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When interest rates rise, the prices of outstanding bonds fall; when rates fall, prices rise. Though this relation might not seem obvious at first, the reasons are fairly simple.
Take this example. Say the U.S. government sells Treasury bonds when prevailing market interest rates are 8%. So, a bond with a face value of $1,000 on issue would pay $80 a year in interest - usually in two half-yearly installments of $40. But if market interest rates were to rise to 10%, then who would want to buy such a bond? So, the market price of the bond would have to fall to a level where that fixed $80 annual payment were the equivalent of a 10% annual yield - in this case, the price would have to fall to $800, so that the annual $80 payment would equal 10% of the purchase price of the bond. (Obviously, this matters only if the holder of the bond wants to sell it in the open market; if he or she wants to keep the bond to maturity, the price fluctuations exist only on paper.) Since bond prices are usually expressed at a percent of face (or "par") value, the price of the bond would be quoted at 80.
Conversely, if market interest rates were to fall to 6%, the price of the bond would rise to $1,333.33 - or 133 11/32 in market jargon. U.S. stock and bond markets don't use decimal pricing. Stock prices are usually quoted in eighths of a point, though sixteenths and even thirty-seconds are used for some low-priced shares; bond prices are usually quoted in thirty-seconds.
Things are actually a bit more complicated than this. A buyer who paid $800 or $1,333 for a bond and held it to maturity would get a return of $1,000 in principal. The buyer who paid a premium would have a capital loss, and the one who bought the bond at a discount from its face value would have a capital gain. So that deviation of market value from face value would have to enter into any calculations of ultimate yield ("yield to maturity," in the jargon). But these simplified examples are enough to illustrate the basic principle of why bond prices move in the opposite direction of interest rates.
When combined, price changes and interest payments are referred to as total return. Someone who bought a bond when interest rates were 8% and held it for a year as they fell to 6% would get not only the 8% interest yield, but a 33% capital gain, for a total return of 41% - not bad for a year's "work." But someone who bought a bond at 6% and held it as rates rose to 8% would suffer a sharp capital loss. Since interest rates rose for most of the period from the early 1950s through the early 1970s, the capital losses far outweighed the interest payments - and that's before adjusting for the corrosive effects of inflation. It's no wonder that rentiers, poor dears, christened bonds "certificates of confiscation" in the late 1970s. But since rates peaked in the early 1980s, bondholders have done marvelously well, enjoying one of the greatest long-term bull markets in the modern history of credit.