HD28
.M414
•
ALFRED
P.
WORKING PAPER
SLOAN SCHOOL OF MANAGEMENT
The Investment Performance of U.S. Equity Pension
Fund Managers: An Empirical Investigation
T. Daniel Coggin
*
Frank
Fabozzi
**
Rahman
***
J.
Shafiqur
WP
#3360-91
EFA
December 1991
MASSACHUSETTS
INSTITUTE OF TECHNOLOGY
50 MEMORIAL DRIVE
CAMBRIDGE, MASSACHUSETTS 02139
The Investment Performance of U.S. Equity Pension
Fund Managers: An Empirical Investigation
T. Daniel Coggin
*
Frank
Fabozzi
**
Rahman
***
J.
Shafiqur
WP
#3360-91
EFA
December 1991
Virginia Retirement System
» *
* * *
Massachusetts Institute of Technology
Portland State University
of authorship is alphabetical to reflect an equal contribution by each. We thank
Jon Christopherson of the Frank Russell Company for providing the pension manager data
used in this study. The paper has benefitted from helpful discussions with John E. Hunter.
The opinions and conclusions offered in this study do not necessarily represent those of the
Virginia Retirement System or the Frank Russell Company.
The order
The Investment Performance of U.S. Equity Pension Fund Managers:
An
Empirical Investigation
ABSTRACT
This paper presents an empirical examination of the selectivity and timing performance of
a sample of U.S. equity pension fund managers. Regardless of the choice of benchmark portfolio
or estimation model, the average selectivity measure
is
negative.
However,
selectivity
benchmark when managers are
variation around the
positive and the average timing measure
does appear to be somewhat sensitive to the choice of a
classified
mean values
is
by investment
for each measure.
style.
The 80%
Meta-analysis revealed some real
probability intervals for selectivity
revealed that the best managers produced substantial risk-adjusted excess returns. Consistent with
previous studies of mutual fund performance,
selectivity
and timing.
we
also found a negative correlation
between
M.I.T.
JAN
1
J 1992
The Investment Performance of U.S. Equity Pension Fund Managers:
An
Each
management
was invested
was invested
in
than the
little
leading
pension assets of $1,876
total
trade
trillion.
The Investment Company
in equities.
a 3:1
investment. Not only
in
a
,
newspaper
for
the
Approximately $750
Institute estimates that
open- and closed-end equity-oriented U.S. mutual funds
snapshot indicates
managers
Investments
pension
industry, profiles the top 1000 public and private U.S. pension funds. At year-end
1990, these funds had
percent)
&
Pensions
year
Empirical Investigation
is
for pension
ratio
at
equity investment versus
$250
is
The
large.
total
mutual fund equity
number of pension fund managers
number of mutual fund managers, by a
ratio of
billion
year-end 1990. This
the dollar difference large, but also the difference in the
each universe
billion (40
is
number of
much
larger
approximately 10:1. Yet surprisingly
research has been done on the investment performance of U.S. equity pension fund
managers. This paper begins to
fill
an important gap
in the literature
by providing empirical
evidence on the investment performance of these managers.
The focus of
this study is
on equity pension fund managers who have been allocated
funds by a pension plan sponsor.
Brinson,
(1987), and Berkowtiz, Finney and
sample of large U.S. pension plans.
different asset categories with their
is
the only study
we know
Hood and Beebower
Logue (1988) examined
(1986), Ippolito and Turner
the investment performance of a
Each plan may be composed of many fund managers
own
specific investment objectives
and
styles.
To
in
date, ours
of which specifically examines the components of the investment
performance of a sample of U.S. equity pension fund managers.
1
The two components we examine
are security selection skill and market timing
skill.
Security selection involves the identification of individual securities which are under- or
overvalued relative to the market
Pricing
Model (CAPM),
returns which
securities
lie
Within the specification of the Capital Asset
in general.
the investment
manager attempts
significantly off the security market line.
which offer an abnormally high
return on the market portfolio. If the
risk
to identify securities with expected
The manager
will then invest in those
premium. Market timing
refers to forecasts of
manager believes he can forecast the market
return, he will
adjust his portfolio risk level accordingly.
According
is
to the efficient
The only
futile.
market hypothesis,
in
However,
the United States.
I
activity
an investment program which cannot outperform a
for)
there exists a very large active pension fund
Our study
will shed
some
funds are behaving rationally to perpetuate
Section
management
an efficient market, plan sponsors would not rationally invest
pay active management fees
market index.
active investment
rational investment choice for a plan sponsor is to invest in a passively
managed market index. Hence,
in (or
all
light
mangement business
on the question of whether or not pension
this business.
Our paper
is
organized as follows.
presents the models of selectivity and market timing used in this paper. Section
describes the data and methodology. Section
presents a meta-analysis of our results. Section
III
V
in
presents the empirical results. Section
II
IV
discusses the results. Section VI concludes our
paper.
I.
It is
Models of
Selectivity
and Timing
important that portfolio managers be evaluated on both selection ability and market
timing
Accordingly
skill.
it
is
necessary to model timing and selectivity simultaneously. Jensen
(1968, 1969) formulated a return-generating model to measure performance of the managed
The model
portfolios.
is:
Rp,
where
R^, is the excess (net
of risk-free
rate) return
the market return and
of security selection
consideration
Indeed,
is
=
a,
+
of risk-free
+
Up R„,
rate) return
on the market portfolio,
Up, is
skill.
fip
Up,
(1)
on the pth
the excess (net
ap
is
to
a measure
This specification assumes that the risk level of the portfolio under
managers may
issue and suggested a
somewhat
the
shift
overall
composition of their portfolio
risk
movements. Fama (1972) and Jensen (1972) addressed
finer
They argued
in
this
breakdown of performance.
Treynor and Mazuy (1966) added a quadratic term
that if the
the return on the market
to equation (1) to test for
manager can forecast market
greater proportion of the market portfolio
when
is
measures the sensitivity of the portfolio
a random error which has expected value of zero,
anticipation of broad market price
proportion
R^i
stationary through time and ignores the market timing skill of the managers.
f)ortfolio
timing ability.
portfolio.
when
is
the return
market
returns, he will hold a
on the market
is
high and a smaller
low. Thus, the portfolio return will be a non-linear
function of the market return as follows:
R,,
A
=
positive value of
ap
-h
iSpR„,
+
y(R^y-
+
e^,
(2)
y would imply good market timing.
Jensen (1972) developed a similar model to detect selectivity and timing
managers.
skill
of
Jensen's measure of market timing performance calls for the fund manager to
forecast the deviation of the market portfolio return
from
its
consensus expected return.
