The Method for Determining Initial Margins

Transcription

1 The Method for Determining Initial Margins RM Office Version 1.0

2 Summary Foreword Types of Initial Margins Calculating the Ordinary Initial Margins Defining the Parameters... 6 a) The Margin Interval... 6 b) The Offset Factor... 6 Page 2 of 7

3 Foreword This document describes the Initial Margin calculation method. First it defines the various types of Initial Margins (section 1), and afterwards it describes, in summary, the TIMS methodology adopted for calculating the Ordinary Initial Margins (section 2). Lastly, it shows the method for defining parameters necessary for using TIMS (section 3). 1. Types of Initial Margins The TIMS methodology provides for the following types of Initial Margins: a) Futures Straddle Margin, calculated only for futures positions having opposite sign on different maturities and relating to the same underlying asset (futures straddle positions). This margin is equivalent to the number of futures straddle positions multiplied by the futures straddle margin fixed by Cassa on the basis of the R 2 determination coefficient observed among the daily price fluctuations of the various maturities. (see enclosure 1). b) Premium Margins, calculated only for stock-style options. It has the purpose of revaluating the theoretical liquidation costs/revenues at the current market values (market-to-market) and therefore represents a theoretical credit 1 for the options buyer and a theoretical debt for the seller. It is equal to the current market value of the option itself, assumed equal to the closing price that is calculated daily. c) Ordinary Margin, calculated on the non-straddle futures positions and on the options positions. It has the purpose of valuating the maximum loss reasonably possible in the hypothesis of market price fluctuations of the underlying asset. The options on individual shares that are exercised/assigned and not yet settled are comprised in calculating the Margins on Premium and Ordinary Margins whereas application of a Delivery Margin is foreseen only on the BTP-Futures being delivered. Such Delivery Margin has the purpose of covering the risk of adverse market trends during the four days running between the last trading day and the delivery day. Starting from the date that will be pointed out in future, the individual and general clearing members will also be requested to set up a Preliminary Initial Margin in cash 1 The theoretical credits are not paid to the favour of the adherent but can be used only for covering the Initial Margins. Page 3 of 7

4 to cover the risk occurring between the day the operation is carried out and the day payment is made for the other Initial Margins that, as it is known, takes place on the working day following the trade day. The amount of the Preliminary Initial Margin will be determined on the basis of a percentage of the daily average of the other Initial Margins paid by each clearing member during the two previous months, and will be subject to monthly verification. 2. Calculating the Ordinary Initial Margins The TIMS methodology is based on the following basic principles: a) all of the futures and options that are considered by Cassa as being significantly correlated to each other in terms of price trend are included in a single Integrated Portfolio that is evaluated unitarily and hence subjected to Initial Margins that are unitarily calculated as well. In fact, TIMS is able to determine the overall exposure to risk both for integrated portfolios relating to the same underlying asset (so-called Class Group ) and for integrated portfolios having different though significantly correlated underlying assets (so-called Product Group ). b) The risk associated with an Integrated Portfolio is assessed by hypothesizing that the prices of the underlying asset change daily for a maximum percentage amount, defined as the Margin Interval, in a way that is adverse to the clearing member s position, and that Cassa must liquidate the positions in the most unfavourable reasonably conjecturable market conditions in case the clearing member is insolvent. In order to establish the maximum loss in the daily market price fluctuation hypothesis, TIMS determines the theoretical liquidation gains/losses 2 of each Integrated Portfolio in correspondence with a series of scenarios of underlying asset prices comprised in the Margin Interval. The Ordinary Initial Margin is set equivalent to the highest of the theoretical liquidation losses calculated for each price scenario. The price scenarios are not restricted to taking into consideration extreme fluctuations. The calculation of the theoretical liquidation gains/losses of each Integrated Portfolio is made also in the hypothesis of intermediate price scenarios in order to assess the risk 2 Options evaluation in the various price scenarios is made with a binomial pricing model (Cox-Ross- Rubinstein). Moreover, for a prudent estimate of the short positions in options that are strongly Out-of- The Money, whether call or put that have a value close to zero and are not very sensitive to the underlying asset s price fluctuations Cassa sets a theoretical minimum liquidation cost (Short Option Adjustment). Page 4 of 7

