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 ).
In this case we are assuming
that trades occur mainly due to replacement of securities
rather than rebalancing across portfolios.
10
See Arnott et al. [2005].
11
See Zanona [2013].
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To order reprints of this article, please contact Dewey Palmieri
at dpalmieri@ iijournals.com or 212-224-3675.
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