Index Changes and Losses to Index Fund Investors

Abstract

Because of arbitrage around the time of index changes, investors in funds linked to the S&P 500 Index and the Russell 2000 Index lose between $1.0 billion and $2.1 billion a year for the two indices combined. The losses can be higher if benchmarked assets are considered, the pre-reconstitution period is lengthened, or involuntary deletions are taken into account. The losses are an unexpected consequence of the evaluation of index fund managers on the basis of tracking error. Minimization of tracking error, coupled with the predictability and/or pre-announcement of index changes, creates the opportunity for a wealth transfer from index fund investors to arbitrageurs.

The growth in popularity of index funds is a testament to portfolio theory and the virtues of diversification. According to Frank Russell Company, about $2,000 billion in assets were benchmarked to major indices as of June 2003—an indication that indices are an important component of the financial landscape. Investors drawn to the broad diversification and low turnover that characterize index mutual funds no doubt expect the fund portfolios to be invested in the companies constituting the index in the proper proportions at any given time. But fund managers rewarded for performance have an incentive to assume more risk than contracted for by their investors. To address this agency problem, fund managers implicitly or explicitly contract to minimize the size and volatility of tracking error. Accordingly, the performance of index fund managers is usually measured in terms of both the cost of managing the fund and its tracking error.

We show that when the predictability and timing of index changes are combined with fund managers’ objective of minimizing tracking error, index fund investors lose a significant amount. The loss to an investor in the Russell 2000 Index is about 130 bps a year but can be as high as 184 bps a year, and S&P 500 Index investors may lose as much as 12 bps a year. Consistent with this finding, we found that the Russell 2000 underperformed other small-cap indices by more than 3 percentage points a year in the 1995–2002 period, even though comparable indices did not entail greater risk. Moreover, the underperformance was concentrated in months surrounding the annual reconstitution of the index.

In dollar terms, the losses range from $1.0 billion and $2.1 billion a year for the two indices together and can be higher if benchmarked assets, a longer pre-reconstitution period, and involuntary deletions are considered. These losses are an unexpected consequence of evaluation of index fund managers by index fund investors on the basis of tracking error in an effort to control agency costs. Minimization of tracking error, coupled with the predictability and/or pre-announcement of index changes, creates the opportunity for a wealth transfer from index fund investors to arbitrageurs.

No type of index is a perfect solution to index arbitrage. An open but not heavily used index is the best short-term solution, but once it becomes popular, it can create significant costs for the index fund. The best long-term solution is a silent index (one that announces changes only after they are made), but it is not permissible under current U.S. SEC regulations. A popular index is not a good solution for small-cap portfolios because index changes are usually large relative to the index’s market cap. A popular index is more acceptable for large-cap portfolios because most changes to the index are small and inconsequential to the overall index return. Fund investors indexed to popular large-cap indices can suffer when large companies—such as Yahoo!, JDS Uniphase Corporation, Goldman Sachs, and United Parcel Service of America (UPS)—are added to the index.

We suggested steps that can be taken by index fund managers, index fund investors, and indexing firms to recoup a significant part of their losses. Managers of index funds can minimize losses by not trading on the effective date because the price pressure is the greatest at that time. To provide the necessary flexibility to fund managers, investors should rely on overall risk and return of the portfolio for performance evaluation instead of focusing on tracking error. Indeed, we found that the risk of funds that used the strategies we outlined would not be greater than the risk of the benchmark index, although the return would be higher. Finally, small individual investors can protect themselves by choosing index funds on the basis of not only expenses and loads but also the likelihood of the fund being timed by arbitrageurs.

We thank Sean Collins, Srikant Dash, Gary Gastineau, Mark Hulbert, Greg Kadlec, Hugh Marble, Ken O’Keeffe, Mahesh Pritamani, Gus Sauter, and Chester Spatt for comments on the broad results and implications of this article. We thank participants at the SEC; the 2004 Financial Management Association International and Southern Finance Association meetings; and the University of Arkansas, University of Washington at Tacoma, and SUNY Albany for comments and suggestions. In addition, we thank Morgan Stanley Capital International (and Neil Blundell), Frank Russell Company, Standard & Poor’s (and Reid Steadman and Maureen O’Shea), and Quotes Plus (at QP2.com) for providing some of the data used in this article. Honghui Chen acknowledges partial financial support from a University of Central Florida summer grant, and Vijay Singal acknowledges partial financial support from a Virginia Tech summer grant.

