Bond duration convexity and yield shock calculator

Duration weights the cash-flow dates

Macaulay duration is the present-value-weighted average time to payment. A coupon bond returns some value before maturity, so its duration is usually shorter than its final maturity. A zero-coupon bond is a useful boundary check because all of its payment arrives at maturity.

Modified duration converts that timing measure into a first-order price sensitivity for the selected nominal-yield convention. A one-percentage-point move is entered as one in the form but becomes 0.01 in the sensitivity formula.

The XIRR and XNPV dated cash flow calculator solves an investor’s dated cash-flow rate. This bond model instead prices regular scheduled coupons at an entered nominal yield and examines local yield sensitivity.

Convexity improves a local approximation

Duration alone models a straight price response around the original yield. Convexity adds curvature. The page calculates both an approximation and a complete repricing at the shocked yield so the difference is visible rather than assuming the approximation is exact.

The convexity expression is analytic for the stated periodic fixed-cash-flow bond. It is not a finite-difference estimate from live market quotes. Bigger yield moves can still produce larger approximation errors, especially when the initial yield and maturity differ substantially.

Keep the settlement convention visible

Settlement is assumed to fall exactly on a coupon date. There is no accrued interest or fractional first coupon period, and the displayed price uses only the remaining regular payments. Actual bond quotations may use another settlement date and day-count rule.

Default risk, callability and changes in market spreads are not modelled. A price sensitivity to a parallel yield move does not establish credit quality or a likely trading return. Use the cash-flow table to check the mechanical model before comparing it with an actual security.

Work through the example

A five-year annual 5 percent coupon bond with face value 100 and yield 5 percent prices at par. Raising its yield to 6 percent lowers the exact price to about 95.79.

Use the worked table to trace where each input enters. Then change one assumption and calculate again, leaving the others fixed. A comparison is easier to interpret when the change has one identifiable cause rather than a different set of measurements, dates and rates all at once.

What this model does not establish

Plain noncallable fixed-coupon bullet bond; coupon-date settlement and whole-year maturity. Nonnegative original and shocked yields. No accrued interest, default, spread curve, irregular coupon, embedded option or live market valuation.

Keep the input assumptions with any exported result. Illustrative values do not become observations merely because the output is precise. For a real purchase, financial reconciliation or technical decision, check the underlying records and applicable requirements before treating this scenario as a final answer.