By
assuming
and the actual return on the market have a joint normal
that the forecasted return
distribution,
Jensen shows that, under this assumption, a market timer's forecasting ability can
be measured by the correlation between the market timer's forecast and the realized return on
He concluded
the market.
selectivity
that,
under the above structure, the separate contributions of
and timing can not be identified unless, for each period, the manager's forecast and
consensus expected return on the market portfolio, E(R^, are known.
Bhattacharya and Pfleiderer (1983) extended the work of Jensen (1972).
an error made
obtain
measures of timing and selection
that the
correcting
Jensen (1972), they show that one can use a simple regression technique to
in
unadjusted forecast of the market return
assume
By
manager
ability.
in the
Jensen assumes that the manager uses the
Bhattacharya and Pfleiderer
timing decision.
adjusts forecasts to minimize the variance of the forecast error.
Sf)ecify a relationship in
terms of observable variables, which
is
They
similar to the Treynor and
Mazuy model:
=
Rp,
a,
+ eE(RJ(\
-
^)R„,
+ ^e(K.d' +
e^6,R„,
+
Up,
(3)
where
6 =
^ =
the fund manager's response to information,
the coefficient of determination between the
return
€,
=
on the market, and
the error of the
This quadratic regression of
as revealed by a^.
cj,
manager's forecast and the excess
manager's forecast
Rp,
on R„, allows us
The disturbance term
= e^€,R„, +
Up,
in
to detect the existence
equation
of stock selection ability
(3):
(4)
contains the information needed to quantify the manager's timing ability.
We
can extract
this
information by regressing (wj- on (R„,)^:
(c.,)'
= &r'(af{R„,y +
(5)
?.,
where
=
?,
The proposed
e^^i'^CR^J^LCeJ^
{of]
+
(Up^
+
2e^R„,6,Up..
regression produces a consistent estimator of
we
(6)
6^^Ve, where
Using the consistent estimator of
of the manager's forecast error.
equation (3),
-
(ct,)^ is
Q^, which we
recover from
This, coupled with knowledge about (aj^, the variance of excess
obtain {a,f.
return on the market, allows us to estimate
^ =
(aJ^/[((Tj^
+
(a,)^]
= p^ where
correlation between the manager's forecast and excess return on the market.
which
calculate p
truly
of timing
It
skill.
forecasting
Pfleiderer
model of equation
(3) is a
is
the first
Rahman
both the Treynor and
model
that analyzes the error
term to identify a manager's
(1990). In the empirical tests reported in Section
Mazuy and
sensitivity
and timing
the Bhattacharya and Pfleiderer
models.
III,
model are
we employed
This will allow us
of results to alternative model specifications.
There are other models
selectivity
we
Such a refinement should make the model more powerful than previous ones.
discussed in Lee and
examine the
Finally,
refinement of the Treynor and
Further detail and econometric issues relating to the Bhattacharya and Pfleiderer
to
the
focuses on the coefficient of the squared excess market return as an indication
It
skill.
is
p
measures the quality of the manager's timing information.
The Bhattacharya and
Mazuy model.
the variance
skills
in
the
literature
that
permit identification and separation of
of portfoloio managers. These are models by Grinblatt and Titman
(1989b), Henriksson and Merton (1981), and an alternative version of the Henriksson and
Merton mcxlel by Kon and Jen (1978, 1979). The Grinblatt and Titman model requires the
observation of the historical sequence of portfolio weights for the manager. Unfortunately, data
on portfolio weights are very costly and time-consuming and often not available. The Henriksson
and Merton model provides no significant advantage over the Bhattacharya and Pfleiderer model.
One weakness of
no
of whether the information
test
Merton model
the Henriksson and
is
is
that information is
being used correctly. The forcasters in
sophisticated than those of the Bhattacharya and Pfleiderer model,
much
better the superior investment will perform. Henriksson
have a coarse information structure
measured but there
in
model are
this
is
less
where they do forecast how
and Merton assume
that
managers
which dichotomous signals are only predictive of the sign
of the excess return of the market relative to the risk-free
of receiving an "up" or a "down" signal
in
rate. In their
no way depends upon how
model, the probability
far the
market will be
"up" or "down."
II.
The
data for this study consist of monthly returns for the period January 1983 through
December 1990 (96 months)
are net of expenses and
market.
Among
Data and Methodology
The
for a sample of 71 U.S. equity pension fund managers.
management
fees.
These managers invest exclusively
data were provided by the Frank Russell
other services, the Frank Russell
Company
Company
in the
Returns
U.S. equity
of Tacoma, Washington.
evaluates the performance of the managers
of a number of pension funds throughout the United States. The Frank Russell
Company
segregates equity managers into four basic investment styles on the basis of managers' portfolio
characteristics.
These
are:
(1)
Earnings Growth, (2) Market-Oriented, (3) Price-Driven, and
(4)
Our sample
Small Capitalization.
Price-Driven, and
consists of 18 Earnings
Appendix
16 Small Capitalization managers.
Monthly observations
investment styles.
Growth, 19 Market-Oriented, 18
for the Treasury bill rate
I.
A
describes these four
was used
as a proxy for the
risk-free rate.
Our study
S&P
uses several alternative equity benchmark portfolios.
500 Index and
like the
S&P
500 Index.
500.
To be more
These
The
Russell
two broad market
specific,
we
3000 Index
is
a broad market index
(for
indices,
we
it
to the
S&P
also use four style indices as
use separate benchmarks for four different investment
style indices are the Russell
2000 index
Russell
3000 Index.
of these are the
Apf)endix I.B describes the Russell 3000 Index and compares
In addition to these
benchmarks.
styles.
the Russell
Two
1000 Index
(for
Market-Oriented managers), the
Small Cap managers), the Russell Price-Driven Index (for Price-Driven
managers), and the Russell Earnings Growth Index (for Earnings Growth managers). Appendix
I.B describes these indices and compares them to broad market indices.
alternative
indices
performance
market,
allow
to alternative
(a,)^,
of Lee and
will
to
examine the
benchmarks.
An
was derived from observed
Rahman
of pension
sensitivity
several
fund manager's
estimate of the variance of the excess return on the
returns for each
benchmark following
the procedure
(1990).
In the empirical test,
and Mazuy
us
The use of
it
is
necessary to correct for heteroscedasticity in both the Treynor
model and the Bhattacharya and Pfleiderer
model, the error term
model.
will exhibit conditional heteroscedasticity
In the
Treynor and Mazuy
because of the fund manager's
attempt to time the market, even though security returns are assumed to be independent and
identically distributed through time.
To
correct this, following Breen, Jagannathan and Ofer
Lehmann and Modest
(1986) and
prof)osed by White (1980),
in
Section
produce the most
and
we
use heteroscedasticity-consistent standard errors
Hansen (1982), and Hsieh (1983). The significance
tests reported
are based on heteroscedasticity-adjusted t-statistics.
