Short‐term
investment
indicator:
How
short‐term
oriented
is
your
fund
manager?
















Short‐term
investment
indicator:


How
short‐term
oriented
is
your
fund
manager?









 Mark
T.
Hömmen
 (1483919)
 
 Instructor:
dr.
Auke
Plantinga
 University
of
Groningen
 Faculty
of
Economics
 
 February
26,
2009

 
 Abstract
 To
supplement
return‐based
mutual
fund
analysis,
an
alternative
holdings‐based
 measure
 called
 the
 STI
 indicator
 is
 developed
 in
 this
 paper.
 It
 describes
 the
 amount
of
the
mutual
fund’s
net
asset
value
allocated
to
short‐term
investments
 (STI)
in
relation
to
trading
activity
(turnover)
for
a
given
period
of
time.
With
the
 STI
 indicator,
 investors
 can
 match
 their
 preference
 for
 short‐term
 orientation
 and
 activeness
 with
 mutual
 funds.
 Behavioral
finance
 concepts
 are
 linked
 with
 this
new
measure
as
well
as
Jensen’s
alpha
that
appears
to
have
a
relation
with
 the
 STI
 indicator.
 
 Using
 the
 STI
 indicator
 in
 conjunction
 with
 other
 ‘rating’
 systems
enables
the
investor
to
better
understand
mutual
funds.

JEL classification: C51, G11

2

1


Introduction





Mutual
 fund
 performance
 measurement
 systems
 are
 a
 popular
 tool
 for
 private
 and
 institutional
 investors
 to
 screen
 investment
 opportunities
 among
 mutual
 funds
 and
 manage
 their
 investment
 portfolios.
 According
 to
 several
 methodologies
developed
by
Morningstar,
LipperLeaders,
and
ValueLine,
certain
 rates
are
assigned
to
different
kinds
of
mutual
funds.
All
these
methodologies
are
 based
 on
 historical
 returns
 of
 mutual
 funds
 in
 the
 calculus
 of
 their
 rating.
 Additionally
a
benchmark
is
often
used
to
measure
‘relative’
performance
of
the
 mutual
fund.
Historical
returns
have
only
very
limited
predictive
power,
as
James
 Montier
states
in
his
book
Behavioural
Investing
published
in
2007:
page
575‐576
 “…
 we
 couldn’t
 find
 any
 evidence
 of
 predictive
 power
 from
 a
 wide
 variety
 of
 leading
indicators.”
The
same
is
the
case
for
equity
returns,
according
to
Montier
 (2007).
Therefore,
it
is
in
my
view
incorrect
just
to
rate
mutual
funds
on
the
basis
 of
 historical
 return
 data.
 A
 further
 observation
 is
 that
 mutual
 fund
 portfolio
 holdings
and
turnover
are
not
examined
whereas
these
elements
certainly
have
a
 considerable
bearing
on
performance.
Using
historical
mutual
fund
performance
 data
 involves
 the
 implicit
 assumption
 that
 the
 derived
 information
 has
 at
 least
 some
 predictive
 content
 for
 the
 future
 (Sharpe,
 1998).
 According
 to
 Markowitz
 (1952)
 the
 way
 of
 constructing
 an
 investment
 portfolio
 takes
 into
 account
 the
 best
possible
estimates
of
relevant
future
risk
and
returns.
In
an
attempt
to
use
 portfolio
 holdings
 instead
 of
 historical
 returns
 to
 ‘rate’
 mutual
 funds,
 a
 two‐ dimensional
 approach
 called
 the
 Short‐Term
 Investment
 (STI)
 indicator
 is
 developed
 in
 this
 paper.
 The
 STI
 indicator
 describes
 the
 amount
 of
 the
 mutual
 fund’s
 net
 asset
 value
 allocated
 to
 short‐term
 investments
 in
 relation
 to
 the
 trading
 activity
 (turnover)
 for
 a
 given
 period
 of
 time.
 In
 addition,
 the
 STI
 indicator
 will
 give
 valuable
 insights
 in
 the
 behavioral
 component
 of
 asset
 management.




 Nowadays,
traditional
mutual
fund
performance
measurement
systems
are
 used
extensively
for
different
reasons.
One
reason
is
the
perceived
convenience
 in
 their
 use
 to
 select
 investment
 opportunities
 and
 their
 goodwill
 among
 many
 investors.
As
Damato
(1996)
showed,
90%
of
the
money
that
has
to
be
invested
 will
 be
 allocated
 to
mutual
 funds
 with
 a
 four
or
 five
 star
 rating
of
 Morningstar.

 Financial
 advisors
 are
 influenced
 by
 their
 clientele
 to
 invest
 preferably
 in
 high
 rated
 mutual
 funds
 and
 as
 a
 mark
 of
 ‘good
 housekeeping
 seal
 of
 approval’;
 institutional
 investors
 of
 401
 (k)
 pension
 funds
 also
 invest
 in
 those
 high
 rated
 mutual
funds
(Franecki,
2000).
The
goodwill
created
by
rating
agencies
is
widely
 used
 in
 marketing
 campaigns
 of
 individual
 mutual
 funds;
 this
 enhances
 the
 reputation
of,
for
example,
the
star
system
from
Morningstar.




 However,
the
popularity
of
the
rating
services
has
another
aspect.
Changes
 in
ratings
of
mutual
funds
can
have
a
 severe
impact
on
the
fund’s
performance.
 Morey
 (2005)
 discovered
 side‐effects,
 for
 example
 like
 subsequent
 to
 receiving
 the
first
five
star
rating
the
mutual
fund
management
decides
to
take
excess
risk
 and
 use
 strategies
 that
 cause
 their
 performance
 to
 suffer.
 According
 to
 Del
 Guercio
 and
 Tkac
 (2002)
 significant
 cash
 outflow
 might
 be
 the
 result
 of
 a
 decrease
in
the
rating
provided
by
rating
services.



performance
 of
 mutual
 funds
 (Reichenstein,
 2004).
 In
 2002
 Morningstar
 Inc
 adjusted
this
system
after
some
criticism
and
extended
the
categories
of
mutual
 funds,
 resulting
 in
 more
 objective
 ratings.
 Investors
 wish
 to
 use
 these
 ratings,
 because
 the
 amount
 of
 mutual
 funds
 available
 to
 them
 is
 too
 large
 to
 analyze
 quickly.
However,
after
the
first
selection
using
mutual
fund
ratings,
the
investor
 should
check
the
prospectuses
of
the
funds
to
come
to
a
sound
decision
instead
of
 making
a
decision
based
on
only
a
fund
rating.
Still,
investors
consider
the
ratings
 for
the
Holy
Grail
and
that
is
not
the
right
attitude
towards
those
rating
services.
 Warshawsky
(2000)
mentions
that
investors
tend
to
use
these
systems
as
vision
 for
the
future,
because
investors
are
in
search
of
systems
that
are
able
to
predict
 future
performance.




 The
 focus
 on
 historical
 performance
 data
 may
 not
 help
 investors,
 as
 historical
performance
is
no
guarantee
for
future
performance.
Alternatively,
it
is
 probably
 better
 to
 study
 the
 allocation
 and
 turnover
 of
 mutual
 funds.
 With
 the
 STI
indicator
the
investor
uses
portfolio
holdings
based
information
and
trading
 activity
of
mutual
funds.
The
STI
indicator
dimensions
give
an
indication
of
how
 short‐term
 oriented
 and
 active
 a
 mutual
 fund
management
 invests
 relative
 to
 a
 population
of
mutual
funds.
Then,
the
investor
can
select
the
fund
that
suits
his
 preferences
 toward
 short‐term
 orientation
 and
 activeness
 according
 to
 the
 STI
 and
turnover
dimension.
For
example,
a
risk‐averse
investor
who
wants
a
secure
 income
 in,
 say,
 five
 years
 would
 choose
 a
 mutual
 fund
 that
 is
 less
 short
 term
 oriented
(relative
small
STI
ratio)
and
with
less
active
management
(relative
low
 turnover
ratio).




 After
 all,
 this
 STI
 indicator
 attempts
 to
 take
 into
 account
 the
 problems
 of
 using
 historical
 performance
 data
 as
 opposed
 by
 different
 authors
 about
 the
 Morningstar
 star,
 LipperLeaders,
 and
 ValueLine
 rating
 mechanisms.
 The
 STI
 indicator
 provides
 the
 investor
 holdings‐based
 information
 and
 matches
 the
 investor’s
 preference
 for
 active
 management
 with
 mutual
 funds,
 compared
 to
 methods
relying
on
historical
returns
only.
To
validate
the
STI
indicator,
it
will
 be
linked
with
mutual
fund
portfolio
alphas
and
betas
and
it
is
examined
if
the
 STI
and
turnover
dimension
are
linearly
related
with
each
other.


