When interest rates rise, bond prices fall. When they fall, bond prices rise. This inverse relationship is the most important rule in fixed income — and a single measure called duration tells you exactly how much price risk you are carrying. In April 2026, with 30-year Treasury yields hovering near 5%, understanding these mechanics has never been more practical.
What Is a Bond?
A bond is a loan you make to a borrower — a corporation, the U.S. Treasury, or a municipality. In return, the borrower promises to pay you periodic coupon payments (interest) plus repayment of the face value (also called par value, typically $1,000) when the bond matures. The coupon rate is expressed as a percentage of face value; a 4% coupon on a $1,000 bond pays $40 per year, or $20 every six months.
As SEC Investor.gov explains, bonds carry several risks — but the one that catches most new investors off guard is interest rate risk: the fact that a bond’s market price changes every time interest rates move.
The Inverse Rule: Why Bond Prices Move
Imagine you buy a newly issued $1,000 Treasury note paying 4%. One year later, the Fed has raised rates and new notes now pay 6%. Who wants to buy your old 4% bond at face value? Nobody — unless its price drops enough to make the yield competitive with the current 6% rate. The price falls until a buyer earns 6% on the lower purchase price. This is the inverse relationship in action.
Conversely, if rates fall to 2%, your 4% bond looks very attractive. Its price rises above $1,000 — to a premium. FINRA states the rule plainly: “When interest rates rise, bond prices generally fall. When interest rates fall, bond prices generally rise.”
Yield to Maturity: The Whole Return Story
The yield to maturity (YTM) is the total annualized return you earn if you buy a bond today and hold it until it matures, assuming all coupon payments are reinvested at the same rate. YTM accounts for both the coupon income and any capital gain or loss between your purchase price and par value at maturity.
- Bond at par ($1,000): YTM equals the coupon rate.
- Bond at a discount (below $1,000): YTM > coupon rate — you earn extra from buying cheap.
- Bond at a premium (above $1,000): YTM < coupon rate — you overpay, which reduces your realized return.
Worked example. You pay $914 for a $1,000 bond with a 4% annual coupon and 5 years to maturity. Your YTM is approximately 5.93% — higher than the 4% coupon because that $86 discount accretes toward par over 5 years.
Bond Pricing: The Math Behind the Inverse Rule
Bond price equals the present value of all future cash flows. For a bond paying a semiannual coupon C over n semiannual periods at a yield of y per period:
Price = Σ [C ÷ (1+y)^t] + FaceValue ÷ (1+y)^n
t = 1 to n
For a concrete illustration, take a $1,000 bond with a 4% annual coupon (semiannual $20 payments) and a 10-year maturity:
- At 4% yield: Price = $1,000 (par)
- At 6% yield: Price ≈ $851 — a 14.9% decline
- At 2% yield: Price ≈ $1,181 — an 18.1% gain
The chart below plots the full price-yield curve for this bond. Notice the curve is not a straight line — it bows outward. That curvature has a name: convexity, discussed below.
Duration: Your Interest Rate Sensitivity Meter
Duration is a single number — expressed in years — that tells you how sensitive a bond’s price is to changes in interest rates. As FINRA describes it: duration “signals how much the price of your bond investment is likely to fluctuate when there’s an up or down movement in interest rates.”
There are two related versions:
Macaulay Duration
The weighted average time — in years — until you receive all of a bond’s cash flows, where each payment is weighted by its present value. A bond that returns most of its value at maturity (low coupon) has a longer Macaulay Duration. A zero-coupon bond’s Macaulay Duration equals its maturity exactly, because there are no interim cash flows at all.
