BOVESPA Indices - BOVESPA Index (Ibovespa)


Presentation

Methodology Aspects

Portfolio Composition - September to December/2008

Current Portfolio Composition - 12/04/2008

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



PRESENTATION

The Bovespa Index is the main indicator of the Brazilian stock market’s average performance. Ibovespa’s relevance comes from two facts: it reflects the variation of BOVESPA’s most traded stocks and it has tradition, having maintained the integrity of its historical series without any methodological change since its inception in 1968.

What is the Bovespa Index?

It is the current value, in Brazilian currency, of a theoretical stock portfolio constituted in 02/01/1968 (base value: 100 points), by a hypothetical investment. No additional investment has been made since this date, apart from the reinvestment of the distributed benefits (such as dividends, subscription rights and stocks bonuses). In that way, the index reflects not only the variation of the stock prices but also the impact of the distribution of benefits, and is considered an indicator that evaluates the total return of its components stocks.

Extremely reliable and with a methodology easily understandable by the market, the Bovespa Index represents faithfully the average performance of the main traded stocks and the profile of the cash market operations carried out on BOVESPA.

(*) The index has suffered, only for disclosure purposes and without any loss to its calculation methodology, the following changes:
1 – division by 100, on 10/03/1983;
2 – division by 10, on 12/02/1985;
3 – division by 10, on 08/29/1988;
4 – division by 10, on 04/14/1989;
5 – division by 10, on 01/12/1990;
6 – division by 10, on 05/28/1991;
7 – division by 10, on 01/21/1992;
8 – division by 10, on 01/26/1993;
9 – division by 10, on 08/27/1993;
10 – division by 10, on 02/10/1994;
11 – division by 10, on 03/03/1997.

Objective

Ibovespa’s basic objective is to be an average indicator of the market performance. For that purpose, its composition aims at reflecting as close as possible the real configuration of the cash market operations (round lot) on BOVESPA.

Ibovespa’s Representativity

  1. In terms of liquidity:
    The stocks that integrate Ibovespa’s theoretical portfolio represent more than 80% of the number of trades and the financial value registered on BOVESPA’s cash market (round lot).

  2. In terms of market capitalization:
    The issuing companies of the stocks that compose the Bovespa Index theoretical portfolio are responsible, in average, for approximately 70% of the sum of all BOVESPA’s companies’ capitalization.

Disclosure and Monitoring

BOVESPA calculates Ibovespa in real time, considering the prices of the last trades carried out in the cash market (round lot) with the stocks that compose its portfolio.

Its disclosure is made through BOVESPA’s diffusion system and is also retransmitted by many "vendors", thus making it possible to monitor the index performance "on line" in any part of Brazil or of the world.

Transparency

Ibovespa’s reliability comes from its simple calculation methodology, and also from the availability of its data to the investor public. The market recognizes the index’s positive characteristics, and this recognition is expressed by the fact that Ibovespa is the only performance indicator of the Brazilian stocks that has a liquid future market (one of the biggest index future market of the world).

Security, Reliability and Independence

Bovespa is responsible for Ibovespa’s management, calculation, disclosure and maintenance. This responsibility assures the strict compliance with the rules and technical procedures contained in the index methodology.

 

METHODOLOGIC ASPECTS

Criteria for Inclusion in the Portfolio

The Ibovespa theoretical portfolio is composed by the stocks that meet the following criteria, in regard to the last twelve months:

  • to be included in the group of stocks whose negotiability indexes added represent 80% of the total value of all individual negotiability indexes;
  • to have a trading value participation higher than 0,1% of the total;
  • to have a trading session presence of more than 80%.

Participation of the Stock in the Theoretical Portfolio

The participation of each stock in the portfolio has a straight relation with its representativity in the cash market – in terms of number of trades and financial value – adjusted to the sample´s size. This representativity is obtained by the negotiability index, calculated according to the following formula:

IN =

where:
IN = negotiability index
ni = number of trades carried out with stock "i" on BOVESPA cash market (round lot)
N = total numbers 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.

