Calculation & Maintenance
Index Maintenance
The ZagadaWaagstein Index Committee consistently and continually evaluates and monitors constituents on the Index to ensure they maintain the capitalization, liquidity and governance standards and rules established by the index committee. Companies may be removed from the Index each quarter at rebalancing. ZagadaWaagstein may also remove companies due to corporate actions resulting in mergers, acquisitions and bankruptcies. Zagada Waagstein rebalances the Index each quarter to ensure each holding represents 1% of the total index value.
Index Calculation
The ZagadaWaagstein Global Outsourcing 100 Index is the exclusive property of Zagada Markets Inc, a U.S. registered entity and Waagstein Research AB, a Swedish registered entity. Both companies have signed a co-publishing agreement. Zagada and Waagstein have jointly contracted with Standard & Poor’s to maintain and calculate the Index. S&P shall have no liability for any errors or omissions in calculating the Index. Standard & Poor’s is a trademark of The McGraw-Hill Companies, Inc.
Equal Weighted Index Calculation
An equal weighted index is one where every stock has equal weight in the index and a portfolio that tracks the index will invest an equal dollar amount in each security. As stock prices move, the weights will shift and exact equality will be lost. Therefore, an equal weighted index must be rebalanced from time to time to re-establish the proper weighting. (In contrast, a cap-weighted index requires no rebalancing as long as there aren’t any changes to share counts, IWFs, returns of capital, or stocks added or deleted.) The overall approach to calculate equal weighted indices is the same as in the capweighted indices; however, the share count is re-defined to be a number that will achieve equal weighting at each rebalancing. Recall two basic formulae:
| Index Level | = Index MarketValue |
|
Divisor |
||
and
Index MarketValue P Shares = Σi Pi x Sharesi
To calculate an equal weighted index, shares are re-defined. Rather than being the actual count of shares outstanding multiplied by the IWF, or other such adjustment factors, the “shares” number is calculated to establish equal weighting. For clarity, this section will refer to the “shares” figure as c_shares for calculated_shares. Not only are these not the true share count, they have essentially no relation to the true share count. Moreover, thec_shares figure may be less than one and will probably not be an integer value. Thec_shares are calculated at each re-balancing.
Since c_shares are being used instead of true shares, the Index Market Value defined in (14) is not the actual market value of the index. For a cap-weighted index, one can say the index market value is the total market value of all the shares. In an equal weighted index, there is no equivalent concept; rather, the Index Market Value is an arbitrary or nominal value for the portfolio used when the c_shares figure is established; therefore it is called c_index market value here for calculated_index market value. Given this, the c_shares are calculated:
| c _ sharesi = | k |
| Pi |
where k is a constant and Pi is the price of stock i at the close of the rebalancing date.
The index divisor is defined based on the index level and c_index market value from equation . The index level is not altered by rebalancing. However, since prices and, therefore, c_shares will have changed since the last rebalancing, the divisor may change at the rebalancing. In a cap-weighted index, the index market value is the total value of all stocks in the index. This provides a link across each divisor change. Given the arbitrary nature of the c_index market value, there is no link from one rebalancing to the next and from one divisor value to the next. This does not matter if the only calculations being made are index levels and total returns. However, if the divisor is used to calculate time series of index fundamentals, such as earnings per share, continuity is required. Therefore, the divisor should be re-calculated at the rebalancing to be consistent across the rebalancing.So:
| (Divisor) after rebalance = | (Index Market Value) after rebalance |
| (Index Value) before rebalance |
where,
Index MarketValue P Shares = Σi Pi x Sharesi
These calculations can be re-stated somewhat differently, but achieving the same results. Instead of defining c_shares as done here, one can calculate an adjustment factor to be applied to the actual share count that assures the equal weight result. Refer to the section titled Index Fundamentals for information on the calculation of earnings per share and other index fundamental values.
Corporate Actions and Index Adjustments
The table shows the necessary adjustments to the index and the divisor for managing an equal weighted index. One key issue is how to handle events when one stock is replaced by another. Given that stock prices move all the time, the index is only truly equally weighted at the rebalancing. Therefore, when stocks are added or deleted either the new stock must assume the actual weight of the old stock or the entire index must be rebalanced. Since index rebalancing generates trading costs for tracker funds, the design decision is usually made to have a new stock assume the weight of the stock being dropped until the next rebalancing.
