Question

Bond A has a 8% coupon rate, paid annually. Maturity is in three years. The bond sells at par value $1000 and has a convexity of 9.3. The duration of the bond is 2.78. If the interest rate increases from 8% to 9.5%, what price would be predicted by the duration-with-convexity rule?

Answer 1

Given about a bond,

Face value = $1000

coupon rate = 8% paid annually,

Years to maturity y = 3 years

Yield = 8%

Since Yield of the bond equals its coupon rate, bond is selling at par and the price of the bond is equal to Face value

So, Price P = $1000

Macaulay duration = 2.78

So, Modified duration = Macaulay duration/(1+y) = 2.78/1.08 = 2.58 years

Convexity C = 9.3

yield changes from 8% to 9.5%

=> change in yield dy = 1.5%

So, Change in price using duration and convexity rule is

dP = -D*P*dy + (1/2)*C*P*dy^2 = -2.58*1000*0.015 + (1/2)*9.3*1000*(0.015)^2 = -37.61

So, price of the bond decreases by $37.61

So, new price is P + dP = 1000 - 37.61 = $962.43