# Inflation Lag Bond Valuation

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.

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             ?