BOVESPA Indices - Brazil Index (IBrX)

Presentation

Portfolio Composition  - September to December/2008

Current Portfolio Composition - 12/04/2008

1st. Preview of the Portfolio -  January to April/2009



PRESENTATION

The Brazil Index – IBrX is an index which measures the return on a theoretical portfolio composed by 100 stocks selected among BOVESPA’s most actively traded securities, in terms of number of trades and financial value. The component stocks are weighted according to the outstanding shares’ market value.


Shares Eligible for the Index

The IBrX will consist of 100 securities chosen from a list of shares classified in descending order according to liquidity, measured by their negotiability index (considering the last twelve months). These stocks must also meet the other inclusion criteria described below.


Criteria for Inclusion in the Portfolio

The index portfolio will include the 100 eligible companies that meet the following criteria:

a) to be among the 100-best classified stocks according to the negotiability index, measured in the last twelve months;
b) to have a trading session presence of at least 70%, measured in the last twelve months.

Companies that are under judicial reorganization, have filed for bankruptcy, are under a special regime or are subject to a trading halt of its security over an extended period of time will not integrate IBrX.


Criteria for Exclusion from the Portfolio

A share will be excluded from the portfolio, during periodical reevaluations, if it no longer meets the criteria for inclusion.

If, during the life cycle of the portfolio, the issuing company enters a regime of judicial reorganization or files for bankruptcy, its shares will be excluded from the index portfolio. In case of a public offering which results in the removal from the market of a significant proportion of shares, the company will be excluded from the portfolio. In such cases, the necessary adjustments will be made to ensure the continuity of the index.


Term of the Portfolio

The theoretical portfolio will be valid for four months, for the periods of January to April, May to August and September to December.

The portfolio will be recalculated at the end of each four-month period, according to the procedures and criteria of this methodology.


Weighting Criterion

The IBrX will measure the return on a theoretical portfolio consisting of the securities that meet all the criteria described above, which are weighted according to the respective market value of the type included in the portfolio.

In order to calculate the market value for the type, only the outstanding shares will be considered. In other words, those belonging to the controller will be excluded.

The base for the IBrX has been set at 1,000 points for the date of December 28th 1995, and its diffusion initiated on January 2nd 1997. In order to adapt to the initial base, the portfolio market value has been adjusted using a reducer (adjustment coefficient), designated by in the index formula. That is,

Initial index = Value of portfolio / = 1,000

The reducer for the index will be altered whenever necessary to accommodate inclusions in or exclusions from the portfolios, on the occasion of the periodical rebalancing or on the occasion of any adjustments arising from benefits/events given by the companies.

The specific weight of each share in the index may be altered during the term of the portfolio, due to the price evolution of each share and/or the benefit distribution by the issuing company.

When the issuing companies of component shares distribute benefits, the necessary adjustments will be made to guarantee that the index reflects not only the share price variations, but also the impact of the benefit distribution. Because of this methodology, the IBrX is considered to be an index that evaluates the total return of the shares comprising its portfolio.


Index Calculation

BOVESPA calculates the IBrX in real time, taking into consideration the prices of the last trades carried out on the cash market (round-lot) with the component shares.


Suspension of Trading

In case of suspension of a component share, the index will use the price of the last trade registered on the Exchange until the resumption of trading. If trading is not permitted for a period of 50 days, as of the date of suspension, or if there are no perspectives that trading will be resumed, or in case of rebalancing of the portfolio, the share will be excluded from the portfolio. In such a case, the necessary adjustments will be made to ensure the continuity of the index.


Procedures for Rebalancing

In the four-month rebalancing the following procedures will be adopted:

1. The rebalancing of the index's theoretical portfolio will occur after the closing of the last trading session of the four-month period and will adopt the index closing value of this day as its base.

2. Once selection (share/type) of the companies that will compose the portfolio for the coming four-month period has been concluded, the respective market value of each company/share in the share type is calculated - the product of multiplying the number of outstanding shares by their closing price -, and the results are summed up. That is, the economic value of the new portfolio is calculated according to the closing prices of the day.