III
In the Bhattacharya
(3)
(1987),
and Pfleiderer model, the procedure discussed
in Section
efficient estimates of the parameters since the disturbance
More
(5) are heteroscedastic.
efficient estimates can
in
equations
be obtained by taking into account
We followed a Generalized
the heteroscedasticity of the disturbance terms.
term
does not
I
Least Squares (GLS)
procedure, which makes a correction for heteroscedasticity, to obtain efficient estmates of
parameters.
This methodology
As noted
is
more
fully described in
Coggin and Hunter (1991), one weakness of the Treynor and Mazuy and the
in
Bhattacharya and Pfliederer models
modify these models
is that
skill.
In the
Such
this is indicative
results in both
forecast the expected return
market return
to
(2), a
when
is
hypothesize that managers
this
means
high.
is
the
may
We
exhibit
manager holds
In the Bhattacharya
of a negative correlation between beta and the market
on the market
it
We
the market return
models could be due
be high when
model of equation
skill.
Treynor and Mazuy model,
a smaller portion of the market portfolio
and Pfleiderer model,
they ignore negative or inferior market timing.
allow negative timing
to
negative ex post timing
return.
Lee and Rahman (1990).
portfolio.
actually
to the inability
Hence
of managers to correctly
these managers
low and vice versa.
In the
would forecast the
Treynor and Mazuy
negative value of 7 would be indicative of poor market timing.
For the Bhattacharya and Pfliederer model, we examine the sign of the coefficient of
(Rrnd^ in equation (3).
this coefficient will
Intuitively, in the spirit
of the Treynor and
be indicative of the nature of timing
8
skill.
Mazuy model,
If the
the sign of
estimated value of this
coefficient
is
negative,
we
designate timing
modification makes these models
Pfleiderer model
was
more
realistic.
Significant Selectivity and
Table
follow,
I
presents
"S&P 500"
A
given by p to be poor or inferior.
This
similar adjustment of the Bhattacharya and
implicitly introduced in Jagannathan and Korajczyk (1986, p. 229).
III.
A.
skill
Empirical Results
Timing
summary
results
Skill
from the two
denotes results based on using the
models. In this table and those that
S&P
"Russell 3000" denotes results based on using the Russell
500 as the benchmark
3000 as the benchmark
portfolio,
portfolio,
and
"Style Index" denotes results based on using each manager's appropriate style index as the
benchmark
portfolio.
negative timing
skill
values exceeds the
These
show some evidence of
results
significant positive selectivity
significant negative selectivity values for both
of the benchmark used. For timing
number of
The number of
on the part of managers.
number of
positive security selection skill and
skill,
the results are just the opposite.
significant negative timing values exceeds the
number of
models regardless
For both models, the
significant positive timing
values regardless of the benchmark used.
—
B.
Mean Values
Table
II
Insert Table
I
about here
—
of Performance Measures
presents the
means of
the subsets of managers classified
the selectivity and timing values for
by investment
style.
all
managers and for
For the entire sample
(All
Managers),
both models show a
f)ositi\e
values are significant
S&P
For the
mean liming value
S&P 500
results using the
3000 Index and
is
two of
However,
models show a
for only
benchmarks. These
For timing
the three benchmarks.
entire sample, both
three alternative benchmarks.
all
500), the
Russell
selectivity value for all three alternative
at the .05 level for
results are just the opposite.
value for
mean
skill,
the
mean timing
negati\'e
one of the three benchmarks
significant at the .05 level for both models.
Hence
(the
the
Index as a benchmark contrast with the results obtained using the
the style indices as benchmarks.
two indices are much more representative of
As shown
the managers'
in
Appendix
I.B. the latter
investment universe
(i.e.,
true
investment opportunities) than the former and, as such, are more appropriate benchmarks than
the former.
The
results in Tables
and
I
pickers than market timers.
confirmed
Rahman
in
Table
(1990),
However,
it
skill in their
Our
suggest that pension fund managers are on average better stock
The
results that
were only hinted
Table
at in
I
are
now
results relating to selection skill are consistent with those of
who found some
They
managers.
II.
II
evidence of superior selection
skill
strongly
Lee and
on the part of mutual fund
also found evidence of superior market timing skill for several managers.
should be pointed out that Lee and
model, while
we allow
Rahman
(1990) ignored negative market timing
negative market timing here.
Our market timing
consistent with those of previous studies on mutual fund performance (see
and Lewellen (1984), Henriksson (1984), Lehmann and Modest (1988),
Coggin and Hunter (1991), and Connor and Korajczyk (1991)).
Kon
results are
(1983),
Cumby and
Chang
Glen (1990),
These studies found more
evidence of negative market timing than positive. These studies also found some evidence of
negative selection
skill for
mutual funds.
10
-
There are differences
and investment
in the portfolio characteristics
styles
among
Earnings Growth, Market-Oriented, Price-Driven, and Small Capitalization managers.
examine performance measures
therefore useful to
II
presents
mean values of the performance measures
However, they do vary somewhat across benchmarks
benchmark.
The period 1983-1990 was
For the eight years,
substantially.
S&P
500 grew
15.60%
at a
the "value" investment style
analog of this style
compares
grew
at a
to the
as
is
all
period
in
grew
However,
3000 grew
also provides
the Price-Driven index
for a given model.
an annualized rate of 14.17%, and
at
this
period (up until the end of 1988)
the market relative to other investment styles.
which grew
at
Our
an annualized rate of 15.53%. This
rate,
a
at
and the Small Capitalization style (represented by the Russell 2(XX)
7.38%
rate. In
if
we
look
Table
II
we
see that, using the broad stock market indices
selectivity value is consistently
is
observed for the growth and
consistent with the preference of the stock market for the
at the Style
Index as a benchmark,
we
other styles) have positive selectivity values. Thus, while
selectivity value across All
which benchmark portfolio
of investment
Table
which the overall stock market was up
For the majority of
was favored by
small capitalization managers. This
well
a
the Russell
rate.
benchmarks, a negative mean
period.
It
is
"growth" investment style (represented by the Earnings Growth index) which
13.72%
index) which
for each style of manager.
It
These ranks do not vary between the models for a given
the aggregated rank of each group.
the
for each investment style separately.
the
Managers
is
for each
benchmark,
it
we
style.
-
Insert Table
II
11
about here
observe a positive mean
does appear to make a difference
used (and, perhaps, which time period)
—
see that these managers (as
—
when we move
to the level
-
Correlation of Performance Measures
C.
To examine
the sensitivity of results to
benchmarks and models, we also examine the
correlation of the performance measures across models and benchmarks.
of association
Tables
II.
III,
Table
-
the Pearson correlation coefficient and the
IV, and
III
V
Spearman rank correlation
coefficient.
