Index Changes and Losses to Index Fund Investors

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.