3. The reducer adjusted for the new portfolio is reached by dividing the economic value, calculated in accordance with item 2, by the closing index of the four-month period.

4. The adjustment of the reducer aims to ensure the continuity of the index, in such a way that the number of index points does not change because of rebalancing. Thus, both the division of the "new market value" of the index theoretical portfolio by the new reducer, and the division of the "market value of the previous theoretical portfolio" by its respective reducer, result in the same index in terms of points.


Index Adjustments

So as to measure the total return on its theoretical portfolio, the IBrX will be adjusted for all benefits distributed by the issuing companies of the shares included in the portfolio.

1. Adjustments for benefits in shares of the same type
(Bonuses/Splits/Reverse Splits/Subscriptions)

After the last trading day prior to the benefit distribution, the market value of the component share/type is recalculated. In order to do so, the theoretical quantity adjusted to the benefit distributed and the "ex-theoretical" price of the share are used. The value thus obtained will be the basis for comparing the evolution of this share on the following trading session.

Example:

Let's consider company XPT which distributed a share bonus of 50% on the share type, D-0 being the last trading day before the benefit distribution.

Date
Price(R$)
Qty. XPTshares in the index
Market value ofXPT share (R$)
Variation (%)
Index (*)
D-0 (1) 300,00 1.000.000 300.000.000,00 - 100
D-0A (2) 200,00 1.500.000 300.000.000,00 - 100
D+1 (3) 220,00 1.500.000 330.000.000,00 + 10,0 110
D+2 230,00 1.500.000 345.000.000,00 + 4,5 115

(1) Closing position of the component share/type on the last trading day before the benefit distribution, that is, the quantity of shares before distribution of the benefit multiplied by the last asset price registered for that day.
(2) Adjusted closing position of the component share/type on the last trading day before the benefit distribution, that is, considering the new quantity of shares and the "ex-theoretical" price. This data will be used as a basis for comparison for the following day.
(3) Closing position of the component share/type on the first "ex-rights" trading day, taking into consideration the new quantity of shares and the "ex-market" closing price.
(*) If necessary, the index reducer will be adjusted to guarantee that the number of index points suffers no alteration due to the adjustment to the benefit.

In the case of reverse splits, the theoretical quantity will be reduced on the proportion determined by the company and a special "ex-theoretical" price will be calculated in order to maintain the economic value of the component share/type unaltered.

Apart from these situations, whenever the issuing company communicates the occurrence of facts that result in changes in its total share quantity (conversion of debentures into shares, cancellation of shares, conversion of one type of share into another, etc.), the relevant adjustments will be carried out.


2. Benefits in cash or other events

After the closing of the trading session of the last trading day prior to benefit distribution, the market value of the component share/type is recalculated, maintaining the theoretical quantities of these shares in the portfolio unaltered and using their "ex-theoretical" price. This value will serve as a basis for comparison of the share prices evolution on the following day.

Example:

Let's consider company YKW which distributed a dividend of R$ 30 per share, D-0 being the last trading day before the benefit distribution.

Date
Price(R$)
Qty. XPTshares in the index
Market value ofXPT share(R$)
Variation (%)
Index (*)
D-0 (1) 250,00 1.000.000 250.000.000,00 - 100,0
D-0A (2) 220,00 1.000.000 220.000.000,00 - 100,0
D+1 (3) 230,00 1.000.000 230.000.000,00 + 4,5 104,5
D+2 235,00 1.000.000 235.000.000,00 + 2,2 106,8

(1) Closing position of the component share/type on the last trading day before the benefit distribution, that is, the position calculated with the last price of that day.
(2) Adjusted closing position of the component share/type on the last trading day before the benefit distribution, that is, considering the same quantity of shares and the "ex-theoretical" price. This data will be used as a basis for comparison for the following day.
(3) Closing position of the component share/type on the first "ex-rights" trading day, taking into consideration the "ex-market" closing price.
(*) If necessary, the index reducer will be adjusted to guarantee that the number of index points suffers no alteration because of the adjustment to the benefit.


