HD28
.M414
no.
ALFRED
P.
WORKING PAPER
SLOAN SCHOOL OF MANAGEMENT
The Investment Performance of U.S. Equity Pension
Fund Managers: An Empirical Investigation
Daniel Coggin
Frank J. Fabozzi
Shafiqur Rahman
T.
W
#3360-91 EFA
*
*~^
*""*
Revised
November 1992
MASSACHUSETTS
INSTITUTE OF TECHNOLOGY
50 MEMORIAL DRIVE
CAMBRIDGE, MASSACHUSETTS 02139
The Investment Performance of U.S. Equity Pension
Fund Managers: An Empirical Investigation
Daniel Coggin
Frank J. Fabozzi
Shafiqur Rahman
T.
W
""
*"'•
*""""
*
**
*~-'""'
Revised
November 1992
#3360-91 EFA
Virginia Retirement System
Journal of Portfolio Management
Portland State University
To be presented at the Annual Meeting of the American Finance
We thank Jon ChristoAssociation, Anaheim, CA January 1993.
pherson of the Frank Russell Company for providing the pension
manager data used in this study. The paper has benefitted from
discussions with John E. Hunter and Charles Trzcinka. The opinions and conclusions offered in this study do not necessarily
represent those of the Virginia Retirement System or the Frank
Russell Company.
,
M TUBRARIES
I
DEC
7 1992
The Investment Performance
An
of U.S. Equity Pension
Fund Managers:
Empirical Investigation
ABSTRACT
This paper presents an empirical investigation of the security selection and market timing
performance of a random sample of 71 U.S. equity pension fund managers using monthly returns
The 71
for the period 1983-1990.
investment advisors
equity fund managers include banks, insurance companies and
who have been
provided by the Frank Russell
allocated funds
by pension plan sponsors. The data were
Company of Tacoma, WA. While
of U.S. equity mutual funds, ours
is
the first such study of
there have been
many
studies
which we are aware of U.S. equity
pension fund managers. The estimates of selectivity and timing were derived using the Treynor
and Mazuy (1966) model and the Bhattacharya and Pfleiderer (1983) model. The
of managers
is
subdivided into four groups by investment
identified for each style.
We
style,
total
sample
and a benchmark portfolio
is
two benchmarks for the broad equity market.
also included
Regardless of the choice of a benchmark portfolio or estimation model, the selectivity measure
is
positive
on average and the timing measure
and timing do appear
to
was performed
results. In
to
negative on average.
be somewhat more sensitive
(and, possibly, the time period)
analysis
is
when managers
to quantify the effect
to the choice
are classified
However, both
of a benchmark portfolio
by investment
80%
style.
A
meta-
of sampling error on the cumulated regression
every case, meta-analysis revealed some real variation (in excess of that attributable
sampling error) around the mean values for both selectivity and timing.
the
selectivity
An
examination of
probability intervals for selectivity revealed that the best managers can deliver
substantial risk-adjusted excess returns. Finally, consistent with previous studies of equity mutual
fund performance,
we
However, we argue
that the
also
found a negative correlation between selectivity and timing.
observed negative correlation in our data
negatively correlated sampling errors for the
two
estimates.
is
largely an artifact of
The Investment Performance
An
Each year Pensions
management
&
of U.S. Equit>' Pension
Empirical Investigation
Investments
industry, profiles the top 1000
,
a
leading
was invested
was invested
in
little
Approximately $750
Institute estimates that
at
billion (40
$250
billion
year-end 1990. This
a 3:1 ratio for p«ision fund equity investment versus mutual fund equity
investment. Not only
than the
trillion.
The Investment Company
in equities.
newspaper for the pension
open- and closed-end equity-oriented U.S. mutual funds
snapshot indicates
managers
trade
pubUc and private U.S. pension funds. At year-«Kl
1990, these funds had total pension assets of $1,876
percent)
Fund Managers:
is
the dollar difference large, but also the difference in the
The
in each universe is large.
total
number of pension fund managers
number of mutual fund managers, by a
ratio
is
number of
much
larger
of approximately 10:1. Yet surprisingly
research has been done on the investment performance of U.S. equity pension fund
managers. This paper begins to
an important gap in the literature by providing empirical
fill
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,
Logue (1988) examined
(1987), and Berkov-tiz, Finney and
sample of large U.S. pension plans.
different asset categories with their
Hood and Beebower
own
examined
the investment
performance of a
Each plan may be composed of many fund managen
specific investment objectives
study containing a wealth of informatioQ about the pension
Shleifer and Vishny (1992)
(1986), Ippolito and Turner
and
management
styles.
in
In a recent
industry, Lakonishok,
the annual returns of a sample of equity pension funds over
the period 1983-1989.
as a
benchmark
Hence
which
However, they made no
portfolio,
S&P
500 Index
and focused on actual (equity only) returns (before management
their results are not
specifically
risk adjustment, used only the
comparable
to ours.
