Q.19I

Expert-verifiedFound in: Page 362

Book edition
9th

Author(s)
Zvi Bodie, Alex Kane, Alan Marcus, Alan J. Marcus

Pages
748 pages

ISBN
9780078034695

**You are managing a portfolio of $1 million. Your target duration is ten years, and you can choose from two bonds: a zero-coupon bond with a maturity of 5 years and an infinity, each yielding 5%.**

**An a. How much of each bond will you hold in your portfolio?**

**b. How will these fractions change next year if the target duration is nine years?**

**Answer**

a. 11/16 and 5/16

b. 12/17 and 5/17

Maturity term = 5 years

YTM = 5%

Duration of perpetuity = ΔP/P = 1.05/ 0.5 = 21 years

The weight (w) of five year maturity period

= (w x 5) + [(1 – w) x 21] = 10

w = 11 / 16

So 11/ 16 of the portfolio will be invested in zero bonds and

(1- 11/16 = 5/16) of the portfolio will be invested in perpetuity bonds.

The following year (as given in question), the bond’s duration would change to 4 years.

Perpetuity = 21 years.

Now to solve weight (w) for duration 9 years:

(w x 4) + [(1 – w) x 21] = 9

= w = 12/17

So the following year, this proportion would change as 12/17 would be invested in zero bonds while (1- 12/17= 5/17) would be invested in perpetuity bonds.

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