Inflation
29 October 2021
14:52
Consider an issue date of 7 April. The relevant index level would be the one for 7 January. Say the 1 January CPI-U
level is 160.5 and the 1 February level 160.6. what is the relevant CPI level
The difference between these two values is: 160.6 -160.5 = 0.10
Dividing this difference by the number of days between 1 January and 1 February gives:
(0.10/31)=0.00322581
and multiplying the result by the number of days in January before the reference date gives:
0.00322581*6=0.01935486
So, the CPI-U for January 7 is 160.5 + 0.019=160.519
TIPS cash flow calculations
TIPS periodic coupon payments and their final redemption payments are both calculated using an inflation
adjustment. Known as the inflation compensation, or IC, this is defined as in
IC set date = (P X IRset date)- P
Where P= Bond's Principal
The semiannual coupon payment, or interest, on a particular dividend date is
calculated using
Interest DIV date = (C/2)X (P+ICDIV date)
where C = Annual coupon rate
Note that the redemption value of a TIPS is guaranteed by the Treasury to be a
minimum of $100 – that is, 100% of the face value.
The principal repayment is computed as
100 X (CPIM-3/CPI0)
where CPI0 = Base CPI level – that is, the level three months before the bond’s issue
date.
TIPS price and yield calculations
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TIPS price and yield calculations
The price of a TIPS comprises its real price plus any accrued interest, both of which are
adjusted for inflation by multiplying them times the index ratio for the settlement
date. The bond’s unadjusted accrued interest is
(C/2) X (d-f)/d
Where f = Number of days from the settlement date to the next
coupon date;
d =Number of days in the regular semi-annual coupon
period ending on the next coupon date;
C = Unadjusted coupon payment.
The TIPS real price is given by
The markets use two main yield measures for all index-linked bonds: the money, or
nominal yield, and the real yield. Both are varieties of yield to maturity.
To calculate a money yield for an indexed bond, it is necessary to forecast all its
future cash flows. This requires forecasting all the relevant future CPI-U levels. The
market convention is to take the latest available CPI reading and assume a constant
future inflation rate, usually 2.5% or 5%
The first relevant future CPI level is computed using equation
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Consider an indexed bond that pays coupons every June and December. To compute
its yield, it is necessary to forecast the CPI levels registered 3 months before June and
8 months before December – that is, the October and April levels. Say this
computation takes place in February. The first CPI level that must be forecast is thus
next April’s. This means that , m = 2. Say the February CPI is 163.7. Assuming an
annual inflation rate of 2.5%,
CPI for the following April is computed as follows:
CPI1= 163.7*(1.025)^(2/12) = 164.3751
For the subsequent relevant CPI level =
The forecast CPI level for the following October is calculated as follows:
CPI2 = 164.4*(1.025)^(1/2)=166.4423
Assuming that the analysis is carried out on a coupon date so that accrued interest is 0, the money yield of a bond
paying semiannual coupons is calculated by solving equation for ri:
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Consider a TIPS issued on 15 January 1998, with a coupon of 3.625% and a maturity date of 15 January 2008. The
base CPI-U level for the bond is the one registered in October 1997. Say this is 150.30. Assume that the CPI for
October 2007, the relevant computing level for the January 2008 cash flows, is 160.5. Using these values, the final
coupon payment and principal repayment per $100 face value will be:
Coupon Payment =
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Coupon Payment =
Principal Repayment =
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