To
date, ours is the only study
fees).
we know
of
examines the components of the investment performance of a sample of U.S.
equity pension fund managers.
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 in general.
Pricing
returns
Model (CAPM),
which
securities
return
the investment manager attempts to identify securities with expected
lie significantly
off the security market line.
which offer an abnormally high
on the market
Within the specification of the Capital Asset
portfolio. If the
risk
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 to the efficient market hypothesis,
is futile.
The only
investment management activity
rational investment choice for a plan sponsor is to invest in
managed market index. Hence,
in (or
all active
in an efficient market, plan sponsors
pay active management fees
for)
would not
a passively
rationally invest
an investment program which cannot outperform a
market index. However, there exists a very large active pension fund management business in
the United States.
Our study begins
to shed
some
light
on
sponsors are behaving rationally to perpetuate this business.
the question of whether or not plan
Our paper
is
organized as follows.
Section I presents the models of selectivity and market timing used in this paper. Section
describes the data and methodology. Section
HI presents
the empirical results. Section
n
IV
presents a meta-analysis of our results. Section
V discusses the results.
Section
VI concludes our
paper.
L Models
It is
important that portfolio managers be evaluated on both security selection ability
and market timing
skill.
timing simultaneously.
Furthermore,
it
become standard
has
Rp,
Rp, is the excess (net
=
ttp
+
of risk-free
Bp
R^ +
model
selectivity
and
expected value of zero and
t
to the
(1)
on the pth portfolio.
rate) return
measures the sensitivity of the portfolio
is:
u^
of risk-free rate) return on the market portfolio, Op
is
R^ is
the excess (net
a measure of security selection
market return,
Up, is
skill, Bp
a random error which has
denotes time. This specification assumes that the risk level of the
portfolio under consideration is stationary through time
Indeed, portfolio managers
the managers.
practice to
Jensen (1968, 1969) formulated a return-generating model to measure
performance of the managed portfolios. The model
where
and Timing
of Selectivity
may
portfolio in anticipation of broad market price
and ignores the market timing
shift the overall risk
movements.
Fama
skill
of
composition of their
(1972) and Jensen (1972)
addressed this issue and suggested a somewhat finer breakdown of performance.
Treynor and Mazuy (1966) added a quadratic term
timing ability.
They argued
that if a
proportion of the market portfolio
proportion
when
the return
manager can
when
on the market
function of the market return as follows:
is
to equation (1) to test for
market
forecast market returns, he will hold a greater
the return on the market is high and a smaller
low. Thus, the portfolio return will be a nonlinear
R^ =
A
positive value of
ttp
+
/3pR^
+
7 would imply
7(R-J'
+
(2)
S.
positive market timing skill.
Jensen (1972) developed a similar model to detect selectivity and timing
skill
of
managers. Jensen's measure of market timing performance calls for a fund manager to forecast
the deviation of the market portfolio return from
that the forecasted return
its
By assuming
consensus expected return.
and the actual return on the market have a joint normal
distribution,
Jensen shows that, under this assumption, a market timer's forecasting ability can be measured
by the correlation between the niarket timer's forecast and the realized return on the market.
He concluded
that,
under the above
structure, the separate contributions
of selectivity and timing
cannot 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).
By
correcting
an error made in Jensen (1972), they show that one can use a simple regression technique to
obtain
measures of timing and selection
ability.
Jensen assumes that the manager uses the
unadjusted forecast of the market return in the timing decision.
assume
that the
manager
Bhattacharya and Pfleiderer
adjusts forecasts to minimize the variance of the forecast error.
specify a relationship in terms of observable variables,
which
is similar to the
They
Treynor and
Mazuy model:
R^ =
ap
+ eE(RJ(l
-
*)R«.
+ *e(IU' +
G^€^
+
u^
(3)
where
o(p
=
9 =
security selection skill (risk-adjusted excess return),
the fund manager's response to information; i.e., risk-level deviation
from the
target risk-level depending
^=
on the optdmal forecast of the market return,
the coefficient of determination between the manager's forecast and the excess
return on the market, and
Ct
=
the error of the manager's forecast
This quadratic regression of Rp, on R^^ allows us to detect the exist^ice of stock selection ability
as revealed
by
The
Op.
disturbance term in equation (3):
= e^e,R^ +
u,
Up.
