Question

You have a 25-year maturity, 10% coupon, 10% yield bond with a duration of 10 years and a convexity of 135. If the interest rate were to increase 125 basis points, your predicted price change for the bond (including convexity) is

Answer 1

The price change for the bond is -10.31%

Step-by-step explanation:

Use the following formula to calculate the price change for the bond

Price change of bond = ( -Modified duration x Change in rate ) + ( 0.5 x Convexity x ( Change in rate )^2 )

Where

Modified duration = Duration / ( 1 + YTM ) = 10 years / ( 1 + 10% ) = 9.0909091

Change in rate = 125 basis point / 100 = 1.25%

Convexity = 135

Placing Values in the formula

Price change of bond = ( -9.0909091 x 1.25% ) + ( 0.5 x 135 x ( 1.25% )^2 )

Price change of bond = -0.11364 + 0.01055

Price change of bond = -0.10309

Price change of bond = -0.1031

Price change of bond = -10.31%