Special Procedures


1. Adjustments in the Case of Company Spin-Off

a) Announcement/effect of the spin-off

The announcement of the issuing company's decision to make a spin-off does not alter its situation in the index theoretical portfolio.

Once the spin-off has been made and while awaiting the resulting companies to be operational and registered, these companies will be considered as a trading unit and will remain in the index portfolio.

For the purposes of trading on BOVESPA, the effect of the spin-off means the act by which the shares of the companies resultant from the spin-off start to be traded on the trading session.


b) Beginning of trading on the stock exchange of the companies resulting from the spin-off

The index theoretical portfolio will include the companies resulting from the spin-off.

For example, company A was spun-off, giving rise to companies B (which holds 45% of the net worth of A), C (which holds 30%) and D (25%). Supposing that the participation of A in the index was 20%, the situations immediately prior to and subsequent to the start of trading of the spun-off companies would be as follows:

Closing of the trading session prior to the start of trading of the spun-off companies:

Company's shares
Qty. of outstanding securities(1)
Share prices(2)
Share weights(1)*(2)
Participationin the index(%)
A 1.000 2,00 20.000.000 20,0
Other 99 shares - - 80.000.000 80,0
Total 100 shares - - 100.000.000 100,0
Reducer     100.000  
Total IBrX points     1.000  

Opening of the trading session of the first trading date of the spun-off companies:

Company's shares
Qty. of outstanding securities (1)
Share prices (2)
Share weights (1)*(2)
Participationin the index (%)
A 10.000.000 0,90 9.000.000 9,0
B 10.000.000 0,60 6.000.000 6,0
C 10.000.000 0,50 5.000.000 5,0
Other 99 shares - - 80.000.000 80,0
Total 102 shares - - 100.000.000 100,0
Reducer - - 100.000  
Total IBrX points     1.000  

Notes:
- The example supposes that, in the spin-off, there was no reduction in the number of shares, but rather the distribution of shares of the companies resulting from the spin-off, in a quantity equivalent to that previously held. If the deliberation of the company is different, the procedures will be adapted, but the logic behind the adjustment will be identical.
- In this example, as the spun-off company gave rise to three companies, the number of shares included in the IBrX would change to 102 while the adjustment phase lasted.


c) Next four-month re-compositions

For the selection of the companies/shares that cumulatively meet the criteria for inclusion, the following procedures will be adopted:

· the companies resulting from the spin-off will be treated as a trading unit and their negotiability data will be considered in conjunction with those of the spun-off company;

· when 12 months have passed following the spin-off BOVESPA will exclude those shares that fail to present a suitable trading profile, based on their presence on the trading session, number of trades and financial value.


2. Adjustments in the Case of Public Offerings

Whenever a company launches a public offering that results in the acquisition of a significant proportion of the outstanding shares, BOVESPA may adopt one of the following procedures:

a) when the acquisition is lower than 2/3 (two thirds) of the outstanding shares, removal from the index of the percentage of outstanding shares bought by the company; or
b)
removal of the share from the index when the acquisition is higher than 2/3 (two thirds) of the outstanding shares, and inclusion of another share in its place (the one in the next position in the list of stocks assorted according to the inclusion criteria, used in the last four-month rebalancing).

In either case, an adjustment will be made to the index reducer.


3. Adjustments in the Case of Mergers

a) Company with shares included in the index merges with company whose shares also belong to the index

The shares of the incorporating company remain in the index and its theoretical quantity is altered in order to reflect the company’s new free float. No other company is included in substitution of the incorporated company.

b) Company with shares included in the index merges with company whose shares do not belong to the index

The shares of the incorporating company remain in the index and its theoretical quantity is altered in order to reflect the company’s new free float.

c) Company with shares included in the index is incorporated by company whose shares are not included in the index

This situation will be analyzed on a case-by-case basis, and BOVESPA may, at its own discretion:

· exclude the share from the index and include another share in its place;
· substitute the share of the incorporated company for shares of the incorporating company.


