Homework answers / question archive / You've learned how to compute price elasticity with respect to changes in interest rates (modified duration) of a bond under the flat term structure of interest rates, and parallel shifts in the term structure

You've learned how to compute price elasticity with respect to changes in interest rates (modified duration) of a bond under the flat term structure of interest rates, and parallel shifts in the term structure

Finance

Share With

You've learned how to compute price elasticity with respect to changes in interest rates (modified duration) of a bond under the flat term structure of interest rates, and parallel shifts in the term structure. In this problem, you are asked to compute the price elasticity of a bond under a non-flat yield curve. The present value (price) of a bond is B =[# 1 (1+r)" CF Now consider the parallel shift of the yield curve by x, i.e. rt + rt+, Vt. Then the price elasticity of the bond with respect to parallel shifts in the yield curve can be written as PE = 1 db=t=1 (1+rojet txCF We can now approximate price changes in response to a small parallel shift Ar in the yield curve as ΔΒ -Βx (PE| x Δη Note that when the yield curve is flat, the absolute value of price elasticity |PE| equals modified duration. Consider the following term structure, which is upward sloping: 1-yr 2-yr 3-yr 4-yr 5-yr 2.1% 2.4% 2.67% 2.88% 3.06% A 5-year Treasury note (T-note) has a face value of $100 and a 2.62% coupon rate (assume annual payments). (a) Compute the price of the T-note. 98.09 (b) Suppose that the yield curve suddenly shifted down by 0.25% (this is a parallel shift, all points on the yield curve shift by the same amount). Compute the new price of the T-note and report the price change relative to the original price computed in (a). 99.14 X