5 even for those trading strategies whose maximum losses occur in correspondence with values of the underlying asset that are comprised among the extreme values. Enclosure 2 illustrates an example of calculating Initial Margins for a FIB-30, whereas enclosure 3 illustrates an example of calculating Initial Margins for a stock option. In the case of instruments relating to a single underlying asset (Class Group), TIMS determines the theoretical liquidation gains/losses of the entire Integrated Portfolio in an integrated manner by algebraically adding the theoretical liquidation gains/losses of each position within the same price fluctuation hypothesis of the underlying asset inside the Margin s Interval. In this way full compensation between theoretical liquidation gains and losses among positions that are influenced by the underlying asset s price fluctuations in opposite ways is permitted. Enclosure 4 illustrates an example of calculation referring to an option strategy in which, among other things, the maximum theoretical loss occurs in an intermediate price scenario. In the case of instruments having different underlying assets but that are wellcorrelated between them (Integrated Portfolio on the Product Group level), the methodology is able to take into account the degree of plausibility of the correlation existing between the various underlying assets. It is for this reason that the theoretical revenues are reduced by applying an Offset Factor of a prudentially adequate size prior to being used in the corresponding scenarios for covering theoretical losses that are instead taken in their entirety. Enclosure 5 illustrates an example of calculation of margins integrated on the Product Group level. Moreover, in order to apply a significant Initial Margin even to those portfolios the ordinary Initial Margin of which is close to or equivalent to zero, a Minimum Margin is defined as well. Among other things, its purpose is to take into account the bid-offer spread existing on the market in the hypothesis that the positions must be liquidated. Enclosure 6 illustrates an example of applying the Minimum Margin to a portfolio made up of FIB-30 and synthetic futures of opposite signs made through MIBO-30 options. Enclosure 7 illustrates an example of applying Initial Margins (Premium and Ordinary) to assigned stock options positions, in one of the three days elapsing between the exercise/assignment date and the settlement date. Page 5 of 7

6 3. Defining the Parameters The quality of the results generated from the TIMS model depends on the quality of the parameters it is supplied with, as is true for any other model. The methods for defining the main parameters used by TIMS are described below. a) The Margin Interval The Margin Interval is determined for each underlying asset on the basis of statistical analyses. It is normally set equal to such a value as to supply a Coverage Level up to 99.8% compared to the daily price fluctuations actually recorded. This Coverage Level makes, among other things, the recourse to Intraday Margins residual (approximately three times a year on the average). Enclosure 8 shows the distribution of the price fluctuations for a share, and also points out the surmountings of the Margin Interval. The standard deviation for the share in question is equivalent to 3.14% related to an certain holding period. Nonetheless, due to the effect of the leptokurtic structure of the distribution (see Enclosure 9), the Coverage Level reached at 3σ (Margin Interval hypothetically equivalent to ±9,42%), proves equal to only 98.3%. Only by putting the Margin s Interval equivalent to 14.5% (equal to 4.6σ), related to the same holding period, a Coverage Level greater than 99.7% is reached. The Margin s Interval is fixed at the end of a valuation process void of automatisms in which, in order to take into account and potentially forecast volatility trends, the results of the analysis of the data obtained both for the long and average periods and for short and very short periods are taken into consideration, as shown in the enclosed table (enclosure 12). b) The Offset Factor The degree of the correlation s plausibility is measured for each pair of underlying assets by calculating the R 2 determination coefficient. In the case of a stable surmounting of significant values as occurs in the case of the MIB-30 and MIDEX indices (see enclosures 13 and 14) a Product Group, the Offset Factor of which is fixed in a basically complementary extent to the determination coefficient detected, is set up so that the higher the correlation is, 3 Historical sets, even covering 10 years, are used for some stock and this explains why revisions of the Margin s Interval take place fairly rarely, as illustrated for example in enclosure 10. If only the short periods are taken into consideration, one may due to the mean reversion end up chasing volatility by raising the level of the low margins at the end of periods of high volatility when, on the other hand, we are presumably at the eve of a volatility period and, to the contrary, by lowering the margins at the end of a low volatility period that may be followed by a high volatility period. Enclosure 11 furnishes an example of historic volatility fluctuating around its average long-term value. Page 6 of 7

