CT1 IFoA Sept 2006 Q11 (ii)

Sorry : Question is from 2006 year exam paper instead of 2009


While calculating Price of bond on real rate 3% convertible half yearly and assumed that investor hold till maturity.....


Solution seems doubtful :

1) Why annuity is taken for 12 half years by multiplying real rate 0.81748??

Since investor hold this till maturity ...that make sense that he purchased on 1st July 2003 and hold for next 6 years.

But confusion comes in play that on July 2003 he or she didn't receive any coupen. And he or she started receiving coupons from 1st Jan 2004. So it only counts 5.5 ... Means only 11 payment were received by investor.


2nd doubt:

Since we are given coupen payment with index number. So can't we directly multiply the coupen rate by index..

i.e. coupen rate*Base index/Current index


To obtain the real rate.

Or is it multiply to monetary term due to effective money rate is not given in question.

Just want to understand a different approach to solve this question.


Please help.

Any other information or suggestions are greatly appreciated in advance.

 

31) The investor receives 12 coupons. 2 in 2004, 2 in 2005, 2 in 2006, 2 in 2007, 2 in 2008 and 2 in 2009. On 1 Jan and 1 July each year. Hence the 12 half-years in the annuity.

2) The question provides a real yield, so we need to set up an equation of value in real terms, ie we need to work out the real value of each payment before discounting them. To do this, the actual monetary amount of each payment is first worked out, using the index values given.

The monetary amount of the first coupon on 1 Jan 2004 after tax has been taken off is 0.8*1*(113.8/110.0), as the payments from an index-linked bond are increased in line with inflation from the date of issue of the bond up to the date of the payment (here with a lag of 8 months).

In real terms on 1 July 2003, this payment is worth 0.8*1*(113.8/110.0)*(1.025)^(-0.5), as inflation is running at 2.5% over the half-year from 1 July 2003 to 1 Jan 2004. (The (1.025)^(-0.5) factor is the same as your base index/current index factor, just with a constant inflation assumption). This amount is then discounted for one half-year to find the present value.

This procedure is repeated for the other payments, ie work out the actual amount of each monetary payment received, then work out the real value of it as at 1 July 2003, then apply the discounting, as shown in the Examiners solution. This is the standard approach to take in index-linked bond questions like this one.

 

Thanks sir !!