Introduction section Examples of calculations

Examples of calculations

EXAMPLE OF INDEXATION COEFFICIENT CALCULATION FOR BTP INDEXED TO EUROPEAN INFLATION

The BTP indexed to European inflation has, as its reference value, "the Harmonized Index of Consumer Prices in the euro area (HICP), excluding tobacco". This index is published monthly on Eurostat's website, at the following address:
https://ec.europa.eu/eurostat/databrowser/view/teicp240/default/table?lang=en

 

To get the indexation coefficient, each day's reference index must be divided by the value taken at the base time, according to the following formula:

ICd,m = Reference Index d,m / Base Index

 

If, for example, we want to calculate the reference index for May 15th, 2022, the payment date of the first coupon of the BTP indexed to European inflation (BTP€i) maturing on May 15th, 2033, the formula will be:

ICd,m = 112.60097 / 107.78267 = 1.04470

 

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Calculation of the reference index

For May 15th, 2022, the Eurostat indexes to be used for calculation are those for February and March 2022:

REFERENCE MONTH EUROSTAT INDEX
February 2022 (m-3)
three months before the month
in which the calculation is made
111.35
March 2022 (m-2)
two months before the month
in which the calculation is made
114.12

Although the reference index is the one of the coupon payment day (May 15th, 2022), the coupon interest accrual period is 14 days, because the coupon payment day (May 15th, 2022) corresponds to the first interest accrual day of the next coupon, exactly as is the case for other BTPs. This value is then divided by the total number of days in the month (in this case May) for which the calculation is made, namely 31.

 

The reference index is then obtained from the following formula:

 

RId,m = EIm-3 + (d-1) / gg * (EIm-2- EIm-3)

 

That is:

 

RId,m = 111.35 + (15 - 1) / 31 * (114.12-111.35) = 112.6009677

 

The index should be truncated to the sixth decimal place (112.600967) and rounded to the fifth digit (112.60097).

 

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Calculation of the base index

For the BTP indexed to European inflation with maturity date as of May 15th, 2033 and a real coupon of 0.10% per annum, the base day is November 15th, 2021, the date of the bond's accrual. For the calculation of the base index, the Eurostat indices to be used are those for August and September 2021:

REFERENCE MONTH EUROSTAT INDEX
August 2021 (m-3)
three months before the month
in which the calculation is made
107.54
March 2022 (m-2)
two months before the month
in which the calculation is made
108.06

Proceeding with the same formula used to calculate the reference index we will have:

BI = 107.54 + (15 - 1) / 30 * (108.06-107.54) = 107.78266666

 

Again, the index should be truncated to the sixth decimal place (107.782666) and rounded to the fifth digit (107.78267).

 

Example of calculation of the indexation coefficient related to each day of May 2022:

DATE REFERENCE INDEX BASE INDEX INDEXATION COEFFICIENT
01/05/2022 111.35000 107.78267 1.03310
02/05/2022 111.43935 107.78267 1.03393
03/05/2022 111.52871 107.78267 1.03476
04/05/2022 111.61806 107.78267 1.03558
05/05/2022 111.70742 107.78267 1.03641
06/05/2022 111.79677 107.78267 1.03724
07/05/2022 111.88613 107.78267 1.03807
08/05/2022 111.97548 107.78267 1.03890
09/05/2022 112.06484 107.78267 1.03973
10/05/2022 112.15419 107.78267 1.04056
11/05/2022 112.24355 107.78267 1.04139
12/05/2022 112.33290 107.78267 1.04222
13/05/2022 112.42226 107.78267 1.04305
14/05/2022 112.51161 107.78267 1.04387
15/05/2022 112.60097 107.78267 1.04470
16/05/2022 112.69032 107.78267 1.04553
17/05/2022 112.77968 107.78267 1.04636
18/05/2022 112.86903 107.78267 1.04719
19/05/2022 112.95839 107.78267 1.04802
20/05/2022 113.04774 107.78267 1.04885
21/05/2022 113.13710 107.78267 1.04968
22/05/2022 113.22645 107.78267 1.05051
23/05/2022 113.31581 107.78267 1.05134
24/05/2022 113.40516 107.78267 1.05217
25/05/2022 113.49452 107.78267 1.05299
26/05/2022 113.58387 107.78267 1.05382
27/05/2022 113.67323 107.78267 1.05465
28/05/2022 113.76258 107.78267 1.05548
29/05/2022 113.85194 107.78267 1.05631
30/05/2022 113.94129 107.78267 1.05714
31/05/2022 114.03065 107.78267 1.05797

Daily values of the indexation coefficient are available on the website of the Department of Treasury-Public Debt at the following address:

 

https://www.dt.mef.gov.it/en/debito_pubblico/dati_statistici/coefficienti_di_indicizzazione_btpei/

 

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