Question

One strategy that is used to hedge interest rate risk is to match the modified duration of assets and liabilities. If we hedge the above bond in question 7 with a zero coupon bond, what would be the maturity of said zero.

Answer 1

Par Value =100
Semi annual Coupon =3
Number of Periods =3*2 =6
Price =98.50
semi annual Rate using financial calculator
N=6;PMT=3;PV=-98.50;FV=100;CPT I/Y =3.279466%
Rate =3.279466%
Macaulay Duration =(1*Coupon1/(1+r)+2*Coupon 2/(1+r)^2+3*Coupon 3/(1+r)^3+4*Coupon 4/(1+r)^4+5*Coupon 5/(1+r)^5+
6*(Coupon 6+Par Value)/(1+r)^6)/Price
=(3/(1+3.279466%)+3*2/(1+3.279466%)^2+3*3/(1+3.279466%)^3+3*4/(1+3.279466%)^4+3*5/(1+3.279466%)^5+103*6/(1+3.279466%)^6/98.50 =5.5759
Macaulay Duration =5.5759/2 =2.79

Modified Duration =Macaulay Duration/(1+YTM/2) =(5.5759/2)/(1+3.279466%/2) =2.74