Bond Prices

• The price of a bond is negatively related to the interest rate. When interest rates rise, bond prices fall and when interest rates fall, bond prices rise.
  
  

Convexity

• How much the price rises or falls depends upon how long the bond will last. A 10-year bond will change price more than a five-year one; a 30-year bond more than a 10-year one. This is called convexity, the difference in reaction of different bonds to a change in interest rates.
  
  

Considerations

• If interest rates rise, then instead of getting the old interest rate on your bond, you could be getting the new one on a new bond. A five-year bond means you have to wait a maximum of five years before you get your money back to put into a new bond. A 30-year one: well 30 years is a long time to wait. The opposite is true of a fall in interest rates: you get the old higher rate for however the bond lasts.
  
  

Mortgage Bond Convexity

• Mortgage bonds are made up of a collection of mortgages. If interest rates fall, then many of those original mortgages will refinance at the new lower rates. So some of the money will come back early and will have to be invested again at the new lower interest rates.
  
  

Negative Mortgage Convexity

• This early repayment of some of the mortgages shortens the duration of the whole bond. So a 30-year mortgage bond, instead of acting like other 30-year bonds, will act more like a 25- or 20-year bond. So we say that the convexity of such a bond is negative: it changes in price less than other bonds in reaction to a change in interest rates.