(4)
contains the information needed to quantify the manager's timing ability.
information by regressing
(coo^
(co,)^
We can
extract this
on (lO^:
= e^^V/(R«.)' +
f t,
(5)
where
C,
The proposed
=
e'^'(R^\ied'
-
icf]
+
(UpJ^
+
2Q-^R^,xx^.
regression produces a consistent estimator of G^^^o^e, where (<tJ^
of the manager's forecast error. Using the consistent estimator of
equation (3),
(6)
we
obtain (ay.
9"*^,
is
which we recover from
This, coupled with knowledge about (aj^, the variance of excess
return on the market, allows us to estimate i'
=
(<Tj^/[(aJ^
+
(crj^]
=
p^,
where p
correlation
between the manager's forecast and excess return on the market.
calculate p
which
truly
of timing
It
skill.
forecasting skill.
is
the
Finally,
we
measures the quality of the manager's timing information.
The Bhattacharya and
Mazuy model.
the variance
Pfleiderer
model of equation
(3) is a
refinement of the Treynor and
focuses on the coefficient of the squared excess market return as an indication
It is
the first
model
that analyzes the error
Such a refmement should make
the
term to identify a manager's
model more powerful than previous ones.
Further detail and econometric issues relating to the Bhattacharya and Pfleiderer
model are
discussed in Section n. In the empirical tests reported in Section HI,
we employed
Trey nor and Mazuy
This will allow us to
examine the
and the Bhattacharya and Pfleiderer
sensitivity
of results to alternative model specifications.
There are other models in the
selectivity
and timing
models.
both the
skills
literature that
of portfolio managers;
i.e.,
permit identification and separation of
models by Grinblatt and Titman (1989b),
Henriksson and Merton (1981), and an alternative to the Henriksson and Merton model by
and Jen (1978, 1979). The Grinblatt and Titman model requires the
portfolio weights (i.e., the
amount invested
on portfolio weights are very
costly,
in each stock) for the
historical
Kon
sequence of
manager. Unfortunately, data
time-consuming and not often available. The Henriksson
and Merton model provides no significant advantage over the Bhattacharya and Pfleiderer model.
The weakness of
the Henriksson and
special information, but
it
does not
Merton model
test
is that it
only
whether the manager has
whether the manager uses the information correctly
(Dybvig and Ross (1985)). The forecasters
in this
model are
less sophisticated than those
Bhattacharya and Pfleiderer model, where they do forecast
investment will perform.
tests
how much
of the
better the superior
Henriksson and Merton assume that managers have a coarse
information structure in which dichotomous signals are only predictive of the sign of the excess
return of the market relative to the risk-free rate. In their model, the probability of receiving an
"up" or a "down" signal in no
way depends upon how
far the
market will be "up" or "down."
n. Data and Methodology
The data
for this study consist of monthly returns for the period January 1983 through
December 1990 (96 months)
for a
random sample of 71 U.S. equity pension fund managers with
complete data for the entire period. The 71 managers were chosen from the Russell pension
manager database by random drawing (with replacement) so as
actual distribution of
and management
that are at least
managers (by investment
fees.
The
and investment advisors
style) in the database.
data include returns on tax-ftee,
$5 million in
size.
to reflect as close as possible the
fiilly
Returns are net of expenses
discretionary equity portfolios
These portfolios are managed by banks, insurance companies
who have been
allocated funds
by pension plan sponsors. The
identities
of the fund managers and sponsors are not included. The managers invest exclusively in the U.S.
equity market.
The random sample of pension fund managers was provided by
Company of Tacoma, Washington. Among
Russell
evaluates the performance of the managers of a
States.
The Frank Russell Company
other services, the Frank Russell
number of pension funds throughout
the
Frank
Company
the United
segregates equity managers into four basic investment styles
on the basis of managers' portfolio
characteristics.
These
are:
Market-Oriented, (3) Price-Driven, and (4) Small Capitalization.
(1)
Earnings Growth, (2)
Our sample
consists of 18
Earnings Growth, 19 Market-Oriented, 18 Price-Driven, and 16 Small Cjq)italization managers.
Appendix
bill
I.
A describes
these four investment styles.
were used as a proxy for the
Our study uses
S&P
Monthly returns on the 91-day Treasury
risk-free rate.
several alternative equity
benchmark
portfolios.
