When Yield to Maturity Exceeds Coupon Rate: Current Yield and Price

Summary

The discussion asks whether a bond’s current yield must exceed its coupon rate whenever its yield to maturity is higher. It also considers the related claim that a bond with yield to maturity above its coupon rate trades below its maturity value. The accepted response points out a boundary case: a zero-coupon bond has a current yield of zero, equal to its coupon rate, so the strict inequality in the first claim does not hold.

That counterexample clarifies why the two statements need not have identical truth conditions. For a coupon-paying, straight option-free bond, the other replies assert that the first relationship does hold: a price below par makes annual coupon divided by price greater than the coupon rate. The thread also notes that embedded options can complicate such relationships. It is a conceptual discussion rather than a full proof, and the replies conflict in scope; conclusions should therefore be tied to bond type and assumptions, particularly whether coupons are positive and the bond is option-free.

Key ideas

• A zero-coupon bond is a counterexample to a strict claim that current yield must exceed coupon rate.
• Current yield equals annual coupon payment divided by the bond’s current price.
• For a coupon-paying straight bond priced below par, current yield exceeds the coupon rate.
• Embedded options may alter the relationship, so bond structure and assumptions matter.

Tags

# YTM and current yield


# YTM and current yield












Which of the following statements is correct?

a. If a bond’s yield to maturity exceeds its coupon rate, the bond’s current yield must also exceed its coupon rate.

b. If a bond’s yield to maturity exceeds its coupon rate, the bond’s price must be less than its maturity value.

The correct answer is b. I would like to know why option a is incorrect.

If bond price is less than maturity value, then current yield = (annual coupon payment)/(current bond price) > coupon rate. Is there anything wrong with this reasoning?

## Answer by ikh (score 1, accepted)

https://quant.stackexchange.com/a/7635

(a) is false

Consider a zero coupon bond. Yield to maturity clearly exceeds the coupon rate, but

$$ Y_\text{current} = 0 = \text{Coupon} $$

while the question asks about a strict inequality.

## Answer by user1627466 (score 0)

https://quant.stackexchange.com/a/7632

No you're right. If YTM > coupon rate, then the bond is selling below par and therefore current yield > coupon rate.

## Answer by jeff m (score 0)

https://quant.stackexchange.com/a/7633

If you're talking about a straight, option-free bond, then A is absolutely correct. It's rather easy to prove doing the math. However, if it's not a straight bond then you may have cases where A wouldn't be true(puttable bonds in some cases), but then B would be false in those cases as well. I think you need to burn whatever book you're reading.

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