4

2


Literature





The
introduction
provided
a
short
overview
on
the
current
use
and
limitations
of
 existing
 mutual
 fund
 performance
 measurement
 systems.
 This
 section
 gives
 an
 impression
 of
literature
on
 mutual
 fund
 performance
 measurement
 systems
 as
 well
as
literature
about
behavioral
issues
in
managing
a
mutual
fund.
At
the
end
 of
each
subsection,
the
literature
is
summarized
and
linked
to
both
dimensions
 of
the
STI
indicator.
 
 2.1 Financial
elements
related
to
the
STI
indicator
 Financial
literature
that
is
not
focused
on
explaining
behavioral
elements
in
asset
 management
offers
a
 variety
of
explanations
that
affect
 both
dimensions
of
the
 STI
 indicator.
 This
 subsection
 provides
 a
 point‐by‐point
 outline
 of
 financial
 elements
affecting
the
STI
indicator.


Wermers
(2000)
examined
comprehensively
the
mutual
fund
industry,
by
 examining
 mutual
 fund
 performance
 through
 skills
 in
 picking
 stocks,
 characteristics
 of
 stock
 holdings,
 costs
 of
 implementing
 the
 style
 of
 a
manager,
 fund
 expenses
 and
 fees
 charged,
 and
 differences
 between
 gross
 stock
 portfolio
 returns
and
net
fund
returns.
The
costs
of
implementing
the
style
of
the
manager
 can
be
significant,
a
study
by
Morey
(2005)
found
that
after
receiving
an
increase
 in
performance
rating,
managers
adapt
their
strategies
in
an
attempt
to
sustain
 those
higher
ratings.
According
to
Morey
2005:
“…investors
should
be
very
wary
 about
using
the
5‐star
rating
as
a
signal
of
future
3‐year
performance.”
Whereas,
 subsequent
 mutual
 fund
 performance
 seems
 to
 suffer
 from
 those
 changes
 in
 strategy.
Wermers
(2000)
states
that
high
turnover
mutual
funds,
although
they
 incur
 more
 transaction
 costs
 and
 charge
 higher
 fees,
 hold
 stock
 with
 much
 higher
 average
 returns
 compared
 to
 low
 turnover
 mutual
 fund.
 He
 concludes:
 “Our
 evidence
 supports
 the
 value
 of
 active
 mutual
 fund
 management.”
 High
 turnover
 means
 that
 the
 portfolio
 holdings
 do
 change
 often
 and
 mutual
 fund
 management
 should
 indeed
 hold
 stocks
 with
 high
 returns,
 otherwise
 the
 transaction
 cost
 will
 not
 be
 covered
 at
 all.
 The
 risk
 of
 such
 stocks
 can
 be
 significant,
because
their
volatility
is
high.




 Marcin
 Kacperczyk
 (2007)
 argues
 that
 professional
 managers
 do
 have
 access
 to
 superior
 information
 and
 that
 this
 is
 related
 to
 the
 skills
 of
 the
 manager.
 He
 developed
 a
 measure
 of
 reliance
 on
 public
 information
 (RPI)
 that
 “…clarifies
whether
traditional
performance
measures
indeed
reflect
skill,
in
that
 managers
 who
 produce
 high
 values
 of
 these
 measures
 should
 also
 have
 low
 sensitivities
 of
 their
 portfolio
 holdings
 to
 changes
 in
 public
 information.”
 Of
 course,
 the
 manager
 can
 adopt
 a
 strategy
 that
 actively
 trades
 on
 information,
 which
can
be
related
to
the
overconfidence
concept,
on
which
will
be
elaborated
 further
 in
 the
 next
 subsection.
 According
 to
 Kacperczyk
 et
 al.
 (2005),
 mutual
 fund
managers
tend
to
concentrate
their
funds
in
industries
where
they
assume
 they
have
informational
advantages
(familiarity).
This
study
found
that
there
is
a
 relation
between
industry
concentration
and
the
performance
of
a
mutual
fund.
 He
found
that
industry
concentrated
funds
tend
to
overweigh
growth
and
small
 stocks;
 whereas
 managers
 of
 more
 diversified
 funds
 hold
 portfolios
 that
 more
 closely
resemble
the
total
market
portfolio.



Perceived
 informational
 advantage
 can
 be
 an
 argument,
 as
 proposed
 by
 Kacperczyk
et
al.
(2005).
They
state
that
asymmetric
information
between
local
 and
 non‐local
 investors
 drives
 the
 preference
 for
 geographically
 proximate
 investments.
 They
 divide
 the
 preference
 into
 two
 categories;
 one
 based
 on
 the
 distance
 from
 the
 home
 country
 and
 the
 other
 which
 relies
 on
 national
 or
 governmental
frictions.


Chevalier
 and
 Ellison
 (1997)
 tested
 the
 relationship
 between
 the
 cash
 inflows
and
the
performance
of
mutual
funds,
they
“…examine
portfolio
holdings
 of
 mutual
 funds
 in
 September
 and
 December
 and
 show
 that
 mutual
 funds
 do
 alter
the
riskiness
of
their
portfolios
at
the
end
of
the
year
in
a
manner
consistent
 with
these
incentives.”
Investors
want
a
secure
return
and
the
fund
management
 would
like
as
many
inflows
of
cash
as
possible.
This
relation
generates
incentives
 for
mutual
funds
to
increase
or
decrease
the
risk
of
their
portfolio.



 Cohen
et
al.
(2005)
developed
a
performance
evaluation
approach
in
which
 the
 skill
 of
 a
 fund
 manager
 is
 judged
 by
 the
 extent
 to
 which
 his
 investment
 decisions
 resemble
 the
 decisions
 of
 managers
 with
 distinguished
 performance
 records.
 This
 proposed
 approach
 uses
 historical
 returns
 and
 the
 holdings
 of
 many
funds.
They
state
that
their
developed
measure
is
useful
in
ranking
mutual
 fund
 managers
 from
 poor
 to
 good
 ones
 and
 “…skilled
 managers
 tend
 to
 make
 similar
investment
decisions,
because
they
interpret
information
similarly.”


Grinblatt,
 Titman,
 and
 Wermers
 (1995)
 analyzed
 the
 extent
 to
 which
 mutual
 funds
 purchase
 stocks
 based
 on
 their
 past
 return.
 They
 find
 that
 77
 percent
 of
 the
 mutual
 funds
 were
 "momentum
 investors,"
 buying
 stocks
 that
 were
 past
 winners;
 however,
 most
 did
 not
 systematically
 sell
 past
 losers.
 On
 average,
 funds
 that
 invested
 on
 momentum
 realized
 significantly
 better
 performance
than
other
funds.




 The
two
dimensions,
STI
and
turnover,
of
the
STI
indicator
are
related
to
 the
 previous
 financial
 literature.
 A
 source
 that
 influences
 the
 STI
 ratio
 is
 the
 adjustment
of
the
investment
strategy
by
fund
managers.
This
can
be
a
result
of,
 for
 example,
 a
 rise
 in
 performance
 rating
 or
managers
 that
 have
 informational
 advantages
 in
 specific
 markets
 and
 tend
 to
 invest
 like
 momentum
 investors.
 Managers
 that
 trade
 due
 to
 change
 in
 strategies
 and
 potential
 superior
 information
 may
 affect
 both
 dimensions.
 Furthermore,
 persistence
 in
 mutual
 fund
 performance
 is
 awkwardly
 interpreted
 from
 historical
 performance
 data.
 Markov
 (1952)
 already
 suggested
 that
 only
 the
 present
 state
 of
 a
 variable
 is
 relevant
for
predicting
the
future
and
the
way
the
present
has
emerged
from
the
 past
is
irrelevant.






2.2




Behavioral
elements
related
to
the
STI
indicator


Behavioral
 finance
 literature
 is
 focused
 on
 explaining
 financial
 decisions
 from
 behavioral
elements
in
asset
management.
Many
circumstances
can
influence
the
 investment
 behavior
 of
 asset
 managers;
 therefore
 managers
 can
 deviate
 from
 their
 initial
 investment
 strategy.
 This
 subsection
 provides
 a
 point‐by‐point
 outline
of
behavioral
finance
elements
affecting
the
STI
indicator.


6 differential
performance
may
simply
reflect
differences
in
transaction
costs
that
 are
incurred.”



Overconfidence
can
be
related
to
turnover,
because
if
investors
think
they
 are
 above
 average
 they
 are
 likely
 to
 trade
 more
 actively
 (Glaser
 and
 Weber
 (2003).
 De
 Bondt
 and
 Thaler
 (1995)
 argue
 that
 overconfidence
 is
 the
 best
 behavioral
indicator
to
reason
about
the
trading
puzzle.


The
illusion
of
knowledge
is
a
source
of
overconfident
trading
behavior,
 where
 investors
 believe
 that
 the
 more
 information
 they
 possess
 the
 more
 accurate
 their
 decisions
 become.
 Theoretically,
 the
 investor
 that
 uses
 his
 superior
 information
 should
 cover
 its
 transaction
 costs,
 so
 its
 active
 trading
 behavior
 is
 justified.
 