Notes

¹ Tracking error has no universally accepted definition. Tracking-error calculations may be based on daily returns, monthly returns, quarterly returns, volatility, correlations, and so on. Two common measures, TE1 and TE2, are as follows (seeAmmann and Zimmermann 2001):
$$\begin{array}{c}TE1=\sqrt{{{\displaystyle {\sum }_k^n\left(R_{pk}-R_{Bk}\right)}}^2/(n-1)}\\ \end{array}$$
and
$$TE2=\sigma \left(R_p\right)\sqrt{1-{\rho }_{pB}^2},$$ 
where R is the return for tracking portfoliop or benchmark portfolio B over n periods,k is an index that goes from 1 to n, and $${\rho }_{pB}$$ is the correlation between returns to the tracking portfolio and the benchmark portfolio. Our definition in the text is one of the simplest.

² Other important reasons for tracking error and expenses are reinvestment of dividends and cash management to meet investor purchases and redemptions. Fund managers are adept at minimizing the impact of dividends and cash flows by using index futures.

³ We distinguish between “passively indexed” and “benchmarked” in our computations. For example, around $264 billion in assets were benchmarked to the Russell 2000 in 2003 (Smith and Haughton 2003) compared with around $43 billion passively indexed to it during that year (Merrill Lynch 2005). We used the passively indexed estimate in our tests.

⁴ The exception is that in 2004, Frank Russell Company commenced adding IPOs to the index on a quarterly basis. We consider this change later.

⁵ Until September 1989, there was no lag between announcement and the actual change to S&P indices. Changes were announced after the close of trading and became effective at the open on the next day.

⁶ Our sample selection process is similar to that in Chen et al. (2004).

⁷ Announcement-day return refers to the return for the trading day following announcement because all announcements are made after the close of markets.

⁸ This result is similar to those in Chen et al. (2004) and in Dash (2002), a study conducted by Standard & Poor’s.

⁹ A negative bias was introduced by our excluding the months of March, April, and May because the change list is known with a high degree of confidence as early as March in any year. The probability of addition/deletion for a company on the list is not 1.0, however, which introduces an additional risk factor into a portfolio of additions or deletions formed earlier than 31 May.

¹⁰ That the mean size of deleted companies is larger than the mean size of added companies implies that several companies deleted from the Russell 2000 moved up to the Russell 1000 Index and, similarly, several companies added to the Russell 2000 are those that moved down from the Russell 1000.

¹¹ Because announcements take place after the exchanges have closed, we essentially bought at the closing price on the day after the announcement. Thus, we lost the announcement-day return. This factor helps explain why the numbers in Table 3 look considerably different from those in Table 1.

¹² The net impacts reported were obtained by multiplying the abnormal returns and total market cap of additions or deletions and dividing by the total market cap of the Russell 2000 as of 30 June.

¹³ The analysis is identical for deletions.

¹⁴ We thank a referee for pointing this out.

¹⁵ As pointed out previously, trading at the open on the day after announcement can generate additional gains. We thank a referee for providing us with an estimate of loss resulting from the deletion of foreign companies.

¹⁶ Year-by-year results are available from the authors.

¹⁷ Short-sale proceeds are not usually available for reinvestment, so the actual savings from this strategy might be marginally smaller than those assumed here.

¹⁸ One would expect gains to arbitrageurs to dissipate with competition. There may be several explanations of why this does not happen in the case of index reconstitution. First, not all arbitrage opportunities are eliminated by competition. For example, arbitrageurs still profit from merger arbitrage, post-earnings-announcement price drift, and price momentum. Second, in the case of index changes, some market participants—namely, indexers—are focused on tracking-error minimization rather than maximizing profit; hence, they trade at the closing price on the date of reconstitution.

¹⁹ Some observers have suggested that the actual trading volume on the effective day is much less than what would be expected if all index fund managers traded on that day. A quick check for all additions to the S&P 500 in the latter half of 2002 revealed, however, that the trading volume is sufficiently large to support all managers trading on that day. The trading volume on the effective date is 9–20 percent of the number of shares outstanding for NYSE stocks and 20–25 percent for NASDAQ stocks (without adjusting the volume for the upward bias in NASDAQ’s reported volume). These percentages compare favorably with the ratio of 11.3 percent indexed value to total value for the S&P 500.

²⁰ The 1 percent cutoff is arbitrary and could be lower or higher.

²¹ As mentioned previously, we assumed that the turnover associated with each index change is the same.