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Explanation:
Correct answer: C) 4.88%
The bond’s price is found by discounting each cash flow using the given spot rates, and then the yield-to-maturity is the single semi-annual-compounded rate that matches that price.
$100 = $3.00$103.00Using the annual spot rates with annual compounding:
$3 / (1.02)^{0.5}$$3 / (1.036)^{1.0}$$3 / (1.044)^{1.5}$$103 / (1.05)^{2.0}$This gives a bond price of approximately $102.10.
Now solve for the semi-annual yield that prices the bond at about $102.10. The yield comes out to:
Because the coupon rate (6%) is above the long-term spot rate (5%), the bond trades above par, so its yield must be below 5.0%. The nearest choice is therefore 4.88%.
Q-713.2. Consider the steep spot (aka, zero) rate curve illustrated below: 2.0% at 0.5 years, 3.60% at 1.0 year, 4.40% at 1.5 years and 5.0% at 2.0 years. Each of these zero rates is per annum with annual compounding.
| Face value; aka, principal, par | $100.00 |
|---|---|
| Semi-annual coupon (per annum) | 6.0% |
We are interested in the yield-to-maturity (aka, yield) of a two-year $100.00 face value bond that pays an 6.0% semi-annual coupon (3.0% coupon every six months). If this yield-to-maturity is expressed with semi-annual compounding (aka, bond equivalent basis), which of the following is nearest to this yield?
A
a) 2.52%
B
b) 3.95%
C
c) 4.88%
D
d) 5.00%
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