 However,
 according
 to
 Barber
 and
 Odean
 (2000):
 “Overconfident
 investors
 will
 overestimate
 the
 value
 of
 their
 private
 information,
causing
them
to
trade
too
actively
and,
consequently,
to
earn
below‐ average
results.”
More
obvious
is
the
result
of
a
study
by
Odean
(1999):
“those
 who
 trade
 the
 most
 lose
 most.”
 Gervais
 and
 Odean
 (2001)
 do
 summarize
 the
 threat
within
overconfidence
in
the
following
quote:
“…overconfidence
does
not
 lead
to
greater
profits,
greater
profits
lead
to
overconfidence.”


The
 position
 of
 overconfidence
 has
 to
 be
 interpreted
 in
 a
 broader
 perspective;
 the
 market
 condition
 should
 also
 be
 considered.
 As
 can
 be
 concluded
 from
 the
 research
 by
 Gervais
 and
 Odean
 (2001);
 investors
 become
 overconfident
 about
 the
 precision
 of
 their
 information
 after
 favorable
 market
 conditions.
 In
 a
 market
 downturn
 investors
 tend
 to
 be
 less
 overconfident
 and
 downsize
their
trading
activity,
however
this
distinction
between
good
and
bad
 market
 times
 is
 not
 symmetrical.
 This
 difference
 explains
 some
 psychological
 elements
in
the
behavior
of
people.
If
an
investor
in
a
good
market
discovers
an
 investment
opportunity,
it
is
surrounded
with
other
investments
that
increase
in
 value.
If
this
investor
sees
the
same
investment
opportunity
in
a
bad
market
he
is
 more
 anxious
 about
 the
 return.
 Therefore,
 the
 uncertainty
 surrounding
 the
 precision
of
their
knowledge
about
an
investment
opportunity
experienced
by
a
 risk
averse
investor
seems
to
be
higher
in
bad
markets.
Before
interpreting
the
 active
 trading
 behavior
 (turnover)
 of
 an
 asset
 portfolio,
 it
 is
 necessary
 to
 be
 aware
of
the
market
conditions.



 Statman
et
al.
(2006)
found
that
market
turnover
tends
to
increase
after
 months
 with
 positive
 market
 returns
 and
 they
 establish
 the
 link
 with
 the
 disposition
 effect.
 This
 effect
 can
 be
 described
 as
 the
 desire
 by
 investors
 to
 realize
 gains
 by
 selling
 stocks
 that
 appreciated
 and
 delaying
 realizations
 of
 losses.
Trading
activity
is
dependent
on
past
returns
and
explains
the
attitude
of
 investors
in
realizing
losses
and
gains
according
to
the
disposition
effect.



 Glaser
 and
 Weber
 (2004)
 consider
 the
 overconfidence
 in
 relation
 with
 trading
 activity,
 but
 in
 addition
 they
 consider
 another
 strand
 of
 literature:
 the
 differences‐of‐opinion
 concept.
 “Differences
 of
 opinion
 can
 arise
 due
 to
 differences
 in
 prior
 beliefs
 or
 due
 to
differences
 in
 the
 way
 investors
 interpret
 public
 information.”
 This
 study
 provided
 a
 psychological
 foundation
 for
 the
 differences
of
opinion
concept
applied
in
examining
trading
activity
and
tries
to
 explain
observed
trading
activity.


market
 clearing
 condition
 requires
 that
 he
 and
 no
 other
 trader
 sees
 the
 profitable
 investment
 opportunity.
 In
 other
 words,
 if
 one
 investor
 has
 information
that
induces
him
to
trade,
other
rational
investors
are
unwilling
to
 trade
 with
 him,
 as
 he
 might
 have
 superior
 information.
 Therefore,
 some
 participants
 in
 the
 financial
 markets
 clearly
 behave
 irrational.
 This
 has
 an
 empirical
 implication:
 the
 introduction
 of
 irrational
 investors
 will
 alter
 the
 behavior
 or
 rational
 market
 participants
 and
 therefore
 change
 the
 nature
 of
 equilibrium
 (Black,
 1986).
 In
 line
 with
 this
 reasoning
 it
 is
 important
 for
 an
 investor
 to
 recognize
 the
 fraction
 of
 opinion
 and
 fraction
 of
 information
 from
 another
 investor’s
 belief
 to
 determine
 the
 reliability
 of
 the
 other
 investor’s
 trading
behavior.




 Differences
 in
 opinion
 are
 caused
 by
 differences
 in
 beliefs,
 risk
 attitudes,
 existing
 portfolio
 holdings,
 hedging
 activities,
 etc.
 To
 link
 the
 difference
 of
 opinion
concept
with
turnover,
the
illusion
of
knowledge
seems
to
be
a
critical
 part.
Trading
is
generated
first
of
all
by
differences
in
opinion
about
prior
beliefs.
 Prior
 belief
 induces
 trading,
 because
 investors
 think
 they
 possess
 superior
 information
 and
 use
 this
 information
 to
 trade.
 Varian
 (1989)
 describes
 the
 relation
between
beliefs
and
asset
values
like:
“An
increase
in
the
"spread"
of
the
 probability
 beliefs
 of
 investors
 may
 increase
 or
 decrease
 equilibrium
 asset
 values
depending
on
the
value
of
a
parameter
of
the
utility
function.”
The
more
 diverse
 the
 differences
 in
 opinion,
 the
 more
 trade
 will
 be
 possible.
 Think
of
 an
 equilibrium,
without
difference
of
opinion,
no
investor
would
have
an
incentive
 to
trade,
as
the
equilibrium
is
assumed
to
be
a
product
of
efficient
market
theory.
 Therefore,
trade
can
only
be
introduced
if
investors
have
different
prior
beliefs
 based
on
their
illusion
of
knowledge.
This
can
explain
the
trading
activity
that
is
 measured
 with
 the
 turnover
 ratio
 used
 in
 the
 STI
 indicator.
 For
 example,
 a
 mutual
 fund
 management
 with
 a
 particular
 strategy
 can
 see
 many
 profitable
 investment
 opportunities,
 based
 on
 this
 the
 management
 seems
 to
 differ
 in
 opinion
with
other
established
mutual
fund
providers
and
market
participants.


8

3


Methodology
and
data
description





This
 section
 provides
 a
 complete
 manual
 of
 how
 the
 STI
 indicator
 has
 been
 developed
and
can
be
used
by
individual
investors
or
mutual
fund
companies.

 The
 essence
 of
 the
 STI
 indicator
 is
 to
 categorize
 mutual
 funds
 according
 to
 trading
 activity
 and
 allocation
 to
 short‐term
 investments.
 By
 using
 the
 STI
 indicator,
 an
 investor
 should
 be
 able
 to
 link
 his
 preference
 toward
 active
 investment
management
with
the
two
dimensions
of
the
STI
indicator.
Both
STI
 dimensions
are
tested
for
the
existence
of
a
linear
relationship
and
a
statistical
 approach
is
suggested
to
test
if
the
alphas
and
betas
do
have
some
explanatory
 power
 if
 they
 are
 used
 in
 conjunction
 with
 the
 STI
 indicator.
 Furthermore,
 summary
 statistics
 explain
 characteristics
 of
 the
 mutual
 fund
 population
 and
 tables
 are
 included
 that
 describe
 the
 distribution
 of
 the
 mutual
 funds
 over
 certain
intervals
of
the
STI
and
turnover.



To
 clarify
 the
 process
 of
 how
 the
 STI
 indicator
 is
 determined,
 an
 ongoing
 example
throughout
this
section
is
developed:
virtual
mutual
fund
X.
This
section
 first
 describes
 the
 derivation
 of
 both
 STI
 indicator
 dimensions.
 Second,
 the
 necessary
data
is
described
and
analyzed.
Third,
both
dimensions
are
combined
 to
 form
 the
 STI
 indicator
 and
 finally,
 the
 STI
 indicator
 is
 applied
 in
 a
 general
 format
on
a
virtual
mutual
fund.






3.1 STI
indicator
fundamentals


The
 next
 four
 subsections
 define
 active
 and
 passive
 management,
 the
 STI
 and
 turnover
 dimension,
 and
 the
 in‐sample
 alpha
 and
 beta,
 which
 serve
 as
 the
 building
blocks
of
the
STI
indicator.






3.1.1 Active
and
passive
management


According
 to
 Elton
 et
 al.
 (2007),
 active
 portfolio
 management
 is
 defined
 as:
 “taking
a
position
(stock
selection)
different
from
that
which
would
be
held
in
a
 passively
managed
portfolio,
based
on
a
forecast
about
the
future.”




