The Market Impact of Passive Trading - August 2015

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only 5% + 15% 2 = 7.25%, or about one-third as much. This difference is not visible to portfolio analysts who rely exclusively on total turnover. 5 Selecting the universe that corresponds to the capweighted benchmark would usually make the weight ratios more meaningful. 6 This approximation assumes that prices follow a normal (not log-normal) distribution; clearly, it won’t work well if the volatility is sufficiently high. In addition, the stocks that moved down in price by a large amount are more likely to be deleted, further lessening the precision of the estimate. 7 Weighted-average market capitalization is defined WAMC = ∑ S ∈P ∑ S∈P wSCS . Here, MC is the market capitalization (of either individual stocks s or the entire portfolio P), and c s is the cap weight of stock s in portfolio P. 8 In fact, we need the weaker but more complex assumption that the turnover is uncorrelated with certain weightrelated measures; however, for our purposes the simpler one will do. 9 Effective turnover will be bounded by turnover (TO) and the square of turnover (TO2 ).

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2 (March/April 2005), pp. 83-99. To order reprints of this article, please contact Dewey Palmieri at dpalmieri@ iijournals.com or 212-224-3675. THE M ARKET I MPACT OF PASSIVE T RADING JOT-AKED.indd 12 SUMMER 2015 6/13/15 8:43:52 AM .