1 Introduction
An active equity fund manager can attempt to outperform the fundís benchmark only by
taking positions that are di§erent from the benchmark. Fund holdings can di§er from the
benchmark holdings in two general ways: either because of stock selection or factor timing
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(or both). Stock selection involves picking individual stocks that the manager expects to
outperform their peers. Factor timing involves time-varying bets on systematic risk factors
such as entire industries, sectors of the economy, or more generally any systematic risk
relative to the benchmark index. Because many funds favor one approach over the other,
it is not clear how to quantify active management across all funds.
Tracking error volatility (hereafter just ìtracking errori) is the traditional way to mea-
sure active management. It represents the volatility of the di§erence between a portfolio
return and its benchmark index return. However, the two distinct approaches to active
management contribute very di§erently to tracking error, despite the fact that either of
them could produce a higher alpha. For example, the T. Rowe Price Small Cap fund is a
pure stock picker which hopes to generate alpha with its stock selection within industries,
but it simultaneously aims for high diversiOcation across industries. In contrast, the Mor-
gan Stanley American Opportunities fund is a ìsector rotatoriwhich focuses on actively
picking entire sectors and industries that outperform the broader market while holding
mostly diversiOed (and thus passive) positions within those sectors. The tracking error of
the diversiOed stock picker is substantially lower than that of the sector rotator, suggesting
that the former is much less active. But this would be an incorrect conclusion nits tracking
error is lower simply because individual stock picks allow for greater diversiOcation, even
while potentially contributing to a positive alpha.
Instead, we can compare the portfolio holdings of a fund to its benchmark index. When
a fund overweights a stock relative to the index weight, it has an active long position in
it, and when a fund underweights an index stock or does not buy it at all, it implicitly
has an active short position in it. In particular, we can decompose any portfolio into a
100% position in its benchmark index plus a zero-net-investment long-short portfolio on
top of that (Asness (2004) discusses the same decomposition, albeit from the point of view
of tracking error alone). For example, a fund might have 100% in the S&P 500 plus 40% in
active long positions and 40% in active short positions.
We propose the size of this active long-short portfolio (40% in the previous example)
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The basic idea has been presented and discussed by Fama (1972), Brinson, Hood, and Beebower (1986),
Daniel, Grinblatt, Titman, and Wermers (1997), and many others.
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