Independent solution

How to solve this Duration and Convexity question

Setup

Setup

Deferring every payment by six years adds six years to Macaulay duration, not directly to modified duration.

(1+j)(9−4)=6⟹j=0.20(1+j)(9-4)=6\Longrightarrow j=0.20

Model

Model

The two supplied modified durations therefore determine one plus yield as 1.2.

−P′(j)=4P(j)=40-P'(j)=4P(j)=40

Compute

Compute

The immediate added payment increases value from 10 to 13 but contributes zero to the price derivative.

Dmod,new=4010+3=4013D_{\mathrm{mod,new}}=\frac{40}{10+3}=\frac{40}{13}

Answer

Answer

Converting the new modified duration back to Macaulay gives 3.69 years, choice C.

DM,new=1.2(40/13)=3.69(C)\boxed{D_{M,\mathrm{new}}=1.2(40/13)=3.69\quad\text{(C)}}