Selection of an Optimal Index Rule for an Index Fund

Abstract

Several empirical studies document a substantial price premium for stocks in the S&P 500 index. For index investors this creates a recurring cost: as the index is updated, they need to buy stocks with the premium and sell stocks without the premium. Different index rules can produce different index premia due to the different frequency and criteria of updating. We build a model to investigate the behavior of the index turnover cost and the portfolio performance of a mechanical index fund under a market-cap rule, an exogenous random rule, and a deterministic rule. We find that the rational anticipation of future index composition reflected in prices today eliminates any first-order differences in index fund performance across the three index rules. As the index investors become a large part of the market, the non-index investors become less diversified, and this induces hedging motives which hurt the index investors especially under a market-cap rule. JEL classification: G12, G14