Index Changes and Losses to Index Fund Investors

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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...