7 Enclosures the lower the abatement applied to the theoretical revenues will be, thus making the cross-margining effect greater. Page 7 of 7

8 Cassa di Compensazione e Garanzia SpA 8,00 7,50 7,00 6,50 6,00 5,50 5,00 4,50 4,00 3,50 3,00 2,50 2,00 1,50 1,00 0,50-0,50-1,00-1,50-2,00-2,50-3,00-3,50-4,00-4,50-5,00-5,50-6,00-6,50-7,00-7,50-8,00 FIB30 Futures Straddle Margins Correlation between first and second maturity price variations. (from 28/11/1994 to 15/1/2001) y = 0,9224x + 36 R² = 0,9184 Second Maturity Price Variations -8,00-7,50-7,00-6,50-6,00-5,50-5,00-4,50-4,00-3,50-3,00-2,50-2,00-1,50-1,00-0,50 0,50 1,00 1,50 2,00 2,50 3,00 3,50 4,00 4,50 5,00 5,50 6,00 6,50 7,00 7,50 8,00 First Maturity Price Variation Enclosure n. 1

9 Cassa di Compensazione e Garanzia SpA TWO LONG FIB-30 MARCH 2001 DOWNSIDE UPSIDE Margin Interval -7,50% -6,00% -4,50% -3,00% -1,50% 1,50% 3,00% 4,50% 6,00% 7,50% Futures Theoretical Value Closing Price Theoretical Liquidation Gain/Loss (Index Points) X 2 Long Positions Theoretical Liquidation Total Gains/Losses ( ) Largest Theoretical Loss Ordinary Initial Margins Class Group Total Initial Margins Debit Debit Enclosure n. 2

10 Cassa di Compensazione e Garanzia SpA TEN SHORT OPTION POSITIONS ENEL CALL 4,10 MAR 2001 Premium Margins (Closing Price x Number of Lots x No. Underlying Shares) 0,17 x 10 x Debit TOTAL Debit DOWNSIDE UPSIDE Margin Interval -1% -8,00% -6,00% -4,00% -2,00% 2,00% 4,00% 6,00% 8,00% 1% ENEL Theoretical Value ( ) 3,60 3,68 3,76 3,84 3,92 4,00 4,08 4,16 4,24 4,32 4,40 Enel Call 4,10 MAR 01Option Theoretical Value 0,040 0,059 0,079 0,103 0,133 0,17 0,206 0,250 0,299 0,352 0,409 Closing Price 0,170 0,170 0,170 0,170 0,170 0,170 0,170 0,170 0,170 0,170 Theoretical Liquidation Gain/Loss ( ) -0,130-0,111-0,091-0,067-0,037 0,04 0,08 0,13 0,18 0,24 X 10 Short Positions 1,30 1,11 0,91 0,67 0,37-0,36-0,80-1,29-1,82-2,39 Theoretical Liquidation Total Gains/Losses ( ) Largest Theoretical Loss Ordinary Initial Margins Premium Margins Class Total Initial Margins Debit Debit Debit Enclosure n. 3

