Bond Duration and Convexity Calculator
Enter a plain fixed-coupon bond and an interest-rate shock to compare duration estimates with a fresh cash-flow valuation. You can start from either yield to maturity or a clean market price.
Exact price after yield change$925.61
- Current bond price
- $1,000.00
- Implied yield to maturity
- 5%
- Macaulay duration
- 7.99 years
- Modified duration
- 7.79 years
- Convexity
- 73.63
- DV01
- $0.78
- Exact price change
- -7.44%
- Duration-only estimated price
- $922.05
- Duration-only error
- -$3.56
- Duration plus convexity estimated price
- $925.74
- Duration plus convexity error
- $0.12
Assumes level fixed coupons, no default, redemption at face value, and a clean price immediately after a coupon date.
Large yield shocks can make both sensitivity estimates materially different from exact cash-flow repricing.
How to use this calculator
- Choose whether the bond’s starting yield or clean market price is known.
- Enter face value, coupon rate, maturity, and the payment frequency stated in the bond terms.
- Enter the known yield or price, then state the parallel yield change in basis points.
- Read the exact repriced value alongside the duration-only and duration-plus-convexity estimates.
How the bond price change is calculated
The calculator treats the bond as a level fixed-coupon security held just after a coupon date. For each remaining payment, it discounts the coupon, and the face value in the final period, at the yield to maturity. If you start with a market price, it uses a bracketed search to find the annual yield that makes those discounted cash flows equal that price.
With face value F, annual coupon rate q, payments per year m, annual yield y, and N = m × T coupon periods, each coupon is c = Fq ÷ m. The clean price is:
P(y) = Σ CFₖ ÷ (1 + y ÷ m)ᵏ
where CFₖ is the coupon before maturity and the coupon plus face value at maturity. Macaulay duration is the present-value-weighted average time to receive those cash flows. Modified duration divides it by 1 + y ÷ m, which gives the first-order sensitivity to a yield change.
For a yield shift Δy, the first-order estimate is P × (1 − modified duration × Δy). The convexity estimate adds 0.5 × convexity × Δy². The exact result shown by the calculator is not an estimate: it discounts every cash flow at y + Δy. The difference between that value and each estimate is the approximation error.
What moves interest-rate sensitivity
Longer maturities normally have greater duration because more value arrives farther in the future. A lower coupon also tends to increase duration, since less cash is returned early. Frequency matters because semiannual and quarterly coupons bring some cash forward and use a periodic yield. DV01 converts modified duration into an approximate dollar change for one basis point, making bonds with different prices easier to compare.
Convexity matters more as the shock becomes larger. Positive convexity means a fixed-rate bond usually loses slightly less than duration predicts when yields rise and gains slightly more when yields fall. It improves the local estimate, but it does not replace exact repricing for a large move.
What this calculation leaves out
This is a clean theoretical price immediately after a coupon date. It excludes accrued interest, settlement timing, bid-ask spreads, taxes, commissions, liquidity, and dealer markups. It also assumes one parallel change in required yield; it does not separate Treasury-rate, credit-spread, or liquidity changes. Callable, putable, convertible, floating-rate, inflation-linked, and amortizing bonds need different cash-flow or effective-duration models.
Worked example
Consider a $1,000 bond with a 5% annual coupon, 10 years remaining, semiannual payments, and a 5% yield. Its coupon is $25 every six months and its current price is $1,000. For a 100-basis-point yield increase, exact cash-flow repricing gives a value of about $925.61.
The bond’s modified duration produces a first-order estimate near $922.05. Adding convexity raises the estimate to about $925.63, much closer to the exact value. The difference is small for this 1% move, but it becomes more important for longer bonds and larger shocks.
Common questions
What is the difference between Macaulay and modified duration?
Macaulay duration is the present-value-weighted average time until a bond pays its cash flows, expressed in years. Modified duration adjusts that value for the yield compounding convention and estimates the percentage price response to a small yield change. Modified duration is the measure used in the calculator’s first-order price estimate.
Why does convexity improve a bond price-change estimate?
Duration draws a straight-line approximation around the current yield, while bond prices follow a curved relationship with yield. Convexity measures that curvature and adds a second-order adjustment. It usually improves the estimate for a fixed-rate bond, especially when the yield move is not small.
How accurate is duration for a 1% interest-rate change?
Duration is a local approximation, so a 1% move can produce a visible error, particularly for long maturities and low coupons. Convexity usually narrows the gap, but exact repricing is the relevant result when the individual bond’s cash flows are known. This calculator displays all three values so the gap is explicit.
What does DV01 mean for an individual bond?
DV01 is the approximate dollar price change from a one-basis-point, or 0.01 percentage-point, increase in yield. The calculator computes it as current price times modified duration times 0.0001. It is a small-move estimate, not a guarantee of the price change for a larger move.
Does duration matter if I hold the bond to maturity?
If the issuer pays as promised and you hold a plain bond to maturity, interim market-price changes do not alter the stated coupons or face value you receive. Duration can still matter if you may sell before maturity, need to report market value, or reinvest coupons at changing rates. Credit risk and inflation can also affect the economic result even when the bond is held to maturity.