Independent solution

How to solve this Portfolio Weight for a Target Duration question

Setup

Setup

Price Bond A and form its time-weighted present-value numerator at 4%.

PA=601.04+601.042+1,0601.043=1,055.5018P_A=\frac{60}{1.04}+\frac{60}{1.04^2}+\frac{1{,}060}{1.04^3}=1{,}055.5018

Model

Model

Divide the timing numerator by price.

DA=60v+2(60)v2+3(1,060)v3PA=2.8381263D_A=\frac{60v+2(60)v^2+3(1{,}060)v^3}{P_A}=2.8381263

Compute

Compute

Let w be the fraction of portfolio market value in Bond A. The zero's duration is one year.

2=w(2.8381263)+(1−w)(1)2=w(2.8381263)+(1-w)(1)

Answer

Answer

Solving gives 54.4%, choice D.

w=0.5440323w=0.5440323
w≈54.4%(D)\boxed{w\approx54.4\%\quad\text{(D)}}