What is relationship between a bond coupon rate and its duration?

Answer 1

bond coupon rates and yield rates have very similar effects and a very similar relationship to duration, lemme explain, by first explain durations effects in relation to interest rates, then yields and finally you can surmise that relationship between yield rates will be the same as coupon rates

Duration can be seen as the elasticity of the bond's price with respect to interest rates. When duration is 7, a 15 year bond will fall 7% in value if interest rates increase by 1%. In the data we've generated we can also determine the relationship between yields and duration by analyzing the change after a 50 basis point decrease in rates. The duration will rise as yields are lowered, and conversely a high coupon rate or high yield will result in lower durations. While a higher yield reduces the present value of all the bond's payments, it reduces the value of payments further in the future by a greater proportional amount. This amounts to a reduction in duration. Merck & Company's bond has the highest yield and therefore one would surmise that the duration for MRK should be lower than the other bonds, this is only true if all other variables are held equal (ceteris paribus). This is not the case. The bonds have wildly different coupons remaining. Eli Lilly's bond has a similar number of coupons remaining-suggesting a relatively good candidate for comparison-and a lower yield than MRK, leading one to expect LLY bond to have a higher duration than MRK. An astute financial student would discourage this comparison, citing that LLY exhibits the highest (7.125%) annual coupon rate, which would in turn reduce the duration. While comparisons between bonds will fail us due to their unique characteristics, it is easy to see the change when examining a single bond and the effect of a 50 basis point decrease in rates has on the bond's duration. Every single bond's duration rose, relative to itself before the basis change, as their yields were lowered. This helps prove our assumption of the inverse relationship between yield and duration.