Passive
 portfolio
 management
 is
 based
 on
 trading
 through
 mechanical
 rules
 by
 using
 past
 data,
 like
 replicating
 an
 index
 or
 form
 a
 portfolio
 of
 a
 specified
 number
 of
 stocks
 based
 on
 mathematical
 programming
 (Elton
 et
 al.,
 2007).





3.1.2
 Short­term
investment
(STI)


The
STI
ratio
of
a
mutual
fund
is
the
fraction
of
the
fund’s
net
asset
value
that
is
 held
less
than
one
year
in
a
portfolio
with
an
investment
horizon
of
at
least
three
 years.
 Typically,
 the
 STI
 is
 characterized
 by
 disposed
 investments
 that
 do
 not
 satisfy
the
goal
of
the
investment
manager’s
strategy.
It
is
possible
to
use
more
 frequent
portfolio
holdings
data,
like
quarterly
holdings
data,
however,
quarterly
 data
has
to
be
compared
with
quarterly
data
and
not
with
yearly
data
and
so
on.
 The
 STI
 is
 combined
 with
 turnover,
 because
 the
 STI
 does
 not
 explain
 total
 activeness
of
mutual
fund
management,
due
to
allocation
in
long
term‐oriented
 positions.
 Section
 3.3
 will
 elaborate
 on
 the
 combination
 of
 both
 dimensions
 of
 the
STI
indicator.


proposed
long‐term
investment
horizon.
Likewise,
from
a
STI
ratio
of
40%
for
a
 long
term
investing
fund
can
be
concluded
that
the
fund
manager
does
not
follow
 its
 proposed
 strategy.
 
 Singleton
 (2005)
 describes
 that
 short‐term
 investments
 (also
called
satellites)
include
the
riskier
part
of
a
portfolio.
However,
Singleton
 (2005)
 argues
 that
 professional
 investors
 should
 all
 use
 the
 core‐satellite
 portfolio
management
model.
Hence,
it
is
not
necessary
to
exhibit
a
core‐satellite
 portfolio
management
structure
for
mutual
funds
to
derive
a
STI
ratio
that
just
 measures
investments
that
last
for
less
than
one
year
in
a
portfolio.


The
 process
 of
 calculating
 the
 STI
 ratio
 of
 a
 mutual
 fund
 portfolio
 is
 straightforward.
 First,
 the
 mutual
 funds
 are
 selected
 that
 have
 portfolio
 data
 over
three
recent
successive
years.
Second,
in
deriving
the
STI
ratio,
we
want
to
 filter
out
investments
that
are
exclusively
apparent
in
the
mutual
fund
portfolio
 of
year
t‐1
(the
middle
year).
Therefore,
we
need
to
compare
the
portfolio
of
year
 t‐1
with
investments
in
portfolios
of
year
t
and
t‐2.
For
example,
this
study
uses
 the
 years
 2005,
 2006,
 and
 2007;
 and
 the
 investments
 held
 exclusively
 in
 2006
 are
called
the
STI
component
of
a
portfolio.
The
virtual
example
of
mutual
fund
X
 and
a
mathematical
explanation
will
clarify
this.



Suppose
fund
X
is
a
defensive
long
term
oriented
mutual
fund,
focused
on
 investing
 worldwide.
 Table
 one
 represents
 the
 latest
 three
 years
 of
 portfolio
 holdings.
Yearly
portfolio
holdings
are
represented
by
t‐2,
t‐1,
and
t,
respectively.
 The
allocated
funds
to
single
securities
in
the
mutual
fund
portfolio
for
each
year
 are
represented
as
percentage
of
the
fund’s
net
asset
value
(NAV)
by
 ! I_i,t,
where
i
 stands
for
an
individual
stock
and
t
stands
for
a
particular
year
(t,
t‐1,
or
t‐2).
For
 example, ! I_2,t"1
represents
stocks
of
ING
relative
to
the
fund’s
NAV
in
year
t‐1.
For
 every
year,
subscript
i
stand
for
the
same
stock.
 
 Table
1:
Portfolio
holdings
fund
X
for
year
t,
t­1,
and
t­2,
holdings
of
mutual
fund
X
relative
to
 NAV,
 represented
 by


!

I_i,t
is
value
of
stock
i
 at
time
t
relative
to
 fund
NAV,
 Portfolio
t
(portfolio
 holdings
 of
 most
 recent
 year),
 Portfolio
 t‐1
 (one
 year
 old
 portfolio
 holdings),
 and
 Portfolio
 t‐2
 (two
 year
 old
 portfolio
 holdings),
 used
 to
 derive
 the
 STI
 component
 of
 fund
 X
 in
 t‐1.
 The
 STI
 component
is
I10,t­1
in
the
shaded
cell.

Portfolio
t Portfolio
t­1 Portfolio
t­2

! I_1,t ! I_1,t"1 ! I_1,t"2 ! I_2,t ! I_2,t"1 ! I_2,t"2 ! I_3,t ! I_3,t"1 ! I_3,t"2 ! I_4,t ! I_4,t"1 ! I_4,t"2 ! I_5,t ! I_10,t"1 ! I_6,t"2 


To
 derive
 the
 STI
 component
 from
 this
 portfolio,
 a
 comparison
 of
 the
 three
portfolios
must
be
made,
respectively
the
portfolios
in
year
t,
t‐1,
and
t‐2.
It
 is
clearly
visible
from
table
one
that
investments
I1,
I2,
I3,
and
I4
are
investments


are
 at
 least
 three
 years
 in
 the
 portfolio.
 These
 investments
 are
 called
 core
 investments
in
the
STI
indicator
methodology.
The
position
of
I6,t­2
is
initiated
in


t‐2
 or
 in
 previous
 years,
 however
 it
 is
 certainly
 disposed
 in
 t‐2,
 so
 I6,t­2
 is
 not


included
in
the
STI
ratio.
I5,t
is
initiated
in
the
current
year
t,
so
it
is
not
possible


to
 judge
 the
 amount
 of
 time
 it
 will
 be
 included
 in
 the
 portfolio
 until
 it
 will
 be
 disposed.
 Therefore,
 I5,t
 is
 not
 included
 in
 the
 STI
 ratio.
 
 I10,t­1
 is
 an
 investment


10 the
criteria
of
a
STI
investment
within
fund
X.
If
the
fund’s
investments
are
not
 stated
relative
to
the
fund’s
net
asset
value,
the
STI
can
be
calculated
according
 to
the
following
equation,
where
Oi,t
represents
the
amount
of
money
allocated
to


stock
i
at
time
t.

 ! STI_x,t"1= O10,t"1 NAV (O_1,t"1,O_2,t"1,O_3,t"1,O_4,t"1,O_10,t"1)= O_10,t"1 O_1,t"1+ O_2,t"1+ O_3,t"1+ O_4,t"1+ O_10,t"1.
 
 According
to
table
one,
a
frank
mathematical
approach
can
be
derived
to
 calculate
 the
 STI
 ratio
 by
 using
 a
 dummy
 variable
 and
 sets
 of
 investment
 portfolios.
 Ii,t
 is,
 as
 stated
 earlier,
 the
 relative
 value
 with
 respect
 to
 the
 mutual


fund’s
net
asset
value
of
stock
i
at
time
t.

A
convenient
way
of
performing
this
 filtering
 process
 is
 to
 compare
 sets
 of
 investments
 (the
 portfolios).
 The
 set
 of
 investments
 in
 t‐1
 we
 call
 St‐1
 and
 is
 compared
 with
 the
 comparison
 set


consisting
 of
 investments
 in
 t
 and
 t‐2.
 The
 comparison
 set
 is
 called
 Sc,
 where


subscript
 c
 refers
 to
 the
 comparison
 set,
 see
 equations
 under
one.
 The
dummy
 variable
equals
one
for
an
individual
investment
if
it
appears
only
in
St‐1
and
not
 in
Sc,
so
that
investment
satisfies
the
STI
definition.
The
dummy
variable
is
zero
 if
a
particular
investment
appears
in
St‐1
as
well
as
in
Sc.
The
dummy
conditions
 are
provided
in
equations
two
and
three.
From
this,
the
last
 step
in
calculating
 the
STI
ratio
is
simply
adding
the
investments
that
are
held
exclusively
in
year
t‐ 1,
like
in
equation
four.





!

S_t"1= {I1,t"1,...,Ii,t"1}
and


!

S_c = {I1,t,...,Ii,t},{I1,t"2,...,Ii,t"2}
 
 
 (1)



 
 ! d_i,t = 1
if
 ! S_t"1# Sc,$i = 1,2,...,n
 
 
 (2)
 ! d_i,t = 0
if
 ! S_t"1# Sc,$i= 1,2,...,n
 
 
 (3)
 
 !