Modified Duration
The practical tool. Modified Duration tells you the approximate percentage price change per 1% (100 basis point) move in yield:
Modified Duration = Macaulay Duration ÷ (1 + yield / periods per year) Price Change % ≈ −Modified Duration × Change in Yield
Worked example. The 10-year Treasury note currently yields about 4.34%. A 10-year note trading at par carries a Macaulay Duration of roughly 8.25 years and a Modified Duration of approximately 8.07 years. If yields rise by 1 percentage point:
- Expected price decline ≈ 8.07 × 1% = 8.07%
- On a $10,000 position, that’s a paper loss of roughly $807
The 30-year T-bond, currently yielding ~4.94%, carries a Modified Duration of approximately 17.5 years. A 1% yield rise implies a price decline of roughly 17.5% — over $1,750 on a $10,000 position. This explains why long-duration bond funds have been among the most volatile assets since the Federal Reserve began raising rates in 2022.
| Security | Current Yield | Approx. Mod. Duration | Est. Price Drop per 1% Yield Rise |
|---|---|---|---|
| 3-Month T-Bill | 3.59% | ~0.25 yr | ~0.25% |
| 5-Year T-Note | 3.95% | ~4.3 yr | ~4.3% |
| 10-Year T-Note | 4.34% | ~8.1 yr | ~8.1% |
| 30-Year T-Bond | 4.94% | ~17.5 yr | ~17.5% |
| 10-Year Zero-Coupon Bond | N/A | 10.0 yr | ~10.0% |
Convexity: Why Duration Is Only an Approximation
Duration predicts price changes as if the price-yield relationship were a straight line. As the chart above shows, it isn’t — the real curve bows outward. That curvature is convexity. The full price-change approximation is:
ΔPrice% ≈ (−Duration × Δy) + (½ × Convexity × Δy²)
Two things to know about convexity for standard bonds:
- It always works in your favor. Convexity means the curve bends toward you. When rates fall, prices rise faster than duration predicts. When rates rise, prices fall less than duration predicts. This is a desirable property, and bonds with higher convexity command a small pricing premium.
- It matters most for large rate moves. For a 25-basis-point shift, the convexity term (½ × Convexity × 0.0025²) is tiny. For a 200-basis-point move, ignoring convexity produces meaningful errors — the straight-line approximation overstates the price decline.
An analogy: duration is the best straight-line estimate of how far you travel on a curved road. Convexity accounts for the bend. For short distances, the straight line suffices. Over long hauls, you need to know the road curves.
What This Means Right Now
With 10-year Treasury yields at 4.34% and 30-year yields near 5% (as of late April 2026, per Yahoo Finance), duration risk is tangible. A long-duration Treasury fund tracking 20-to-30-year bonds carries a modified duration of roughly 16–18 years. A 1 percentage point further rise in long-end yields would subtract approximately 16–18% from that fund’s price — far exceeding the current annual coupon income. The math explains why bond fund investors experienced steep losses during the 2022–2023 rate-hiking cycle, the fastest in four decades.
Investors who shortened their bond duration — moving from 30-year Treasuries to 3-month T-bills — captured the current 3.59% yield with almost zero interest rate exposure. The trade-off: no upside if yields fall. Understanding duration lets you make that choice consciously.
Common Mistakes
- Confusing coupon rate with yield. The coupon is fixed at issuance. Yield fluctuates every second in the market.
- Treating Treasuries as “safe” from price volatility. Treasuries have zero credit risk but very real duration risk at long maturities. A 30-year T-bond can lose more in price than a high-yield corporate bond in a rising-rate environment.
- Applying duration to large rate moves without a convexity correction. For moves above 1%, the linear approximation overstates losses.
- Assuming YTM equals realized return. YTM assumes coupons are reinvested at the same rate. In a falling-rate environment, reinvestment income is lower, so realized returns fall short of the original YTM.
What to Learn Next
- The Yield Curve Explained — what the shape of the yield curve signals about the economy and recession risk
- Credit spreads and bond ratings — why corporate bonds yield more than Treasuries and what that premium compensates for
- Bond fund strategies — duration targeting, laddering, and how fund managers manage rate exposure
Sources
- SEC Investor.gov — Introduction to Bonds
- FINRA — Understanding Bonds: Interest Rate Risk and Duration
- Yahoo Finance — U.S. Treasury Yields, April 28, 2026
Disclosure: This article was produced with AI assistance and reviewed before publication. It is for informational purposes only and is not investment advice.