How Coupon Size Affects a Bond’s Relative Interest Rate Risk
Summary
The document explains why higher-coupon bonds are generally described as having less interest rate risk, even though larger coupon payments can mean larger dollar losses when rates rise. It separates absolute exposure from relative exposure: dollar changes depend on how much is invested, while percentage sensitivity depends on the timing of the bond’s cash flows. Coupons bring some value forward, reducing the cash flows’ average maturity and typically lowering duration relative to a lower-coupon bond with otherwise comparable features.
The discussion is conceptual and gives no numerical example or full derivation. It frames duration as the key explanation, but does not specify assumptions such as matching maturity, yield, or other bond terms. The simplified coupon-only comparison in the question also omits the principal repayment, which matters when comparing a bond’s total price sensitivity. The takeaway is therefore a general relationship, not a complete risk calculation for every bond.
Key ideas
- Higher coupon payments can increase absolute dollar exposure when more cash is invested in the bond.
- Relative interest rate sensitivity is measured as a price change compared with the bond’s value.
- Higher coupons generally shorten a bond’s duration by shifting more value into earlier cash flows.
- Duration comparisons require other relevant bond characteristics to be held constant.
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Full text
# Interest rate risk of a bond as a function of the coupon
# Interest rate risk of a bond as a function of the coupon
This SEC document claims that increasing the ocupon on a bond decreases the interest rate risk (bottom of page 3):
And the Finra SIE exam states the same also.
I cannot understand the logic behind this statement, it just seems wrong to me. If we consider a simple example where we have a flat interest rate of $r$, and a bond that pays semiannually, then the value of the bond can be written as:
$$ B = \frac{1}{(1+r)^{t_n}} + c \sum_{i=0 \ldots n} \frac{1}{(1+r)^{t_i}}$$
Where if we're just comparing two bonds to each other then, for the sake of comparison, the principal repayment can be ignored, and we can then look at the interest rate risk of the coupons. Here, we can happily say that the rate risk is linear in the coupons, and if we have larger coupons then we must have more risk.
So how is it that the SEC can say that a lower coupon bond has more interest rate risk? What am i missing?
## Answer by Mats Lind (score 3, accepted)
https://quant.stackexchange.com/a/70632
Yes, the point made in the question is true; more fixed coupons all else equal leads to more interest rate risk. More precisely: more fixed coupons trivially (but well spotted) gives you more losses in USD per increase in the quoted market interest rate (in bps for example).
But what SEC refers to is the interest rate risk per invested USD, equal to the relative (in percentage point) loss you make per increase in the rate. And that increases with the maturity of the cashflows and is insensitive to the amount invested.
So the more you dilute the long bullet with the shorter coupons, the less average maturity you have and the less relative interest rate risk.
Still absolute interest risk increases the more you invest.
## Answer by AlRacoon (score 4)
https://quant.stackexchange.com/a/70630
Since duration is the primary risk of a bond, higher coupons tend to decrease the duration, and the risk of the bond.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.