I
and
represents the correlation of a performance measure (selectivity or timing) with
There
significant at the .0001 level.
broad market indices
-
S&P
the
is
All the correlations reported in the table are
a very high correlation between the results based on the
500 Index and
the Russell
measures based on these benchmarks are somewhat
indices.
use two measures
provide correlational summaries of the results presented in Tables
between benchmarks for a given model.
itself
We
These
results are consistent for both
3000 Index.
The performance
less correlated with those
based on style
models and also for both the timing and
selectivity
measures.
Table IV presents the correlation of a performance measure (selectivity or timing)
with
between models for a given benchmark.
itself
significant at the .(XX)! level.
The
results in Tables III
These correlations are very high and
and IV indicate high ranking consistency
among benchmarks and between models.
Finally,
we
present the correlation between selectivity and timing
for a given benchmark.
significantly negative.
These correlations are presented
These
results indicate that
in
Table V.
good (poor)
to say
about
this in Section
—
selectivity
All these correlations are
Insert Tables III, IV,
12
V
about here
—
poor
This implies that fund
and timing simultaneously.
V.B.
-
within a model
selectivity is associated with
(good) timing ability regardless of the benchmark or model used.
managers can not accomplish both
skill
We
will
have more
IV.
Meta-analysis
is
a statistical methodology for the cumulation of results across studies.
contribution of meta-analysis
mean and standard
Meta-Analysis of Results
The
offer a statistical technique to produce direct estimates of the
is to
deviation of population values. Thus, meta-analysis allows
more
statistically
powerful inferences from data than are possible using more traditional disaggregated analyses.
Following
to
its
early beginings in physics and psychology, meta-analysis has recently been applied
cumulate results across studies
(1990) and Trotman and
Dimson and Marsh
Wood
in several other disciplines including
accounting (Christie
(1991)), finance (Coggin and Hunter (1983, 1987, 1991) and
(1984)), and marketing (Farley and
Lehman
(1986)). Recent comprehensive
on meta-analysis include Hedges and Olkin (1985) and Hunter and Schmidt (1990).
texts
There are a number of "study
artifacts"
which can cause the
different or even contradictory to those of another.
Among
the
results of
one study
more prominent
to
appear
artifacts are
sampling error, error of measurement, and restriction of range on the dependent variable. These
artifacts are discussed in detail in
we
Hunter and Schmidt (1990, Chapters 2 and
3). In this
paper,
focus on sampling error in the regression values for selectivity and market timing across
managers. Meta-analysis has been primarily developed for correlational data. However, the time
series
regressions
performed
measurement model) across
meta-analysis,
we
in
our paper have identical
specifications
(by performance
the sample of pension fund managers. Thus, for the purpose of
can consider each of the 71 managers as a "study," cumulate the results and
apply meta-analysis. Appendix
II to this
paper presents a brief discussion of the meta-analysis
technique for regression coefficients used in this section.
13
Table VI presents the results of the meta-analysis of the selectivity and timing coefficients
based on three benchmark portfolios and using heteroscedasticity corrected t-values.
row of
b; the
second row gives estimates of the standard deviation of the observed values,
the standard deviation of the papulation values,
Sbi
the fourth
s^j;
the third
row gives
estimates of the frequency-weighted average squared deviation of the observed values,
fifth
row gives estimates of
total
row gives estimates
Insert Table
VI about here
s/ZSb'.
—
Selectivity
For
selectivity,
the
mean monthly values are
However, on an annualized
basis, these
positive in every
3000), and 1.97% (Style Index).
selectivity values are
to the
the Bhattacharya
% (S&P 500), .93%
(Russell
For the Treynor and Mazuy model, the annualized mean
.51% (S&P 500), .96%
see that for both models, managers
compared
case but very small.
numbers become more meaningful. For
and Pfleiderer model, the annualized mean selectivity values are .41
we
last
observed variance accounted for by sampling error,
—
the
the chi-square value for the
of the observed variance to the sampling error variance; and the
of the proportion of
A.
row gives
Sb^;
row gives
the variance of the population values, s/; the sixth
estimates of the sampling error variance, s/; the seventh
ratio
first
frequency-weighted mean of the observed values for each parameter,
this table gives the
row gives estimates of
The
do
broader market indices.
(Russell 3000), and
better
on average
This result
is
1.99%
(Style Index).
relative to their
instructive, since
own
14
style index as
much of
investment wisdom implies that investment managers "can't beat the market."
Hence
the
common
This result
suggests that such a
used
comment begs an important
management
three
remind the reader
of investment
benchmarks
are significant at the .05 level or less for the selectivity values using
for both models.
This implies that there
attributable to sampling error) around the
B.
that these returns are net
fees.
The chi-square values
all
We
evaluating a manager.
in
question regarding which benchmark should be
mean
is real
selectivity value in
variation (in excess of that
each case.
Timing
For market timing, the mean values are negative
the results of
(1988),
Kon
(1983),
in
each case. This result
Chang and Lewellen (1984), Henriksson (1984),
Lehmann and Modest
(1988),
Cumby
Pfleiderer
at
consistent with
Grinblatt and Titman
and Glen (1990), Coggin and Hunter (1991), and
Connor and Korajczyk (1991) who examined mutual fund
values are significant
is
returns.
Furthermore, the chi-square
the .10 level or less in each case except for the Bhattacharya
model using the
S&P
500 benchmark.
Thus
in
almost every case there
is
and
evidence
of real variation around the negative mean timing value.
C.
The 80%
If there
would be
of
Probability Intervals for Selectivity and
were no
real variation
around the observed mean value, then the observed mean
the true value for each of the 71 managers.
real variation in
in perspective,
almost every
we
can look
set
Timing
However,
in
our case, there
of selectivity and market timing values.
at the last
row of Table VI
for each
To
is
evidence
put these results
model and examine the
proportion of total observed variance accounted for by sampling error. For the Bhattacharya and
15
Pfleiderer model, the percentage of observed variance in selectivity accounted for by sampling
71%
error goes from
to
57%
to
50%
across benchmarks; while the percentage of variance in
timing accounted for by sampling error goes from
the Treynor and
Mazuy model,
across benchmarks;
benchmarks.
95%
to 81
%
of variance attributable
68%
across benchmarks.
go from 71%
the percentages for selectivity
while the timing percentages go from
We should
to
18%
17%
to
to
to
57%
to
14%
For
50%
across
note that, as discussed in Hunter and Schmidt (1990), these percentages
sampling error
to
may
well contain other unaccounted for study artifacts
(such as measurement error).
Assuming
80%
selectivity
and market timing
to
be normally distributed,
probability intervals (i.e., the lower and upp)er
90%
selectivity
(i.e.,
result is
80%
both the observed and the population values for
there
is
real variation in selectivity
and timing values
80%
probability intervals for selectivity are
all
in
every case except
Using the
at
S&P
500
shifted towards positive values,
probability intervals for timing are all shifted towards negative values.
confirmed by the significance counts for positive and negative
values in Table
can look
probability intervals in Table
timing values from the Bhattacharya and Pfleiderer model using the
benchmark). The
while the
The
and market timing.
