IMI Desk Notes

NEW Btp Inflation linked: good for investors and good for the Treasury

Cristiana Corno

Desk rates & Inflation - Structuring

Milan, 16 th March 2012

1

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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

5

New Btp inflation linked versus Outstanding Btp-i

Btp Italia

Indexation coefficient is linked to semi annual inflation, for both coupon and capital

Semi annual revaluation of capital, paid at coupon date

Floor on capital and coupon, during

the life of the bond

Italian inflation (itcpiunr Index)

Btp-i

Indexation coefficient is linked to inflation accrued from settlement date of the security

Capital is revalued at maturity

Floor on capital only at maturity

European Inflation (cptfemu Index)

6

Indexation mechanism

Btp Italia pays a semi annual coupon revalued on the semester’ inflation. At time t the flow will be*:

where is the level of the inflation index at time t and is the level of the inflation index at preceding coupon

date.

On the contrary a Btp-i pays a flow equal to:

where is the level of inflation at time t and is the level of inflation at the initial accrual date of the security.

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.

)6

(*100*2 −

=tI

tICtF

tI6−tI

)0

(*100*2 I

tICtF =

tI 0I

*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

7

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

0

5

10

15

20

25

-2.0

0%

-1.7

5%

-1.5

0%

-1.2

5%

-1.0

0%

-0.7

5%

-0.5

0%

-0.2

5%

0.00

%

0.25

%

0.50

%

0.75

%

1.00

%

1.25

%

1.50

%

1.75

%

2.00

%

2.25

%

2.50

%

3.00

%

On the contrary, at present, we are

in a situation of negative real ratesin the short end, due to liquidity

abundance and LTRO carry

speculation and high inflation.

On this argument at present

situation favors Btp-i over Btp Italia,

where flows are re-invested at

inflation rate.

Bloomberg data, IMI calculations

8

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-i104.00 coupon index coefficient revalued coupon index coefficient revalued coupon106.08 1.02 1 1.02 1.02 1.02 1.02108.20 1.02 1 1.02 1.02 1.04 1.04110.37 1.02 1 1.02 1.02 1.06 1.06112.57 1.02 1 1.02 1.02 1.08 1.08114.82 1.02 1 1.02 1.02 1.10 1.10117.12 1.02 1 1.02 1.02 1.13 1.13119.46 1.02 1 1.02 1.02 1.15 1.15121.85 1.02 1 1.02 1.02 1.17 1.17

Compounded

inflationIMI calculations: simulation of indexation coefficients for Btp Italia and Btp-i

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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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-i104 index coeff icient coupon revalued coupon revalued capital total f low s revalued coupon revalued capital total f low s

104.7 1.0067 1.00 1.0067 0.67 1.68 1.0067 1.01106.1 1.0134 1.00 1.0134 1.34 2.35 1.0202 1.02106.8 1.0066 1.00 1.0066 0.66 1.67 1.0269 1.03108.2 1.0131 1.00 1.0131 1.31 2.32 1.0404 1.04108.9 1.0065 1.00 1.0065 0.65 1.65 1.0471 1.05110.4 1.0138 1.00 1.0138 1.38 2.39 1.0615 1.06111.1 1.0063 1.00 1.0063 0.63 1.64 1.0683 1.07112.6 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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Capital revaluation

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.00

1 2 3 4 5 6 7 8

Btp ItaliaBtp-i

Positive for Investors: credit risk is less

concentrated at maturity, therefore the break

even inflation between nominal and real

bonds will translate more correctly the Italian

inflation rate. Contrarily at what happened

with Btp-i during the crisis.

Negative for investors: tax to be paid earlier

Due to lack of inflation uplift, credit

risk is more comparable to nominal

Btps !!!

Flows related to coupon and capital revaluation for Btp Italia and Btp-i

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FloorBoth 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 modif ied ic rule20/09/2012 103.6 0.99615 104 1.00000 deflation: index to 120/03/2013 106 1.02317 104 1.01923 inflation and level greater than any level preiously registered: index goes to 106/10420/09/2013 104.7 0.98774 106 1.00000 deflation: index to 120/03/2014 105.8 1.01051 106 1.00000 inflation but level is not greater than the higher level previously registered: index to 120/09/2014 107 1.01134 106 1.00943 inflation and level greater than any level preiously registered: index goes to 107/10620/03/2015 103 0.96262 107 1.00000 deflation: index to 120/09/2015 102 0.99029 107 1.00000 deflation: index to 120/03/2016 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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FloorThe 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

.

-4.00%

-3.00%

-2.00%

-1.00%

0.00%

1.00%

2.00%

3.00%

4.00%

5.00%

6.00%

Jul-0

1

Jul-0

2

Jul-0

3

Jul-0

4

Jul-0

5

Jul-0

6

Jul-0

7

Jul-0

8

Jul-0

9

Jul-1

0

Jul-1

1

itcpi Indexcptfemu Curncy Historically we had brief periods

of negative semester inflation

as outlined from chart (6m

rolling inflation from 2000

onwards)

6m rolling Italian and European inflation, Bloomberg data, IMI calculations

13

Italian inflationBtp 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

-0.50%

0.00%

0.50%

1.00%

1.50%

2.00%

2.50%

3.00%

3.50%

4.00%

4.50%

Sep

-05

Jan-

06

May

-06

Sep

-06

Jan-

07

May

-07

Sep

-07

Jan-

08

May

-08

Sep

-08

Jan-

09

May

-09

Sep

-09

Jan-

10

May

-10

Sep

-10

Jan-

11

May

-11

Sep

-11

Jan-

12

realized inflationquoted inflation

What is interesting is that the market

seems to systematically underestimate

Italian inflation with an average error of

0.20% on 1y point from 2004 onwards.

Quoted 1y inflation and inflation realized in the subsequent period. Bloomberg data, IMI calculations

14

Italian inflationThe 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.

-0.80%

-0.60%

-0.40%

-0.20%

0.00%

0.20%

0.40%

0.60%

0.80%

1.00%

Sep

-05

Jan-

06

May

-06

Sep

-06

Jan-

07

May

-07

Sep

-07

Jan-

08

May

-08

Sep

-08

Jan-

09

May

-09

Sep

-09

Jan-

10

May

-10

Sep

-10

Jan-

11

May

-11

Sep

-11

Jan-

12

Eu-Italian inflation spread realized

Eu-Italian inflation spread quoted

At present inflation swap market is

implying a lower Italian inflation

than European.

Historically, Italian inflation has come down more slowly than implied by the inflation swap market.

Quoted and realized spread between European and Italian inflation 1y point. Bloomberg data, IMI calculations

15

Possible approaches to valuationDifficult 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

100

105

110

115

120

125

130

2013 2014 2015 2016 2017 2018 2019 2020 2021 2022

MIDOFFER

Inflation index data as derived from Itlaian inflation swap, Bloomberg data

16

Possible approaches to valuationb) 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.

!!!!!!!

17

Further information

http://www.dt.tesoro.it/en/debito_pubblico/btp_italia/index.html

http://www.tesoro.it/primo-piano/btp.asp