Question

19. A 20-year, 6.500% annual payment bond settles on a coupon date. The bond's yield to maturity is 9.400%.

(a)   What is the bond’s Macauley Duration (show your work, like you did in problem (16) above.)

(b) What is the bond’s approximate modified duration? Use yield changes of +/- 30 bps around the yield to maturity for your calculations.

20. Consider the bond from problem (19) above.

(a) Calculate the approximate convexity for the bond.

(b) Calculate the change in the full bond price for a 40 bps change in yield.

All prices and interest rates must be expressed to THREE decimal places. You must show your work

i need answer for 20

Answer 1

N= 20

Ytm =9.4%
cupon =6.5%

face value = 1000

19)

a)Duration= V(-)-V(+)/2V0*(chage in yield )=0.09522
Chage yield by 30 basis point

b)Macauley Duration = ( 1+ytm)* modified Duration

= (1+9.4%)*0.09522
= 0.1041

20)

a)convexity = V(+) + V(-) -2V0 / 2 * V(0) * chage in yield ^2

= 0.007

b) chage in yield by 40 basis point

Duration = 0.09522

convexity = 0.007

chage in price = - duration * chage in yield + 1/2* convexity * chage in yield ^ 2

= - 0.09522 * 0.004 + 1/2 * 0.007* 0.004^2

=0.0003808