Criteria for Exclusion from the Portfolio

A stock selected to compose the portfolio will only be excluded when it no longer meets at least two of the criteria of inclusion.

Companies that are in a regime of judicial reorganization, files for bankruptcy, are in a special situation or subject for a long period of trade suspension will not integrate Ibovespa.

Calculation of Bovespa Index

The Bovespa Index is the sum of the weights (stock theoretical quantity multiplied by its last price) of the stocks that integrates the theoretical portfolio. In this sense, it can be calculated, at any time, according to the following formula:

Ibovespa t =


where:
Ibovespa t = Bovespa Index at moment "t"
n = total number of stocks that compose the theoretical portfolio
P = last price of stock "i" at moment "t"
Q = theoretical quantity of stock "i" in the portfolio at moment "t"

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.

Term of the Portfolio

To ensure Ibovespa’s representativity along the time, its portfolio is recalculated at the end of each four months, according to the procedures and criteria of this methodology. At the rebalancings, the changes in the relative participation of each stock in the index are identified, as well as their maintenance or exclusion, and possible inclusions of new papers are defined.

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

Procedures for Rebalancing

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

  • BOVESPA calculates the negotiability index for each traded stock considering the last twelve months. These indexes are ranked in decreasing order, and a column shows the accumulated sum of the indexes from the highest to the lowest one. Then the participation of each individual negotiability index is calculated in relation to the total sum, and the stocks whose accumulated participation reaches 80% are listed.
  • The listed stocks will compose the index portfolio once they meet the two other criteria of inclusion. A stock which does not meet these criteria will be substituted by the following stocks in the list which meet those parameters.
  • The next step is to identify, between the stocks that belong to the current portfolio, if any of them will be excluded.
  • The negotiability index of the chosen stocks are listed again, and the participation percentage of each stock in relation to the total sum of all negotiability indexes is calculated.
  • The adjusted participation of each stock multiplied by the index value of the last day of the previous four month period will determine the initial "weight" (number of index points) of each stock.
  • Each stock’s theoretical quantity, resulting from the division of its share in the index composition (weight) by its closing price of the last day of the previous four month period, will remain constant for the four months of the new portfolio, and will only be modified in the case of a benefit distribution (dividends, stock bonuses, subscriptions, etc.) by the issuing company.

See example of Ibovespa rebalancing and calculation

Portfolio´s Previews

Aiming at helping the market participants who use Ibovespa portfolio as an instrument to elaborate their investment polices, BOVESPA regularly discloses three previews of the new composition 30 days before, 15 days before and 1 day before of the new portfolio for the next four months. In special situations, however, Bovespa may anticipate the previews disclosure and/or increase their number in order to calm the market.

Index Adjustments

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

The adjustment is made considering that the investor sold the stocks at the closing price of the last trading day prior to the benefit distribution and used the resources to buy the same shares without the benefit (i.e., at the "ex-theoretical" price).

Formula for adjustments in the theoretical quantity

(in the case of benefit distribution)

where:
Qn = adjusted share quantity
Qo = previous share quantity
Pc = last price before the benefit distribution
Pex = ex-theoretical price, calculated based on Pc

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

Special Procedures

1. Adjustments in the Case of Company Spin-Off

1.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.

1.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. The participation presented by the original company in the theoretical portfolio will be distributed among the resulting companies.

For each company included in the index, the share quantity and the theoretical price will be determined in function of the spin-off ratio informed by the company.

