INTEREST RATE AND BOND PRICE PRIMER

Understanding stock movements is relatively straight forward. Rising earnings, dividends and stock prices is generally considered a good thing for equity investors. When considering bonds, the first thought would be that rising interest rates would be positive for bond investors as they would be paid higher interest rates. The reality is a little different in that rising interest rates results in declining bond prices. Bond prices and interest rates have an inverse correlation. So why is it that rising interest rates is negative for bond prices and bond holders?
The easiest way of explaining this is by example. If you buy a ten year bond at $100 that has a 2% coupon, you will earn $20 in interest over the life of the bond. Assuming rates never change and ignoring interest com-pounding (for simplicity), the price of the bond will remain at $100 till the $100 principle is repaid in ten years.

Bonds, like stocks, do trade on a secondary market. You can buy ten year bonds when they are issued (which we will call "new" bonds for our example) or you can buy "used" ten year bonds on the secondary market. For our example, a "used" ten year bond will be considered any ten year bond that has less than ten years to maturity. A "new" bond will turn into a "used" bond the day after they are issued.

Buying a "used" bond with a maturity of ten years less a day is virtually identical to a "new" ten year bond. For our example, we will assume that they are equivalent. If we buy a "new" 2% ten year bond, and the following day interest rates for ten year bonds pop to 3%, "new" bonds issued after the change in interest rates would be priced to yield 3%. These "new" bonds would pay $3 of interest per year or $30 over the ten year life of the bond. Since the bond we bought yesterday (with a 2% coupon) only pays $20 interest over its ten year life, it is obviously less attractive than a bond that pays 3%. There needs to be another mechanism to entice buyers to buy our now "used" 2% ten year bond on the secondary market. This mechanism is price. For buyers to get a 3% equivalent yield from a "used" 2% coupon ten year bond, the price of the "used" 2% bond would drop from $100 to $90 at the same time that interest rate rise to 3%. A buyer (but not the initial holder) of the "used" 2% bond would then realize interest of $20 and capital gains of $10 over the ten year life of the bond (assuming the bond is held to maturity). This is the same as a buyer of a "new" 3% bond receiving interest of $30 over 10 years with a return of principle that is equal to what was paid for the bond. Of course, the initial buyer of the 2% bond (when it was considered "new") would realize a capital loss of $10 / bond when interest rates rose from 2% to 3%. This is why bondholders lose when interest rates rise. Their bonds are re-priced to reflect the higher interest rates.

What happens to the "used" 2% bond over the intervening years? Assuming interest rates remain at 3%, the price of the 2% bond will rise approximately 1% per year. This means that the bond holder will receive both 2% of interest plus 1% in capital gains each and every year. The math also means that the further out the maturity for any bonds held, the larger the loss on the price of the bonds when rates rise, all else being equal. We have already seen an example of what happens when rates rise and how it impacts a ten year bond. If the same example is applied to a five year bond, a rise in interest rates from 2% to 3% will result in the price of a "used" five year bond dropping to $95. The reason the bond price only drops $5 (vs. $10 for the "used" ten year bond) is because buyers of the bond need only a 5% discount to offset the five years of receiving a 2% coupon, in-stead of 3% for the more recently issued "new" bonds.

These examples are extreme, as bonds rarely have such big overnight moves (2% to 3%). While rapid and significant decreases in bond prices do happen, they tend to play out over a number of days and weeks rather than overnight as we have illustrated. While rising interest rates are positive for prospective bond purchasers (as they receive higher rates), they are negative for existing bondholders due to bond price declines.