Effective duration FI

CFA Level I
#1

The following information on Bonds A and B was obtained:

Bond Effective Duration Effective Convexity
A 7.48621 29.35972
B 7.23852 –321.75618

Compare the interest rate risk of Bond A and Bond B.

  1. Bond A is riskier than Bond B.
  2. Bond B is riskier than Bond A.
  3. Bond A and Bond B have approximately the same interest rate risk.

Answer is Option 2.
I didnt understand how B is riskier
If we assume 100bps decrease
% change for A= -7.48621 x -0.01 + 1/2 x 29.35972 x 0.01^2 = 7.633%
% change for B= -7.23852 X -0.01 + 1/2 x -321.75618 x 0.01^2 = 5.63%

#3

How? Sorry I didn’t understand

#4

Sorry my maths went all to pot but the overall point still stands.
You want to examine when rates rise and prices fall nor when rate fall and prices rise.

100bp rise Duation effect C effect Combined
Duration Convexity -D x 0.01 0.5 x C x 0.01 * 0.01
A 7.47621 29.35972 -7.476% 0.147% -7.329%
B 7.23852 -321.75618 -7.239% -1.609% -8.847%
100bp fall Duation effect C effect Combined
Duration Convexity -D x -0.01 0.5 x C x 0.01 * 0.01
A 7.47621 29.35972 7.476% 0.147% 7.623%
B 7.23852 -321.75618 7.239% -1.609% 5.630%

Bond B has more downside and less upside.