Chapter 3: 10-3CP (page 334)
A convertible bond has the following features:
Coupon | 5.25% |
Maturity | June 15, 2020 |
Market price of bond | \(77.50 |
Market price of underlying common stock | \)28.00 |
Annual Dividend | $1.20 |
Conversion ratio | 20.83 shares |
Calculate the conversion premium for this bond.
a. $191.76
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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?
a. Which set of conditions will result in a bond with the greatest price volatility?
(1) A high coupon and short maturity.
(2) A high coupon and a long maturity.
(3) A low coupon and a short maturity.
(4) A low coupon and a long maturity.
b. An investor who expects declining interest rates would be likely to purchase a bond that has a _____________ coupon and a _____________ term to maturity.
(1) Low, long
(2) High, short
(3) High, long
(4) Zero, long
c. With a zero-coupon bond:
(1) Duration equals the weighted-average term to maturity.
(2) Term to maturity equals duration.
(3) Weighted-average term to maturity equals the term to maturity.
(4) All of the above.
d. As compared with bonds selling at par, deep discount bonds will have:
(1) Greater reinvestment risk.
(2) Greater price volatility.
(3) Less call protection.
(4) None of the above.
The historical yield spread between AAA bonds and Treasury bonds widened dramatically during the credit crisis in 2008. If you believed the spread would soon return to more typical historical levels, what should you have done? This would be an example of what sort of bond swap?
Find the convexity of a seven-year maturity, 6% coupon bond selling at a yield to maturity of 8%. The bond pays its coupons annually.
( Hint: You can use the spreadsheet from this chapter’s Excel Application on Convexity, setting cash flows after year 7 equal to zero. The spreadsheet is available at www.mhhe.com/bkm; link to Chapter 11 material.)
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?
Year | 1 | 2 | 3 | |
Spot rate of Forward rates? | 10.00% | 12.00% | 14.00% | |
Spot rate of Forward rates? | 10.00% | 14.0364% | 18.1078% |
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