500 Index and the Russell 3000 Index. The Russell 3000 Index
index like the
S&P 500
to both
S&P
Index.
is
Two
of these are the
a broad equity market
500. Appendix I.B describes the Russell 3000 Index and compares
The
idea of investment "style management"
is
it
to the
becoming increasingly important
academic studies and professional investment management
(see,
e.g.,
Tiemey and
Winston (1991)). Therefore,
style indices as
in addition to the
To be more
benchmarks.
different investment styles.
two broad equity market
These
specific,
The use of
indices
the procedure of
and Mazuy
examine the
An
test, it is
to
broad market indices.
sensitivity
of pension fund
estimate of the variance of the excess
was derived from observed
Lee and Rahman
In the empirical
the Russell Price-Driven Index
and compares them
manager's performance to alternative benchmarks.
(<r,)^,
1000 Index (for Market-Oriented
Cap managers),
several alternative indices will allow us to
return on the market,
use four
and the Russell Earnings Growth Index (for Earnings Growth
Appendix I.B describes these
managers).
we also
use separate benchmarks for four
style indices are the Russell
managers), the Russell 2000 Index (for Small
(for Price-Driven managers),
we
indices,
returns for each
benchmark following
(1990).
necessary to correct for heteroscedasticity in both the Treynor
model and the Bhattacharya and Pfleiderer
model.
In the Treynor and
Mazuy
model, the error term will exhibit conditional heteroscedasticity 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.
(1986) and
Lehmann and Modest
To
(1987),
correct this, following Breen, Jagannathan and Ofer
we
use heteroscedasticity-consistent standard errors
proposed by White (1980), Hansen (1982), and Hsieh (1983). The significance
in Section
HI are based on
tests reported
heteroscedasticity-adjusted t-statistics.
In the Bhattacharya and Pfleiderer model, the procedure discussed in Section I does not
produce the most efficient estimates of the parameters since the disturbance term in equations
(3)
and
(5) are heteroscedastic.
More
efficient estimates
the heteroscedasticity of the disturbance terms.
can be obtained by taking into account
We followed a Generalized Least Squares (GLS)
8
procedure, which makes a correction for heteroscedasticity, to obtain efficient estimates of
parameters.
This methodology
As noted
in
more
is
fully described in
Lee and Rahman (1990).
Coggin and Hunter (1993), one weakness of the Treynor and Mazuy and the
Bhattacharya and Pfliederer models
modify these models
is that
they ignore negative or inferior market timing.
to allow negative timing skUl.
negative ex post timing
skill.
In the Treynor and
We hypothesize that
Mazuy model,
a smaller portion of the market portfolio when the market return
and Pfleiderer model,
the market return.
this is indicative
Such
forecast the market return to
Mazuy model of equation
means the managers hold
high.
In the Bhattacharya
models could be due to the inability of managers to
on the market
be high when
(2),
is
managers can exhibit
of a negative correlation between the manager's beta and
results in both
correctly forecast the expected return
this
it is
portfolio.
actually
Hence
these managers
this coefficient will
a negative value of 7 would be indicative of poor market timing.
Intuitively, in the spirit
modification
Pfleiderer
makes
we
designate timing
these models
model was
more
skill
realistic.
A
skill.
coefficient of
Mazuy model,
the sign of
If the estimated value of this
(given by p) to be poor (negative).
This
similar adjustment of the Bhattacharya and
and Korajczyk (1986,
implicitiy introduced in Jagannathan
m.
A.
of the Treynor and
be indicative of the nature of timing
coefficient is negative,
would
low and vice versa. In the Treynor and
For the Bhattacharya and Pfliederer model, we examine the sign of the
(Rjof in equation (3).
We
p. 229).
Empirical Results
Significance Tests for Performance Measures
Table
I
presents
summary
results
from the two
models. In
this table
and those
that
follow, 'SScP 500" denotes results based
on using the
S&P 500
"Russell 3000" denotes results based on using the Russell
"Style Index" denotes results based
benchmark
portfolio.
negative timing
skill
values exceeds the
These
on
on using each manager's appropriate
The number of
the part of managers.
skill,
security selection skill and
significant positive selectivity
the results are just the opposite.
significant negative timing values exceeds the
portfolio,
style index as the
significant negative selectivity values for both
of the benchmark used. For timing
number of
benchmark
3000 as the benchmark portfolio, and
show some evidence of positive
results
number of
as the
number of
models regardless
For both models,
the
significant positive timing
values regardless of the benchmark used.
—
B.
