The market impact, or implementation cost, of passive trading is composed of both explicit and implicit costs. The explicit cost is often referred to as implementation tracking error, defined as the observed difference between a fund’s performance and the index against which it is benchmarked. The implicit cost is the unobserved reduction in performance of the benchmark index as a result of trading activity. The relative contribution of each component is primarily determined by the implementation strategy. This article focuses on the implicit cost, which is harder to measure, and which is often the main component of an index fund’s implementation cost.
The authors use a linear price impact model to derive implicit costs. Empirical evidence supports a linear model as a reasonable approximation for price in index rebalancing trades when trade size is less than average daily volume. In practice, it is likely that individual implementers are unaware of rebalancing trade size in the aggregate and unknowingly cluster trading at the market close.
The authors consider the change in a security’s price as a function of trading execution to be an implementation cost, because the price change will disappear over the security’s holding period. The aggregate implicit implementation cost of a rebalancing is the summation of such costs across all stocks traded in the rebalancing.
With some simplifying assumptions, five factors are responsible for the implicit costs associated with rebalancing:
- The first factor is base impact, which is the ratio of the assets under management to the dollar value of shares traded daily across all stocks in the universe, scaled by a constant.
- Effective turnover, the second factor, is impacted by both replacement turnover and reweighting turnover. This factor reflects the obvious, that if there were no rebalancing, there would be no implementation cost.
- The third factor is tilt, the weighted-average ratio of the actual weight of a fund to the volume weight of the index, with a volume-weighted index having the lowest implementation cost.
- The ratio of the total trading volume of the index constituents to the total trading volume of the entire universe is the fourth factor, which is coverage. A portfolio that contains every stock in the universe has coverage of 1.
- The fifth factor is rebalance frequency. More frequent rebalancing, all things being equal, is associated with lower implicit intraperiod market impact costs. The rebalance frequency applies at the individual stock level, not at the index level.
Aked and Moroz analyze nine portfolios to measure their respective rebalancing impact costs. Three types of portfolio weighting strategies—a Cap 1000; Equal-Weight 1000, using the same constituents as the Cap 1000; and Fundamental 1000, an index whose constituents are selected and weighted by an average of book, sales, dividends, and income—are implemented in each of three regions: the United States, developed markets ex U.S., and emerging markets.
All portfolios begin with the same strategy size and rebalance frequency. The market impact costs of net investment flows are not measured. Because the coverage for these broad portfolios is close to 1, the majority of the differences in market impact costs among the portfolios can be explained by base impact, effective turnover, and tilt.
Base impact is a function of the total trading volume of the universe. Effective turnover has two sources: 1) turnover associated with constituent additions/deletions, and 2) turnover from reweighting existing portfolio constituents. Effective turnover is higher for fundamental- versus capitalization-weighted portfolios. Although the turnover for additions and deletions is lower, the reweighting turnover is higher because fundamental-weighted portfolios must rebalance against price movements. The equal-weighted strategy has the highest effective turnover because the rebalancing due to constituent additions and deletions occurs at larger weights than the cap-weighted strategy. For all three weighting schemes, effective turnover is highest in the nondeveloped markets, due in large part to their higher idiosyncratic volatility. Index tilt is also highest in the emerging markets.
When these three sources of market impact are combined, the authors’ analysis shows that rebalancing implementation costs increase relative to the U.S. Cap 1000 portfolio (1.00) for the developed ex U.S. Cap 1000 portfolio (2.36) and even more for the EM Cap 1000 portfolio (19.14). Likewise, market impact rises relative to the U.S. Cap 1000 portfolio for the U.S. Fundamental 1000 (2.68) and U.S. Equal-Weight 1000 (12.89) portfolios. The same pattern is observed across the Fundamental 1000 portfolios as is observed across the Cap 1000 portfolios: market impact is greater for the developed ex U.S. (4.19) portfolio than for the U.S. portfolio (2.68), and even greater for the EM portfolio (33.01). The case is similar across the Equal-Weight 1000 portfolios. The largest market impact cost is measured at 180.85 for the EM Equal-Weight 1000 portfolio, which compares to 1.00 for the U.S. Cap 1000 portfolio.
Because the assets tracking cap-weighted indexes are so much greater than those tracking fundamental-weighted indexes ($7 trillion vs. approximately $100 billion), the market impact model predicts that the costs of cap-weighted index investing would be substantially greater, in fact, roughly 25 times greater, than those of fundamental-weighted index funds. Not encompassed in the authors’ analysis, however, are several real-world adaptations that have served to mitigate market impact costs.
Summarized by Kay Jaitly, CFA.