# How to Calculate Bond Convexity

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Convexity is one of several tools used to evaluate the volatility of a bond portfolio. It measures how sensitive the term of a bond is to a change in its interest rate. The convexity is positive when terms shorten because of rises in the interest rate or when terms lengthen because the rates have fallen. The convexity is negative in reverse situations. A bond that has less sensitivity to interest rate changes will have a higher convexity than a bond with more sensitivity.

### Things You'll Need

• Pencil
• Paper
• Calculator

Use an online source (see resources) or a newspaper such as the Wall Street Journal or Barron's to find the information you will need to calculate your bond's convexity.

Calculate the convexity of a bond by using an online tool (see resources). You will need information on the bond's par value, its coupon rate expressed as a percentage, the number of elapsed coupons, the number of remaining coupons, its yield expressed as a percentage and the frequency.

Manually calculate the approximate convexity using a simplified formula such as:

convexity equals (B3 + B2 - 2 B1) ÷ 2 B1((I2-I1)(I2-I1)). B1 is the initial bond price, B2 is the bond price when interest rates increase, B3 is the bond price when rates decrease, I2 is the new interest rate and I1 is the old interest rate. Both interest rates are expressed in decimal form.

For example, if interest rates increase from 3.5% to 3.8%, the original bond price is \$10,000 and the new bond price is \$9,600, then the approximate convexity is -5.77.

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