The Distribution of Asset Holdings and Capital Gains
Presentazione Btp
1. IMI Desk Notes
NEW Btp Inflation linked: good for investors and good for the Treasury
Milan, 16 th March 2012
Cristiana Corno
Desk rates & Inflation - Structuring
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5. New Btp inflation linked versus Outstanding Btp-i
We will go in details in the features of the new Btp,”BTP Italia” with focus to:
Different indexation mechanisms: semi annual versus inflation accrued from settlement date of the security
Semi annual revaluation of capital versus maturity revaluation of capital
Floor on capital and coupon versus floor on capital at maturity
Italian inflation versus European one
Possible approaches to valuation
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6. New Btp inflation linked versus Outstanding Btp-i
Btp Italia Btp-i
Indexation coefficient is linked to Indexation coefficient is linked to
semi annual inflation, for both inflation accrued from settlement
coupon and capital date of the security
Semi annual revaluation of capital, Capital is revalued at maturity
paid at coupon date
Floor on capital and coupon, during Floor on capital only at maturity
the life of the bond
Italian inflation (itcpiunr Index) European Inflation (cptfemu Index)
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7. Indexation mechanism
Btp Italia pays a semi annual coupon revalued on the semester’ inflation. At time t the flow will be*:
C I
F = *100 * ( t )
t 2 I
t −6
where It is the level of the inflation index at time t and I is the level of the inflation index at preceding coupon
t −6
date.
On the contrary a Btp-i pays a flow equal to:
C I
F = *100 * ( t )
t 2 I
0
where I is the level of inflation at time t and I is the level of inflation at the initial accrual date of the security.
t 0
This actually means that in the second case inflation is re-invested at subsequent period inflation rate, while in the first
case it is re-invested at nominal rates. The second indexation mechanism is superior to the first for the investor, if
nominal rates are higher than inflation rate.
*We are not considering the lag in indexation, being the same for Btp-i and Btp Italia. Detailed info avaiable on Tesoro website, link at end of
presentation
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8. Indexation mechanism
If we look at 6m Italian inflation rate versus 6m Bot yield, we find that nominal rates have generally been higher
than inflation rate by approximately 0.30% (6m real rate, histogram in chart below, data from Jan 2000,
calculated as difference between 6m yield and realized inflation in the subsequent 6 months)
6 m Real Rate
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On the contrary, at present, we are
20 in a situation of negative real rates
in the short end, due to liquidity
15 abundance and LTRO carry
speculation and high inflation.
10
On this argument at present
situation favors Btp-i over Btp Italia,
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where flows are re-invested at
0
inflation rate.
-2.00%
-1.75%
-1.50%
-1.25%
-1.00%
-0.75%
-0.50%
-0.25%
0.00%
0.25%
0.50%
0.75%
1.00%
1.25%
1.50%
1.75%
2.00%
2.25%
2.50%
Bloomberg data, IMI calculations 3.00%
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9. Indexation mechanism
Assuming for simplicity, an constant annul 2% inflation rate and a 2% semi annual coupon, we get the
following indexation coefficients for a hypothetical 4y Btp Italia and a Btp-i with the same features in terms of
maturity and coupon
inflation rate 2.00% Btp Italia Btp-i
104.00 coupon index coefficient revalued coupon index coefficient revalued coupon
106.08 1.02 1 1.02 1.02 1.02 1.02
108.20 1.02 1 1.02 1.02 1.04 1.04
110.37 1.02 1 1.02 1.02 1.06 1.06
112.57 1.02 1 1.02 1.02 1.08 1.08
114.82 1.02 1 1.02 1.02 1.10 1.10
117.12 1.02 1 1.02 1.02 1.13 1.13
119.46 1.02 1 1.02 1.02 1.15 1.15
121.85 1.02 1 1.02 1.02 1.17 1.17
IMI calculations: simulation of indexation coefficients for Btp Italia and Btp-i Compounded
inflation
This table aims to show the difference in inflation coumpounding in Btp Italia (current pay bonds) and standard Btp-i
linkers (capital indexed bonds). For more info on this argument see link
http://www.nuclearphynance.com/User%20Files/3877/Inflation-linked%20Bonds%20Explained.pdf
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10. Capital revaluation
The next big difference between Btp Italia and Btp-i is that, in first case, capital revaluation is done semi annually and
paid together with the coupon with the same indexation method described in previous pages.
