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The price of a bond changes as interest rates change. Specifically, price moves in the opposite direction to the change in interest rates. That is, if interest rates increase, the price of a bond will decline; if interest rates decrease, the price of a bond will increase. This is the reason a bond will sell above its par value (i.e., sell at a premium) or below its par value (i.e., sell at a discount). The risk that the price of a bond or bond portfolio will decline when interest rates increase is called interest rate risk.
The sensitivity of the price of a bond to changes in interest rates depends on the following factors:
? The bond’s coupon rate
? The bond’s maturity
? The level of interest rates
Specifically, the following relationships hold:
? All other factors being constant, the lower the coupon rate, the greater the price sensitivity of a bond for a given change in interest rates.
? All other factors being constant, the longer the maturity, the greater the price sensitivity of a bond for a given change in interest rates.
? All other factors being constant, the lower the level of interest rates, the greater the price volatility of a bond for a given change in interest rates.
Consequently, the price of a zero-coupon bond with a long maturity is highly sensitive to changes in interest rates. The price sensitivity is even greater in a low interest rate environment than in a high interest rate environment. For money market instruments, since their maturity is less than one year, the price is not very sensitive to changes in interest rates.
The price sensitivity of a bond to changes in interest rates can be estimated. This measure is called the duration of a bond. Duration is the approximate percentage change in the price of a bond for a 100-basis- point change in interest rates. For example, if a bond has a duration of 8, this means that for a 100-basis-point change in interest rates, the price will change by approximately 8%. For a 50-basis-point change in interest rates, the price of this bond would change by approximately 4%.
Given the price of a bond and its duration, the dollar price change can be estimated. For example if our bond with a duration of 8 has a price of $90,000, the price will change by about 8% for a 100-basis- point change in interest rates and therefore dollar price change will be about $7,200 (8% times $90,000). For a 50-basis-point change, the price would change by about $3,600.
The concept of duration applies to a bond portfolio also. For example, if an investor has a bond portfolio with a duration of 6 and the market value of the portfolio is $1 million, this means that a change in interest rates of 100 basis points will change the value of the portfolio by approximately 6% and therefore the value of the portfolio will change by approximately $60,000. For a 25-basis-point change in interest rates, the portfolio’s value will change by approximately 1.5% and the portfolio’s value will change by approximately $15,000.