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Answer: If the zero curve is upward-sloping, the zero rate for a particular maturity is greater than the par yield for that maturity; specifically, if $r(t2) > r(t1)$, then $\text{zero}(t2) > \text{par yield}(t2)$
**Correct answer: A** The statement in **A** is the exception because, on an upward-sloping zero curve, the **par yield is typically greater than the zero rate** for the same maturity, not smaller. Why the others are true: - **B**: On an upward-sloping zero curve, longer forward rates exceed shorter zero rates. - **C**: A two-year semiannual coupon bond provides enough information to bootstrap the zero curve out to 2 years. - **D**: For a bond selling at a premium, the relationship is indeed: \[ \text{coupon rate} > \text{current yield} > \text{YTM} \] So the false statement is **A**.
Author: Manit Arora
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Question-163.1. With respect to interest rates, EACH of the following is necessarily TRUE except for:
A
If the zero curve is upward-sloping, the zero rate for a particular maturity is greater than the par yield for that maturity; specifically, if , then
B
If the zero curve is upward-sloping, the forward rate is greater than the zero rate; specifically, if ,
C
If we only have the price and coupon rate for a two-year semi-annual coupon bond, we have enough information to construct the zero rate curve up to two years (but not beyond two years)
D
Let current yield = annual dollar coupon interest / current price of bond. If a bond is selling at a premium, the coupon rate > current yield > yield to maturity
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