Question: Consider a generic bond with face value X and coupon rate c. The bond has T periods to maturity and the term structure of interest

Consider a generic bond with face value X and coupon rate c. The bond has T periods to maturity and the term structure of interest rates is constant at rate r.

(i) Write down an expression for the price of the bond and from this derive the elasticity of the bond's price with respect to the gross spot rate, 1+r. Explain the links between this elasticity and the Macauley duration of the bond.

(ii) Consider two bonds with identical features aside from their coupon rates. Which of the bonds would one expect to have a larger Macauley duration and why?

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