Morningstar Magazine - August/September 2018 - 44

Strategies

Altogether, this gave us 5,500 unique fund and
fund-category-adjusted-index histories that were
used to calculate the funds' LUPs and LOPs.
The Results
The results paint a reasonably benign picture
of the active-fund global universe on the one hand,
and a striking one on the other.
E X H I B I T 1 shows the averages and distributions
of LUPs for the funds that outperformed their
benchmarks over the 15-year period considered.
Roughly two thirds-3,790 out of 5,500-
of the funds' gross returns beat their benchmarks
over the 15-year period considered. Nonetheless,
the results also reveal that for the 3,790
funds that did outperform, the average incomplete
LUP was 133 months, which is just more
than 11 years, and the average complete LUP
was 106 months, which is just short of nine years.
Hence, on average, investors who were
hoping to hold outperforming funds over this

States (112 months) and the United Kingdom (95),
respectively. For incomplete LUPs, they
were Canada (141) and the United Kingdom
(120), respectively.

the number of trials that result in LUPs being
undefined, incomplete, and complete,
and the ratio of the number of incomplete LUPs
to the number of complete LUPs.

E X H I BI T 2 tells the other side of the story. Funds
that have long periods of outperformance
can ultimately underperform. Of the 1,710 funds
that ultimately underperformed over the
15-year period, 1,164 had an average complete
LOP of 132 months (11 years), and 546 had
an incomplete LOP with an average of 145 months
(just more than 12 years). Hence, it would
be a mistake to judge a fund's ability
to outperform its benchmark on a track record
as long as 11 years.

The first line of EXHIB IT 3 serves as a reality check
on our simulations. Note that the number of
trials that result in LUPs being undefined matches
the assumed skill level. In the case of positive
skill, we set the failure rate to 25% and the number
of trials with undefined LUPs is about 25%
of the 10,000 trials. We have a similar result for
the other skill levels. Also note the ratio of
incomplete to complete LUPs increases as the
skill level decreases.

These results are counterintuitive enough that
a question naturally arises: Are they due
to the peculiarity of the time period or the fund
sample under consideration? We investigated
this question by running a Monte Carlo

EXHIBIT 3

Monte Carlo Simulation Results: Counts of Types of LUPs
Positive Skill

No Skill

Negative Skill

Undefined

2,529

5,041

7,473

Incomplete

1,227

964

568

Complete

6,244

3,995

1,959

0.20

0.24

0.29

Incomplete/Complete
Source: Morningstar.

15-year period not only needed to pick the right
funds but have the patience to endure
periods of underperformance of nine to 11 years
at some point within that period!

These results aggregate over all the regions
considered, but the averages did not
vary much across regions. The longest and shortest
average complete LUPs were for the United

simulation of "positive skill," "no skill," and
"negative skill" managers; these were defined
as managers who had a 75%, 50%, and
25% chance of outperforming their benchmarks
over a 15-year period, respectively. We ran
10,000 Monte Carlo trials.
E X H I BI TS 3 & 4 present the results of the Monte
Carlo simulation for LUP.1 EXHIB IT 3 shows

EXHIB IT 4 shows the averages of incomplete and
complete LUPs as well as various percentiles
of the distributions. Note that, as we are reporting
LUPs, we are conditioning the results shown
here on having outperformed the benchmark over
the entire 15-year period. For the skilled
manager, the average complete LUP is 115 months
and the median is 114 months. Thus, a fund
manager who has the skill to outperform
the benchmark over a 15-year period with a 75%
probability could easily end up with a 9.5-year run
of underperformance even when ultimately
outperforming the benchmark over the full
15 years. From the 5 th and 10th percentiles, we see
that there is a 5% to 10% chance of about
a four- to five-year stretch of underperformance.
For the lower skill levels, these stretches
are longer, but in practice, there is no easy way
of telling whether a bad stretch is attributable
to luck or skill.

These results were largely consistent with
the empirical results presented in this
article. For example, the average complete and
incomplete LUPs for our simulated skilled
managers were 115 and 132 months, respectively,
not far off the results of 106 and 133
months that we got from actual funds (on the
assumption that outperforming the
index over 15 years is a decent proxy for being
a "skilled" manager).

1 We show only the results for LUPs, as the results for LOPs are just their mirror image. For example, the results for LOP for the manager with negative skill are very similar to the results for LUP
for the manager with positive skill.

Morningstar August/September 2018

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