Chapter 3: 10-13I (page 329)
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.
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Question: Consider a bond with a settlement date of February 22, 2012, and a maturity date of March 15, 2020. The coupon rate is 5.5%. If the yield to maturity of the bond is 5.34% (bond equivalent yield, semi-annual compounding), what is the list price of the bond on the settlement date? What is the accrued interest on the bond? What is the invoice price of the bond?
How can perpetuity, which has an infinite maturity, have a duration as short as 10 or 20 years?
Question: A two-year bond with par value \(1,000 making annual coupon payments of \)100 is priced at $1,000. What is the yield to maturity of the bond? What will be the realized compound yield to maturity if the one-year interest rate next year turns out to be:
( a ) 8%,
( b ) 10%,
( c ) 12%?
Question: The yield to maturity on one-year zero-coupon bonds is 8%. The yield to maturity on two-year zero-coupon bonds is 9%.
a. What is the forward rate of interest for the second year?
b. If you believe in the expectations hypothesis, what is your best guess as to the expected value of the short-term interest rate next year?
c. If you believe in the liquidity preference theory, is your best guess as to next year’s short-term interest rate higher or lower than in ( b )?
One common goal among fixed-income portfolio managers is to earn high incremental returns on corporate bonds versus government bonds of comparable durations. The approach of some corporate-bond portfolio managers is to find and purchase those corporate bonds having the largest initial spreads over comparable-duration government bonds. John Ames, HFS’s fixed-income manager, believes that a more rigorous approach is required if incremental returns are to be maximized. The following table presents data relating to one set of corporate/government spread relationships (in basis points, bp) present in the market at a given date:
CURRENT AND EXPECTED SPREADS AND DURATIONS
OF HIGH-GRADE CORPORATE BONDS (ONE-YEAR HORIZON)
Bond Ratings | Initial spread over governments | Expected horizon spread | Initial duration | Expected duration one year from now |
Aaa | 31 bp | 31 bp | 4 years | 3.1 Years |
Aa | 40 | 50 | 4 years | 3.1 Years |
a. Recommend purchase of either Aaa or Aa bonds for a one-year investment horizon given a goal of maximizing incremental returns.
b. Ames chooses not to rely solely on initial spread relationships. His analytical framework considers a full range of other key variables likely to impact realized incremental returns, including call provisions and potential changes in interest rates. Describe other variables that Ames should include in his analysis, and explain how each of these could cause realized incremental returns to differ from those indicated by initial spread relationships.
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