Insert Table I about here
Mean
Values of Performance Measures
Table
n presents
the subsets of
managers
the
means of
both models show a positive
the selectivity and timing values for all
by investment
classified
mean
—
style.
For the
entire
sample (All Managers),
selectivity value for all three alternative
values are significant at the .05 level for two of the three benchmarks.
results are just the opposite.
value for
S&P
all
entire sample, both
three alternative benchmarks.
500), the
mean timing
results using the
Russell
For the
S&P
value
500 Index
benchmarks. These
For timing
skill,
benchmark
the .05 level for both models.
Hence
(the
the
contrast with the results obtained using the
3000 Index and the Style Indices as benchmarks. As shown
two indices are much more representative of
the
models show a negative mean timing
However, for only one of the three benchmarks
is significant at
as a
managers and for
in
Appendix LB,
the latter
the managers' investment universe (i.e., true
10
investment opportunities) than the fonner and, as such, are more appropriate benchmarks than
the former.
The
results in
Tables
I
and
pickers than market timers.
supported in Table n.
Rahman
(1990),
However,
it
skill in their
suggest that pension fund managers are on average better stock
The
results that
were only hinted
at in
Table I are
now
results relating to selection skill are consistent with those
who found some
They
managers.
Our
II
evidence of superior selection
skill
strongly
of 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
Rahman
(1990) ignored negative market timing
allow negative market timing here.
consistent with those of previous studies
Our market timing
on mutual fund performance (see Kon (1983), Chang
and Lewellen (1984), Henriksson (1984), Lehmann and Modest (1988),
and Connor and Korajczyk (1991)).
results are
Cumby and 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.
There are differences
in the portfolio characteristics
and investment styles among the
Earnings Growth, Market-Oriented, Price-Driven, and Small Capitalization managers.
therefore useful to
examine performance measures
for each investment style separately.
n presents mean values of the performance measures for each style of manager.
the aggregated rank of each group.
benchmark.
However, they do vary somewhat across benchmarks
For the eight years,
Table
also provides
These ranks do not vary between the models for a given
The period 1983-1990 was a period
substantially.
It
It is
the Russell
in
which the overall stock market was up
3000 grew
11
for a given model.
at
an annualized rate of 14.17%, and
the
S&P
500 grew
at
a 15.60%
the "value" investment style
rate.
For the majority of
was favored by
the market relative to other investment styles.
for this style is the Price-Driven index
benchmark
period (up until the end of 1988)
this
which grew
Our
an annualized rate of 15.53%.
at
This compares to the "growth" investment style (represented by the Earnings Growth index)
which grew
at a
13.72%
index) which grew at a
rate,
7.38%
as benchmarks, a negative
and the Small Capitalization
rate. In
mean
Table
selectivity value is consistently
if
we
managers
(as well as all other styles)
a positive
mean
benchmark,
period)
it
selectivity value
is
Finally,
look at the Style Index as a benchmark,
see that these
we
observe
and a negative mean timing value across All Managers for each
is
used (and, perhaps, which time
the results for the four investment styles.
size of the timing values.
At a
by looking
at the
Treynor-Mazuy model the impact of timing on portfolio return
is, in
one needs to be somewhat concerned about the
one can
assess the significance of the timing values
statistical
level,
t-tests.
However,
in the
effect,
measured by multiplying a rather small decimal
.
we
have positive selectivity values. Thus, while
purely
fraction, (R„J^
observed for the Earnings
consistent with the preference of the stock
does begin to matter which benchmark portfolio
when we examine
by the Russell 2000
n we see that, using the broad stock market indices
Growth and Small Capitalization managers. This
market for the period. However,
style (represented
Thus,
at the level
fraction, 7,
by a squared decimal
of actual portfolio returns, there
is
a relatively small
reward/penalty to this activity in our data. Further research in the area of the measurement and
assessment of market timing would help clarify
—
this issue.
Insert Table II about here
12
—
Correlation of Performance Measures
C.
To examine
the sensitivity of results to
benchmarks and models,
correlation of the performance measures across models and benchmarks.
of association
-
the Pearson correlation coefficient and the
Tables HI, IV, and
n.
V
we
also
examine the
We use two measures
Spearman rank correlation
coefficient.
provide correlational summaries of the results presented in Tables
I
and
Table HI represents the correlation of a performance measure (selectivity or timing) with
itself
between benchmarks for a given model.
significant at the .0001 level.
broad market indices
-
the
There
S&P
is
All the correlations reported in the table are
a very high correlation between the results based on the
500 Index and
the Russell
3000 Index.
The performance
measures based on these benchmarks are somewhat less correlated with those based on style
indices.
