Fixed Income & Treasury Risk Lab

Bond Duration & Convexity Calculator

Calculate Macaulay Duration, Modified Duration, Convexity, and DV01 to measure bond price sensitivity and interest rate risk with exact repricing.

Bond Inputs Yield Sensitivity Matrix Fixed Income Theory FAQ

Fixed Income Presets

Load calibrated bond portfolio structures.

Step 1: Bond Terms, Yield to Maturity & Rate Shock

Bond Characteristics & Rate Shift

📜 Bond Characteristics

📈 Market Yield & Rate Shock

100 basis points (bps) = 1.00% yield shift. Positive shift reflects rising interest rates; negative shift reflects falling interest rates.

Current Bond Price
$980.20
98.02% of Par (Discount)
Macaulay Duration
8.04 Yrs
Weighted average cash flow receipt time
Modified Duration
7.86 Yrs
Convexity: 76.54 | -7.86% per 100 bps
DV01 (Dollar Value of 1 bp)
$0.7704
Dollar Value of 1 Basis Point (0.01% shift)

Interest Rate Risk Sensitivity Matrix (-300 bps to +300 bps)

Compares linear Duration estimates, Convexity-adjusted estimates, and exact DCF repricing across parallel interest rate shifts.

Yield Shift (bps) New YTM (%) Repriced Bond Price ($) Dollar Impact ($) Duration Est (%) Duration + Convexity (%) Exact Repriced (%)

Fixed Income Mathematics

Understanding Duration & Convexity

Key fixed income principles used in portfolio management and banking ALM:

  • Macaulay Duration: Measures the effective maturity of a bond by weighting the present value of each cash flow by the time of its receipt.
  • Modified Duration: Measures the percentage change in bond price for a 100 bps (1.00%) change in yield-to-maturity.
  • Convexity Advantage: Because bond price-yield curves are convex, bond prices rise more when yields drop than they fall when yields rise by the same amount.
  • DV01 (Dollar Value of 01): Measures the exact dollar risk per basis point, vital for interest rate swap hedging and treasury immunization.

Model corporate dividend streams in the Dividend Discount Lab.

Mathematical Formulation

Bond duration equations

Macaulay_Duration (D_Mac) = ( 1 / Price ) × ∑ [ ( t / k ) × CF_t / ( 1 + y / k )^t ]

Modified_Duration (D_Mod) = D_Mac / ( 1 + y / k )

Convexity (Cx) = [ 1 / ( Price × (1 + y/k)^2 ) ] × ∑ [ (t/k)(t/k + 1/k) × CF_t / (1 + y/k)^t ]

ΔPrice / Price ≈ -D_Mod × Δy + 0.5 × Cx × (Δy)^2

DV01 = D_Mod × Price × 0.0001

Evaluate firm bankruptcy exposure in the Altman Z-Score Lab.

FAQ

Bond duration & interest rate risk questions

What is the difference between Macaulay Duration and Modified Duration?

Macaulay Duration measures the weighted average time (in years) required to receive all coupon and principal cash flows from a bond. Modified Duration converts Macaulay Duration into a direct percentage price sensitivity metric for a 1% change in yield-to-maturity: Modified Duration = Macaulay Duration / (1 + y/k).

Why is Convexity important when measuring bond price changes?

Duration provides only a linear first-order approximation of bond price changes. Because the true price-yield curve is convex (curved), Duration underestimates price increases when yields fall and overestimates price drops when yields rise. Convexity adds a second-order correction to provide an accurate estimate.

What is DV01 (Dollar Value of 01)?

DV01 (Dollar Value of a Basis Point) is the dollar price change of a bond resulting from a 1 basis point (0.01%) parallel shift in yield: DV01 = Modified Duration x Bond Price x 0.0001.

Why does a zero-coupon bond have a duration equal to its maturity?

Because a zero-coupon bond makes no intermediate coupon payments, 100% of its cash flow is received at maturity. Therefore, its Macaulay Duration exactly equals its years to maturity.

Can I export the bond duration and interest rate sensitivity audit to CSV?

Yes. You can export complete Macaulay duration, Modified duration, Convexity, DV01, and yield shift revaluation tables across -300 bps to +300 bps as a UTF-8 CSV spreadsheet with formula defense.

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