As noted above,
one
in
can also examine the
probability values) for the spread of
the observed and population values presented in Table VII.
VII clearly show the amount of variation
we
selectivity
This
and timing
I.
80%
probability intervals for the population selectivity values in Table VII,
the true spread in pension
manager excess returns
benchmarks. The return for the top 10% of managers
16
is
for the
we
two models across
obtained by annualizing the appropriate
upp)er
bound return
in
10% of managers
Table VII, and the return for the bottom
annualizing the appropriate lower bound return in Table VII.
Pfleiderer
model using the
S&P
500 benchmark,
4.52%
using the Russell 3000, the true spread
is
5.49%
-1.78); and using the style index, the true spread
is
5.44%
(top
10% = 3.71%, bottom 10% =
(top
10% = 4.72%, bottom 10% = -.72%).
annualized spread in returns using the
bottom 10%
=
performance
=
use.
-.90%).
Hence
substantial
Rahman
models the
there
is
10% = 3.04%,
(top
5.55%
is
(top
10% = 3.77%,
5.86%
(top
10% =
evidence in our data that the best pension fund
is
risk-adjusted excess returns,
(1990), and Coggin and Hunter (1991)
in their studies
no matter which model or
at the last line
style index
who found
evidence of superior
of mutual funds.
The Correlation between
Looking
5.01%
is
This complements the results of Grinblatt and Titman (1989a), Ippolito
—
D.
S&P 500 benchmark
-1.78%); and using the style index, the true spread
managers can deliver
(1989), Lee and
For the Tryenor and Mazuy model, the true
-1.97%); using the Russell 3000, the true spread
4.96%, bottom 10%
benchmark we
For the Bhattacharya and
is
10% = 2.69%, bottom 10% = -1.83%);
=
obtained by
the true annualized spread in returns
(top
bottom 10%
is
Insert Table VII about here
Selectivity and
of each panel
benchmark
in
Timing
Table VI
results in the least
of the selectivity and timing values.
If
we
—
treat
(S(,^/Sb^),
we
see that in each case for both
amount of sampling error
sampling error as analogous
in the variation
to
measurement
error, then (adopting the language of classic psychometric reliability theory) the estimates of
selectivity
and market timing using the style index benchmark have a higher
17
"reliability" than
This
the other estimates.
more
is
consistent with our earlier observation that the style indices are
representative of the managers' true investment universes. Hunter and Schmidt (1990, pp.
115-116) show that the attenuating effect of sampling error on correlations
attenuating effect of
measurement
corrected for sampling error
error, or unreliability, in
In the
psychometric
error.
They then show
same way
in the
we
observed correlations can thus be
as the psychometric correction for
reliability
T = true
model, the
reliability
of variable x
score and x=observed score.
variables to be correlated are actually estimates of the
If
two parameters,
the psychometric two-sided correction for attenuation formula
The observed
now
=
observed corr./
[v/(reliability
of x)
V
selectivity
Mazuy model. This
/
=
-.359
/
While we can correct
can substitute into
(1982)):
in
(7)
Table V.
=
-.61 for the
Kon
We
can
Thus, for the
[v/.500 *'\/.318]
[v/.500* V.855]
Connor and Korajczyk
is
and market
of y)]
were given
further confirms the results of previous studies (see
(1984), Coggin and Hunter (1991), and
we
for the effect of sampling error.
benchmark, we have corrected correlation
the Bhattacharya and Pfleiderer model, and -.399
denoted r„ and
is
(Thomdike
* "/(reliability
correlations between selectivity and timing
correct the observed correlations in Table
style index
measurement
In the present context, the
estimate the "reliability" of each parameter as s//Sb^ then
corrected corr.
analogous to the
psychometric terminology.
defined as a-^lo^\ where
timing.
that
is
=
-.90 for
Treynor and
(1983), Henriksson
(1991)).
the observed correlations for sampling error,
we cannot
in
any
uncomplicated way correct for the possibility of a negative correlation between the two described
in
Jagannathan and Korajczyk (1986).
They show
that
it
is
possible to observe a negative
correlation between selectivity and timing in a sample of mutual funds if the
18
common
stocks held
by the funds are more/less option-like than the stocks
in the
finding of a negative correlation
all
believe
it
is
is
replicated across
Sensitivity of Results to
Our
since our
portfolios in Table V,
we
general finding
is
Discussion
Benchmarks and Models
that selectivity
models and benchmarks. The
all
benchmark
However,
unlikely that our observed correlations are seriously affected by this problem.
V.
A.
market proxy.
managers up by investment
positive and timing
results in Tables III
performance measures are not very sensitive
However, we did observe some
is
These
negative on average across
and IV indicate
to alternative
that the
rankings of both
benchmarks and models
sensitivity to the choice of a
style.
is
in
our data.
benchmark when we divided
results contrast with those of
the
Lehmann and Modest
(1987) and Grinblatt and Titman (1989a).
It
analysis.
and
APT
should be pointed out that there
They examined
models.
is
a problem in the
Lehmann and Modest (1987)
selectivity in the context of a Jensen-like
Market timing and
measure using the
CAPM
factor timing activities are not included in their analysis.
Market timing was also ignored by Grinblatt and Titman (1989a). Grant (1977) explained how
market timing actions
He showed
to
that
will affect the results of empirical tests that focus only
market timing
be downwardly biased.
ability will
The
results of
on selection
skill.
cause the observed regression estimate of selectivity
Lee and Rahman (1990) are consistent with Grant's
(1977) contention.
A
Henriksson (1984).
Moreover, as Jensen (1972), Admati and Ross (1985), Dybvig and Ross
similar conclusion
was drawn by Chang and Lewellen (1984) and
19
(1985), and Grinblatt and Titman (1989b) have shown, the Jensen-like measure
may
penalize the
performance of market timers.
B.
Negative Correlation Between Selectivity and Timing
As
discussed in Sections
selectivity
III
and market timing
several other studies.
The
in
and IV, we calculate a strongly negative correlation between
our data.
literature
summary and
(1986) for a
know of which documents
model here
of mutual fund managers (see Chua and
ability
extention of these studies).
this finding for f)ension
to explain the negative correlation,
we
to
do well consistently.
As many
Indeed,
dimension taken separately. This has resulted
clients only
one of these
skills.
There
is
also
that
much
number of pension plan sponsors do not believe
basis,
and therefore do not hire managers
between
selectivity
selectivity are not
and timing
good
in
at timing,
said to include
who
we
we
no formal
is
tasks: picking
very difficult
only the best managers do well on either
opting to market to prospective
anecdotal evidence indicating that a growing
that
market timing
attempt
and those managers
20
offer
two separate
it.
