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Bond Convexity Calculator

Calculate bond convexity to evaluate interest rate risk and price curves.

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Calculation Parameters

Specify your inputs below.

Calculated Result

Bond Convexity Measure 18.80
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Expert Tip

Convexity is a useful risk management tool, accounting for the curvature of the bond price-yield curve where duration is not constant.

How this Calculator Works

This calculator computes bond convexity, which measures the curvature of the relationship between bond prices and interest yields. Because duration only provides a linear approximation, convexity is used to improve the accuracy of price changes during large interest rate fluctuations.

Formula & Methodology

Convexity = [ Sum (t^2 + t) * C_t / (1 + r)^t ] / [ Price * (1 + r)^2 ] - C_t is the cash flow at time t. - r is the discount rate per period. - Price is the current bond price.

Step-by-Step Calculation Example

Here is a step-by-step example showing how the calculations are performed:

A 2-year bond pays a $50 coupon annually. Discount rate is 5%. Par value is $1,000. Price is $1,000. 1. Year 1 (t=1): (1^2 + 1) * $50 / 1.05^1 = 95.24. 2. Year 2 (t=2): (2^2 + 2) * $1,050 / 1.05^2 = 5,714.28. 3. Sum components: 95.24 + 5,714.28 = 5,809.52. 4. Divide by Price * (1 + r)^2: 5,809.52 / [ 1,000 * 1.05^2 ] = 5.27. Result: The bond convexity is 5.27.

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Detailed Insights & Expert Guide

ℹ️ About this Calculation

This fixed income and debt investment calculator analyzes bond pricing, coupon yield to maturity (YTM), Macaulay/modified duration, credit risk spreads, and debt coverage ratios based on Wall Street fixed income analytics.

Variable Glossary

Input

Fixed Income Data

Par value ($1,000), coupon rate %, payment frequency, maturity years, corporate credit spread, or tax rate %.

Parameter

Bond Performance

Yield to Maturity (YTM %), present bond price ($), modified duration (years), or Tax-Equivalent Yield (TEY).

How to Calculate Step-by-Step

1

Step 1

Input bond face value, annual coupon interest rate, or corporate credit default swap (CDS) basis points.

2

Step 2

Select payment schedule frequency (annual, semi-annual) and years remaining until maturity date.

3

Step 3

Review calculated yield to call/maturity, interest rate sensitivity duration, or debt service coverage (DSCR).

FAQ

How does bond duration measure interest rate risk?
Modified duration estimates the approximate percentage change in a bond's price for a 1% (100 bps) shift in interest rates. Higher duration indicates greater price sensitivity to rate moves.
What is Tax-Equivalent Yield (TEY) for municipal bonds?
Tax-Equivalent Yield = Municipal Tax-Exempt Yield / (1 - Marginal Tax Rate). It shows the pre-tax yield a taxable bond would need to equal the after-tax yield of a tax-free municipal bond.
Can fixed income calculators guarantee bond trading outcomes?
No. Bond pricing models assume clean compounding yields and fixed reinvestment rates. Secondary market prices fluctuate based on liquidity, credit rating revisions, and market interest rate movements.