When stocks enter and exit the index, index-tracking fund managers attempt to trade as much as 10% of an entire company, with their intentions publicly known in advance. This opens up the possibility of other market participants profiting at their expense, creating an additional cost for passive investors that is not reflected in tracking error.

Standard and Poor’s (S&P) determine the rules governing the composition of the S&P 500, which amount to a trading system for an index-tracking fund. Since October 1989, S&P announce changes in the composition of their index early enough to allow index fund managers to buy (or sell) stocks added to (or removed from) the index in a timely fashion.

For equity investors, the costs associated with turnover can be split into two: 1) commissions that are paid for brokerage services; and 2) market impact, often referred to as “slippage”, which forces investors buying large blocks of shares to pay a premium. We focus on the latter as commissions are very low; even assuming a high rate of 10 basis points per transaction, the resulting cost is less than 2 basis points per year.

We start by detailing the data we use for this analysis and how it was collected. We then analyse S&P 500 turnover since 1989, and estimate the commissions paid, before estimating the price impact of changes to index constituents.

Most stock-level data – and especially index membership information – is provided by S&P, together with various index level-data such as market capitalisation, price and total-return index values. We checked the data against other providers, and it was consistent except for minor glitches in earlier years.

S&P do, however, define price and dividend returns in a way that might be misleading some. For instance, S&P include large special dividends (such as the one paid by Microsoft in 2004) in the price return and not in the dividend return.

To assess price impact, we needed historical prices for stocks when they were not in the S&P 500. For that, we used Centre for Research in Security Prices (CRSP) data.

Finally, for index additions and deletions, S&P have announced changes to constituents five days in advance, whenever possible since 1989. In practice, this varied substantially. S&P provided us with data they had collated for earlier studies, but we had to collect original press releases from various archives and online sources for the remaining announcements.

Market-cap weighting means that an S&P 500 tracker does not trade most days, but a number of events cause turnover:

• Additions and deletions: When S&P modify the index constituent list, the manager has to sell the stocks removed from the index and buy the newly added ones.
• Share issues and buybacks: When a company issues new shares or buys back those in issue, the manager has to buy or sell stocks to adjust the weight of that company.
• Free-float changes: When S&P changes the fraction they consider to be the free-float shares of a company, the company index weight changes.
• Reinvestment of cash proceeds: Dividends need to be reinvested when tracking the total-return index.
• Net rebalancing: When company weights change due to additions/deletions or share issues/buy backs, rebalancing of the remaining stocks in the index must also take place.

Estimates of the turnover caused by these changes are provided in Table 1, which suggest that the manager has to buy and sell 6.8% of the portfolio each year on average.

We only assess the effect of index additions and deletions in this study as these trades are confined to a few stocks, so the price impact will be most visible (rebalancing trades and cash reinvestment are diluted across all constituents).

We also exclude free-float changes, which cause minimal turnover, and share issues and buybacks (the market impact is offset by the supply or demand from the company itself).

Additions to the index are caused by two types of event:

1) When S&P decide to add an already listed and traded stock to the index, such as Yahoo. In this case, managers have to buy the newly added stock.

2) When a company already listed in the S&P 500 index spins off a new entity, and S&P decide to include the spin-off in the index. These new spin-offs do not create turnover as the fund receives the new stock, due to holding the corresponding shares in the previous entity. But trading may be required by S&P removing a stock from the index.

Between January 1990 and December 2011, 537 stocks have been added to the S&P 500. Of these, 483 (90%) were type 1), and 54 (10%) were type 2). We focus on type 1) additions here.

There are three types of index deletions:

1) S&P decides to remove a stock, which requires the manager to trade of out of their position.

2) A stock is acquired by a company, either inside or outside of the S&P. No action is required here except for the rebalancing or reinvestment of cash proceeds.

3) The rare case when a stock is delisted. This can correspond to a variety of situations, but we do not analyse this further as it only relates to a few cases.