The
is
possible on a consistent
strongly negative correlation
our data suggests that those managers
selectivity.
the first study
shown, each of these jobs
many managers
in
is
can offer some observations.
studies have
we show
Ours
fund managers. While
The job of equity investment management can be
stocks and timing the market.
with the results of
this is consistent
on investment management contains a number of studies
documenting the negative market timing
Woodward
Furthermore,
who
are
good
at
who
are
good
timing are not good
at
at
This intuitively makes sense, because the two investment activities are largely separate and
distinct.
However,
selectivity
and timing
that the general
recall
is
the nonlinear
econometric formulas quickly reveals
model are negatively
correlated.
However, we note
two.
between
selectivity
that
functional form of our estimating equation for
Treynor-Mazuy model.
An
inspection of the standard
sampling errors for the two coefficients
that the
in this
This clearly contributes to the negative correlation between the
Connor and Korajczyk (1991)
also found a negative correlation
and timing using a "new version of the Henriksson-Merton model," which
does not appear to suffer from
problem.
this
This suggests that our result
may
not be entirely
arti factual.
Finally,
one needs
to
be somewhat concerned about the size of the timing values.
At a
one can assess the significance of the timing values by looking
at the
purely
statistical
level,
t-tests.
However,
in the
effect,
measured by multiplying a rather small decimal
fraction, (R^^)-
.
reward/penalty to
Thus,
Treynor-Mazuy model
at the level
this activity in
the impact of timing on portfolio return
7,
our data.
in
by a squared decimal
of actual portfolio returns, there
is
a relatively small
Further research in the the area of the measurement
and assessment of market timing would help clarify
C.
fraction,
is,
this issue.
Sur\'ivorship Bias
The
issue of survivorship bias
is
well
known
in studies
of investment performance.
A
recent
study by Brown, Goetzmann, Ibbotson and Ross (1991) highlights this issue with regard to
performance measurement.
The
basic issue here is as follows.
managers with complete data from 1983
to
1990.
21
Our study
includes 71 pension
Hence, any manager
who may have
disappeared through merger or poor performance
is
To
not included in our data.
the extent that
our sample underrepresents such managers, our results are biased in favor of more successful
managers.
We do not know
and Titman (1989a) suggest
the true extent of this bias in our results, but the results in Grinblatt
that
it
is
VI.
not large.
Summary and Conclusion
This paper presents an empirical examination of the selectivity and timing performance of
a sample of U.S. equity pension fund managers.
results
on
estimation
selectivity
and timing are only mildly sensitive
findings are as follows.
to
the
benchmark
The
portfolio or
Moreover, regardless of the choice of benchmark portfolio or
model used.
estimation model, the selectivity measure
negative on average.
Our major
However,
is
selectivity
positive on average; and the timing
measure
is
does appear to be somewhat sensitive to the choice
of a benchmark (and, possibly, the time period) when managers are classified by investment
style.
In almost every case,
meta-analysis revealed
attributable to sampling error) around the
the
80%
mean values
real
variation (in excess of that
for each measure.
An
examination of
probability intervals for selectivity revealed that the best equity pension fund managers
can deliver substantial risk-adjusted excess returns.
fund performance,
Much work
we
Consistent with previous studies of mutual
also found a negative correlation between selectivity and timing.
remains
be done
to
losing ground to passively
in this area.
managed index funds,
largest fraction of the equity
some
some
While active equity managers are currently
actively
managed
component of corporate pension funds.
represent the
equities
still
We
do not know why
still
active managers are able to provide substantial risk-adjusted performance, while most
22
cannot.
Identifying the characteristics of successful
future research.
is
While there are some
money managers should be one
interesting hypotheses,
we
still
focus of
do not know why there
a consistently negative correlation between the selectivity and timing ability of active equity
managers.
This
is
another
fertile
area for study.
23
Appendix
This appendix
is
I
based on Haughton and Christopherson (1989).
A.
Style Descriptions
1.
Earnings Growth:
Earnings Growth managers focus predominantly on earnings and
revenue growth and attempt to identify companies with above-average growth prospects.
In general,
(a)
two basic categories of
securities are
companies with consistent above-average
owned by Earnings Growth managers
(historical
and prospective)
profitability
-
and
growth, and (b) companies expected to generate above-average near-term earnings
momentum
2.
based upon company, industry, or economic factors.
Market-Oriented:
Market-Oriented managers are broadly diversified managers
The
participate in all sectors of the market.
portfolios of these
who
managers may either be
well diversified, or take meaningful sector/ factor bets relative to the market toward both
growth and value over time. Market-Oriented managers typically are willing
to consider
companies representative of the broad market when seeking investment opportunities.
3.
Price-Driven:
Price-Driven managers focus on the price and value characteristics of a
security in the selection process.
These managers buy stocks from the low price portion
of the market, and are sometimes called value or defensive/yield managers.
these managers focus on securities with
low valuations
24
In general,
relative to the broad market.
4.
Small Capitalization: Small Capitalization managers focus on small capitalization stocks.
These companies may be unseasoned and rapidly growing but sometimes are simply
Typical characteristics of small capitalization
small businesses with long histories.
portfolios are below-market dividend yields, above-market betas, and high residual risk
relative to broad
B,
market indices.
Description of Russell Indices
Benchmarks
for
Aggregate Portfolios
The
Russell 3000 Index:
Russell 3000 Index includes the top 3000 U.S. companies
ranked by capitalization. Haughton and Christopherson (1989) discussed two reasons for
choosing the Russell 3000 Index over the
(1)
The
S&P
500 spans only 75% of
S&P
500 Index.
the investable U.S. equity market.
has a large capitalization bias but, within large cap stocks,
companies.
It
also includes non-U. S. companies, so
equity market benchmark.
There
ownership of shares, resulting
it
in the
covers only 500 companies,
it
no adjustment
in
is
such,
it
excludes some large
not strictly a U.S.
the index
for cross-
overweighting of certain companies.
Since
does not reflect many of the long-term bets
managers take away from the index.
25
is
it
it
As
(2)
The
Russell
3000 covers 98% of
market sectors according
all
the investable U.S. equity market.
investment opportunities, and
to their
U.S. companies and hence has no foreign exposure.
It
is
is
It
weights
confined to
adjusted for cross-
ownership, thereby reflecting true investment opportunities; and spans nearly
of the stocks
in
which a manager
is
Hence, the index
likely to invest.
all
is
relatively unbiased.
Style Indices
Broad market benchmarks
who
evaluating pension managers
pension
managers specialize
performance benchmarks
managers
is
The Frank
needed
Russell
that
Company
500 and
the Russell
use the whole market as a base.
subsets
more
of the market.
