Question

The price of a bond is $100 and it has a Macaulay duration of 18.72 years and a convexity of 2400 as per annum. If rates decrease from 8% to 7.5% per annum compounded semiannually then algebraically find the approximate new price of the bond. Your final answer should be correct to 2 places after the decimal point.

Answer 1

Given about a bond,

Price P = $100

Macaulay duration = 18.72 years

convexity C = 2400

rates decrease from 8% to 7.5%

=> Modified duration of the bond D = Macaulay duration/(1+old yield) = 18.72/(1.08) = 17.33 years

change in yield dy = 7.5 - 8 = 0.5%

Change in price of a bond is calculated as

dP = -D*P*dy + (1/2)*C*P*dy^2 = -17.33*100*(-0.005) + (1/2)*2400*100*(-0.005)^2 = 11.67

So, price increase by $11.67

So, new price = old price + dp = 100 + 11.67 = $111.67