dstefan
06-06-2008, 12:46 AM
Chapter 2, Problem 15
A five year bond with duration 3.5 years is worth 102. Find an approximate price of the bond if the yield decreases by fifty basis points.
Solution:
First note that, since the yield of the bond decreases, the value of the bond must increase.
Recall that the percentage change in the price of the bond can be approximated by the duration of the bond multiplied by the parallel shift in the yield curve, with opposite sign, i.e., \frac{\Delta B}{B} ~\approx~ - \Delta y ~D
For B = 102, D = 3.5 and \Delta y = - 0.005 (since 1% = 100 bp), we find that \Delta B ~=~ B_{new} - B ~\approx~ - \Delta y ~D ~B ~=~ 1.785.
The new value of the bond is B_{new} ~=~ B + \Delta B ~=~ 103.75.
A five year bond with duration 3.5 years is worth 102. Find an approximate price of the bond if the yield decreases by fifty basis points.
Solution:
First note that, since the yield of the bond decreases, the value of the bond must increase.
Recall that the percentage change in the price of the bond can be approximated by the duration of the bond multiplied by the parallel shift in the yield curve, with opposite sign, i.e., \frac{\Delta B}{B} ~\approx~ - \Delta y ~D
For B = 102, D = 3.5 and \Delta y = - 0.005 (since 1% = 100 bp), we find that \Delta B ~=~ B_{new} - B ~\approx~ - \Delta y ~D ~B ~=~ 1.785.
The new value of the bond is B_{new} ~=~ B + \Delta B ~=~ 103.75.