Question

A 30-year bond making annual payments has a coupon rate of 12%,a duration of 11.54years, and convexity of 192.4.The bond is currently selling at a yield to maturity of 8%. Use the duration-with -convexity approximation to predict the new price of the bond iftheyield to maturitydeclines from 8% to 7%.Assume a facevalue of 1000.

Answer 1

Given about a bond,

Face value = $1000

Coupon rate = 12% paid annually,

=> Annual coupon = 12% of 1000 = $120

YTM = 8%

years to maturity = 30 years

Price of the bond can be calculated on financial calculator using following values:

FV = 100

PMT = 120

I/Y = 8

N = 30

Compute for PV, we get PV = -1450.31

So, price of the bond = $1450.31

duration of the bond = 11.54 years

So, modified duration D = duration/(1+y) = 11.54/1.08 = 10.69 years

Convexity C = 192.40

change in yield dy = -0.01

So, price change dP using duration-with -convexity approximation is

dP = -D*P*dy + (1/2)*C*P*dy^2 = -10.69*1450.31*(-0.01) + (1/2)*192.40*1450.31*(-0.01)^2 = $169

New price = P + dP = 1450.31 + 169 = $1619.31