Coupon Effect on Price Sensitivity
Coupon Effect on Price Sensitivity
A bond paying a high coupon will swing less in price when yields change. A bond paying a low coupon will swing more. The coupon directly determines interest-rate risk.
Key takeaways
- A lower-coupon bond has more of its return concentrated in the principal repayment at maturity, making it more sensitive to discount-rate changes.
- A higher-coupon bond receives more of its return as near-term cash flows, buffering it from rate changes.
- A zero-coupon bond is the extreme: all return is at maturity, so it is the most price-sensitive bond of any given maturity.
- For bonds with the same maturity, the lower-coupon bond will experience a larger price decline when yields rise.
- This is why TIPS, zeros, and other low-coupon securities are riskier than higher-coupon Treasury or corporate bonds with the same maturity.
Why coupon affects sensitivity: the return structure
Every bond's total return comes from two sources: coupon income and principal appreciation or depreciation. A bond paying a high coupon receives a large portion of its return immediately as cash. A bond paying a low coupon receives most of its return as the principal repayment at the end.
This difference matters when yields change. When yields rise, all bonds lose value. But a high-coupon bond has already collected a substantial amount of coupon cash, reducing its dependence on principal repayment. A low-coupon bond depends almost entirely on principal repayment, so it is exposed to a larger portion of the discount-rate change.
Comparing two bonds: high-coupon vs. low-coupon
Let us compare two 5-year bonds, both with face value $1,000, but with different coupons:
Bond A: 5% coupon
- Annual coupon: $50
- Cash flows: $50, $50, $50, $50, $1,050
- At 5% yield: Price = $1,000 (par)
Bond B: 1% coupon
- Annual coupon: $10
- Cash flows: $10, $10, $10, $10, $1,010
- At 5% yield: Price = ?
For Bond B at 5% yield: $10 / 1.05 + $10 / 1.05^2 + $10 / 1.05^3 + $10 / 1.05^4 + $1,010 / 1.05^5 = $9.52 + $9.07 + $8.64 + $8.23 + $791.09 = $826.55
Now suppose yields rise to 6%. What happens to each bond?
Bond A at 6% yield: $50 / 1.06 + $50 / 1.06^2 + $50 / 1.06^3 + $50 / 1.06^4 + $1,050 / 1.06^5 = $47.17 + $44.50 + $42.01 + $39.67 + $784.59 = $957.94
Price change: $957.94 - $1,000 = -$42.06 or -4.2%
Bond B at 6% yield: $10 / 1.06 + $10 / 1.06^2 + $10 / 1.06^3 + $10 / 1.06^4 + $1,010 / 1.06^5 = $9.43 + $8.90 + $8.40 + $7.92 + $754.13 = $788.78
Price change: $788.78 - $826.55 = -$37.77 or -4.6%
The low-coupon bond (Bond B) experienced a larger percentage decline (-4.6% vs. -4.2%) even though both experienced the same yield increase (100 basis points). This is the coupon effect: lower coupon means higher price sensitivity.
With a larger yield increase (say, to 8%), the gap widens even further. Bond A falls to around $920 (8% decline), while Bond B falls to around $740 (10.5% decline). The low-coupon bond is riskier.
Zero-coupon bonds: the extreme case
A zero-coupon bond has a 0% coupon. It pays no interim cash flow and returns only the face value at maturity. All return comes from the discount at purchase. This makes zeros the most price-sensitive bonds.
Consider a 5-year zero with face value $1,000. At a 5% yield, the price is:
$1,000 / 1.05^5 = $783.53
At a 6% yield, the price is:
$1,000 / 1.06^5 = $747.26
Price change: $747.26 - $783.53 = -$36.27 or -4.6% for a 1% yield increase.
Compare this to Bond B (1% coupon) above, which fell -4.6% for the same yield increase. The zero and Bond B are nearly tied in this case. (The zero is slightly more sensitive in absolute terms, but the percentage impact is similar because Bond B is also heavily dependent on principal repayment.)
Now extend the maturity to 20 years. A 20-year zero at 5% yield:
$1,000 / 1.05^20 = $376.89
At 6% yield:
$1,000 / 1.06^20 = $311.80
Price change: $311.80 - $376.89 = -$65.09 or -17.3% for a 1% yield increase.
The long-maturity zero is extremely price-sensitive. This is why zero-coupon bonds (including TIPS and Treasury Strips) are considered high-risk for interest-rate movements, even though they are backed by the US government. The coupon effect is dramatic.
Real-world example: TIP bonds vs. Treasury bonds
Treasury Inflation-Protected Securities (TIPS) have a coupon that adjusts with inflation, but the base coupon is often quite low (1–2%). Traditional Treasuries might pay 3–4%. In 2022, when yields rose sharply, TIPS fell hard in price because their low coupons made them sensitive to the discount-rate increase. Investors who expected TIPS to be safer because they protect against inflation were surprised by short-term price declines. The low coupon was the culprit.
Similarly, long-term Treasury bonds (30-year Treasury, or TLT in fund form) fall more sharply than intermediate-term bonds (TLH, Vanguard Intermediate-Term Treasury) when yields rise, partly because their longer maturity extends the sensitivity, but also because their coupons are lower relative to the yield increase.
Why this matters for portfolio construction
Understanding the coupon effect is essential for managing risk. If you want a stable, low-volatility bond fund, you avoid low-coupon and long-maturity bonds. If you are building a portfolio and yields are about to rise (or you expect them to), bias toward higher-coupon bonds. If you expect yields to fall, low-coupon bonds offer greater capital-appreciation potential because their price swings are larger in both directions.
For income investors, higher-coupon bonds are attractive because you collect more cash annually. For total-return investors, lower-coupon bonds can offer higher capital gains if yields fall. The coupon is not just a payment; it is a key determinant of interest-rate risk.
Flowchart
Next
The coupon effect tells us that low-coupon bonds are more sensitive to yield changes. But there is another dimension that makes bonds even more sensitive: maturity. A long-maturity, low-coupon bond is doubly exposed to interest-rate risk. In the next article, we explore how longer maturities compound the price sensitivity beyond what coupon alone determines.