STI_t"1= I_i,t"1# di,t i=1

n

$


 
 
 (4)
 





The
core
ratio
is
calculated
according
to
the
same
principle
as
in
equation
 four,
 however
 by
 adding
 positions
 that
 last
 for
 at
 least
 three
 years.
 Again,
 the
 portfolios
of
year
t,
t‐1,
and
t‐2
have
to
be
compared.
Yet,
the
dummy
conditions
 of
equation
two
and
three
have
to
be
adjusted,
instead
of
using
a
comparison
set,
 we
need
a
particular
set
for
t
and
t‐2.
The
set
for
t
and
t‐2
will
become
St
and
St­2,
 respectively.
The
dummy
becomes
one
if
an
investment
in
t‐1
is
also
present
in
t
 and
t‐2,
like
in
equation
five.
With
a
dummy
of
zero,
the
particular
investment
is
 not
present
in
both
years
t
and
t‐2,
as
in
equation
six.
Though
it
is
possible
that
 an
investment
is
present
in
one
of
the
years
t
or
t‐2,
but
than
it
does
not
satisfy
 the
 definition
 of
 the
 core
 component.
 With
 changed
 dummy
 conditions,
 the
 formula
of
equation
five
will
transform
into
one
used
to
calculate
the
core
ratio
 in
t‐1
by
replacing
STI
with
CORE
as
in
equation
seven.
 
 ! d_i,t = 1
if
 ! S_t"1# St$ St"2,%i= 1,2,...,n

 
 
 (5)
 ! d_i,t = 0
if
 ! S_t"1# St$ St"2,%i= 1,2,...,n

 
 
 (6)
 
 !

CORE_t"1= I_i,t"1# di,t

n=1 n

3.1.3
 Turnover


The
 turnover
 ratio
 is
 defined
 according
 to
 the
 generally
 accepted
 description
 offered
 by
 the
 Center
 for
 Research
 in
 Security
 Prices
 (CRSP)
 as
 the
 minimum


aggregate
purchases
or
sales
of
securities
divided
by
the
average
total
net
assets
of
 a
 mutual
 fund
 over
 a
 calendar
 year.
 According
 to
 this
 definition
 the
 turnover


ratios
used
in
the
STI
indicator
are
based
on
the
annual
reports
of
mutual
funds.

 Turnover
 does
 not
 make
 any
 difference
 in
 what
 allocation
 of
 investments
 generates
 it,
 therefore
 it
 is
 combined
 with
 the
 STI
 that
 concentrates
 on
 short‐ term
investments.









Turnover
ratios
are
calculated
in
order
to
give
investors
insight
in
trading
 activity
and
transaction
costs
involved
and
is
formulated
as
in
equation
eight:




!

turnover =value sales and purchases of investments " subscriptions " redemptions

net asset value 

(8)




 In
the
literature
section
the
turnover
ratio
was
introduced
with
additional
 background
information
in
combination
with
behavioral
finance
literature.

 
 3.1.4
 Alpha
and
beta
 According
to
Elton
et
al.
2007
the
Jensen’s
alpha
is
described
as
the
excess
return
 of
 a
 stock
 or
 portfolio
 of
 stocks
 relative
 to
 the
 return
 of
 the
 benchmark
 index
 adjusted
 for
 risk
 with
 the
 risk‐free
 rate
 (treasury
 rate).
 The
 beta
 of
 a
 stock
 or
 portfolio
 of
 stocks
 can
 be
 described
 as
 a
 measure
 of
 volatility
 relative
 to
 the
 market.
The
in‐sample
Jensen’s
alpha
and
in‐sample
beta
are
calculated
using
a
 single
 index
 model
 (Elton
 et
 al.,
 2007)
 as
 of
 equation
 nine.
 Ri,t
is
 the
 return
 of


stock
i
at
time
t
and
Rf,t
is
the
risk‐free
treasury
rate
at
time
t.
The
alpha
is
(αi,t)


and
 the
 beta
 (βi,t)
 for
 stock
 i
 at
 time
 t,
 respectively.
 Rm,t
is
 the
 return
 of
 the


benchmark
at
time
t.
 


!

R_i,t" Rf ,t =#i,t+$i,t(Rm,t" Rf ,t)

 
 
 (9)





The
beta
for
stock
i
at
time
t
is
calculated
by
dividing
the
covariance
of
the
return
 of
 the
 stock
 i
 at
 time
 t
 (Ri,t)
 and
 return
 of
 the
 market
 at
 time
 t
 (Rm,t)
 with
 the


variance
 (σ2m,t) of
 Rm,t
 (equation
 10).
 The
 second
 step
 to
 calculate
 the
 beta
 of


the
portfolio
p
at
time
t
is
adding
all
betas
for
the
stocks
included
in
the
portfolio
 according
to
portfolio
weights
Xi,t
(equation
11).
The
annualized
three‐year
beta


12 equation
 13;
 and
 dividing
 the
 outcome
 by
 three
 to
 calculate
 the
 annualized
 three‐year
Jensen’s
alpha
(called
alpha
in
the
rest
of
the
paper).





!

"i,t = Ri,t# Rf ,t #$i,t(Rm,t# Rf ,t) (12)


 ! "_p,t = X_i,t i=1 n

#

"_i,t
 
 
 (13)
 


In‐sample
 three‐year
 annualized
 alphas
 and
 betas
 are
 used
 in
 this
 paper
 and
 section
3.5
describes
how
to
test
for
the
significance
of
alpha
and
beta
in
the
STI
 indicator.






3.2
 Data
description


This
 subsection
 provides
 data
 requirements
 and
 assumptions
 to
 perform
 the
 mutual
 fund
 analyses
 according
 to
 the
 STI
 indicator.
 Four
 topics
 are
 covered,
 namely
 population
 selection,
 data
 on
 holdings,
 data
 on
 turnover,
 and
 data
 on
 alpha
and
beta.





3.2.1
 Population
selection


The
 mutual
 funds
 that
 are
 used
 in
 this
 paper
 are
 selected
 according
 to
 the
 following
conditions:


• The
mutual
fund
has
portfolio
holdings
and
allocation
data
over
the
past
 three
years;


• Yearly
 turnover
 ratio
 is
 available
 in
 annual
report
of
mutual
fund
and
is
 calculated
according
to
equation
eight;


• Only
 all‐equity
 open‐end
 mid‐
 to
 long‐term
 investing
 mutual
 funds
 are
 included.


sample.
 Comparing
 the
 geographical
 versus
 the
 sector
 sample
 shows
 that
 the
 median
 and
 average
 values
 for
 the
 turnover
 and
 STI
 are
less
 and
 that
 the
 core
 ratio
and
number
of
positions
held
are
larger.
The
median
and
average
turnover
 for
the
geographical
and
sector
oriented
sample
are
66%
and
96%,
and
83%
and
 102%,
respectively.
The
sector‐oriented
sample
does
have
a
maximum
turnover
 of
 378%.
 The
 population’s
 standard
 deviation
 with
 respect
 to
 turnover
 is
 approximately
70%.


14 
 Table
2:
Summary
statistics
of
data,
panel
a,
b,
and
c
of
this
table
represent
summary
statistics
for
 the
population,
geographical
sample,
and
sector
sample,
respectively.
The
turnover,
STI,
core
ratio,
 three‐year
annualized
alpha
and
beta
are
calculated
using
the
definitions
presented
in
section
three.
 The
net
asset
value
(NAV)
in
€
times
106
_{is
the
value
of
the
mutual
fund’s
assets
and
positions} represent
the
number
of
holdings
within
a
mutual
fund
(excluding
cash
and/or
equivalents).
The
 Morningstar
rating
shows
the
number
of
stars.
The
summary
statistics
include
a
median,
a
minimum
 and
maximum
value,
a
mean,
a
standard
deviation
(SD)
and
the
number
of
observations
(#obs)
of
 individual
mutual
funds.
All
the
figures
are
calculated
using
data
from
table
one
in
appendix
A. Panel
a:
Summary
statistics
for
the
population

Median Minimum Maximum Average SD #obs

Table
3:
Population
(2006)
of
all­equity
mutual
funds,
sorted
by
the
STI
dimensions.
 The
 mutual
 funds
are
classified
in
intervals
 for
STI
and
 turnover
ratio.
 The
amounts
of
 mutual
funds
that
lie
within
a
certain
interval
for
the
STI
or
turnover
ratio
are
summed
 up
 in
 the
 last
 column
 (for
 STI)
 and
 last
 row
 (for
 turnover).
 The
 STI
 and
 turnover
 ratio
 satisfy
the
definitions
as
mentioned
in
section
three.
 