Note: In any situation, adjustments will be made to the reducer and the new quantities of shares will be used. Also, on the occasion of the four-month reevaluations, the negotiability data of the incorporated company will be added to those of the incorporating company.


CALCULATION FORMULA AND PROCEDURES

Negotiability Index

The negotiability index is calculated according to the following formula:

where:

IN = negotiability index
ni = number of trades carried out with stock "i" on BOVESPA cash market (round-lot)
N = total number of trades carried out on BOVESPA cash market (round-lot)
vi = financial value generated by the trades carried out with share "i" on BOVESPA cash market (round-lot)
V = total financial value of BOVESPA cash market (round-lot)

Note: In the calculation of the negotiability index, cross trades are not considered.

Formula for Calculating the IBrX

The IBrX may be calculated using the following formulas:

a) without using the reducer:

where:

IBrX (t) = index value on day "t"
IBrX (t - 1) = index value on day "t-1"
n = number of shares included in the index theoretical portfolio (100)
= theoretical quantity of share "i" available for trading on day "t-1". In the event of distribution of shares of the same type by the company, it refers to the theoretical quantity of share "i" available for trading on day "t-1", recalculated because of such benefit.
= price of share "i" at closing of day "t"
= closing price for share "i" on day "t-1", or its ex-theoretical price, in the case of benefit distribution on this day.


b) using the reducer:

where:

Index t = index value at moment "t"
n = total number of companies (in the share/type) included in the index theoretical portfolio
= last price of share "i at moment "t"

= quantity of share "i in the theoretical portfolio at moment "t"

= reducer used to adjust the index value to the current base


Adjustment Procedure for Benefits

The theoretical quantities of the companies in the share/type (i.e. their number of outstanding shares) will remain constant during the portfolio's four month period, and will only be altered in the event of benefit distribution in shares of the same type by the issuing companies (bonuses, splits, subscription, etc.).

The adjustment of the theoretical quantities in the exact proportion to the distributed benefit is carried out after the closing of BOVESPA's trading session, on the last day prior to the ex-date of the corporate action.

The following formula is used:

Qn = Qa * (1 + B + S)

where:

Qn = adjusted share quantity
Qa = previous share quantity
B = percentage of bonus and/or split, in index number
S = percentage of subscription, in index number

In the event that an approved benefit is partially homologated, or is not homologated, the quantity of shares in the portfolio will be proportionally reduced to reflect the real quantity of outstanding shares.

This adjustment will be carried out on the trading session after the date of receipt, by BOVESPA, of the communication expedited by the issuing company providing information of these facts. The index reducer will be adapted so that the index value suffers no alteration.

General Formula for Calculation of the "Ex-theoretical" Price


where:

Pex = ex-theoretical price
Pc = last price before the benefit distribution
S = percentage of subscription, in index number
Z = issuing value of the share to be subscribed, in Brazilian currency
D = dividends received per share, in Brazilian currency
J = interest on capital, in Brazilian currency
Vet = theoretical economic value per share, resulting from benefits distributed in another share type/asset
B = percentage of bonus (or split), in index number


Note: The Vet is calculated considering the financial amount which would be obtained from the sale of shares of another type and/or other assets (debentures, shares of another company, etc.) received. For example, suppose that company A is distributing to its shareholders, free of charge, one share of company B for every two shares held of company A, and that the shares of company B are evaluated at $ 5.00/share. In this case, the Vet will be equal to $2.50.

Example of IBrX calculation and rebalancing

For the calculation of the new portfolio all transactions carried out on BOVESPA's cash market (round lot) during the last twelve months are considered. For example purposes, the data shown below will represent the whole stock market, and the calculation of the negotiability index will be made based on the market total figures (and not based on the daily average figures).

