The most important interpretation of the duration of a bond is how sensitive is the price of the bond to changes in market interest rates. The estimate of the percentage change in the bond price for a 100 basis points (1%) change in the interest rate is called duration.
Different bonds have different durations. Depending upon the investment strategy, an investor may look for bonds with higher (long) or lower (short) durations. A more accurate calculation is made using calculus or a bond-pricing model. A reliable valuation model is a pre-requisite to accurate calculation of duration.
Computation of duration
The formula for duration is:
price if yields decline – price if yields rise
2 x (initial price) x (change in yield in decimals)
Yield curve risk
There are various interest rates in the market. Interest rates differ from each other depending upon the maturities and the credit risks of the fixed-income securities.
When these different interest rates/yields are plotted against their respective maturities, the graphical description is called the yield curve. The yield curve is subject to change in the form of parallel shifts, i.e. when every interest rate in the yield curve changes by the same amount and the same direction, or nonparallel shifts, where the interest rates in the yield curve do not change by the same amount and/or direction.
A bond portfolio consists of a variety of bonds with different maturities and coupon rates. The different patterns of interest rate changes will affect the value of the individual bonds in the portfolio differently. The risk that affects a bond portfolio due to different patterns of the changes of the various interest rates in the economy is called the yield curve risk.
Because of this, a single duration number is not sufficient to explain the interest rate risk of a portfolio of bonds. A rate duration, which is defined to be the sensitivity of the change of bond price with respect to a particular (spot) rate, is a more useful measure.
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