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
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.
Which of the following most accurately describes the behavior of credit default swaps?
a. When credit risk increases, swap premiums increase.
b. When credit and interest rate risk increases, swap premiums increase.
c. When credit risk increases, swap premiums increase, but when interest rate risk increases, swap premiums decrease
A 30-year maturity bond making annual coupon payments with a coupon rate of 12% has duration of 11.54 years and convexity of 192.4. The bond currently sells at a yield to maturity of 8%. Use a financial calculator or spreadsheet to find the price of the bond if its yield to maturity falls to 7% or rises to 9%. What prices for the bond at these new yields would be predicted by the duration rule and the duration-with-convexity rule?
What is the percent error for each rule? What do you conclude about the accuracy of the two rules?
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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