Stock
Number of Trades
Value (R$)
Trading Session Presence*
Closing Quotation
Quantity of Issued Stocks
"Free Float" Percentual
on D+0
on D+1
AAA ON 15.000 150.000 171 2,50 2,60 5.000.000 35%
AAA PN 150.000 3.000.000 200 2,80 2,90 5.000.000 80%
BBB ON 80.000 400.000 195 100,00 95,00 25.000.000 25%
BBB PN 230.000 1.150.000 220 85,00 83,00 50.000.000 85%
CCC ON 95.000 600.000 230 50,00 48,00 18.000.000 40%
CCC PNA 105.000 800.000 245 62,00 65,00 25.000.000 95%
DDD ON 10.000 105.000 230 15,00 16,00 2.500.000 45%
DDD PNB 20.000 250.000 170 15,50 16,50 5.600.000 90%
EEE ON 15.000 220.000 210 105,00 115,00 10.000.000 35%
EEE PNA 55.000 500.000 200 120,00 123,00 13.000.000 85%
FFF ON 3.000 320.000 195 0,80 0,85 6.000.000 49%
FFF PN 8.000 70.000 200 0,95 1,03 6.500.000 78%
GGG ON 2.000 30.000 180 225,00 224,00 12.000.000 30%
GGG PN 10.000 80.000 205 230,00 229,00 18.000.000 70%
HHH ON 9.500 55.000 180 10,00 9,90 15.000.000 45%
HHH PN 120.000 1.500.000 250 10,50 10,45 10.000.000 75%
III ON 15.000 150.000 195 32,00 33,00 8.000.000 35%
III PN 3.000 35.000 220 33,00 34,00 9.000.000 90%
JJJ ON 4.000 50.000 130 45,00 46,00 7.500.000 25%
JJJ PN 25.000 200.000 205 47,00 47,50 8.500.000 80%
KKK ON 12.000 130.000 205 130,00 132,00 4.500.000 34%
KKK PN 3.000 31.000 240 125,00 129,00 6.000.000 98%
LLL ON 2.500 30.000 205 18,00 18,50 11.000.000 35%
LLL PN 8.000 144.000 140 17,00 17,00 9.000.000 100%
Total 1.000.000 10.000.000 -        

(*) There were 250 trading sessions at the period.

The first step for the index calculation consists in calculating the stock participation in terms of trading value, number of trades and trading session presence, and also to calculate their negotiability index, as shown in the table below.

Stock
Participation (%)
Negotiability Index
Presence*
"Free Float" Quantity
No. Trades (1)
No. Trades (2)
Part. %
Trading Sessions
Part. %
AAA ON 1,50 1,50 1,50 1,56 171 68,40 1.750.000
AAA PN 15,00 30,00 21,21 22,08 200 80,00 4.000.000
BBB ON 8,00 4,00 5,66 5,89 195 78,00 6.250.000
BBB PN 23,00 11,50 16,26 16,93 220 88,00 42.500.000
CCC ON 9,50 6,00 7,55 7,86 230 92,00 7.200.000
CCC PNA 10,50 8,00 9,17 9,54 245 98,00 23.750.000
DDD ON 1,00 1,05 1,02 1,07 230 92,00 1.125.000
DDD PNB 2,00 2,50 2,24 2,33 170 68,00 5.040.000
EEE ON 1,50 2,20 1,82 1,89 210 84,00 3.500.000
EEE PNA 5,50 5,00 5,24 5,46 200 80,00 11.050.000
FFF ON 0,30 3,20 0,98 1,02 195 78,00 2.940.000
FFF PN 0,80 0,70 0,75 0,78 200 80,00 5.070.000
GGG ON 0,20 0,30 0,24 0,25 180 72,00 3.600.000
GGG PN 1,00 0,80 0,89 0,93 205 82,00 12.600.000
HHH ON 0,95 0,55 0,72 0,75 180 72,00 6.750.000
HHH PN 12,00 15,00 13,42 13,96 250 100,00 7.500.000
III ON 1,50 1,50 1,50 1,56 171 78,00 2.800.000
III PN 0,30 0,35 0,32 0,34 220 88,00 8.100.000
JJJ ON 0,40 0,50 0,45 0,47 130 52,00 1.875.000
JJJ PN 2,50 2,00 2,24 2,33 205 82,00 6.800.000
KKK ON 1,20 1,30 1,25 1,30 205 82,00 1.530.000
KKK PN 0,30 0,31 0,30 0,32 240 96,00 5.880.000
LLL ON 0,25 0,30 0,27 0,29 205 82,00 3.850.000
LLL PN 0,80 1,44 1,07 1,12 140 56,00 9.000.000
Total 100,00 100,00 96,09 100,00 - -  

