# Inverse Relationship Between Bond Prices & Interest Rates

by Cam Merritt, studioD

How bonds get priced is a mystery to many novice investors, but just about anyone can grasp the fundamental relationship between bond prices and interest rates. It's an inverse relationship: When interest rates are rising, bond prices will fall; when interest rates are falling, bond prices will rise. Why this happens becomes clear when you examine how bonds actually work.

## Coupon Rates

The typical corporate or government bond has a "par value" and a "coupon rate." The par value, or face value, is the money you will receive when the bond matures or comes due; bonds usually have a par value of \$1,000. The coupon rate tells you how much interest you'll receive each year until the bond matures, expressed as a percentage of the par value. So a bond with a \$1,000 par value and a coupon rate of 4.5 percent will pay \$45 per year in interest. The par value and the coupon rate of a bond never change.

## Competitive Investments

Interest rates are constantly rising and falling, and a bond has to stay competitive with other investments; otherwise, no one will want it. It wouldn't make sense to buy a bond that pays 4.5 percent interest, for example, if there were another bond that presented an equal amount of risk but was offering 5 percent interest. At the same time, it wouldn't make sense for a bond to pay 4.5 percent interest if equivalent investments were paying only 4 percent. The question is how a bond with an unchangeable coupon rate can compete in an environment of changing interest rates. The answer lies with the price of the bond.

## Prices and Yields

Say you have a \$1,000 bond with a 4.5 percent coupon rate, meaning it pays \$45 per year. You want to sell it, but similar bonds are offering 5 percent interest. So you offer to sell the bond for \$900. The buyer will still receive \$45 a year in interest -- but that \$45 is actually 5 percent of \$900. On the other hand, if similar bonds were offering only 4 percent interest, you could have raised the price to \$1,125. The \$45 annual interest payments would be equal to 4 percent of \$1,125. By changing the price, then, you've changed the effective interest paid rate by the bond. That effective rate is known as the yield rate. Whatever's happening with interest rates, you can adjust yields to match market rates by adjusting the price.

## Inverse Relationship

Bond pricing in practice is somewhat more complicated than in this example, because it involves calculating the present value of the future interest payments and of the payment at maturity. Nevertheless, the example demonstrates the basics of the inverse relationship between bond prices and yields. Prices and yields always move in opposite directions. It's impossible for them not to, as one dictates the other. If a bond is selling for more than par value -- selling at a premium -- the yield rate will be lower than the coupon rate. If a bond sells for less than par value -- selling at a discount -- the yield rate is higher than the coupon rate.

#### References (2)

• "Financial Accounting for MBAs," Fourth Edition; Peter Easton, et al
• "Corporate Finance: The Core," Second Edition; Jonathan Berk and Peter DeMarzo