Dear Ask the Economist:

How do bonds work? Why do bond prices rise as interest rates fall, and vice versa?

Bonds are debt instruments that pay a fixed income over their life and then pay a principal to the bondholder upon their maturity.  The typical bond has a principal of $1,000 and for the purpose of answering your questions, that's what my example below will assume.
 
When a $1,000 bond is first issued, it has a stated "coupon rate" of some fixed percentage that is usually close to prevailing interest rates in the marketplace at that time.  Let's suppose a particular $1,000 bond carries a coupon rate of 5 percent.  That means it will pay interest of $50 to the bondholder, most likely twice a year in payments of $25.00 each time.  When the bond matures, it will pay the bondholder $1,000.
 
During the life of the bond, market conditions are likely to change substantially (including such major factors as the state of the economy, people's confidence in investing, rates of return on competing investment opportunities, etc.).  And of course, being a bondholder doesn't mean you have to buy and hold the bond for its entire life; in fact, most bondholders don't do that.  They buy and sell bonds all the time.  For the bond we're talking about in the above paragraph to remain attractive and competitive in the marketplace during its life, its rate of return must adjust upwards or downwards accordingly.  The promise to pay $1,000 at maturity never changes.  The $50 per year interest payment never changes.  What does change is the bond's market price, which could go above or below the face value of $1,000.
 
Let's say market conditions change in this way: Interest rates rise, for whatever combination of reasons.  A bond offering $1,000 at maturity and payments of $50 per year is no longer attractive at $1,000 if interest rates on similar, competing investment opportunities rise to, say, 6 percent.  For the 5-percent bond to be attractive, its price must fall until the $50 per year represents a rate of return in the neighborhood of 6 percent.  Its price might fall to $950 or lower.  Conversely, if interest rates in the general market fall to, say, 4 percent, then people will gladly bid more than $1,000 for that bond in order to get the $50 per year interest payments.  The price might rise to $1,050 or more.
 
The rule on bonds is indeed that as interest rates rise, bond prices fall and that as interest rates fall, bond prices rise.  This is, as the example above shows, because bond prices have to fluctuate so that their interest return changes to reflect conditions in the marketplace, especially changes in interest rates.
 

"During the life of a bond, market conditions are likely to change substantially."

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