The Evolution Of Equal Weighting

December 15, 2010

Additional measures can be taken in the daily maintenance of the index to avert turnover in the index between reweighting periods, which might otherwise be caused by corporate actions affecting the constituents. For example, not applying month-end share adjustments and not increasing a company’s weight when a company acquires another company from different size tiers can reduce turnover between reweighting periods.

Rebalancing Frequency
Sector equal-weighted indexes assign a weight to each security at each rebalancing period. However, between rebalancing periods, the weights of each security will deviate from this target weight due to daily changes in price. A perfect implementation of the sector equal-weight strategy would require sectors and constituents to rebalance daily. Daily rebalancing would be impractical to implement as a passive strategy; it would require selling and buying constituents’ shares daily to keep the weights constant, and thus bring about high transaction costs for replicated portfolios.

Thus, a trade-off is required between representation of the strategy and turnover. To keep portfolio turnover down, we reweight less frequently but incur some tracking error to a hypothetical portfolio that is reweighted daily. To test the impact of different reweighting periods, we simulate sector equal-weighted strategy indexes based on different reweighting time frames—daily, monthly, quarterly, semiannually and annually. Intuitively, we should see tracking error maximized for the scenario with the longest reweighting period and turnover maximized for the shortest reweighting period.

We measure the tracking error of each reweighting time frame against the theoretical perfect implementation of daily reweighting. We also calculate the turnover of the portfolios for each of the different reweighting time frames. These results are presented in Figure 5 for the Russell 1000 and Russell 2000 sector equal-weighted indexes.

Figure 5

The results are as expected. When the frequency of reweighting increases, so does the turnover of the portfolio. However, as the frequency is increased, the tracking error of the portfolio decreases. A daily reweighted large-cap portfolio has turnover of more than 175 percent. The turnover is more pronounced for the daily reweighted small-cap portfolio, where it is more than 250 percent. Turnover decreases dramatically for both the large-cap and small-cap portfolios when the reweighting is done on a monthly basis, becoming less than a quarter of that of the daily reweighted portfolio. The annually reweighted large-cap portfolio has the least turnover (16 percent), but also the highest tracking error (4.6 percent).

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