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a. What is the duration of a two-year bond that pays an annual coupon of 10 percent and has a current yield to maturity of 12 percent? Use $1,000 as the face value. ( LG 3-6 )
b. What is the duration of a two-year zero-coupon bond that is yielding 11.5 percent? Use $1,000 as the face value.
c. Given these answers, how does duration differ from maturity?
( LG 3-6 )
The estimation of the effect of maturity and coupon rates on the sensitivity of bond prices to changes in interest rates, as discussed in the previous section, is complex and using these relationships as the basis for decision making is difficult in dealing with multiple bonds. Duration, on the other hand, provides a simple measure that allows for a straightforward calculation of a bond’s interest rate sensitivity. In this section, we show that the price sensitivity of a bond, or the percent change in the bond’s fair present value, for a given change in interest rates (as discussed above) can be more directly measured by a concept called duration (or Macauley’s duration). We also show that duration produces an accurate measure of the price sensitivity of a bond to interest rate changes for relatively small changes in interest rates. The duration measure is a less accurate measure of price sensitivity the larger the change in interest rates. Duration is the weighted - average time to maturity on a financial security using the relative present values of the cash flows as weights. On a time value of money basis, duration measures the weighted average of when cash flows are received on a security. In addition to being a measure of the average life of an asset or liability, duration also has economic meaning as the sensitivity, or elasticity , of that asset or liability’s value to small interest rate changes (either required rate of return or yield to maturity). ^{16} Duration describes the percentage price, or present value, change of a financial security for a given (small) change in interest rates. That is, rather than calculating present value changes resulting from interest rate changes, as we did in the previous sections, the duration of a financial security can be used to directly calculate the price change. Thus, for investors and financial managers duration is a tool that can be used to estimate the change in the value of a portfolio of securities or even firm value for a given change in interest rates.
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