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Methodological Aspects
Portfolio Composition - September to December/2008
Current Portfolio Composition - 12/04/2008
1st. Preview of the Portfolio - January to April/2009
METHODOLOGICAL ASPECTS
Presentation
The Valor Bovespa Index - 2nd Tier (IVBX-2) was jointly developed by BOVESPA and the newspaper Valor Econômico, in the aim of measuring the return on a hypothetical portfolio consisting exclusively of securities issued by companies of excellent image among investors, classified from the 11th position down, both in terms of market value and liquidity of their shares.
Shares Eligible for the Index
The IVBX-2 index will consist of 50 securities chosen from a list of shares classified in descending order according to liquidity, measured by their negotiability index (considering the last twelve months). Given the purpose of the index, those shares that present the 10 highest negotiability indexes will not be included in the portfolio, nor will those issued by the companies with the 10 highest market values within the sample. Thus, the portfolio will be made up of the 50 best shares whose negotiability indexes are classified from the 11th position down, which meet the other inclusion criteria described below.
Criteria for Inclusion in the Portfolio
The index portfolio will include the 50 eligible companies that meet the following criteria:
a) to be classified from the 11th position down, in terms of negotiability index measured in the last twelve months;
b) do not present the 10 highest market values within the sample;
c) do not have any other share type classified among the 10 highest negotiability indexes;
d) to have a trading session presence of more than 70%.
A company will only be included in the portfolio with its most liquid share type (the one which presents the highest negotiability index for the period).
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.
When, in a periodical reevaluation, there are indications that the type of a component share which is included in the index should be substituted by another, BOVESPA reserves the right not to carry out such a substitution if any atypical trades have occurred with that security.
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 a case, 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 IVBX-2 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 those shares available for trading will be considered. In other words, those belonging to the controller will be excluded.
The base for the IVBX-2 has been set at 1,000 points, for the date of December 30th 1999. In order to adapt to the initial base, the market value of the portfolio has been adjusted using a reducer (adjustment coefficient), designated by a in the index formula. That is,
Initial index = Value of portfolio / a = 1,000
The divisor 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 eventual 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 evolution of the prices for each share and/or the distribution of benefits 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 IVBX-2 is considered to be an index that evaluates the total return on the shares comprising its portfolio.
Index Calculation
BOVESPA calculates the IVBX-2 every 30 seconds, taking into consideration the prices for 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 -, followed by the sum of all these figures. 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 IVBX-2 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$) |
Qty. XPT
shares in
index |
Market
value of XPT
share (R$) |
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$) |
Qty. YKW
shares in the
index |
Market
value of the YKW
share (R$) |
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-Offs
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:
Opening of the trading session of the first trading date of the spun-off companies:
Company
Shares |
Qty. Securities
in public hands
(1)Share Prices
(2)Weight of Shares
(1)*(2) |
% Participation
in the index |
| A |
10,000,0000.909,000,000 |
9.0 |
| B |
10,000,0000.606,000,000 |
6.0 |
| C |
10,000,0000.505,000,000 |
5.0 |
| Other 49 shares |
--80,000,000 |
80.0 |
| Total 52 shares |
--100,000,000 |
100.0 |
| Reducer |
--100.000 |
|
| Total IVBX-2 points |
1,000 |
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Note:
1) 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.
2) In this example, as the spun-off company gave rise to three companies, the number of shares included in the IVBX-2 would change to 52 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 two 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 a 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
1. Negotiability Index
| IN |
= |
 |
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.
2. Formula for Calculating the IVBX-2
The IVBX-2 may be calculated using the following formulas:
a) without using the reducer:
| IVBX-2 (t) = IVBX-2 (t - 1) * |
 |
where:
| IVBX-2 (t) |
= |
index value on day "t" |
| IVBX-2 (t - 1) |
= |
index value on day "t-1" |
| n |
= |
number of shares included in the index theoretical portfolio (50) |
 |
= |
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:
| Indext |
= |
 |
= |
 |
where:
| Índicet |
= |
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" |
| µ |
= |
reducer used to adjust the index value to the current base |
3. 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 quantity of shares
Qa = previous quantity of shares
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.
4. 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.
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