Bond Convexity Calculator - Duration and Convexity

Bond Convexity Calculator estimates the curve in a bond's price-yield relationship by comparing the current price with two prices from equal yield shocks. Use it when you already have model prices, broker analytics, or spreadsheet repricing for a fixed-income position and want to test whether duration alone is too flat for the rate move you are considering.

• • Rate-shock review: Compare the estimated price move for a bond or portfolio when yields rise or fall by a scenario amount.
• • Duration check: Measure effective duration from the same shocked prices before adding the convexity adjustment.
• • Bond comparison: Compare two bonds that have similar duration but different curvature around the current yield.
• • Model audit: Check whether a pricing model's up-yield and down-yield outputs imply reasonable convexity.

Convexity is useful because bond price changes are not perfectly straight as yields move. Duration gives the first-order slope; convexity adds the second-order curve. With positive convexity, the estimate usually shows a slightly smaller loss when yields rise and a slightly larger gain when yields fall than duration alone would show.

Keep the inputs on one pricing basis. If your current price is clean, use clean prices for the up-yield and down-yield cases. If your model includes accrued interest, option adjustments, or spread shifts, keep that same convention across all three prices.

This calculator is for scenario analysis, not a buy, sell, or hold recommendation. It does not forecast interest rates, credit spreads, liquidity, taxes, settlement, reinvestment, or executable prices. Treat the output as a sensitivity estimate that belongs beside the bond's offering documents and your own risk limits.

For base yield and cash-flow work before this risk step, the Bond Calculator gives a broader bond-pricing workflow.

The calculator uses symmetric repricing around the current yield. Enter the price if yield falls by Δy, the price if yield rises by Δy, and the current price.

• P0: Current bond price on the same pricing basis as the shocked prices.
• Pdown: Price after the yield falls by the one-sided repricing shock.
• Pup: Price after the yield rises by the same one-sided repricing shock.
• Δy: One-sided yield shock as a decimal rate. A 100 bps shock is 0.01.
• scenarioΔy: The yield change you want to estimate after duration and convexity are calculated.

The yield shock is entered in basis points because bond-market moves are commonly discussed that way. A 25 bps shock is 0.0025 as a decimal yield change. The shock should be the same one used to generate both repriced values.

NYU Stern valuation notes describe bond value as discounted expected cash flows and use duration to measure interest-rate sensitivity. That present-value relationship is why a price-yield curve can be summarized with duration and convexity around a starting point.

If you need to translate a rate move before entering it here, the Basis Point Calculator keeps basis points, percentage points, and decimal rates aligned.

These concepts help you read the output without treating one metric as the whole bond-risk story.

Duration and convexity are local estimates. They describe behavior around the current price and the shock size you supplied. If the bond's credit spread changes, the yield curve twists, or embedded-option assumptions change, the realized price can differ from this approximation.

Do not confuse convexity with yield. Current yield measures annual income relative to price, while convexity measures price curvature around a yield shock. A high-yielding bond can still have weak convexity, high credit risk, or limited liquidity.

When income yield is the immediate question, the Bond Current Yield Calculator is the closer tool.

Use the Bond Convexity Calculator after you have three comparable prices from a bond model, quote system, or spreadsheet. The calculator does not create those prices; it turns them into a duration and convexity estimate.

1. 1 Enter the current price: Use the bond price that anchors the scenario. Keep clean or dirty price treatment consistent.
2. 2 Enter the down-yield price: Use the price from a lower yield by the stated repricing shock.
3. 3 Enter the up-yield price: Use the price from a higher yield by the same repricing shock.
4. 4 Set the shock size: Enter the one-sided repricing shock in basis points, such as 25, 50, or 100.
5. 5 Add a scenario move: Enter the yield change you want to estimate. Positive values are rising yields; negative values are falling yields.
6. 6 Read the estimate: Compare duration-only price change with the convexity-adjusted result before using the scenario price.

Suppose a portfolio note says a municipal bond has a current model price of 980, a price of 1,018 after a 50 bps yield decline, and a price of 943 after a 50 bps yield increase. Enter those values and use -75 bps as a falling-rate scenario. The calculator estimates duration near 7.6531, convexity near 40.8163, and a scenario price near 1,037.38. That output is a rate-risk estimate, not a tax-adjusted return.

If you are comparing municipal income with taxable alternatives, the Taxable Equivalent Yield Calculator can help keep yield context separate from price-risk context.

A convexity estimate helps when a duration-only shortcut is too flat for the yield move you are testing. It is especially useful for longer maturities, larger rate scenarios, and securities where option behavior can change cash-flow timing.

• • Better rate-scenario notes: Show the duration-only move and the convexity adjustment side by side in investment memos or risk reviews.
• • Clearer bond comparisons: Two bonds can have similar duration but different convexity, which can matter during larger yield moves.
• • Model output checks: Large, tiny, or negative convexity values can prompt a review of pricing inputs, call assumptions, or cash-flow treatment.
• • Cleaner communication: Basis-point inputs and percent outputs make the result easier to share with treasury, investment, or advisory teams.
• • Scenario discipline: Separating current price, shocked prices, and scenario yield change reduces the chance of mixing model inputs with forecast assumptions.

The output is most useful when you already have reliable shocked prices. It gives a compact explanation of why a bond's estimated gain from falling yields may not mirror the estimated loss from rising yields.

Convexity also helps with post-trade review. If a bond's realized price move was far from the duration-only estimate, compare the size of the yield move, the convexity adjustment, spread movement, liquidity, and any call or prepayment behavior.

A convexity scenario is not the same as realized performance because it leaves out coupon income, purchase price, sale price, and the actual holding period.

For realized total-return work after coupon income and sale price are known, use the Holding Period Return Calculator instead of treating a convexity scenario as performance.

Several inputs and market conventions affect how much trust to place in the convexity result.

• • The calculator does not compute the three bond prices from coupon, maturity, call schedule, day count, or yield curve. It needs comparable prices supplied by a model, quote system, or spreadsheet.
• • The estimated scenario price is an approximation around the current yield. For large rate moves, stressed credit conditions, or option-embedded securities, rerun the bond model at the scenario yield.

FINRA's investor alert on duration explains that duration estimates how much bond value may change when interest rates rise or fall, and that higher duration means more interest-rate sensitivity. Convexity refines that idea, but it does not remove other bond risks.

SEC Investor.gov's bond overview notes that interest-rate changes can affect bond value and that selling before maturity may produce a price above or below face value. That is why the scenario price should be read as market-risk context, not as a maturity payoff.

For long-horizon portfolio decisions, remember that fees, coupon reinvestment, taxes, and credit selection still matter.

When fee drag is part of the fixed-income product comparison, the Investment Fees Calculator can sit beside this convexity estimate.