On May 30, 2009, Janice Kerr is considering the newly issued 10-year AAA corporate bonds shown in the following exhibit:
Sentinal due, May 30, 2019
Collina due, May 30, 2019
a. Suppose that market interest rates decline by 100 basis points (i.e., 1%). Contrast the effect of this decline on the price of each bond.
b. Should Kerr prefer the Colina over the Sentinal bond when rates are expected to rise or to fall?
c. What would be the effect, if any, of an increase in the volatility of interest rates on the prices of each bond?
a. The Sentinal bond will increase in value to 107.79 while The price of the Colina bond will increase, but only to the call price of 102
b. If rates are expected to fall, the Sentinal bond is more attractive while If rates are expected to rise, Colina is a better investment.
c. An increase in the volatility of rates increases the value of the firm’s option to call back the Colina bond.
a. The maturity of each bond is 10 years.
Let’s assume that coupons are paid semiannually.
Since both bonds are selling at par value, the current yield to maturity for each bond is equal to its coupon rate.
If the yield declines by 1%, to 5% (2.5% semiannual yield), the Sentinal bond will increase in value to 107.79 [n=20; i = 2.5%; FV = 100; PMT = 3]
The price of the Colina bond will increase, but only to the call price of 102. The present value of scheduled payments is greater than 102, but the call price puts a ceiling on the actual bond price.
b. If rates are expected to fall, the Sentinal bond is more attractive: because
(i) it is not subject to being called,
(ii) its potential capital gains are higher.
On the other hand, If rates are expected to rise, Colina is a better investment because:
(i) Its higher coupon will provide a higher rate of return than the Sentinal bond.
c. An increase in the volatility of rates increases the value of the firm’s option to call back the Colina bond. This makes the Colina bond less attractive to the investor.
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?
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?
Question: The following table contains spot rates and forward rates for three years. However, the labels got mixed up. Can you identify which row of the interest rates represents spot rates and which one the forward rates?
Spot rate of Forward rates?
Spot rate of Forward rates?
Fill in the table below for the following zero-coupon bonds, all of which have par values of $1,000
Yield to Maturity
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