Between January 1990 and December 2011, 537 stocks have been deleted from the S&P 500 index. Of these, 220 (41%) were type 1), and 317 (59%) were type 2) or 3). We focus on type 1) deletions in this study.

Figure 1 shows the cumulative excess returns of stocks added to the index, conditioned on the offset to the addition date.

Similarly, to obtain Figure 2, we compute an average price impact for stocks deleted from the index, conditioned on the offset to the deletion day.

Looking at both curves, it is apparent that stock additions and deletions have a marked effect on equity prices. Index trackers are buying the newly added stocks at a premium, and selling the deleted stocks at a discount.

Estimating the cost of this effect on an index tracker is difficult, as we need to compare how the price relative to the market would have changed to if the stock had not been added to the index. We also need to distinguish between permanent impact and reverting impact (which can be defined as slippage).

Two different views are represented in the literature. The first uses a reference price of zero, relative to the market. In the case of the additions in Figure 1, a simple fit finds an impact of 6.9% from 10 days prior to the addition. This reverts to 5.3% by 10 days after the addition, indicating a reverting effect over this period of 1.6%, as shown in Figure 3.

A similar graph can be drawn for deletions. Table 2 summarises the permanent and temporary impacts and the resulting cost to the investor.

For this study we only looked 10 days either side of the event, but the event could have an effect outside of this period. If this is the case, the price impact and cost to the investor would amount to a total of 14.2 basis points of the portfolio per year.  

The authors of [1] and [4] argue against this framework. Intuitively, the stock has been added to the index because its market capitalisation has recently been increasing relative to the index. Therefore, on average, stocks due to be added to the index exhibit positive momentum. Similarly, for a stock to leave the index, it must have fallen in the recent period. We therefore expect deletions to have negative momentum.

Further, in [4] the authors argue that price impact of an addition to the index is reverting and has no permanent effect.

This framework implies a different reference price, and a modification to the diagram of permanent and reverting impact, as shown in Figure 4.

Assuming the permanent impact is zero, and the temporary impact is larger than before, then we end up with Table 3.

The total cost to the investor according to these estimates is 26.4 basis points per year, compared to 14.2 basis points using the initial framework.

Another way to assess the cost is to compare the performance of a less naïve strategy, with one that minimises tracking error by buying exactly at the close of the addition or deletion day.

We call this alternative an arbitraging tracker strategy. For any addition, it buys the new constituent in the following way:

• Buy at the first possible closing once the addition is announced;
• Sell the stock at closing of the announced addition day, when trackers are supposed to buy;
• Buy again five days after the marked addition day.

The arbitraging tracker would potentially increase their tracking error but add value. A similar approach (with the opposite trades) is used for deletions from the index.

Figure 5 shows the cumulative gains for the arbitraging tracker, relative to a standard tracker. We display another theoretical, “with hindsight” curve for an arbitraging tracker strategy that trades first at the close of the day of S&P’s announcement, instead of the next close. This is not normally possible as S&P tend to publish their decisions after close.

The realistic arbitraging tracker beats a naïve tracker by 17.2 basis points per year. The arbitraging tracker with hindsight beats the naïve tracker by an additional 10.7 basis points, so a total of almost 28 basis points per year. This would suggest that knowing S&P’s decisions ahead of time is worth an additional 10 basis points per year.

The actual gain that can be made is between these extremes. A tracker can buy earlier than at the next closing – for example, any time during the trading day – so 17.2 basis points figure is a lower bound.

From our two methods to measure the hidden cost that index-tracking investors pay, we estimate costs in the range of 14 to 26 basis points and 17 to 27 basis points per year, respectively. An impact between 17 to 26 basis points would therefore be a sensible overall estimate.

The effect that we document is well known within the quantitative investment community, where index arbitragers seek to profit at the expense of index investors. Whenever large sums of money follow a prescribed set of investment rules, we think it likely that other market participants will be motivated to profit by “trading ahead”.