11 Cassa di Compensazione e Garanzia SpA 10 LONG STRADDLE ENEL 4,10 MAR 01: { TEN LONG OPTION POSITIONS ENEL CALL 4,10 MAR 2001 TEN LONG OPTION POSITIONS ENEL PUT 4,10 MAR 2001 Premium Margins (Closing Price x Number of Lots x No. Underlying Shares) 0,17 x 10 x Credit 0,25 x 10 x Credit TOTAL Credit DOWNSIDE UPSIDE Margin Interval -1% -8,00% -6,00% -4,00% -2,00% 2,00% 4,00% 6,00% 8,00% 1% ENEL Theoretical Value ( ) 3,60 3,68 3,76 3,84 3,92 4,00 4,08 4,16 4,24 4,32 4,40 Enel Call 4,10 MAR 01Option Theoretical Value 0,040 0,059 0,079 0,103 0,133 0,17 0,206 0,250 0,299 0,352 0,409 Closing Price 0,170 0,170 0,170 0,170 0,170 0,170 0,170 0,170 0,170 0,170 Theoretical Liquidation Gains/Losses ( ) -0,130-0,111-0,091-0,067-0,037 0,04 0,08 0,13 0,18 0,24 X 10 Long Positions -1,30-1,11-0,91-0,67-0,37 0,36 0,80 1,29 1,82 2,39 Theoretical Liquidation Total Gains/Losses ( ) Enel Put 4,10 MAR 01 Option Theoretical Value 0,500 0,47 0,406 0,351 0,300 0,25 0,211 0,177 0,146 0,119 0,100 Closing Price 0,250 0,250 0,250 0,250 0,250 0,250 0,250 0,250 0,250 0,250 Theoretical Liquidation Gains/Losses ( ) 0,250 0,216 0,156 0,101 0,050-0,04-0,07-0,10-0,13-0,15 X 10 Long Positions 2,50 2,16 1,56 1,01 0,50-0,39-0,73-1,04-1,31-1,50 Theoretical Liquidation Total Gains/Losses ( ) Theoretical Liquidation Gains/Losses Totali ( ) Largest Theoretical Loss -3 Ordinary Initial Margins Premium Margins Class Total Initial Margins -3 Debit 4.20 Credit 4.17 Credit Enclosure n. 4

12 Cassa di Compensazione e Garanzia SpA TWO LONG POSITIONS FIB-30 MARZO 2001 FOUR SHORT POSITIONS MIDEX FUTURES MARCH 2001 DOWNSIDE UPSIDE Margin Interval -7,50% -6,00% -4,50% -3,00% -1,50% 1,50% 3,00% 4,50% 6,00% 7,50% FIB-30 Theoretical Value Closing Price Theoretical Liquidation Gains/Losses (Index Points) X 2 Long Positions Theoretical Liquidation Total Gains/Losses ( ) (60% Credit Reduction) DOWNSIDE UPSIDE Margin Interval -6,50% -5,20% -3,90% -2,60% -1,30% 1,30% 2,60% 3,90% 5,20% 6,50% Valore Teorico del MIDEX Futures Closing Price Theoretical Liquidation Gains/Losses (Index Points) X 4 Short Positions Theoretical Liquidation Total Gains/Losses ( ) (60% Credit Reduction) DOWNSIDE UPSIDE Theoretical Liquidation Total Gains/Losses ( ) FIB (60% Credit Reduction) Theoretical Liquidation Total Gains/Losses ( ) MIDEX Futures (60% Credit Reduction) Theoretical Liquidation Total Gains/Losses ( ) Equity Indices Product Group Largest Theoretical Loss Ordinary Initial Margins Product Group Total Initial Margins Debit Debit Enclosure n. 5

