Question

1. Two new issue bonds are being evaluated by a portfolio manager. The first bond is a 5-year 3.8% semiannual coupon and the second bond is a 20-year 4.4% semiannual coupon. Both bonds are expected to be issued at par.

a. Calculate the modified duration for each bond using a 10bp change

b. Calculate the convexity for each bond using a 10bp change.

Someone help please!

Answer 1

1 A) BOND 1=

ASSUME FV=1000, I/Y=3.8/2= 1.9, N=5*2= 10, PMT=0, COMPUTE PV= -828.4345

Now, a 10bp change = 0.1% change

Thus, a 0.1% increase will lead to I/Y= 3.9, Put PV=1000, I/Y=3.9/2= 1.95 N=5*2= 10, PMT=0, COMPUTE PV= -824.3805

Similarly, a 0.1% decrease will lead to I/Y= 3.7, Put PV=1000, I/Y=3.8/2= 1.85 N=5*2= 10, PMT=0, COMPUTE PV= -832.5104

Thus, approximate modified duration = (832.5104-824.3805)/ (2*828.4345*0.001)= 4.9068

A) BOND 2=

ASSUME FV=1000, I/Y=4.4/2= 1.9, N=20*2= 40, PMT=0, COMPUTE PV= -418.7590

Now, a 10bp change = 0.1% change

Thus, a 0.1% increase will lead to I/Y= 4.5, Put PV=1000, I/Y=4.5/2= 2.25 N=20*2= 40, PMT=0, COMPUTE PV= -410.6458

Similarly, a 0.1% decrease will lead to I/Y= 4.3, Put PV=1000, I/Y=4.3/2= 2.15 N=20*2= 40, PMT=0, COMPUTE PV= -427.0367

Thus, approximate modified duration = (427.0367-410.6458)/ (2*418.7590*0.001)= 19.6046

1 B) BOND 1

CONVEXITY= (V_- + V₊ - 2V₀)/ (CHANGE IN YTM)^2*V₀

_{= (1656.8909-1656.8690)/ 0.0008= 27.3750}

BOND 2

CONVEXITY= (V_- + V₊ - 2V₀)/ (CHANGE IN YTM)^2*V₀

_{= (837.6825-837.5180)/ 0.0004= 392.8274}