A
aika1
Member
Hi,
I am a little bit confused with calculation of the actual coupons on the index-linked bonds:
For instance, past exam September 2006 (q.11).
-On 1 July 2002, the government of a country issued an index-linked bond of
term seven years. Coupons are paid half-yearly in arrears on 1 January and 1
July each year. The annual nominal coupon is 2%. Interest and capital
payments are indexed by reference to the value of an inflation index with a
time lag of eight months.
Date Inflation index
November 2001: 110.0
May 2002: 112.3
November 2002: 113.2
May 2003: 113.8
I understand that to find the actual amount of coupon say for 31/12/2003 we need to multiply coupon=1 by ‘Index May 2003’ and divide by ‘Index November 2001’.
What I don’t understand is why the coupon should be multiplied by 0.8.
The official solution is: 0.8×1× (Index May 2003/Index November 2001)=
0.8×1×113.8/110
However, here is a similar question from April 2004 (q.7).
A government issued a number of index-linked bonds on 1 June 2000 which were redeemed on 1 June 2002. Each bond had a nominal coupon rate of 3% per annum, payable half yearly in arrears, and a nominal redemption price of 100. The actual coupon and redemption payments were indexed according to the increase in the retail price index between 6 months before the bond issue date and 6 months before the coupon or redemption payment dates.
The values of the retail price index in the relevant months were:
Date Retail price index
December 1999: 100
June 2000: 102
December 2000: 107
June 2001: 111
December 2001: 113
June 2002: 118.
In the solution provided the coupon at 1 December 2000 is 1.530 (ie. 1.5×(Index June 2000/Index December 1999), I mean it is not multiplied by any other number, in contrary to the previous example.
My concern and questions then are:
1) If and when we need to multiple the coupon by another number?
2) What is the meaning of 0.8 in the first example, how to interpret it? How it is derived? I mean if it is 8 months ×0.1, then where this 0.1 comes from?
Hope someone can clarify.
Thank you.
I am a little bit confused with calculation of the actual coupons on the index-linked bonds:
For instance, past exam September 2006 (q.11).
-On 1 July 2002, the government of a country issued an index-linked bond of
term seven years. Coupons are paid half-yearly in arrears on 1 January and 1
July each year. The annual nominal coupon is 2%. Interest and capital
payments are indexed by reference to the value of an inflation index with a
time lag of eight months.
Date Inflation index
November 2001: 110.0
May 2002: 112.3
November 2002: 113.2
May 2003: 113.8
I understand that to find the actual amount of coupon say for 31/12/2003 we need to multiply coupon=1 by ‘Index May 2003’ and divide by ‘Index November 2001’.
What I don’t understand is why the coupon should be multiplied by 0.8.
The official solution is: 0.8×1× (Index May 2003/Index November 2001)=
0.8×1×113.8/110
However, here is a similar question from April 2004 (q.7).
A government issued a number of index-linked bonds on 1 June 2000 which were redeemed on 1 June 2002. Each bond had a nominal coupon rate of 3% per annum, payable half yearly in arrears, and a nominal redemption price of 100. The actual coupon and redemption payments were indexed according to the increase in the retail price index between 6 months before the bond issue date and 6 months before the coupon or redemption payment dates.
The values of the retail price index in the relevant months were:
Date Retail price index
December 1999: 100
June 2000: 102
December 2000: 107
June 2001: 111
December 2001: 113
June 2002: 118.
In the solution provided the coupon at 1 December 2000 is 1.530 (ie. 1.5×(Index June 2000/Index December 1999), I mean it is not multiplied by any other number, in contrary to the previous example.
My concern and questions then are:
1) If and when we need to multiple the coupon by another number?
2) What is the meaning of 0.8 in the first example, how to interpret it? How it is derived? I mean if it is 8 months ×0.1, then where this 0.1 comes from?
Hope someone can clarify.
Thank you.