13 Cassa di Compensazione e Garanzia SpA TWO SHORT POSITIONS FUTURE MIB-30 MAR 01 TWO "SYNTHETIC" LONG POSITIONS FUTURE MIB-30 MAR 01 { FOUR LONG POSITIONS CALL MIB-30 MAR 01 FOUR SHORT POSITIONS PUT MIB-30 MAR 01 Premium Margins (Closing Price x Number of Lots x Index Point Value) 2273 x 4 x Credit 2236 x -4 x 2, Debit TOTAL 370 Credit DOWNSIDE UPSIDE Margin Interval -7,50% -6,00% -4,50% -3,00% -1,50% 1,50% 3,00% 4,50% 6,00% 7,50% FIB-30 Theoretical Value Closing Price Theoretical Liquidation Gains/Losses (Index Points) X 2 Short Positions Theoretical Liquidation Total Gains/Losses ( ) MIB-30 Theoretical Value MIB-30 Variation Call MAR 01 Option Theoretical Value Closing Price Theoretical Liquidation Gains/Losses (Index Points) X 4 Long Positions Theoretical Liquidation Gains/Losses ( ) Put MAR 01 Option Theoretical Value Closing Price Theoretical Liquidation Gains/Losses (Index Points) X -4 Short Positions Theoretical Liquidation Gains/Losses ( ) Theoretical Liquidation Total Gains/Losses ( ) Largest Theoretical Loss 0 Minimum Margins Ordinary Initial Margins Premium Margins Class Group Total Initial Margins -780 Debit -780 Debit 370 Credit -410 Debit Enclosure n. 6

14 Cassa di Compensazione e Garanzia SpA TWO ASSIGNED GENERALI OPTIONS CALL 29,00 MAR 00 Premium Margins (In-The-Money Amount x No. Of Lots x No. Underlying Shares) (30-29) x -2 x Debit TOTAL Debit Reference DOWNSIDE UPSIDE Price Margin Interval -7,50% -6,00% -4,50% -3,00% -1,50% 3 1,50% 3,00% 4,50% 6,00% 7,50% Generali Theoretical Value ( ) 27,75 28,20 28,65 29,10 29,55 30,45 30,90 31,35 31,80 32,25 Strike Price Generali Call 29,00 MAR 00 29,00 29,00 29,00 29,00 29,00 29,00 29,00 29,00 29,00 29,00 "Exercised Option Theoretical Value" ("Theoretical In-The- Money Amount ") -1,25-0,80-0,35 0,10 0,55 1,45 1,90 2,35 2,80 3,25 In-The Money Amount 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 Theoretical Liquidation Gains/Losses ( ) -2,25-1,80-1,35-0,90-0,45 0,45 0,90 1,35 1,80 2,25 X 2 Assigned Positions 4,50 3,60 2,70 1,80 0,90-0,90-1,80-2,70-3,60-4,50 Theoretical Liquidation Total Gains/Losses ( ) Largest Theoretical Loss Ordinary Initial Margins Premium Margins Class Total Initial Margins Debit Debit Debit Enclosure n. 7

15 Cassa di Compensazione e Garanzia SpA Options on Alitalia SpA ord. Shares Underlying Daily Price Variation Distribution From 16/12/1993 to 15/1/ ,85 16,51 16,84 6,28 9,42 12,56 15,70 18,84 21,98 25,12 Percent Price Variations Outside of margin Interval Margin Interval -24,64-28,26-25,12-21,98-18,84-15,70-12,56-9,42-6,28-3,14 3,14 17-dic feb apr giu-94 2-set-94 7-nov gen mar mag lug set-95 1-dic-95 8-feb apr giu ago ott dic-96 6-mar mag lug set nov gen-98 2-apr-98 8-giu ago ott dic feb apr-99 1-lug-99 2-set-99 5-nov gen mar mag lug set nov-00 Enclosure n. 8

16 Cassa di Compensazione e Garanzia SpA Options on Alitalia SpA ord. Shares Underlying Daily Price Variation Distribution From 16/12/1993 to 15/1/ Numbe er of Eventus Normal Distribution Actual Distribution x<-5-5<x<-4-4<x<-3-3<x<-2-2<x<-1-1<x<0 0<x<1 1<x<2 2<x<3 3<x<4 4<x<5 x >5 Standard Deviation: 3,14 Enclosure n. 9

