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Essentials Of Investments
Found in: Page 362
Essentials Of Investments

Essentials Of Investments

Book edition 9th
Author(s) Zvi Bodie, Alex Kane, Alan Marcus, Alan J. Marcus
Pages 748 pages
ISBN 9780078034695

Short Answer

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?


a. 11/16 and 5/16

b. 12/17 and 5/17

See the step by step solution

Step by Step Solution

Step by Step Solution Step 1: Given information

Maturity term = 5 years

YTM = 5%

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

Step 2: Calculation of weight of zero-coupon bond and Perpetuity bond ‘a’

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.

Step 3: Calculation of weight of zero-coupon bond and Perpetuity bond ‘b’

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.

Most popular questions for Business-studies Textbooks

Spice asks Meyers (see the previous problem below) to quantify price changes from changes in interest rates. To illustrate, Meyers computes the value change for the fixed-rate note in the table. He assumes an increase in the interest rate level of 100 basis points. Using the information in the table, what is the predicted change in the price of the fixed-rate note?

Frank Meyers, CFA, is a fixed-income portfolio manager for a large pension fund. A member of the Investment Committee, Fred Spice, is very interested in learning about the management of fixed-income portfolios. Spice has approached Meyers with several questions. Specifically, Spice would like to know how fixed-income managers position portfolios to capitalize on their expectations of future interest rates.

Meyers decides to illustrate fixed-income trading strategies to Spice using a fixed rate bond and note. Both bonds have semi-annual coupon periods. All interest rate (yield curve) changes are parallel unless otherwise stated. The characteristics of these securities are shown in the following table. He also considers a nine-year floating-rate bond (floater) that pays a floating rate semi-annually and is currently yielding 5%.

Spice asks Meyers about how a fixed-income manager would position his portfolio to capitalize on expectations of increasing interest rates. Which of the following would be the most appropriate strategy?

a. Shorten his portfolio duration.

b. Buy fixed-rate bonds.

c. Lengthen his portfolio duration.


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