The stated yield to maturity and realized compound yield to maturity of a (default-free) zero-coupon bond will always be equal. Why?
A zero-coupon bond has the same values for YTM and realized compound yield because there is no reinvestment rate uncertainty.
The bonds which do not pay interests but trade at a deep discount from their face value is known as zero coupon bond.
Zero coupon bonds provide no coupons for reinvestment. Therefore the final value of the coupon comes from the principal of the bond and is independent of the rate at which this could be reinvested. There is no reinvestment rate uncertainty with zeros.
Currently, the term structure is as follows: One-year bonds yield 7%, two-year bonds yield 8%, three-year bonds and greater maturity bonds all yield 9%. You are choosing between one-, two-, and three-year maturity bonds all paying annual coupons of 8%, once a year. Which bond should you buy if you strongly believe that at year-end the yield curve will be flat at 9%?
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.
A 12.75-year maturity zero-coupon bond selling at a yield to maturity of 8% (effective annual yield) has a convexity of 150.3 and a modified duration of 11.81 years. A 30-year maturity 6% coupon bond making annual coupon payments also selling at a yield to maturity of 8% has a nearly identical modified duration—11.79 years—but considerably higher convexity of 231.2.
a. Suppose the yield to maturity on both bonds increases to 9%. What will be the actual percentage of capital loss on each bond? What percentage of capital loss would be predicted by the duration-with-convexity rule?
b. Repeat part ( a ), but this time assume the yield to maturity decreases to 7%.
c. Compare the performance of the two bonds in the two scenarios, one involving an increase in rates, the other a decrease. Based on their comparative investment performance, explain the attraction of convexity.
d. In view of your answer to ( c ), do you think it would be possible for two bonds with equal duration, but different convexity, to be priced initially at the same yield to maturity if the yields on both bonds always increased or decreased by equal amounts, as in this example? Would anyone be willing to buy the bond with lower convexity under these circumstances?
Question: Masters Corp. issues two bonds with 20-year maturities. Both bonds are callable at $1,050. The first bond is issued at a deep discount with a coupon rate of 4% and a price of $580 to yield 8.4%. The second bond is issued at par value with a coupon rate of 8.75%.
a. What is the yield to maturity of the par bond? Why is it higher than the yield of the discount bond?
b. If you expect rates to fall substantially in the next two years, which bond would you prefer to hold?
c. In what sense does the discount bond offer “implicit call protection”?
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