17 Cassa di Compensazione e Garanzia SpA Options on Generali SpA ord. Shares Underlying Daily Price Variation Distribution from 2/1/1991 to 15/1/2001 Percent Price Variation Margin Interval Applied Current Margin Interval Outside Margin Interval 9,60 8,00 7,20 7,05 6,67 6,40 4,80 3,20 1,60-1,60-3,20-4,80-6,40-6,93-8,00-9,60-9,90 Enclosure n dic set giu mar dic set-99 2-lug-99 6-apr-99 4-gen set-98 3-lug-98 3-apr-98 5-gen-98 1-ott-97 3-lug-97 3-apr-97 2-gen set-96 2-lug-96 1-apr-96 3-gen set giu mar dic set-94 1-lug-94 1-apr-94 3-gen-94 1-ott-93 6-lug-93 7-apr-93 8-gen-93 6-ott-92 9-lug-92 9-apr gen-92 3-ott-91 4-lug-91 3-apr-91 3-gen-91-11,20

18 Cassa di Compensazione e Garanzia SpA Options on Banca Intesa SpA ord. Shares Daily Annualized Volatily calculated on a monthly basis From 2/1/1994 to 15/1/ gen-94 8-mar mag-94 8-lug-94 8-set-94 9-nov gen mar mag lug set nov gen mar mag lug set nov gen-97 3-apr-97 5-giu-97 5-ago-97 6-ott-97 4-dic feb apr giu ago ott dic feb apr giu ago ott dic feb apr giu ago ott dic-00 Enclosure n. 11

19 Telecom Italia SpA Rnc. Cassa di Compensazione e Garanzia SpA From: To: 2-gen gen-01 Current Margin Interval: 10,75% Number of Standard Deviations: 4,80 Applied since: 19-giu-00 Coverage Level Obtained: 99,80% Unitary Minimum Margin ( ): 25,00 Multiplier (No. Of Shares): MARGIN INTERVAL TOTAL 10 Years 9 Years 8 Years 7 Years 6 Years 5 Years 4 Years 3 Years 2 Years 1 Year 6 Months3 Months 1 Month 1 Week Standard Deviation of Daily Variations 2,24 2,24 2,30 2,23 2,23 2,24 2,31 2,36 2,42 2,28 2,09 1,65 1,73 2,04 2,25 Absolute performance: 760,42% 809,41% 581,73% 651,28% 311,77% 255,62% 326,85% 118,51% 46,44% 14,50% 12,27% -10,65% 11,88% 5,40% 5,28% Annualized Performance: 23,97% 27,85% 23,82% 28,73% 22,45% 23,60% 33,74% 21,63% 13,58% 7,02% 12,27% -20,10% 55,84% 88,34% 1249,01% No. Of Days: Annualized Daily Volatility: 35,63% 35,66% 36,58% 35,43% 35,47% 35,61% 36,80% 37,60% 38,48% 36,19% 33,18% 26,29% 27,49% 32,40% 35,79% Coverage Level Desired: 99,74% Events to Include: 2.527, , , , , , , ,37 756,03 503,69 252,34 126,67 63,83 20,95 4,99 Events to Exclude: 6,59 6,57 5,91 5,25 4,60 3,94 3,28 2,63 1,97 1,31 0,66 0,33 0,17 0,05 0,01 Largest Variations: Upside 11,62% 11,62% 11,62% 11,22% 11,22% 11,22% 11,22% 11,22% 11,22% 11,10% 11,10% 4,20% 4,20% 4,20% 4,20% 11,22% 11,22% 11,22% 11,10% 11,10% 11,10% 11,10% 11,10% 11,10% 9,38% 6,44% 3,98% 3,98% 3,80% 2,55% 11,10% 11,10% 11,10% 9,38% 9,38% 9,38% 9,38% 9,38% 9,38% 7,88% 5,68% 3,80% 3,80% 2,90% 0,13% 9,38% 9,38% 