Question

There is a par 10 year, 16% bond. What is the % alteration, if the ytm alters by 3%? Do it with duration alone. Then, find the change, if you include convexity also. The convexity is 60.

Answer 1

ASSUMING YIELD DECREASE

Using duration alone:
% alteration=-1/1.16*(-3%)*(1*16/1.16+2*16/1.16^2+3*16/1.16^3+4*16/1.16^4+5*16/1.16^5+6*16/1.16^6+7*16/1.16^7+8*16/1.16^8+9*16/1.16^9+10*16/1.16^10+100*16/1.16^10)/100=18.0172%

Using convexity also:
% alteration=0.5*60*(3%)^2+18.0172%=20.7172%

ASSUMING YIELD INCREASE

Using duration alone:
% alteration=-1/1.16*(3%)*(1*16/1.16+2*16/1.16^2+3*16/1.16^3+4*16/1.16^4+5*16/1.16^5+6*16/1.16^6+7*16/1.16^7+8*16/1.16^8+9*16/1.16^9+10*16/1.16^10+100*16/1.16^10)/100=-18.0172%

Using convexity also:
% alteration=0.5*60*(3%)^2-18.0172%=-15.317%