Morningstar Magazine - August/September 2018 - 42

Strategies

How Long Can a Good Fund Underperform?
Winning long-term managers trail
their benchmark for a decade on average.
Tax Wise
	

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Holding Bonds Under the New Tax Law

	

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Filling in the Gaps

	

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Investment Research
Mind the Gap 2018

	

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Maciej Kowara and Paul D. Kaplan

to underperform within that period? Conversely,
there has been no analysis of how long
a period of outperformance a fund might enjoy
before ultimately underperforming.

The performance of an actively managed mutual
fund is regularly compared against the
performance of its benchmark to determine
whether it is fulfilling its mandate to outperform
that benchmark. While this seems like a
straightforward exercise, it is complicated by
the fact that a fund that ultimately outperforms
its benchmark may go through a stretch
of underperformance. For example, a fund that
ultimately outperforms its benchmark over
a 15-year period could have gone through an
eight-year subperiod in which it underperformed.
At the end of such a bad stretch, investors
who evaluated the fund solely based on eight
years of performance would have missed the
subsequent outperformance.

The purpose of this study is to fill that gap. We
do so by introducing two new performance-related
measures: Longest Underperformance Period,
or LUP, and Longest Outperformance Period,
or LOP. We define LUP as the longest subperiod of
underperformance within a given period of
outperformance and LOP as the longest subperiod
of outperformance within a given period
of underperformance. Note that LUP and LOP are
in units of time and do not measure the magnitude
of under- or outperformance, nor do they
measure probabilities. However, as we discuss
below, we estimate their probability distributions
with Monte Carlo simulation.

RESEARCH

Quant U

Best Ideas

Manager: Good by Any Measure
Passive: Balancing Act
Equity: Winning by a Wide Margin

The converse is also true. A fund that ultimately
underperforms its benchmark over a 15-year
period could very well have gone through an
eight-year subperiod of outperformance,
enticing performance-chasing investors to buy the
fund, only to be disappointed by subsequent
underperformance.
Most relative performance metrics such as alpha,
beta, and information ratio take the period
of analysis as given, typically three or five years.
To our knowledge, there has been no systematic
analysis of how long a period of underperformance
an investor may have to bear while waiting
for a fund to ultimately outperform its benchmark.
Put differently, given that a manager is skilled
and has a good chance of beating the benchmark
over a set time period, over how long a
stretch can that manager be reasonably expected

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Morningstar August/September 2018

Definitions and Data
Over a given period, say, 180 months, the LUP
of a fund is the longest subperiod (in months)
over which the fund underperformed its
benchmark. In other words, the cumulative return
of the fund was less than the cumulative
return of the benchmark over a subperiod of
LUP months.

While this definition of LUP seems simple enough,
there are a few complications that we need
to address when measuring LUP. This is because
there are three possible patterns of relative
cumulative values that we must deal with:
1 The fund underperforms over the full period.

In this case, LUP is not defined.
2 The fund outperforms over the full period, but

toward the end of the full period, a subperiod of
Table of Contents for the Digital Edition of Morningstar Magazine - August/September 2018