These
results are consistent for both
models and for both the
measures.
Table IV presents the correlation of a performance measure
with
between models for a given benchmark.
itself
significant at the .0001 level.
The
results in Tables
selectivity
and timing
(selectivity or timing)
These correlations are very high and
in and IV indicate high ranking consistency
among benchmarks and between models.
Finally,
for a given
we
present the correlation between selectivity and timing skill within a model
benchmark.
significantly negative.
These correlations are given
We
will
—
have more
Insert Tables
IV.
Meta-analysis
is
a parametric
in
Table V.
All these correlations are
to say about this result in Section
m,
IV,
V
about here
V.B.
—
Meta-Analysis of Results
statistical
technique for the cumulation of results across studies
13
The
or units of analysis.
contribution of meta-analysis
is to
offer a statistical technique to
produce direct estimates of the mean and standard deviation of population values. Thus metaanalysis allows
more
statistically
powerful inferences from data than are possible using more
Following
traditional disaggregated analyses.
its
early beginnings in physics
and psychology,
meta-analysis has recentiy been applied to cumulate results across studies in several other
disciplines including accounting (Christie (1990)
and Trotman and
Wood
(1991)), finance
(Coggin and Hunter (1983, 1987,1993) and Dimson and Marsh (1984)), and marketing (Farley
and Lehman (1986)). Recent comprehensive
texts
on meta-analysis include Hedges and Olkin
(1985) and Hunter and Schmidt (1990).
There are a number of "study
different or
even contradictory
artifacts"
to those
which can cause the
of another.
Among
the
results
of one study to appear
more prominent
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
in
our paper have identical specifications (by performance
measurement model) across the sample of pension fund managers. Thus, for the purpose of
meta-analysis,
we 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.
As discussed
in
Appendix n, the standard meta-analysis formulas must be adjusted
the effect of correlated regression residuals. Table
14
VI presents the average
for
correlations between
the regression residuals for the 71 managers for the entire sample period across
benchmarks and
models. These average correlations were used in the adjusted formulas to calculate the metaanalysis results given in Tables
Vn and
—
Table
Vn
coefficients based
The
first
row of
the third
row
Sb^;
Insert Table
—
and timing
selectivity
on three benchmark portfolios and using heteroscedasticity corrected
this table gives the
row
t-values.
frequency-weighted mean of the observed values for each
gives estimates of the standard deviation of the observed values,
row gives estimates of
the standard deviation of the population values,
s^;
the fourth
gives estimates of the frequency-weighted average squared deviation of the observed values,
the fifth
row gives
estimates of the variance of the population values,
estimates of the sampling error variance,
ratio
s^^;
the seventh
row gives
total
s^^;
the sixth
last
row gives
observed variance accounted for by sampling error,
—
Insert Table
Vn about
here
row gives
the chi-square value for the
of the observed variance to the sampling error variance; and the
of the proportion of
A.
VI about here
presents the results of the meta-analysis of the
parameter, b; the second
s^;
Vin.
estimates
s^Js^^.
—
Selectivity
For
small.
selectivity, the
mean monthly
However, on an annualized
values in Table
basis, these
Vn
are positive in every case but very
numbers become more meaningful. For the
Bhattacharya and Pfleiderer model, the annualized mean selectivity values are .41%
.93%
(Russell 3000), and
annualized
mean
1.97%
(Style Index).
selectivity values are
(S&P 500),
For the Treynor and Mazuy model, the
.51% (S&P 500), .96% (RusseU 3000), and 1.99%
15
(Style
"
Index).
Hence we see
compared
style index as
of the
that for both models,
common
managers do better on average relative
to the broader market indices.
This
resxilt is instructive,
to their
since
own
much
investment wisdom implies that investment managers "can't beat the market.
This result suggests that such a
comment begs an important question regarding which benchmark
should be used in evaluating a manager.
We
remind the reader that these returns are net of
investment management fees.
The chi-square values are
three
all
significant at the .05 level or less for the selectivity values using
benchmarks for both models. This implies
attributable to
sampling error) around the mean
selectivity value in
each case.
Timing
B.
For market timing, the mean values
is
that there is real variation (in excess of that
consistent with the results of
Grinblatt and
Kon
in
(1983),
Table
Vn
are negative in each case.
This result
Chang and Lewellwi (1984), Henriksson
(1984),
Titman (1988), Lehmann and Modest (1988), Cumby and Glen (1990), Coggin and
Hunter (1993), and Connor and Korajczyk (1991)
who examined mutual fund
returns.