As
3000 are
Many
such,
suitable for
U.S. equity
a finer set of
closely match the investment styles of individual
maintains four style indices
-
one for each investment
style.
characteristics of each style index are similar to the equity profile
of a typical manager of that
comprise the
S&P
ensure identification of elements attributable to investment styles.
to
The key fundamental
in
like the
style.
This indicates that the subuniverse of stocks that
style indices contains the type
would normally choose;
i.e.,
of stocks from which each style of managers
they constitute rough "normal" portfolios.
These
benchmarks are much more representative of the specialized managers'
style
selection
universes than the broad market and hence should provide better tools for performance
evaluation.
These
style indices are:
26
1.
Russell
The
1000 Index:
1000
Russell
Market-Oriented style managers.
It
is
benchmark recommended
the
is
composed of
Russell 3000 Index ranked by capitalization.
for
the top 1000 stocks in the
Hence,
it
focuses on the broad-
based large cap segment of the market and encompasses about
90%
of
all
the
equity opportunities in the U.S. equity market.
2.
The
Russell 2000 Index:
Russell
2000
is
the small cap
for evaluating small capitalization managers.
It is
benchmark and
composed of
is
useful
2000
the smallest
Of the 10% of the
stocks in the Russell 3000 Index ranked by capitalization.
total
U.S. equity market comprised of small stocks, the Russell 2000 Index covers
about 8%.
3.
Earnings Growth Index: Earnings Growth Index
style
managers, and
is
composed of those
have above-average growth prospects.
according to their
4.
valuation"
is
that
securities in the Russell
1000 Index
that
Securities in this style index are weighted
Price Driven Index
a capitalization-weighted index
1000 Index
an index for Earnings Growth
total capitalization.
Price Driven Index:
It is
is
is
an index for Price Driven managers.
composed of those
have low valuations relative
to
securities in the Russell
the
broad
market.
"Low
defined by examining financial ratios such as the P/E ratio, dividend
yield, the price/book ratio,
and the price/sales
27
ratio.
Appendix
II
The Meta-Analysis of Regression Values
Theoretical Meta-Analysis Parameters
A.
This appendix
taken from a
is
more
detailed presentation given in
Coggin and Hunter
(1991). Meta-analysis was developed as a methodology to cumulate results across studies. In this
we
appendix,
initially
will use the
assume
number of managers
that the
sampling error due
words "study," "manager," and "portfolio" interchangeably.
to a finite
to
is
population values as
e
= b-/3
or
and sampling error as
b
=
The average observed value
b
We
identical across managers.
/3,
/3
+
e.
also
We
large
enough
that
we
can ignore
assume
error in
that the specification
Thus:
(A-1)
e
is:
= ^ + E
we
(A-2)
bi
=
e, will
be zero;
are comparing the portfolios of pension fund managers,
by the subscript
/3,
we
thus b=/3.
denote each manager
Then:
i.
+
Across portfolios,
(A-3)
e,
/3
and e will be uncorrelated, so that the variance of observed values, o^, will
be larger than the variance of population values, a^, by the amount of sampling error,
a^
From
of each
denote observed regression values as b,
Across a large number of managers, the average error,
Since
is
number of managers, and concentrate on sampling
regression estimates for individual managers.
regression equation
be analyzed
We
= a/ +
a^^:
(A-4)
a,'
equation (A-4), the variance of the population regression values can be written as:
28
o,'
The key
known
=
o,'
(A-5)
o,'
-
to meta-analysis is the fact that the
sampling error variance, a,^ can be computed using
Thus equation (A-5) becomes
statistical theory.
a formula to
compute
the population
variance, o/.
Estimating Meta-Analysis Parameters
B.
In the previous section,
we assume
that the
number of
studies to
be cumulated
Specifically, this implies that the observed variance of the sampling errors
theoretical sampling error variance. If the
number of
studies
is
is
large.
would equal the
small, then the observed variance
of the sampling errors will differ by chance from the theoretical sampling error variance. Hence
we
use the notation "s"" for the estimated variances below.
If a
population value
where
b, is
=
E[N,
assumed be constant across
of that value
that the best estimate
b
is
b,]/
E
studies.
Hunter and Schmidt (1990) show
frequency-weighted average:
is its
(A-6)
N,
the observed value in study
and N,
i
is
the
number of observations
corresponding observed variance estimate across studies
is
in study
i.
The
the frequency-weighted average
squared deviation:
Sb-
=
i:[N,(b,
-
hf-V
The observed variance
in
population values
(if
E N.
(A-7)
a confounding of two sources of variation:
variation
any) and variation in observed values due to sampling error.
Thus an
estimate, Sb^
is
estimate of the variation in population values can only be obtained by correcting the observed
variance estimate,
s^,^,
for sampling error.
Hunter and Schmidt (1990) show
29
that
sampling error
across studies behaves like error of measurement, and the resulting formulas are comparable to
the standard formulas in classic psychometric
From
classic
psychometric theory (Thomdike (1982)),
=
Observed value
where
=
Observed variance
In meta-analysis,
e,
true variance
+
reliability theory.
have:
measurement
(A-8)
Hence:
error variance
(A-9)
similarly true that the population regression values, ^,
is
=
s/
The sampling
we
measurement are uncorrelated.
population variance
The observed variance
=
error of
=
Sb'
s,^
it
+
are uncorrelated across studies.
,
Observed variance
above.
true value
the true value and error of
sampling error,
measurement theory or
+
+
Therefore
we
and the
can write:
sampling error variance
(A- 10)
(A-11)
s,'
estimate,
,
s^^, is
the frequency-weighted average squared deviation defined
error variance estimate required by meta-analysis
E[N,(standard error hj^]/
is
then:
L N,
The population variance (sometimes
(A-12)
called the "corrected variance") can thus be estimated
as:
s/
=
(A- 13)
s,' - s,'
Equation (A- 13)
is
the fundamental estimating equation for the theoretical values in equation
(A-5).
The population variance
zero, the inference
is that
sampling error.
That
across studies
positive,
is
estimate, s^^ can be positive, negative or zero.
there
is, all
it
is
no variation
in
still
be
trivial in size.
30
it
is
negative or
observed values that cannot be attributed to
variance in observed values
may
If
is
artifactual. If the corrected variance
A
C.
Significance Test for Real Variation Across Studies
The hypothesis
ratio of the
that there is
no
real variation in
observed variance estimate
to the
observed values has a
statistical test.