 Turnover
(%)
 STI
 (%)
 0‐30
 30‐ 60
 60‐ 90
 90‐ 120
 120‐ 150
 150‐ 180
 180‐ 210
 210‐ 240
 240‐ 270
 >270
 All
 55‐60
 
 
 1
 
 
 
 1
 50‐55
 
 
 0
 45‐50
 
 
 1
 
 
 1
 40‐45
 
 
 0
 35‐40
 
 
 
 1
 1
 
 
 2
 30‐35
 
 
 2
 
 1
 
 
 1
 4
 25‐30
 
 
 1
 
 
 1
 20‐25
 1
 
 
 2
 3
 2
 1
 
 
 1
 10
 15‐20
 1
 3
 1
 3
 2
 
 
 1
 11
 10‐15
 1
 6
 7
 3
 
 
 1
 
 
 
 18
 5‐10
 1
 6
 8
 4
 1
 2
 
 
 22
 0‐5
 11
 4
 2
 3
 2
 
 1
 
 
 
 23
 All
 15
 19
 19
 16
 11
 4
 5
 1
 0
 3
 93
 


Table
 4:
 Median
 net
 asset
 value
 and
 expense
 ratio’s,
 calculated
 from
 the
 population
consisting
of
all
equity
open‐end
mutual
funds
in
2006.
The
median
 values
 for
 certain
 intervals
 of
 STI
 and
 turnover
 are
 based
 on
 at
 least
 three
 observations.
 Panel
 a
 displays
 the
 median
 net
 asset
 value
 in
 €
 x
 106
_derived

16

3.2.2
 Data
on
positions


Portfolio
 positions
 are
 acquired
 through
 Morningstar
 and
 meet
 the
 criteria
 as
 stated
 above,
 so
 only
 all
 equity
 open‐end
 mutual
 funds
 are
 selected.
 The
 most
 important
part
of
the
holdings
data
is
the
fraction
of
each
investment
to
the
total
 net
 asset
 value
 (on
 which
 also
 the
 turnover
 ratio
 is
 based
 on).
 Table
 two
 provides
summary
statistics
for
the
data
of
the
number
of
positions
held
within
 mutual
funds.
The
median
number
of
positions
held
within
a
mutual
fund
of
the
 population
 is
 76.
 The
 median
 and
 average
 number
 of
 positions
 held
 within
 a
 mutual
funds
in
the
geographical
and
sector
oriented
sample
are
96
and
51,
and
 147
and
66,
respectively.






3.2.3 Data
on
alpha,
beta,
and
Morningstar
rating


The
three‐year
annualized
in‐sample
alphas
and
betas
of
the
population
show
a
 large
 gap
 between
 the
 minimum
 and
 maximum
 values,
 according
 to
 table
 two.
 For
example,
the
population
has
a
minimum
and
maximum
value
for
the
three‐ year
annualized
alpha
of
approximately
‐29%
and
19%,
respectively.
The
three‐ year
beta
of
the
population
varies
from
0.69
to
1.92.
The
sector
sample
includes
 these
 maximum
 and
 minimum
 values
 for
 the
 three‐year
 annualized
 alpha.
 The
 average
 three‐year
 annualized
 alpha
 and
 beta
 for
 the
 sector
 sample
 are
 large,
 compared
 to
 the
 geographical
 one.
 The
 median
 values
 of
 the
 three‐year
 annualized
alpha
and
beta
for
the
population
are
‐0.41%
and
1.09,
respectively.


The
Morningstar
rating
ranges
from
zero
to
five
stars,
as
is
also
applicable
 to
this
population
with
an
average
rating
of
three
stars,
according
to
table
two.
 The
 geographical
 sample
 does
 have
 a
 minimum
 amount
 of
 stars
 equal
 to
 zero,
 whereas
the
sector
sample
does
have
one
star
as
minimum
amount.






3.3
 Value
of
combining
of
both
dimensions


The
 combination
of
 the
 STI
 and
 turnover
 (the
STI
 indicator)
 gives
 the
 investor
 insight
in
the
short‐term
orientation
and
trading
activity
of
his
or
her
investment
 manager.
The
drawback
of
using
the
dimensions
separately
is
that
the
turnover
 dimension
 concentrates
 on
 the
 activeness
 of
 a
 mutual
 fund
 and
 does
 not
make
 any
 difference
 in
 what
 generates
 the
 turnover
 (portfolio
 allocation
 changes
 within
STI
or
long
term
investments).
Separate
use
of
the
STI
dimension
will
not
 explain
the
total
activeness
of
the
mutual
fund
management,
due
to
allocation
in
 core
 and
mid‐term
 investments.
 Single
 use
 of
the
 dimensions
 would
only
 be
 of
 value
 if
 they
 where
 compared
 with
 a
 benchmark
 of
 mean
 turnover
 or
 STI
 component
 of
 a
 sample
 of
 other
 mutual
 funds.
 The
 STI
 dimension
 is
 different
 from
 the
 Active‐Share,
 as
 is
 proposed
 by
 Cremers
 and
 Petajisto
 (2007),
 in
 that
 the
 STI
 dimension
 does
 not
 need
 a
 benchmark
 to
 compare
 for
 dissimilarities
 with
 that
 benchmark.
 For
 example,
 the
 mutual
 fund
 ‘g1’
 from
 table
 one
 in
 appendix
A
has
a
turnover
of
130%
with
a
STI
component
of
2.4%.
It
is
unlikely
 that
this
STI
component
is
responsible
for
the
trades
having
a
value
of
1.3
times
 the
net
asset
value
of
the
mutual
fund
‘g1’.
Therefore,
a
possible
explanation
is
 that
in
2006
the
fund’s
management
decided
to
change
the
strategy
and
bought
 many
 new
 investments
 or
 sold
 investments
 that
 where
 in
 portfolio
 more
 than
 one
year,
but
less
than
three.




geographical
and
sector
sample
are
characterized
with
an
r‐squared
of
47%
and
 7%,
respectively
for
the
linear
relationship
between
STI
and
turnover.
Results
of
 the
 F‐test
 and
 coefficients
 of
 determination
 are
 summarized
 in
 table
 five
 and
 include
the
same
analysis
for
CORE
investments.






18 The
graph
of
figure
two
is
divided
into
four
quadrants
based
on
median
 values
 of
 the
 STI
 and
 turnover
 from
 a
 population.
 The
 first
 quadrant
 includes
 mutual
funds
with
the
relative
lowest
STI
and
turnover
and
the
second
quadrant
 contains
mutual
funds
with
the
relative
lowest
STI,
but
relative
highest
turnover.
 Quadrant
three
and
four
represent
mutual
funds
with,
respectively,
the
relative
 highest
 STI
 and
 lowest
 turnover
 and
 relative
 highest
 STI
 and
 highest
 turnover.
 All
the
quadrants
represent
values
for
STI
and
turnover
based
on
a
population
of
 mutual
funds.
For
example,
geographical
oriented
investing
mutual
funds,
as
in
 the
 samples
 above,
 are
 characterized
 by
 relative
 low
 turnover
 and
 STI
 ratios
 (quadrant
 one).
 The
 fund’s
 management
 invests
 long
 term
 oriented
 and
 initial
 investments
 are
 likely
 to
 become
 core
 investments
 with
 the
 passage
 of
 time.
 Short‐term
 investing
 and
 quick
 response
 to
 market
 circumstances
 is
 not
 a
 common
habit
for
these
mutual
funds,
this
can
be
concluded
from
the
fact
that
 both
STI
dimensions
have
relative
low
values.

 
 
 
 
 







3


 
 
 








4


 






S T I 
 
 








1


 
 
 








2

0 






Turnover 


Figure
 2:
 STI
 indicator
 graph
 with
 four
 quadrants
 separated
 by
 median
 values
 of
 STI
 and
 turnover,
based
on
the
underlying
population.


Especially
 quadrant
 four
 is
 important
 in
 examining
 behavioral
 finance
 elements
 within
 mutual
 fund
 management,
 because
 it
 includes
 funds
 with
 relative
 large
 STI
 and
 turnover.
 If
 a
 particular
 mid‐
 or
 long‐term
 investing
 mutual
fund
from
the
population
stays
more
than
one
year
in
quadrant
four,
one
 may
argue
that
this
fund’s
management
exhibits
overconfident
behavior.
Unless,
 of
course,
if
the
fund’s
alpha
is
positive.
Overconfident
behavior
can
be
caused
by
 the
illusion
of
knowledge
and,
consequently,
results
in
more
trading.
According
 to
many
studies,
low
turnover
funds
eventually
outperform
high
turnover
funds
 in
 the
 long
 term.
 The
 investment
 focus
 of
 these
 fund
 managers,
 suffering
 from
 the
illusion
of
knowledge,
is
concentrated
on
new
and/or
small
companies
that
 are
 risky
 short‐term
 investments
 (Statman
 et
 al.,
 2006).
 These
 short‐term
 oriented
 investments
 are
 captured
 by
 the
 STI
 ratio
 and
 enhance
 the
 fund’s
 overall
turnover.



investments,
modern
portfolio
theory
statistics
and
the
STI
and
turnover.
Using
 the
 contents
 of
 table
 six,
 we
 are
 able
 to
 apply
 the
 STI
 indicator.
 Make
 the
 assumption
that
the
median
values
for
the
STI
and
turnover
are
15%
and
80%,
 respectively.





