Morningstar - Q4 2021 - 23

TRENDS
Half-Lifes and Overlaps: A New Way to Measure How Active a Manager Is
Understanding the two reasons portfolios change
and distinguishing between these reasons
can provide key insight into how active a fund
manager is.
Portfolio change starts with the uneven evolution
of price movements in the instruments funds
hold. Even if a manager doesn't sell or buy
anything, a stock that returns twice as much as
another will have a different weight than it did
before. The manager is holding the same names,
but the portfolio is different because the weights
are. Second, adding to, trimming, or exiting
holdings, as well as buying new ones, introduces
further change: Not only are the weights
different because of uneven price movements,
but the manager has also altered positions.
The first reason is especially applicable to passive
vehicles. Although indexes reconstitute and
companies drop out either because they go out of
business or merge away, the uneven evolution
of the weights of their underlying instruments is
the primary reason passive portfolios change. The
second reason also applies to active managers,
who try to add value by buying new positions
they consider undervalued while selling those
they deem fully or overvalued. Active managers'
portfolios change as a result of the uneven
evolution of prices among their positions and the
decisions they make.
It isn't easy to disentangle these two reasons
for change, and common measures like portfolio
turnover don't really do the job, in addition
to having their own flaws.1
But we can compare
a portfolio's " common holdings score " over
time, which provides a record of the overlap of
a fund's portfolio at a specified date (most
conveniently the most recent, although that is not
necessary) with its own historical portfolios.
Overlap here means a sum of the lesser of weights
50
The " half-life " of a fund is the point when its
rate of portfolio change drops below 50%.
12/31/2003
12/31/2009
Source: Morningstar, author's calculations. Data as of 06/30/2021.
12/31/2015
06/30/2021
of all the holdings that are common to portfolios
at two points in time. So, if a portfolio held 50%,
25%, and 25% in stocks A, B, and C, respectively, at
one point and 50% each in stocks A and B at
another, the overlap would be 75%-with 50%
coming from stock A and 25% from stock B.
Because Morningstar holds historical portfolios of
all the publicly available funds, this calculation
is readily accessible.
A comparison of the active offering American Funds
Growth Fund of America AGTHX with the
passive Vanguard Growth Index VIGIX using their
respective June 2021 portfolios as a base provides
a real-life example as shown in the exhibit.2
Growth Fund of America's common holdings score
with itself declines much more rapidly as we
travel back in time than Vanguard Growth Index's.
But how much more rapidly? The concept of
half-life can help us answer this question. Half-life
is the time required for a quantity to reduce
to half of its initial value. This concept could be
used to compare an initial portfolio to subsequent
ones, or as we are doing here, a portfolio's last
incarnation to its prior ones. The half-life of Growth
Fund of America's June 2021 portfolio relative
to its own history is three years. Going backward,
the first time its self-similarity drops below 50%
is June 2018. The index fund's half-life, by contrast,
is five years and nine months. So, now we
can say that, based on that measure, Growth Fund
of America's rate of portfolio change is about
twice that of this passive fund.
Combining a history of the common holdings score
with the concept of half-life turns out to be
a new way to measure how active a manager is
relative to a passive fund or benchmark.
Maciej Kowara, Ph.D., CFA, is associate director of
manager research, quantitative research, at Morningstar
Research Services LLC.
Historical Self-Overlap Using June 2021 Portfolios as a Base
Growth Fund of America
Vanguard Growth Index
The index fund's half-life, by contrast, is
five years, nine months, meaning Growth
Fund of America's rate of portfolio change
is about twice that of the passive fund.
The half-life of Growth Fund of America's
June 2021 portfolio occurred in June
2018, meaning its half-life is three years.
Overlap
100%
75
50
1 On the problems with this SEC-mandated measure, see " How Important Is Turnover? " by Russel Kinnel, Morningstar.com. https://www.morningstar.com/articles/561475/how-important-is-turnover
2 The overlap of the most recent portfolio with itself may be less than 100% because the common holdings score is based only on stock holdings, as can be seen from the Growth Fund of
America example; the overlap calculation excludes cash or other nonequity holdings.
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https://www.morningstar.com/funds/xnas/agthx/quote https://www.morningstar.com/funds/xnas/vigix/quote https://www.morningstar.com/authors/2089/maciej-kowara https://www.morningstar.com/articles/561475/how-important-is-turnover http://www.Morningstar.com

Morningstar - Q4 2021

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