Answer:
To calculate the requested measures for bonds A and B, we need to use the following formulas:
Duration = (PV- - PV+) / (2 x PV x ∆y)
Macaulay duration = Duration / (1 + y/n)
Modified duration = Macaulay duration / (1 + y/n)
where PV- is the price of the bond when yield decreases by a small amount, PV+ is the price of the bond when yield increases by a small amount, PV is the current price of the bond, ∆y is the change in yield, y is the current yield, n is the number of coupon payments per year.
Using the given information and assuming semi-annual payments:
1.) Calculate the duration for the two bonds by changing the yield up and down 25 basis points:
For Bond A:
PV- = 100.369, PV+ = 99.643
Duration = (100.369 - 99.643) / (2 x 100.000 x 0.0025) = 13.697
For Bond B:
PV- = 103.987, PV+ = 104.122
Duration = (103.987 - 104.122) / (2 x 104.055 x 0.0025) = -0.653
2.) Calculate the duration for the two bonds by changing the yield up and down by 10 basis points:
For Bond A:
PV- = 100.141, PV+ = 99.862
Duration = (100.141 - 99.862) / (2 x 100.000 x 0.001) = 13.397
For Bond B:
PV- = 104.028, PV+ = 104.081
Duration = (104.028 - 104.081) / (2 x 104.055 x 0.001) = -0.257
3.) Calculate the Macaulay duration for the two bonds:
For Bond A:
Macaulay duration = 13.697 / (1 + 0.08/2) = 13.184
For Bond B:
Macaulay duration = -0.653 / (1 + 0.09/2) = -0.630
4.) Calculate the modified duration for the two bonds:
For Bond A:
Modified duration = 13.184 / (1 + 0.08/2) = 12.924
For Bond B:
Modified duration = -0.630 / (1 + 0.09/2) = -0.609
Note that the negative duration and modified duration for Bond B indicate that the bond is a short-term bond and is less sensitive to interest rate changes compared to Bond A.