Which of the following statements is CORRECT?
A) a bond's current yield must always be either equal to its yield to maturity or between its yield to maturity and its coupon rate.
B) if a bond sells at par, then its current yield will be less than its yield to maturity.
C) if a bond sells for less than par, then its yield to maturity is less than its coupon rate.
D) a discount bond's price declines each year until it matures, when its value equals its par value.
E) assume that two bonds have equal maturities and are of equal risk, but one bond sells at par while the other sells at a premium above par. the premium bond must have a lower current yield and a higher capital gains yield than the par bond.

Question

Quizplus · Accepted Answer

Answer b is incorrect because a bond selling at par must have a current yield equal to its YTM. Answer c is incorrect because a bond selling at below par must have a YTM > the coupon rate. Answer d is incorrect because a discount bond's price must rise over time. Answer e is incorrect because a premium bond must have a negative capital gains yield. That leaves Answer a as the only possibly correct answer. Note that YTM = Cur Yld +/σ Cap gains Yld., so Cur Yld = YTM +/σ Cap gain yld. The cap gains yld will be positive or negative depending on whether the coupon rate is above or below the YTM. That means that the Cur yld must either equal the YTM or be between the YTM and the coupon rate. a's correctness is also demonstrated below:
 $$\begin{array} { l r r c } 
\text { Par } & \text { Par bond } & \text { Premium } & \text { Discount } \
\text { Maturity } & 1000 & 1000 & 1000 \
\text { Coup rate } & 10 \% & 10 & 10 \
\text { YTM } & 10.00 \% & 10.00 \% & 10.00 \% \
\text { Arn coup } & \$ 100.00 & \$ 110.00 & \$ 90.00 \
\text { Price } & \$ 1,000.00 & \$ 1,061.45 & \$ 938.55 \
\text { Cur Yield } & 10.00 \% & 10.36 \% & \mathbf { 9 . 5 9 \% } \text { aqual to or between YTM } \
\text { Cap gain } & 0.00 \% & - 0.36 \% & 0.41 \%
\end{array}$$

Which of the Following Statements Is CORRECT