Applying an Inflation Lag to Index-Linked Bond Cash Flows
Summary
The example concerns an investor buying an index-linked government bond between issue and maturity and asks how to calculate real yield when coupons and redemption are tied to inflation with an eight-month lag. The answer explains that each payment date uses the inflation index from eight months earlier. The earlier index value supplied at issuance establishes the base for scaling the bond’s nominal principal.
To obtain a coupon, first adjust the nominal principal by the ratio of the relevant lagged index to the base index, then apply the annual coupon rate for the payment period. The response also distinguishes the coupon rate from the resulting coupon amount: inflation-adjusted principal changes the cash payment. When the required index date falls between published observations, the bond’s terms typically specify interpolation, often linear. The answer does not calculate the requested yield or settle how to project future index values; it notes that the question’s assumed inflation path may differ from the issuer’s official index schedule.
Key ideas
- Apply the index value dated eight months before each payment date.
- Scale nominal principal by the ratio of the relevant index to the base index.
- Calculate each coupon by applying the periodic coupon rate to adjusted principal.
- Use the bond’s stated convention to interpolate when a lagged date falls between published index values.
- The response explains cash-flow construction but does not compute the investor’s real yield.
Tags
Full text
# Inflation Lag Bond Valuation # 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 ? ``` ## Answer by Phil H (score 1) https://quant.stackexchange.com/a/42200 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.
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