Inflation Lag Bond Valuation

Question

Question: On 1st March 2006 a government issued a large tranche of an index-linked bond having a term of 6 years. Coupons of 4% p.a. were payable half-yearly in arrears and the bond was redeemed at 102%. Coupons and redemption amounts were indexed with respect to an inflation index with an 8-month time-lag applying.

An investor purchased €100 nominal of the bond on 1st September 2009 for a price of €113 just after the coupon payment had been made on that date and held the bond until its redemption on 1st March 2012.

You are given the following values of the inflation index:

   Date              Index Value
1st July 2005        120
1st March 2006       121.5
1st July 2009        127
1st September 2009   128

Calculate the annual real yield achieved by the investor on the bond transaction as at the purchase date of 1st September 2009. Assume that the inflation index increases continuously from its value on 1st September 2009 at the rate of 4% p.a.

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I found the further inflation index values to be:

Date              Index Value
1st September 2010    133.12
1st September 2011    138.44

The problem I'm having is the 8 month inflation lag, I'm unsure of how to address this problem to get the real cash flow values

I have created a table using the inflation lag to calculate the coupon value, however I am index values at several times. How do I find the coupon values at these times

(Time)   (Index)  (Inflation w.r.t lag)  (Coupon)
1/9/09    128            128/120           2.13
1/3/10     ?              ?/120             ?
1/9/10    133.12        133.12/120         2.21
1/3/11     ?              ?/120             ?
1/9/11    138.44        138.44/120        2.307
1/3/12     ?              ?/120             ?

Answer 1

The 8 month lag just means that the index to use for a given coupon date is the one dated 8m prior. This is why you are given the Jul 2005 index value; it is 8m before the bond's issue date of Mar 2006.

The coupon payment won't be €2, incidentally: the coupon rate is per unit principal, and it is the principal which is varied. So if after some time the the index reaches 130, then the principal is P = €100 x (130/120) = €108.333, and the coupon is P x (4% / 2) = €2.167.

The index itself is published at certain intervals by the relevant government agency, and the bond itself has a defined way to interpolate between those published values. Usually to prevent ambiguity it is a simple linear interpolation between published points.

In the original question it mentions inflation being 4% beyond the given values, but it's not clear whether you should just calculate the required index values from that or generate them according to the schedule of the govt authority (which would presumably be more correct)? It shouldn't make much difference to the figures either way.