Which one of the following applies to a premium bond?

Question

BlackTom AI · Accepted Answer

A premium bond sells above par, so its coupon rate exceeds both the current yield and the yield to maturity.

1. Relevant knowledge points and concepts
- Coupon rate = annual coupon payment / face (par) value. It is fixed by the bond.
- Current yield = annual coupon payment / current market price.
- Yield to maturity (YTM) = internal rate of return if the bond is held to maturity, accounting for coupon payments and capital gain or loss as price moves to par.
- For a premium bond (price > par), the coupon rate > current yield, and YTM is lower than current yield because the investor incurs a capital loss as the price converges down to par.

2. Step-by-step reasoning
- Coupon payment is based on par, so coupon rate is independent of market price.
- If price > par, dividing the same coupon by a larger price produces a smaller current yield than the coupon rate.
- Additionally, buying above par means you will receive par at maturity (lower than purchase price), producing a capital loss that reduces the overall return; thus YTM < current yield.

3. Calculation example (all intermediate steps)
- Assume par = $1,000, coupon rate = 6% → annual coupon = $60.
- Suppose market price = $1,100 (premium).
- Current yield = 60 / 1,100 = 0.054545 = 5.4545%.
- Approximate YTM (5-year example) using the approximation YTM ≈ (coupon + (par − price)/n) / ((par + price)/2):
  - (60 + (1000 − 1100)/5) / ( (1000 + 1100)/2 ) = (60 − 20) / 1050 = 40 / 1050 = 0.038095 = 3.8095%.
- Ordering: coupon rate 6% > current yield 5.4545% > YTM 3.8095%.

4. Why the correct answer is correct
- The coupon rate is measured against par, current yield against a higher market price (thus lower), and YTM incorporates the capital loss to par (thus lowest). Therefore coupon rate > current yield > YTM for a premium bond.

5. Why other options are incorrect
- A: YTM > current yield > coupon rate — this would imply coupon rate is smallest, which describes a discount bond scenario, not a premium bond.
- B: coupon = current yield = YTM — true only for a par bond (price = par), not a premium bond.
- C: coupon rate > YTM > current yield — places YTM above current yield; for a premium bond the capital loss makes YTM the lowest, so this ordering is wrong.

6. Conclusion
- The correct ordering for a premium bond is coupon rate > current yield > yield to maturity, which matches answer D.

Which one of the following applies to a premium bond?单项选择题

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