Independent solution

How to solve this Duration Around Coupon Date question

Setup

Setup

Use the annuity-due duration identity at 5% for the bond immediately before and immediately after its coupon date. Removing the immediate coupon reduces the first duration measure by one.

d0=a¨8‾∣ 0.05=6.7864,d1=d0−1=5.7864d_0=\ddot a_{\overline8|\,0.05}=6.7864,\quad d_1=d_0-1=5.7864

Model

Model

The quantities are d₁ = 5.7864 after the first adjustment and d₂ = 6.0757 for the corresponding seven-period annuity-due.

d2=a¨7‾∣ 0.05=6.0757d_2=\ddot a_{\overline7|\,0.05}=6.0757

Compute

Compute

Their ratio is 5.7864/6.0757 = 0.9524.

d1/d2=0.9524d_1/d_2=0.9524

Answer

Answer

The calculation gives 0.95 for duration around coupon date, matching published choice C.

d1/d2=0.9524(C)\boxed{d_1/d_2=0.9524\quad\text{(C)}}