G
Gbob1
Member
Specifically referring to question 14 part ii) of 2000 April paper:
'A pension fund has a liability to pay 100,000 pounds at the end of 1 year, 105,000 pounds at the end of 2 years, and so on, the amount increasing by 5000 pounds each year to 195,000 pounds at the end of 20 years, this being the last payment. The fund values these payments using an effective interest rate of 7% pa. This is also the interest rate at which the current prices of all bonds are calculated.
The fund invests an amount equal to the present value of these liabilities in the folowing 2 assets:
A) a zero coupon bond redeemable in 25 years, and
B) a fixed interest bond redeemable at par in 12 years' time which pays a coupon of 8% pa annually in arrears'
Calculate the present value and the duration of the liabilities'
Ok I've managed to calculate the present value of the liabilities, that was simple. But then I don't know what else to do next - I've looked up the formula for duration but I don't understand it. How do I work out the numerator of the duration. From the answer scheme I'm assuming the present value of the liabilities is the denominator. So what does: the sum of tk*Ctk*v(i)tk mean (i.e. the numerator)? In the answers it says it's: 95*increasing annuity for 20 yrs in arrears + 5[v + 2.2v^2 +...+ 20.2v^20] I don't understand this at all...
'A pension fund has a liability to pay 100,000 pounds at the end of 1 year, 105,000 pounds at the end of 2 years, and so on, the amount increasing by 5000 pounds each year to 195,000 pounds at the end of 20 years, this being the last payment. The fund values these payments using an effective interest rate of 7% pa. This is also the interest rate at which the current prices of all bonds are calculated.
The fund invests an amount equal to the present value of these liabilities in the folowing 2 assets:
A) a zero coupon bond redeemable in 25 years, and
B) a fixed interest bond redeemable at par in 12 years' time which pays a coupon of 8% pa annually in arrears'
Calculate the present value and the duration of the liabilities'
Ok I've managed to calculate the present value of the liabilities, that was simple. But then I don't know what else to do next - I've looked up the formula for duration but I don't understand it. How do I work out the numerator of the duration. From the answer scheme I'm assuming the present value of the liabilities is the denominator. So what does: the sum of tk*Ctk*v(i)tk mean (i.e. the numerator)? In the answers it says it's: 95*increasing annuity for 20 yrs in arrears + 5[v + 2.2v^2 +...+ 20.2v^20] I don't understand this at all...