1.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;
  • the individual participation of each new stock in the portfolio will be defined at BOVESPA’s discretion and based on the elapsed period, in function of the effective negotiability of each stock or in function of the price level of each asset;
  • until an entire rebalancing period of the trading of the individual companies is complete (minimum of four months, maximum of seven months), BOVESPA will maintain in the index portfolio the stocks with the same theoretical quantity;
  • at the recompositions made after this minimum period, BOVESPA will continue to use on the analysis of the last 12 months the data as described above, but the participation of each company in the Ibovespa will be defined in function of its individual performance considering the available period of individual trading;
  • when 12 months have passed following the spin-off BOVESPA will exclude those stocks that fail to present a suitable trading profile, based on their presence on the trading session, number of trades and financial value.

See example of adjustment in case of Spin-off

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:

  1. 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 and distribute the relative participation of this percentage proportionality to the other component stocks; or
  2. removal of the share from the index when the acquisition is higher than 2/3 (two thirds) of the outstanding shares, and distribute its relative participation in the portfolio proportionality to the other component stocks (the same procedure adopted for companies that enter a regime of judicial reorganization, bankruptcy or are no longer listed on the stock exchange).

3. Adjustments in the Case of Mergers

3.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 adjusted in function of the exchange ratio between the stocks of the incorporated and of the incorporating companies.

3.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 with the same theoretical quantity.

3.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, redistributing its participation for the other stocks of the portfolio;
  • substitute the share of the incorporated company for shares of the incorporating company, making the necessary adjustments in the theoretical quantity in function of the exchange ratio between the stocks.

Note: In any situation, on the occasion of the four-month reevaluations, the negotiability data of the incorporated company will be added to those of the incorporating company.

Example of Ibovespa Rebalancing and Calculation

 In 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 figures).

Stock
Number of Trades
Value (R$)
Trading Session**Presence
Closing Quotation
On T+0
On T+1
* AAA PN

150.000

3.200.000

235

2,80

2,90

BBB ON

80.000

400.000

190

100,00

95,00

* BBB PN

230.000

1.200.000

245

85,00

83,00

CCC PNA

105.000

800.000

245

620,00

610,00

DDD ON

10.000

105.000

195

15,00

16,00

EEE ON

15.000

220.000

206

105,00

115,00

EEE PNA

55.000

500.000

240

120,00

123,00

FFF PN

8.000

70.000

200

0,95

1,03

* GGG ON

2.000

8.000

180

225,00

224,00

HHH ON

12.000

130.000

201

10,00

9,90

* HHH PN

120.000

1.600.000

250

10,50

10,45

* III ON

15.000

150.000

205

320,00

330,00

JJJ ON

4.000

50.000

130

45,00

46,00

JJJ PN

20.000

250.000

197

47,00

47,50

Total

826.000

8.683.000

-

-

-

 

*Shares included in the old portfolio.

**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**

N° Trades (1)

Value (R$) (2)

Part. %

Trading Sessions

Part. %

* AAA PN

18,16

36,85

25,87

26,85

235

94,00

BBB ON

9,69

4,61

6,68

6,93

190

76,00

* BBB PN

27,85

13,82

19,62

20,36

245

98,00

CCC PNA

12,71

9,21

10,82

11,23

245

98,00

DDD ON

1,21

1,21

1,21

1,26

195

78,00

EEE ON

1,82

2,53

2,15

2,23

206

82,40

EEE PNA

6,66

5,76

6,19

6,43

240

96,00

FFF PN

0,97

0,81

0,88

0,92

200

80,00

* GGG ON

0,24

0,09

0,15

0,16

180

72,00

HHH ON

1,45

1,50

1,47

1,53

201

80,40

*

HHH PN

14,53

18,43

16,36

16,98

250

100,00

* III ON

1,82

1,73

1,77

1,84

205

82,00

JJJ ON

0,48

0,58

0,53

0,55

130

52,00

JJJ PN

2,42

2,88

2,64

2,74

197

78,80

Total

100,00

100,00

96,34

100,00

-

-

 *Shares included in the old portfolio.
**There were 250 trading sessions at the period.

The stocks should then be classified in descending order according to the negotiability index, and it should be verified if they meet or not the inclusion/exclusion criteria.