(*) There were 250 trading sessions at the period.

The next step is to select the stocks that will compose IBrX. In our example, the index will be composed by the top-10 stocks considering their negotiability index, which also meet the criteria of trading session presence. In order to effect the selection, the stocks must be ranked in descending order according to the negotiability index.

Stock
Neg. Index Part. %
Presence (%)
Quantity of Issued Stocks
Quantity of Portfolio Stocks
AAA PN 22,08 80,00 5.000.000 4.000.000
BBB PN 16,93 88,00 50.000.000 42.500.000
HHH PN 13,96 100,00 10.000.000 7.500.000
CCC PNA 9,54 98,00 25.000.000 23.750.000
CCC ON 7,86 92,00 18.000.000 7.200.000
BBB ON 5,89 78,00 25.000.000 6.250.000
EEE PNA 5,46 80,00 13.000.000 11.050.000
JJJ PN 2,33 82,00 8.500.000 6.800.000
EEE ON 1,89 84,00 10.000.000 3.500.000
III ON 1,56 78,00 8.000.000 2.800.000

Based on the selected portfolio stocks and on their quotation on T+0 the calculation of the portfolio's total value and of the reducer is made, so that the index is equal to 3.500 points at the opening of the first trading session of the new portfolio.

Stock
Quantity of Portfolio Stocks (1)
Quotations on T+0 (2)
Portfolio Weight (1)*(2)
AAA PN 4.000.000 2,80 11.200.000,00
BBB PN 42.500.000 85,00 3.612.500.000,00
HHH PN 7.500.000 10,50 78.750.000,00
CCC PNA 23.750.000 62,00 1.472.500.000,00
CCC ON 7.200.000 50,00 360.000.000,00
BBB ON 6.250.000 100,00 625.000.000,00
EEE PNA 11.050.000 120,00 1.326.000.000,00
JJJ PN 6.800.000 47,00 319.600.000,00
EEE ON 3.500.000 105,00 367.500.000,00
III ON 2.800.000 32,00 89.600.000,00
Total     8.262.650.000,00
Reducer     2.360.757,14
Index     3.500,00

O índice do pregão seguinte deve ser calculado considerando-se as cotações das ações componentes em D+1. Com base nesses preços, pode-se também calcular a variação do índice e as variações individuais de cada ação entre D+0 e D+1.

Stock
Quantity of Portfolio Stocks (1)
Quotations on T+1 (2)
Portfolio Weight (1)*(2)
Variation (%) on T+1
AAA PN 4.000.000 2,90 11.600.000,00 3,57
BBB PN 42.500.000 83,00 3.527.500.000,00 -2,35
HHH PN 7.500.000 10,45 78.375.000,00 -0,48
CCC PNA 23.750.000 65,00 1.543.750.000,00 4,84
CCC ON 7.200.000 48,00 345.600.000,00 -4,00
BBB ON 6.250.000 95,00 593.750.000,00 -5,00
EEE PNA 11.050.000 123,00 1.359.150.000,00 2,50
JJJ PN 6.800.000 47,50 323.000.000,00 1,06
EEE ON 3.500.000 115,00 402.500.000,00 9,52
III ON 2.800.000 33,00 92.400.000,00 3,13
Total     8.277.625.000,00 0,18
Reducer     2.360.757,14  
Index     3.506,34 0,18
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