# 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?

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Where does that come from? CFA exercises? – SRKX Mar 28 '13 at 13:06
It comes from the book 'Essentials of Financial Management' – Ong Junjie Mar 29 '13 at 2:17

(a) is false

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

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

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Wow ! Nice one. – user1627466 Mar 29 '13 at 12:20
The answer would be more complete if you restated the definitions of the 3. – SRKX Mar 29 '13 at 17:16

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

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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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