interest payment is a return of 12 percent.

Actually, the price will not fall quite this far. Because the bond will pay off at $1,000 in five years, the total return to investing in this bond is the stream of five $100 interest payments, plus a capital gain due to the rise in bond price to $1,000 over these five years. The yield to maturity, which is what economists mean by an interest rate, would be higher than 12 percent. For the yield to maturity to be 12 percent, the price need only fall to $927.90. For those interested, this calculation is explained in appendix 10.1.

An opposite result would occur if the interest rate were to fall to 8 percent. Everyone would want to buy your bond if it were priced at $1,000, because the 10 percent return on your bond would be higher than the 8 percent return available elsewhere. As a result, potential buyers would bid up the price of your bond in their efforts to obtain it, in this case to $1,250 because the $100 return is 8 percent of $1,250. Once again, this is not quite correct. In five years this bond will pay off at $1,000, so holders will experience a capital loss if they buy it for a higher price, implying that the yield to maturity is lower than 8 percent. The price will be bid up to only $1,079.85.

A discount bond is a bond without a coupon (and is therefore sometimes called a zero-coupon bond). The return to holding such a bond comes entirely from buying it at a price below its face value. The most common example is a U.S. government Treasury bill, called a T-bill, sold originally at weekly auctions for maturity periods of three months, six months, and a year (and then, like all other bonds, available for resale on the regular money market). If the interest rate is 10 percent, the price for a one-year $10,000 T-bill will be $9,090.91 since the return of $10,000 - $9,090.91 = $909.09 is 10 percent of the $9,090.91 price paid.

If the interest rate were higher, say 12 percent, the price of the T-bill would be lower—in this case $8,928.57—to make the return of $10,000 - $8,928.57 = $1,071.43 be 12 percent of the $8,928.57 purchase price. If the interest rate were lower, say 8 percent, the price of the T-bill would be higher, in this case $9,259.26.

Regardless of the type of bond, there is an inverse relationship between interest rates and bond prices. This relationship is as close to a true economic law as it can get: interest rates and bond prices are instantly connected, with the causal force going in either direction. If someone decides to sell a bond, for whatever reason, and drops the bond price to sell it, the interest rate instantly rises. And if the interest rate rises, for whatever reason, the market reacts instantly to push down bond prices.

It should now be evident why this relationship between interest rates and bond prices is so important. A change in the interest rate, which happens on a daily basis, can create substantial capital gains or losses for those holding bonds, particularly for those holding long-term bonds. It is for this reason that the financial pages of newspapers provide so much commentary on the future course of the interest rate.

Why are the capital gains and losses greater for longer-maturity bonds? Let’s look at the earlier example of a $1,000 face-value coupon bond with coupon $100 and time to maturity five years. A rise in the interest rate to 12 percent dropped the bond price to $927.90. Suppose there had only been one year to maturity; then the price would have fallen to $982.14. Someone buying this bond would, during the remaining year of its life, receive the $100 coupon plus that year’s capital gain, $17.86, generating a 12 percent return on outlay. If there had been five years to maturity, however, there would have to be five such annual capital gains as the bond price crawls up to its face value over the five years. Consequently, the price must fall further for a longer maturity bond. Capital losses and gains are much larger on long-term bonds than on short-term bonds.