Furthermore, the chi-square values are significant at the .05 level or less in each case. Thus in
every case there
If there
is
evidence of real variation around the negative mean timing value.
were no
real variation
around the observed mean value, then the observed mean
would be the true value for each of the 71 managers. However,
in our case, there is evidence
of real variation in every set of selectivity and market timing values.
perspective,
of
total
we can
look
at the last
row of Table
To
put these results in
Vn for each model and examine the proportion
observed variance accounted for by sampling error. For the Bhattacharya and Pfleiderer
16
model, the percentage of observed variance in selectivity accounted for by sampling error goes
from 57%
57%
to
to
50%
across benchmarks; while the percentage of variance in timing
accounted for by sampling error goes from
73%
Treynor and Mazuy model, the percentages for
to
74%
selectivity
benchmarks; while the timing percentages go from
We
14%
to
63%
across benchmarks.
go from 57%
to
15%
to
to
13%
57%
to
For the
50%
across
across b«ichmarks.
should note that, as discussed in Hunter and Schmidt (1990), these percentages of variance
attributable to sampling error
measurement
C. The
well contain other unaccounted for study artifacts (such as
error).
80%
Assuming
80%
may
Probability Intervals for Selectivity
selectivity
and market timing
to
and Timing
be normally distributed,
probability intervals (i.e., the lower and upper
90%
the observed and population values presented in Table
Vin
clearly
selectivity
show
the
amount of
The 80%
positive values, while the
values.
This result
and timing values
Using the
is
in
80%
80%
also
examine the
probability values) for the spread of
VIQ. The probability
intervals in Table
variation in both the observed and the population values for
and market timing. As noted above, there
values in every case.
we can
is real
variation in selectivity and timing
probability intervals for selectivity are all shifted towards
probability intervals for timing are all shifted towards negative
confirmed by the significance counts for positive and negative
Table
selectivity
I.
probability intervals for the population selectivity values in Table
VDI, we
can look at the true spread in pension manager excess returns for the two models across
benchmarks. The return for the top 10% of managers
17
is
obtained by annualizing the appropriate
10% of managers
upper bound return in Table Vin, and the return for the bottom
by annualizing the appropriate lower bound return
Pfleiderer
model using the
S&P
500 benchmark, the
(top
10% = 3.26%, bottom 10% = -2.37%);
(top
10% = 3.86%, bottom 10% =
(top
10%
=
4.83%, bottom 10%
-1.93);
=
bottom
10% = -2.42%);
bottom
10% = -1.92%); and
=
5.05%, bottom 10%
true annualized spread in returns is
and using the
S&P
For the Bhattacharya and
5.79%
style index, the true spread is
5.65%
For the Tryenor and Mazuy model, the true
500 benchmark
5.93%
is
using the RusseU 3000, the true spread
is
5.84%
using the style index, the true spread
-.98%). Hence there
5.63%
is
using the Russell 3000, the true spread
-.82%).
annualized spread in returns using the
Vm.
Table
in
obtained
is
is
is
10% = 3.51%,
(top
(top
10% = 3.92%,
6.03%
(top
10% =
evidence in our data that the best pension fund
managers can deliver substantial risk-adjusted excess returns, no matter which model or
benchmark we
(1989),
This complements the results of Grinblatt and Titman (1989a), Ippolito
use.
Lee and Rahman (1990), and Coggin and Hunter (1993) who found some evidence of
superior performance in their studies of mutual funds.
—
Insert Table
VHI
about here
—
V. Discussion
A.
Sensitivity of Results to
Our general
all
finding
Benchmarks and Models
is that selectivity is
models and benchmarks. The
positive and timing is negative
results in Tables
HI and IV
indicate that the
on average across
overall rankings
of both performance measures are not very sensitive to alternative benchmarks and models
our data. However,
we
did observe
some
sensitivity
18
in
of results to the choice of a benchmark
when we
divided up the managers by investment style in Table n.
Our
basic results differ from those of Lehraann and
Titman (1989a), who found
portfolios. It should
and
APT
be pointed out
They examined
analysis.
that
performance results varied across models and benchmark
that there is
a problem in the Lehmann and Modest (1987)
selectivity in the context
Market timing and
models.
Modest (1987) and Grinblatt and
of a Jensen-like 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 will affect the results of empirical
He showed
to
that
market timing
be downwardly biased.
ability will
The
results
tests that
focus only on selection
skill.
cause the observed regression estimate of selectivity
of 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
(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
selectivity
in Sections
and market timing
several other studies.