In table below we have summarized the cash flows of Btp Italia and of a Btp-i with the same features (maturity, coupon).
The big difference is that the inflation uplift is diluted through time (chart in next page).
104 Btp Italia Btp-i
104 index coefficient coupon revalued coupon revalued capital total flow s revalued coupon revalued capital total flow s
104.7 1.0067 1.00 1.0067 0.67 1.68 1.0067 1.01
106.1 1.0134 1.00 1.0134 1.34 2.35 1.0202 1.02
106.8 1.0066 1.00 1.0066 0.66 1.67 1.0269 1.03
108.2 1.0131 1.00 1.0131 1.31 2.32 1.0404 1.04
108.9 1.0065 1.00 1.0065 0.65 1.65 1.0471 1.05
110.4 1.0138 1.00 1.0138 1.38 2.39 1.0615 1.06
111.1 1.0063 1.00 1.0063 0.63 1.64 1.0683 1.07
112.6 1.0135 1.00 1.0135 1.35 2.36 1.0827 8.27 9.35
The first column simulates a pattern for the inflation index, in the second column we calculate the indexation coefficients for Btp Italia. In the
following columns, assuming a 2% real annual coupon, we determine revaluted capital and coupons for both Btp Italia and Btp-i
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11. Capital revaluation
Positive for Investors: credit risk is less
10.00
concentrated at maturity, therefore the break
9.00 Btp Italia
Btp-i even inflation between nominal and real
8.00
bonds will translate more correctly the Italian
7.00
inflation rate. Contrarily at what happened
6.00
with Btp-i during the crisis.
5.00
Negative for investors: tax to be paid earlier
4.00
3.00
2.00
1.00
0.00
1 2 3 4 5 6 7 8
Due to lack of inflation uplift, credit
Flows related to coupon and capital revaluation for Btp Italia and Btp-i
risk is more comparable to nominal
Btps !!!
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12. Floor
Both Btp Italia coupons and capital are floored each semester, while Btp-i is only floored on capital at maturity.
Floor mechanism
If inflation index at coupon date x is lower than inflation at previous coupon date, the indexation coefficient is set to 1.
After that, if inflation level increases the indexation coefficient remains unchanged, unless the inflation level is higher than
the maximum inflation level scored in the preceding semesters. Below an example of how it works. Basically once the
indexation rate goes to 1 due to semester deflation, the indexation index base becomes dynamic.
.
start date 104 ic inflation max modified ic rule
20/09/2012 103.6 0.99615 104 1.00000 deflation: index to 1
20/03/2013 106 1.02317 104 1.01923 inflation and level greater than any level preiously registered: index goes to 106/104
20/09/2013 104.7 0.98774 106 1.00000 deflation: index to 1
20/03/2014 105.8 1.01051 106 1.00000 inflation but level is not greater than the higher level previously registered: index to 1
20/09/2014 107 1.01134 106 1.00943 inflation and level greater than any level preiously registered: index goes to 107/106
20/03/2015 103 0.96262 107 1.00000 deflation: index to 1
20/09/2015 102 0.99029 107 1.00000 deflation: index to 1
20/03/2016 99 0.97059 107 1.00000 deflation: index to 1
Example of floor mechanism, for further info see “ESEMPI DI CALCOLO” in www.debitopubblico.it , links at the end of presentations.
Dates are hypotetical.
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13. Floor
The floor gives protection to investor in case of temporary deflation. Valuation requires implementation of Monte Carlo
simulation and it is more a theoretical valuation, than tradable price.