Table
 6:
 Data
 for
 mutual
 fund
 X
 to
 apply
 STI
 indicator,
 summary
 of
 STI,
 core,
 and
 turnover
 ratio
 and
 the
 strategy
 of
 the
 investment
 managers
 in
 t‐1,
 supplemented
 with
 NAV,
 number
 of
 positions
(#pos),
alpha
and
beta,
Sharpe
ratio,
and
strategy.


STI
%
 Core
%
 Turnover
%
 Strategy


10%
 60%
 30%
 Defensive
Worldwide


LT


NAV
 #pos
 Alpha/Sharpe
 Beta


6
billion
 150
 7%/‐0,5
 0,95





The
 result
 of
 the
 STI
 indicator
 of
 mutual
 fund
 X
 is
 presented
 in
 figure
 three;
the
spot
marked
with
‘X’
in
quadrant
one
indicates
the
position
associated
 with
 the
 STI
 (10%)
 and
 turnover
 (30%).
 The
 median
 values
 of
 the
 STI
 and
 turnover
are
represented
by
the
horizontal
and
vertical
line
and
have
values
of
 15%
and
80%
based
on
the
population,
respectively.

 
 
 
 






Y
 







3


 
 
 








4









Z 






S T I





 
 





1 5%  
 






X
 







1


 
 
 








2

0 






80%
 






Turnover 
 Figure
3:
STI
indicator
for
mutual
fund
X


20 can
speculate
that
the
mutual
fund
management
of
fund
X
did
some
major
new
 investments,
or
sold
those
to
become
cash
or
equivalents.



To
 provide
 an
 investor
 with
 a
 pallet
 of
 information,
 the
 mutual
 fund
 provider
can
design
a
fact
sheet
with
the
STI
indicator
as
a
supplementary
tool.
 The
principle
of
applying
the
STI
indicator
will
not
change,
however
the
investor
 is
 able
 to
 weigh
 all
 alternatives
 according
 to
 its
 risk
 preferences.
 For
 example,
 the
modern
portfolio
statistics
as
the
alpha
and
beta
can
be
used
to
accompany
 the
 quadrants
 of
 the
 STI
 indicator.
 In
 combination
 with
 return‐based
 or
 style‐ based
 mutual
 fund
 rating
 systems
 the
 STI
 indicator
 provides
 the
 investor
 maximum
possibility
to
select
mutual
funds
according
to
a
snapshot
of
important
 information.
The
STI
indicator
used
in
practice
is
elucidated
in
section
four.
 
 3.5 How
to
test
for
significance
of
alphas
and
betas
in
quadrants
 This
subsection
describes
a
statistical
test
that
can
be
used
to
assess
if
the
alphas

 and/or
betas
from
the
STI
quadrants
deliver
additional
insight
that
is
statistically
 significant
 using
 a
 t‐test.
 This
 t‐test
 compares
 the
 mean
 from
 a
 sample
 (one
 of
 the
four
quadrants)
with
the
known
value
of
the
population
mean.


An
 unpaired
 one‐sample
 Student’s
 t‐test
 that
 assumes
 a
 normal
 distribution
is
used
to
test
if
the
alpha
and/or
beta
for
a
particular
quadrant
has
 any
 explanatory
 power.
 The
 test
 is
 unpaired,
 because
 there
 is
 no
 one‐to‐one
 correspondence
between
the
samples,
likewise
the
samples
are
independent
of
 each
 other.
 Although
 the
 sample
 size
 of
 two
 quadrants
 is
 less
 than
 30
 observations,
 it
 is
 not
 suitable
 to
 use
 a
 non‐parametric
 test,
 like
 a
 Wilcoxon
 signed
 rank
 test.
 The
 samples
 consist
 of
 data
 based
 on
 direct
 measurements
 instead
 of
 ordinal
 data
 that
 can
 be
 arranged
 in
 a
 particular
 order.
 We
 need
 to
 clarify
 if
 the
 sample
 mean
 alpha
 for
 each
 quadrant
 differs
 significantly
 (at
 5%
 and
 10%
 significance
 level)
 from
 the
 population
 mean
 alpha.
 The
 main
 and
 alternative
hypotheses
stated
below
are
used
to
test
for
significance
of
alpha
or
 beta
in
each
quadrant’s
sample
(Q1,
Q2,
Q3,
and
Q4).
 
 H0:
 the
quadrant’s
mean
alpha/beta
does
not
differ
from
the
population
mean
 alpha.
 
 H1:
 the
quadrant’s
mean
alpha/beta
does
differ
from
population
mean
alpha.

 
 Calculating
the
t‐statistic
as
is
defined
in
equation
14
will
test
these
hypotheses.
 
 ! t = X " µ0 #_x/ n_x ,
 
 
 (14)
 
 where
 ! Xis
the
sample
mean
and
 ! µ0is
the
mean
of
the
population,
 ! "x
and
 ! nxare


4

Results:
STI
indicator
in
practice





In
practice
the
STI
indicator
can
be
used
as
a
stand‐alone
and
as
a
supplementary
 tool
 in
 combination
 with
 other
 return
 or
 style
 based
 mutual
 fund
 rating
 mechanisms.
This
section
will
test
if
the
alphas
and
betas
for
each
quadrant
do
 have
explanatory
power
and
a
selection
of
two
mutual
funds
from
the
population
 will
be
used
to
apply
the
STI
indicator.
 
 4.1
 Determining
quadrants
and
validation
of
STI
indicator
 To
determine
the
relative
position
of
an
individual
mutual
fund,
the
STI
indicator
 graph
is
divided
into
four
quadrants
based
on
median
STI
and
turnover
values
 from
the
population.
In
this
case,
the
population
of
93
mutual
funds
does
have
a
 rounded
median
value
for
STI
and
turnover
of
11%
and
80%,
respectively.
The
 STI
 indicator
 graph
 for
 this
 paper’s
 population
 is
 presented
 in
 figure
 four.
 In
 addition
of
the
scatter
plot
from
figure
one
of
section
three,
the
four
quadrants
 are
 drawn
 into
 figure
 four
 based
 on
 the
population’s
 median
 values
 of
STI
 and
 turnover
and
the
93
mutual
funds
are
plotted.
Quadrant
one
is
characterized
by
a
 three‐year
 annualized
 mean
 alpha
 and
 beta
 of
 ‐1.72
 and
 1.09
 based
 on
 35
 observations,
 respectively.
 Quadrant
 two
 has
 a
 three‐year
 annualized
 mean
 alpha
and
beta
based
on
14
observations
of
1.18
and
1.14,
respectively.
The
third
 quadrant
has
14
observations
and
a
three‐year
annualized
mean
alpha
and
beta
 of,
respectively
4.14
and
1.25.
Quadrant
four
has
a
three‐year
annualized
mean
 alpha
of
0.96
and
a
mean
beta
of
1.17
based
on
30
observations.
From
this
small
 population
one
can
observe
that
the
funds
are
not
equally
distributed
among
the
 quadrants,
 however
 there
 is
 an
 indication
 for
 the
 alpha
 and
 beta
 in
 each
 quadrant.
From
this
data,
it
is
possible
to
conclude
that
high
turnover
and
a
high
 STI
 ratio
 (quadrant
 four)
 has
 a
 small
 positive
 alpha.
 The
 mutual
 funds
 with
 quadrant
 one
 characteristics
 (low
 STI
 and
 turnover
 ratio)
 do
 have
 a
 negative
 alpha
 that
 may
 be
 explained
 that
 very
 passive
 investing
 fund
 do
 not
 produce
 excess
return
on
their
benchmark.


22 


Table
7:
T­statistics
for
testing
significance
of
three­year
annualized
mean
alpha
and
beta
 for
each
quadrant:
the
mean,
standard
deviation
(SD)
and
sample
size
(#obs)
for
alpha
and
beta
 of
the
quadrants
are
used
to
calculate
the
t‐value.
Panel
‘a’
shows
t‐
and
p‐values
for
one‐year
 average
 in‐sample
 alpha
 and
 panel
 ‘b’
 gives
 the
 t‐
 and
 p‐values
 for
 the
 in‐sample
 beta.
 The
 figures
 in
 panel
 ‘a’
 are
 based
 on
 average
 one‐year
 in‐sample
 alpha.
 The
 row
 represented
 by
 ‘Pop’
contains
the
mean,
standard
deviation,
and
size
of
population
for
alpha
and
beta.

