Maturity Effect on Price Sensitivity
Maturity Effect on Price Sensitivity
A 30-year bond will swing wildly in price when yields change. A 2-year bond will barely move. Maturity is the dominant factor determining interest-rate risk.
Key takeaways
- Longer-maturity bonds are more price-sensitive to yield changes because the discount-rate change affects cash flows far into the future.
- A 1% yield change on a 30-year Treasury might move the price 15–20%. The same 1% change on a 2-year Treasury moves the price only 1–2%.
- The relationship is not linear: doubling maturity more than doubles the price sensitivity (an acceleration effect).
- This is why bond duration (a measure of weighted-average maturity) is the standard metric for interest-rate risk.
- For conservative investors, shorter-maturity bonds offer greater price stability, albeit at the cost of lower yields.
The mathematics of maturity and discounting
The present-value formula shows why maturity matters. The price of a bond is:
P = \sum_{t=1}^{n} \frac{C}{(1+y)^t} + \frac{FV}{(1+y)^n}
The exponent n appears in the denominator, raising (1 + y) to an increasingly large power as maturity lengthens. A cash flow 30 years away is discounted by (1 + y)^30. A 1% increase in y dramatically reduces (1 + y)^30 compared to (1 + y)^2.
Example: (1.05)^2 = 1.1025, and (1.06)^2 = 1.1236. The ratio is 1.019, or about 2% change.
Contrast: (1.05)^30 = 4.3219, and (1.06)^30 = 5.7435. The ratio is 1.329, or about 33% change.
A 1% yield increase raises the discount factor for 30-year cash flows by about 33%, versus only 2% for 2-year cash flows. This is why long bonds are so much more volatile.
Comparing bonds of different maturities
Let us compare three Treasury bonds, all with a 4% coupon and face value $1,000, but different maturities:
2-Year Treasury:
- At 4% yield: Price = $1,000 (par, coupon equals yield)
- At 5% yield: Price ≈ $981
Price change: -$19 or -1.9%
10-Year Treasury:
- At 4% yield: Price = $1,000 (par)
- At 5% yield: Price ≈ $922
Price change: -$78 or -7.8%
30-Year Treasury:
- At 4% yield: Price = $1,000 (par)
- At 5% yield: Price ≈ $828
Price change: -$172 or -17.2%
For the same 1% yield increase, the 2-year bond fell 1.9%, the 10-year fell 7.8%, and the 30-year fell 17.2%. The longer bonds are far more volatile. This is the maturity effect in action.
Why the effect accelerates with maturity
The acceleration is due to the exponential nature of discounting. Adding one more year to a short-maturity bond does not add much price sensitivity; adding one more year to a long-maturity bond adds a lot. The effect is not linear but accelerating.
The reason is intuitive: a very distant cash flow (say, 29 years away) is already discounted heavily. Adding one more year to make it 30 years away increases the discount substantially, because you are raising a large exponent by one. But adding a year to a 1-year cash flow (making it 2 years) does not increase the discount as much.
This is captured in the concept of duration, which measures the weighted-average time to receive a bond's cash flows. Duration is always less than or equal to maturity but rises steeply with maturity. A bond with 30-year maturity might have a duration of 18–20 years, depending on its coupon. A bond with 2-year maturity might have a duration of 1.9 years. The duration difference (18 vs. 1.9) is much larger than the maturity difference (30 vs. 2), reflecting the acceleration of the maturity effect.
Real-world example: 2022 bond market sell-off
In 2022, the Federal Reserve raised its policy rate from near 0% to 4.25%, and long-term yields rose from around 1.5% to 3.9%—a 240 basis point increase. The impact on bond funds was dramatic and varied by maturity:
- Very short-term bonds (1-year maturity): Lost about 1–2% in price.
- Intermediate-term bonds (5–7 year maturity): Lost about 8–10% in price.
- Long-term bonds (20+ year maturity): Lost 15–25% in price.
The same yield increase caused vastly different losses based on maturity. Long-duration funds like TLT (30-year Treasuries) dropped nearly 30% in the first half of 2022. Shorter-duration funds like IEF (7–10 year Treasuries) dropped about 12%. Money market funds (1-year or less) dropped about 1%. The maturity effect explains the disparities.
Volatility and yield curve shape
The maturity effect is also why the yield curve (the graph of yields across all maturities) matters. When the Fed raises short-term rates but long-term yields do not rise as much, the curve flattens. In this case, longer-maturity bonds experience less price decline than they would if yields rose uniformly across all maturities. When the entire curve rises in parallel, longer bonds suffer more.
Curve flattening was observed in 2022: the short end (1-year, 2-year) rose steeply, but the long end (10-year, 30-year) rose less. This meant that longer-bond investors suffered losses (rising yields), but not as much as they would have in a parallel shift. A ladder portfolio (holding a mix of maturities) benefits from curve flattening, as longer bonds hold up better.
Portfolio implications: choosing maturity
The maturity effect has major implications for portfolio construction. Conservative investors or those uncomfortable with volatility should tilt toward shorter-maturity bonds. BND and AGG (broad bond funds) have durations around 5–6 years, giving them moderate rate sensitivity. IEF (7–10 year Treasuries) has a duration around 8 years. TLT (30-year Treasuries) has a duration around 18 years, making it much riskier in a rising-rate environment.
For income-seeking investors, this is a trade-off: longer-maturity bonds typically offer higher yields, but with higher interest-rate risk. A barbell strategy holds both very short and very long bonds, avoiding intermediate maturities. A ladder strategy holds bonds of many maturities, spreading risk evenly. The choice depends on your risk tolerance and interest-rate outlook.
In the current environment (yields around 4–5% across the curve), longer-maturity bonds offer higher yields but expose you to the risk that yields will rise further. Shorter-maturity bonds offer lower yields but greater price stability. The maturity effect quantifies this trade-off.
Flowchart
Next
Now we understand that both coupon and maturity affect price sensitivity. A zero-coupon bond with 30-year maturity is the most volatile bond possible: zero coupons mean all return depends on principal, and 30 years means the principal repayment is far away and heavily discounted. In the next article, we explore the mathematics and behavior of this extreme case.