Why a Bond Purchased Above Par Has a Lower Yield Than Its Coupon

Summary

The question asks how a bond with a 7% coupon could yield about 6.7% when purchased for 101 per 100 of face value. It tries to reproduce the quoted yield by discounting coupon and principal payments, but the result depends on the timing assumed for the first coupon and the bond’s call date. The distinction is between the coupon rate, calculated from face value, and yield, which relates the purchase price to the scheduled cash flows.

The accepted response cautions against treating a coupon as arriving immediately at no discount and says the stated yield is only approximate. The excerpt does not supply a full cash-flow schedule, settlement date, or detailed yield calculation, so it cannot establish the exact yield. To verify the figure, one needs the dates and amounts of each payment, the redemption or call assumptions, and the yield convention used.

Key ideas

• A bond’s coupon rate is based on face value, while its yield reflects the purchase price and cash-flow timing.
• Paying above par generally lowers the yield relative to the coupon rate, all else equal.
• The timing assigned to the first coupon affects a discounted cash-flow calculation.
• The excerpt lacks enough schedule and convention details to verify the quoted yield precisely.

Tags

# How are they getting a 6,7 % yield in this article?


# How are they getting a 6,7 % yield in this article?












Ì am reading this article:

https://www.sterling.com.jm/blog/difference-between-yield-and-interest-rate

They write:

> A large French Bank has a bond with a 7% coupon and a 2028 call date. If you pay US 100 for US 100 worth of this bond, you will have both a 7% yield and a 7% interest rate. If you pay US 101 for US 100 worth of this bond, you will enjoy a 6.7% yield.

I am wondering how they get the 6,7 % yield?

I was thinking something like this:

The article is from december 2022, so the first payment is in 2023? But I get:

$7+7/1,067+7/1,067^2+7/1,067^3+7/1,067^4+107/1,067^5=108,24$.

If I assume the first payment is in 2022 I get:

$7+7/1,067+7/1,067^2+7/1,067^3+7/1,067^4+7/1,067^5+107/1,067^6=108,44$.

Could you please help me?

## Answer by KaiSqDist (score 3, accepted)

https://quant.stackexchange.com/a/80668

I don't think you should get a coupon payment immediately (no discount).

The yield is not 6,7%, but it is pretty close.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.