Stock

Participation (%)

Negotiability Index

Presence**

Value (R$)

Index

Part. %

Accum. Part. %

* AAA PN

94,00

36,85

25,87

26,85

26,85

* BBB PN

98,00

13,82

19,62

20,36

47,21

* HHH PN

100,00

18,43

16,36

16,98

64,19

CCC PNA

98,00

9,21

10,82

11,23

75,43

BBB ON

76,00

4,61

6,68

6,93

82,36

EEE PNA

96,00

5,76

6,19

6,43

88,79

JJJ PN

78,80

2,88

2,64

2,74

91,53

EEE ON

82,40

2,53

2,15

2,23

93,75

* III ON

82,00

1,73

1,77

1,84

95,59

HHH ON

80,40

1,50

1,47

1,53

97,12

DDD ON

78,00

1,21

1,21

1,26

98,38

FFF PN

80,00

0,81

0,88

0,92

99,30

JJJ ON

52,00

0,58

0,53

0,55

99,84

* GGG ON

72,00

0,09

0,15

0,16

100,00

Total

-

100,00

96,34

100,00

-

 *Shares included in the old portfolio.
**There were 250 trading sessions at the period.

The next step is to select the stocks that will compose the new portfolio.

Stock

Trading Session Presence** (%)

Neg. Ind.

Neg. Ind. Adjust. Part. %

* AAA PN

94,00

25,87

32,08

* BBB PN

98,00

19,62

24,33

* HHH PN

100,00

16,36

20,29

CCC PNA

98,00

10,82

13,42

EEE PNA

96,00

6,19

7,68

* III ON

82,00

1,77

2,20

Total

-

80,63

100,00

 *Shares included in the old portfolio.
**There were 250 trading sessions at the period.

The new portfolio is then established supposing that the closing index of T+0 has been 10.000 points (referent to the previous portfolio).

Stock

Neg. Ind. Adjust. Part. % (a)

Index Points (a)*10.000=(b)

Quotations on T+0 (c)

Theoretical Quantity (b) / (c)

AAA PN

32,0832

3.208,3209

2,80

1.145,8289

BBB PN

24,3283

2.432,8298

85,00

28,6215

HHH PN

20,2912

2.029,1203

10,50

193,2496

CCC PNA

13,4214

1.342,1369

620,00

2,1647

EEE PNA

7,6793

767,9334

120,00

6,3994

III ON

2,1966

219,6587

320,00

0,6864

Total

100,00

10.000,00

-

1.376,9506

Once the portfolio is constituted, the calculation of the index at the end of T+1 is effected based on the prices of the component stocks for this day, as explained below:

Stock

Theoretical Quantity (d)

Quotations on T+1 (e)

Index Points (d)*(e)

Variation (%) on T+1

AAA PN

1.145,8289

2,90

3.322,9038

3,57%

BBB PN

28,6215

83,00

2.375,5867

-2,35%

HHH PN

193,2496

10,45

2.019,4578

-0,48%

CCC PNA

2,1647

610,00

1.320,4896

-1,61%

EEE PNA

6,3994

123,00

787,1317

2,50%

III ON

0,6864

330,00

226,5231

3,13%

Total

1.376,9506

-

10.052,09

0,52%

 

Example of Adjustment in Case of Spin-off

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

Theoretical Quantity (1)

Share Price (2)

Ibovespa Points (1)x(2)

Participation in the Index (%)

A

1.000

2,00

2.000

20,0

Other stocks

-

-

8.000

80,0

Ibovespa

-

-

10.000

100,0

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

Company´s Shares

Theoretical Quantity (1)

Share Price (2)

Ibovespa Points (1)x(2)

Participation in the Index (%)

B

1.000

0,90

900

9,0

C

1.000

0,60

600

6,0

D

1.000

0,50

500

5,0

Other stocks

-

-

8.000

80,0

Ibovespa

-

-

10.000

100,0

Note: 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.


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