Panel
a:
information
for
calculus
on
significance
of
(one‐year
average)
alpha
for
quadrants

Mean SD #obs t‐value p‐value

Q1 ‐0,5735 2,4187 35 ‐1,7652* 0,0865 Q2 0,3655 1,6425 14 0,4951 0,6288 Q3 1,3793 2,1551 14 2,1375* 0,0521 Q4 0,3199 2,0801 30 0,4522 0,6545 Pop 0.1482 2.2397 93 ‐ - Panel
b:
information
for
calculus
on
significance
of
beta
for
quadrants Q1 1.0877 0.2125 35 ‐1.6365 0.111 Q2 1.1346 0.1868 14 ‐0.2377 0.8159 Q3 1.2500 0.2700 14 1.4343 0.1751 Q4 0.9597 6.2404 30 0.4473 0.6578 Pop 1.1465 0.2244 93 ‐ ‐ t‐values
significant
at
the
10%
significance
level
are
marked
with
an
asterisk
(*) 


Figure
4: STI indicator for the population used in this paper, the horizontal and vertical lines represent median values of STI and turnover, respectively.





To
 deliver
 the
 investor
 quick
 and
 understandable
 information
 about
 short‐term
 allocation
 and
 activity
 of
 the
 mutual
 fund,
 figure
 three
 may
 be
 too
 complex.
 Therefore,
 in
 the
 application
 of
 the
 STI
 indicator
 the
 format
 of
 figure
 one
in
section
three
will
be
used.



mutual
funds
in
quadrant
four
have
relative
large
net
asset
values
contrasted
by
 relative
small
net
asset
values
for
funds
in
quadrant
one.
From
panel
‘b’
of
table
 four
can
be
argued
that
funds
in
quadrant
four
that
have
relative
large
net
asset
 values
do
have
relative
low
expense
ratios.
Tables
like
table
three
and
four
can
 be
 useful
 to
 show
 investors
 the
 characteristics
 of
 the
 quadrants
 from
 the
 STI
 indicator
at
a
glance.





4.2
 STI
indicator
applied


This
 subsection
 proposes
 an
 application
 format
 for
 the
 STI
 indicator
 on
 two
 mutual
 funds
 selected
 from
 this
 paper’s
 population.
 The
 selection
 is
 characterized
by
geographical
and
sector
investment
focus.
Each
selected
mutual
 fund
is
accompanied
with
its
investment
policy
and
mutual
fund
related
ratio’s
 and
 modern
 portfolio
 statistics
 as
 well
 as
 with
 return
 and
 style
 based
 rating
 systems.



First
 the
 STI
 indicator
 will
 be
 applied
 as
 a
 stand‐alone
 measure;
 thereafter
 the
 STI
 indicator
 is
 used
 as
 a
 supplementary
 tool
 with
 return‐based
 performance
measures.
The
selected
mutual
funds
are
Fortis
Obam
(flagship
of
 Fortis
Investments)
and
the
ING
Daily
Consumer
Goods
(sector
oriented).

 
 4.2.1 STI
indicator
for
Fortis
Obam
 Fortis
Obam
is
a
mutual
fund
of
the
population
as
is
described
in
section
three
 and
is
denoted
by
‘g4’
in
table
one
of
appendix
A.
The
chairman
of
the
board
of
 supervisory
 directors
 of
 Fortis
 Obam
 (prof
 R.A.H.
 van
 der
 Meer)
 describes
 the
 strategy
of
the
fund
in
the
annual
report
of
2006/2007
as
in
the
next
paragraph.



 “Fortis
OBAM
aims
at
a
balanced
international
portfolio
of
listed
shares
with
 interests
 in
 Europe,
 the
 United
 States
 of
 America,
 South
 East
 Asia
 and
 Japan
 and
 strives
 for
 increase
 of
 the
net
 assets
 in
 the
 long
 term.
 Traditional,
 a
 considerable
 part
 of
 the
 assets
 are
 invested
 in
 Dutch
companies.
 Within
 the
 portfolio
 of
 Fortis
 OBAM
there
is
special
attention
for
large
companies
that
are
strongly
international
 orientated
and
capable
of
adjusting
well
to
the
global
investment
climate,
but
also
 for
smaller
companies.“



The
quadrants
of
the
STI
indicator
are
based
on
median
values
form
the
 population
of
the
STI
(11%)
and
turnover
(80%)
in
2006.
The
STI
and
turnover
 ratio
 of
 Fortis
 Obam
 are
 1,0625%
 and
 20,66%
 in
 2006,
 respectively.
 Quadrant
 one
 in
 figure
 five
 displays
 the
 relative
 position
 of
 Fortis
 Obam
 within
 the
 population
in
the
STI
indicator.
 
 
 





3
 
 
 




4
 







 



 ST I
 







 


1 1% 
 
 
 





1
 ●
 
 




2
 







0
 






80%
 







Turnover
 Figure
5:
STI
indicator
for
Fortis
Obam
in
2006,
the
spot
in
quadrant
one
represents
the
place
of
 Fortis
 Obam
 in
 the
 STI
 Indicator
 with
 an
 STI
 and
 turnover
 ratio
 of
 1,0625%
 and
 20,66%,
 respectively.


24 population.
The
STI
component
of
the
portfolio
is
considerably
low
in
a
way
that
 it
 cannot
 produce
 a
 turnover
 of
 20%.
 Turnover
 can
 be
 generated
 by
 new
 investments
 or
 by
 selling
 of
 core
 or
 mid‐term
 investments.
 To
 add
 more
 perspective
 to
 the
 STI
 indicator,
 table
 seven
 delivers
 a
 wide
 variety
 of
 return
 based
mutual
fund
ratios.
Nearly
seventy
percent
of
Fortis
Obam
its
investments
 last
 for
 at
 least
 three
 years
 and
 20%
 of
 NAV
 is
 allocated
 to
 the
 top
 10
 investments.
 
 With
 the
 portfolio
 composition
 and
 strategy
 of
 Fortis
 Obam
 in
 2006
 it
 gained
 a
 five
 star
 rating
 from
 Morningstar
 to
 reflect
 good
 historical
 return‐based
performance.
The
alpha
of
nearly
10%
reflects
that
the
long‐term
 investment
approach
with
little
room
for
short‐term
investments
pays
off.






Table
 8:
 Summary
 statistics
 for
 Fortis
 Obam
 2006,
 three­year
 annualized
 return
 is
 based
 on
 fund
values
in
2005,
2006,
and
2007;
the
core
ratio
are
positions
within
Fortis
Obam
that
last
for
 at
least
three
years;
Morningstar
indicates
past
performance;
alpha
is
the
excess
abnormal
return
 of
 a
 portfolio
 compared
 to
 prediction
 from
 the
 CAPM,
 NAV
 is
 the
 net
 asset
 value;
 #inv
 is
 the
 number
of
positions
held;
%NAV
in
top10
explains
the
percentage
of
NAV
allocated
to
10
major
 positions;
and
beta
is
defined
as
a
measure
of
systematic
risk
compared
to
the
benchmark.



3Y
ann.
return%
 Core
%
 Morningstar
 Alpha


18,80
%
 70%
 
 9,8%


NAV
 #inv
 %NAV
in
top10
 Beta


€4,21
billion
 245
 20,50%
 1,92





4.2.2 STI
indicator
for
ING
Basic
Materials
Fund


The
 sector
 fund
 is
 identified
 by
 ‘s33’
 in
 table
 one
 of
 appendix
 A
 and
 ING
 Fund
 Management
B.V.
describes
in
the
prospectus
 the
investment
strategy
as
in
the
 next
paragraph.


“The
ING
Basic
Materials
Fund
uses
active
management
to
outperform
the


result
 in
 investments
 that
 are
 risky,
 short
 term
 oriented,
 and
 producing
 high
 turnover
for
this
long
term
oriented
ING
Basic
Materials
Fund.



Additional
 return‐based
 information
 is
 summarized
 in
 table
 nine,
 explains
 that
 that
 the
 historical
 performance
 is
 valued
 with
 four
 stars
 from
 Morningstar
 relative
 to
 its
 peer
 group
 at
 Morningstar.
 However,
 the
 fund
 does
 not
 outperform
 its
 benchmark
 as
 is
 intended
 by
 the
 mutual
 fund
 investment
 objective
with
an
alpha
of
‐1,92%.
The
active
management
is
resulting
in
that
the
 portfolio
is
20%
more
volatile
as
the
benchmark
(beta
equals
1,2).







Table
9:
Summary
statistics
for
ING
Basic
Materials
Fund
2006,
three­year
annualized
return
 is
 based
 on
 fund
 values
 in
 2005,
 2006,
 and
 2007;
 the
 core
 ratio
 are
 positions
 within
 ING
 Basic
 Materials
Fund
that
last
for
at
least
three
years;
Morningstar
indicates
past
performance;
alpha
is
 the
excess
abnormal
return
of
a
portfolio
compared
to
prediction
from
the
CAPM,
NAV
is
the
net
 asset
value;
#inv
is
the
number
of
positions
held;
%NAV
in
top10
is
the
fraction
of
NAV
allocated
 to
the
10
major
positions;
and
beta
is
a
measure
of
systematic
risk
compared
to
the
benchmark.


3Y
ann.
return%
 Core
%
 Morningstar
 Alpha


23,04%
 45%
 
 ‐1,92%


NAV
 #inv
 %NAV
in
top10
 Beta