9,38% 9,35% 9,35% 9,35% 9,35% 9,35% 9,35% 7,13% 5,26% 3,11% 3,11% 2,55% % 9,35% 9,35% 9,35% 9,02% 9,02% 9,02% 9,02% 9,02% 9,02% 6,89% 5,20% 2,90% 2,90% 1,35% % 9,02% 9,02% 9,02% 8,24% 8,24% 8,24% 8,24% 8,24% 8,24% 6,65% 4,75% 2,78% 2,69% 1,02% --- 8,60% 8,60% 8,60% 7,88% 7,88% 7,88% 7,88% 7,88% 7,88% 6,44% 4,62% 2,69% 2,64% 0,68% --- Largest Variations: Downside 20,91% 20,91% 20,91% 15,27% 15,27% 15,27% 15,27% 15,27% 8,32% 6,74% 6,74% 5,65% 4,40% 4,34% 1,37% 15,27% 15,27% 15,27% 8,32% 8,32% 8,32% 8,32% 8,32% 7,95% 6,70% 5,65% 4,40% 4,34% 2,76% 0,11% 9,58% 9,58% 8,32% 7,95% 7,95% 7,95% 7,95% 7,95% 6,74% 6,02% 5,30% 4,34% 2,76% 1,62% % 8,32% 8,32% 7,95% 7,00% 6,74% 6,739% 6,74% 6,74% 6,72% 5,65% 4,40% 2,76% 2,19% 1,37% % 7,95% 7,95% 7,67% 6,74% 6,72% 6,72% 6,72% 6,72% 6,70% 5,64% 4,35% 2,42% 1,97% 1,13% % 7,67% 7,67% 7,32% 6,73% 6,70% 6,70% 6,70% 6,70% 6,02% 5,34% 4,34% 2,41% 1,62% 0,82% --- 7,49% 7,49% 7,00% 6,72% 6,02% 6,02% 6,02% 6,02% 5,65% 5,33% 4,11% 2,26% 1,61% 0,44% --- Supposed Margin Interval (Max): 9,35% 9,35% 9,35% 9,30% 9,30% 9,35% 11,05% 11,05% 11,05% 11,05% 11,05% 5,70% 5,20% 6,10% 6,75% Supposed Margin Interval (Min): 9,35% 9,35% 9,35% 9,05% 9,05% 9,35% 9,40% 9,40% 9,40% 9,40% 6,75% 5,70% 5,20% 6,10% 6,75% No. of Standard Deviations (Max): 4,17 4,17 4,07 4,17 4,17 4,18 4,78 4,67 4,57 4,86 5,30 3,45 3,01 2,99 3,00 No. of Standard Deviations (Min): 4,17 4,17 4,07 4,06 4,06 4,18 4,06 3,98 3,89 4,13 3,24 3,45 3,01 2,99 3,00 Events Included: Events Excluded: Obtained Coverage Level: 99,72% 99,72% 99,74% 99,75% 99,72% 99,74% 99,76% 99,70% 99,74% 99,80% 99,60% 10% 10% 10% 10% N.B.: Until July 18, 1997 STET Ord. Enclosure n. 12

20 Cassa di Compensazione e Garanzia SpA MIB30/MIDEX Product Group Offset Factor: Correlation between MIB30 and MIDEX indices daily value variations froml 2/01/1995 to 15/1/2001 MIDEX index variation 6,00 5,00 4,00 3,00 2,00 1,00-1,00-2,00-3,00-4,00-5,00-6,00-7,00-8,00 y = 0,621x + 0,0348 R² = 0,6313-9,00-8,00-7,00-6,00-5,00-4,00-3,00-2,00-1,00 1,00 2,00 3,00 4,00 5,00 6,00 7,00 8,00 MIB30 index variations Enclosure n. 13

21 0,90 0,80 0,70 0,60 0,50 0,40 0,30 0,20 0,10 Cassa di Compensazione e Garanzia SpA MIB30/MIDEX Product Group Offset Factor: Correlation betwen MIB30 and MIDEX indices calculated from 2/1/1995 to 15/1/2001 on a quarterly basis Correlation Factore 31-mar giu ago ott-95 9-feb gen mar-96 4-giu ago ott-96 3-gen mar mag-97 4-ago ott dic-97 6-mar mag lug-98 1-ott dic feb-99 6-mag lug set nov apr giu-00 7-set nov-00 Enclosure n. 14