The
sampling error variance estimate has a chi-square
distribution with k-1 degrees of freedom:
x'
where
=
k= number
This
statistic
statistical
(A-14)
kSfcVs,^
of studies.
can be used as a formal
power and may
test
of no variation; although
reject the null hypothesis given
even a
trivial
if
k
is
amount of
(Hedges and Olkin (1985), Cohen (1988), and Hunter and Schmidt (1990)).
square value
studies.
is
not significant, there
However,
if
reduced as discussed
D.
the
strong evidence that there
is
no
it
has high
real variation
Thus
if
the chi-
real variation across
k studies are not independent, then the power of the chi-square
in the
test is
next section.
Independence
Given a
set
of regression estimates, there
the preceding discussion,
would
is
large,
itself
differ
only
it
was assumed
is
a corresponding set of sampling errors.
that the variance
In
of sampling errors across the studies
by sampling error from the hypothetical error variance across
independent replications. This
is
true for
most applications of meta-analysis and follows
immediately from the independence of the estimates across studies. However,
true.
31
this is
not always
In this study the
impact of the market proxy
equity pension fund managers
common
may
overlap.
two
controlled.
Hence
However,
the securities the
the portfolios of
to the residuals
two
two portfolios have
will contribute their particular returns to both portfolio return sequences.
of those securities will thus contribute
the
is
of the two portfolios.
The
in
residuals
This means that
portfolios will not have residual time series that are entirely independent.
Thus the
sampling errors for the two portfolio regressions will also be nonindependent and positively
correlated.
Consider the
r,
set
of sampling errors for two portfolios.
If the correlation
between errors
is
then the variance across portfolios will not be Var(e), but rather the product [(l-r)Var(e)].
The corresponding formulas
Var(b)
=
Var(i3)
+
Var(/3)
=
Var(b)
-
Var(i3)
=
[Var(b)
for meta-analysis are:
(A- 15)
(I-r)Var(e)
(A- 1 6)
(l-r)Var(e)
-
Var(e)]
+
r
(A- 17)
Var(e)
Thus, traditional meta-analysis formulas will underestimate the variance of
variances for timing and selectivity estimated in this paper are too low by
/3.
In particular, the
some amount. The
adjusted formula for chi-square would thus be:
x'
=
k Var(b)/[(l-r)Var(e)]
(A- 18)
X-
=
[l/(l-r)][k Var(b)/Var(e)]
(A- 19)
Hence, the
traditional test statistic for
homogeneity of regression values given
earlier in equation
(A- 14) would be an underestimate and thus would have somewhat lower than optimal power to
detect departures
from homogeneity.
Therefore the traditional chi-square
"conservative" test for heterogeneity.
32
test
would be a
The
size of the correlation
overlap between the portfolios.
effort to diversify risk.
between residuals for two portfolios depends on the extent of
Most equity pension managers
management
Thus, our working hypothesis
is
small enough to
make
little
style, asset allocation,
that the overlap is small in
securities in an
difference in our analysis.
Data on individual
securities held in the
for this study.
33
and rebalancing of portfolios.
magnitude and hence the correlation
While we believe
be reasonable, we know of no study of portfolio overlap which
validity.
many
Moreover, pension fund managers are independent of each other and
typically differ significantly in
r is
invest in
we
this
hypothesis to
could consult
to
check
its
managers' portfolios were not available to us
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A
Direct
•c
8.
u
"5.
E
w
Vi
c
^
Table
III
Correlations of a Performance Measure Between Benchmarks*
Each model was estimated for all managers for the entire period using each of the three
Panel A presents the Pearson and Spearman correlations between
benchmark portfolios.
selectivity values for each pair of benchmark portfolios for each model. Panel B presents the
Pearson and Spearman correlations between timing values for each pair of benchmark portfolios
for each model.
Panel A:
Selectivity
Style Index
Bhattacharya
&.
Pfleiderer
Russell 3000
Model
Pearson
.806
Style Index
Treynor and Mazuy Model
Russell 3000
Style Index
.804
Spearman
.744
S&P
500
Pearson
Spearman
.997
.994
.832
.761
Table IV
Correlation of a Performance Measure Between Models*
Each model was estimated for all managers for the entire period using each of the three
benchmark portfolios. This table presents the Pearson and Spearman correlations between
selectivity values for each model for each benchmark, and the Pearson and Spearman
correlations between timing values for each model for each benchmark.
Timing
Selectivity
Pearson
Spearman
Pearson
Spearman
Benchmark
Russell 3000
.992
.988
.901
.923
Style Index
.991
.990
.835
.930
S«&P500
.990
.985
.866
.894
*A11 correlations are significant at the .0001 level
42
Table
V
Correlation Between Selectivity and Timing
Each mcxlel was estimated
benchmark portfolios. This
selectivity
managers for the entire period using each of the three
table presents the Pearson and Spearman correlations between the
and timing values for each model for each benchmark.
for
all
Bhattacharya and Pfleiderer Model
Treynor and Mazuy Model
Benchmark
Pearson
Spearman
Pearson
Russell 3000
-.447
-.488
-.485
Style Index
-.359"
-.315^
-.399"
.487
-.504
-.467
S&P500
•
significant at the .0002 level
''
significant at the .0006 level
'
significant at the .0008 level
''
significant at the .0021 level
'
significant at the .0075 level
All other correlations are significant at the .0001 level
43
Spearman
-.427'
.359^
-.387
Table VI
Meta-Analysis Results
This table presents the meta-analysis results for the selectivity and timing values based on the three benchmark
portfolios and using heteroscedasticity-corrected t-values, for the entire period (N = 71 managers).
Panel A:
Bhattacharya and Pfleiderer Model
Table
80%
Probabilrty Intervals for
This table presents the
80%
Observed and Population
probability intervals for the
managers for the entire
and the population values are bounded by b±
market timing using
VII
all
Panel A:
period.
Selectivity
observed and population values of selectivity and
The observed values are bounded by b± 1.28(%),
1.28(Sfl).
Bhattacharya and Pfleiderer Model
Observed Values
Selectivity
Benchmark
S&P500
Russell
Lower
-.003121
3000 -.002687
Style Index
-.001606
Upper
.003800
.004255
.004854
Population Values
Market Timing
Selectivity
Lower
Upper
Lower
-.181391
.087434
-.001538
-.155203
.136814
-.001500
.168703
Panel B:
.148697
-.000604
Selectivity
S&P500
Style Index
Upper
Lower
-.003019
.003864
.004223
.004912
-1.092766
-.001622
Market Timing
Lower
Upper
.002217
.076345
-.017613
.003038
.003852
-.073481
-.099569
.055092
.079563
Population Values
Market Timing
Lower
Russell 3000 -.002632
Upper
Treynor and Mazuy Model
Observed Values
Benchmark
and Market Timing Values
-.848546
-.830330
Upf>er
.532916
.683034
.689144
45
Selectivity
Lower
Upper
Market Timing
Lower
Upper
-.001657
.002502
-1.013962
.454111
-.001499
.003091
-.780893
.615381
-.000750
.004040
-.773271
.632085
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