On our valuation it could be worth around 0.20% in terms of real coupon, versus approx 0.05% value of a standard floor
on Btp-i 2016
. 6.00%
itcpi Index
cptfemu Curncy
Historically we had brief periods
5.00%
of negative semester inflation
4.00% as outlined from chart (6m
3.00%
rolling inflation from 2000
onwards)
2.00%
1.00%
0.00%
Jul-01
Jul-02
Jul-03
Jul-04
Jul-05
Jul-06
Jul-07
Jul-08
Jul-09
Jul-10
-1.00% Jul-11
-2.00%
-3.00%
6m rolling Italian and European inflation, Bloomberg data, IMI calculations
-4.00%
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14. Italian inflation
Btp italia will be linked to Italian inflation via Foi. We will not go in depth in describing the index, rather we will focus on
relation with quoted and realized inflation. Italian inflation is quoted on as zero coupon swap. Quotes are available at
Bloomberg page SWIL, still not very liquid prices. In following analysis we focus on 1y point.
First thing to notice is that quoted inflation is a bad forecaster of subsequent period realized inflation (r2=0).
Same old true for 5y point and for quoted EU inflation
4.50%
realized inflation
4.00%
quoted inflation
3.50%
What is interesting is that the market
3.00% seems to systematically underestimate
2.50% Italian inflation with an average error of
2.00%
0.20% on 1y point from 2004 onwards.
1.50%
1.00%
0.50%
0.00%
May-06
May-07
May-08
May-09
May-10
May-11
Jan-06
Jan-07
Jan-08
Jan-09
Jan-10
Jan-11
Jan-12
Sep-05
Sep-06
Sep-07
Sep-08
Sep-09
Sep-10
Sep-11
-0.50%
Quoted 1y inflation and inflation realized in the subsequent period. Bloomberg data, IMI calculations
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15. Italian inflation
The same is evident by looking at the spread between realized and quoted spread between Italian and European
inflation. Quoted spread is more volatile and less sticky than realized inflation spread.
1.00%
Eu-Italian inflation spread realized
0.80% Eu-Italian inflation spread quoted
At present inflation swap market is
0.60%
implying a lower Italian inflation
0.40% than European.
0.20%
Historically, Italian inflation has
come down more slowly than
0.00% implied by the inflation swap
May-06
May-07
May-08
May-09
May-10
May-11
Jan-06
Jan-07
Jan-08
Jan-09
Jan-10
Jan-11
Jan-12
Sep-05
Sep-06
Sep-07
Sep-08
Sep-09
Sep-10
Sep-11
-0.20%
market.
-0.40%
-0.60%
-0.80%
Quoted and realized spread between European and Italian inflation 1y point. Bloomberg data, IMI calculations
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16. Possible approaches to valuation
Difficult to estimate a fair value for the real yield, due to scarce liquidity of Italian swap Inflation and non-linearity in
the floor pay off. We have followed 2 approaches:
a.) Using the inflation swap market (mid) to forward the indexation coefficient and the Btp zero curve to discount the
flows we get that a real coupon of 1.70% to have a initial par price.
To this we have to add a liquidity premium for inflation linked securities. In order to value the liquidity premium we
apply valuation at point 1 for a btp-linkers of the same maturity and we estimate a liquidity premium of around 0.50%.
This gives us a real coupon of 2%, once we subtract an estimation of the floor premium
ITCPI FORWARD DERIVED FROM QUOTED INFLATION
130
MID
125
OFFER
120
115
110
105
100
2013 2014 2015 2016 2017 2018 2019 2020 2021 2022
Inflation index data as derived from Itlaian inflation swap, Bloomberg data
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17. Possible approaches to valuation
b) If we use the breakeven level of Btp-i 2016, around 1.23% (European inflation) less 0.15% (quoted difference
between Italian and European inflation on same maturity) to forecast Italian inflation (1.08%) and subtract the
inflation rate from a comparable nominal yield (Btp Apr 16, yielding 3.30%), we get a real coupon rate of 2.22%.
Again subtracting the floor value we get to 2.02%.
In summary we could see a real coupon of around 2% with same upside given the different tax profile.
!!!!!!!
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