Question

You own two bonds that both have R1000 face values. Bond A has a coupon rate of 7%, 3 years to maturity and a yield to maturity of 10%. Bond B has a coupon rate of 8%, 7 years to maturity and a yield to maturity of 9%. Calculate the duration of your bond portfolio (Bond A and B combined).

Answer 1

Since we have to calculate the bond portfolio's duration, we can assume each cash flow separately and calculate the combined duration. Hence, duration will be given as:

Duration = Summation(n x PVn)/Summation(PVn)

Duration = (1 x 70/1.1 + 2 x 70/1.1^2 + 3 x 1070/1.1^3 + 1 x 80/1.09^1 + 2 x 80/1.09^2 + 3 x 80/1.09^3 + 4 x 80/1.09^4 + 5 x 80/1.09^5 + 6 x 80/1.09^6 + 7 x 80/1.09^7 + 8 x 1080/1.09^8)/(70/1.1 + 70/1.1^2 + 1070/1.1^3 + 80/1.09^1 + 80/1.09^2 + .... + 1080/1.09^8) = 8399.787/1870.046 = 4.492 years.