The
HI and IV, we observe a strong negative correlation between
in
our data.
literature
(1986) for a
summary and
know of which documents
this is consistent
with the results of
on investment management contains a number of
documenting the negative market timing
Woodward
Furthermore,
ability
of mutual fund managers (see Chua and
extension of these studies).
this finding for
pension
19
studies
fiind
managers.
Ours
is
the
first
study
we
The negative
correlation
interpretation. Hunter,
They show
correlated.
selectivity
and timing presents a problem of
Coggin and Rahman (1992) show
in this study, the correlation
negative.
between
between the estimates of
that this is
The magnitude of
that, for the regression
selectivity
models used
and timing will necessarily be
because the sampling errors for the two estimates are negatively
the negative correlation between the
the magnitude of the negative correlation between the
two estimates
two sampling
is
the
errors. Thus,
same as
once
we
account for the effect of negatively correlated sampling errors, selectivity and timing are largely
uncorrelated in our data.
The
correlation between selectivity and market timing
in the literature.
the
currently an unsettied question
Coggin and Hunter (1993) calculated a corrected correlation of about -.64
Lee and Rahman (1990)
errors for the
is
data, but noted that this
two estimates. They
was
in
also an artifact of correlated sampling
also calculated an observed correlation
funds) between "Overall Selectivity" and "Overall Timing" in
Kon
of .04
(N=37
(1983, Table 5),
mutual
who
used
a different model of market timing. Using the Henrikkson and Merton (1981) model, Henrikkson
(1984) and Connor and Korajczyk (1991) report a negative correlation.
Lehmann and Modest
(1987, fn. 33) report basically no "substantive correlation" between the two. Jagannathan and
Korajczyk (1986) have presented an argument that the observed negative correlation between
selectivity
and timing could also be the
result
of some other phenomenon, such as changes in
firms' debt/equity ratios in relationship to that of the
Titman (1989b) have shown
model which seeks
selectivity
that
many of the
benchmark portfolio. Finally, Grinblatt and
desirable properties of a performance measurement
to estimate both selectivity
and timing are correlated.
20
and market timing
skill
are not present
if
C. Survivorship Bias
The
issue of survivorship bias
is
well
known
in studies of investment performance.
A recent
study by Brown, Goetzmann, Ibbotson and Ross (1992) highlights this issue with regard to
performance measurement. The basic issue here
managers with complete data from 1983
is
as follows.
1990.
to
disappeared through merger or poor performance
is
Our
study includes 71 pension
Hence, any manager
not included in our data.
who may have
To
the extent that
our sample underrepresents such managers, our results are biased in favor of more successful
managers.
We do not know the true extent of this bias in our results,
and Titman (1989a) suggest
that
it is
but the results in Grinblatt
not large.
VI. S ummary and Conclusion
This paper presents an empirical investigation of the security selection and market timing
performance of a random sample of 71 U.S. equity pension fund managers for the period 19831990.
Our major
findings are as follows. Regardless of the choice of
estimation model, the selectivity measure
negative on average.
However, both
sensitive to the choice of a
classified
by investment
A
positive
selectivity
benchmark
style.
is
benchmark
on average and the timing measure
(and, possibly, the time period)
when managers
meta-analysis of the regression results
was performed
some
80%
are
to
real variation
of that attributable to sampling error) around the mean values for each measure.
examination of the
is
and timing do appear to be somewhat more
quantify the effect of sampling error. In every case, meta-analysis revealed
(in excess
portfolio or
An
probability intervals for selectivity revealed that the best equity pension
21
fund managers can deliver substantial lisk-adjusted excess returns.
studies of equity mutual fund performance,
selectivity
and timing. However,
we
we
also found a negative correlation between
argue that the observed negative correlation in our data
largely an artifact of negatively correlated sampling errors for the
Much work
remains to be done in
losing ground to passively
some
active
cannot.
this area.
managed index funds,
managers are able
to
While active equity managers are currently
actively
do not have a
managed
satisfactory substantive
ability
still
represent the
We still do not know why
money managers should be one
Furthermore, while there are some interesting
and market timing
equities
provide substantial risk-adjusted performance, while most
Identifying the characteristics of successful
future research.
is
two estimates.
of the equity component of corporate pension funds.
largest fraction
Consistent with previous
model of the
of active equity managers.
22
statistical
relationship
This
is
explanations,
focus of
we
still
between the security selection
another
fertile
area for study.
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:
participate in
either
aU
Market-Oriented managers are broadly diversified managers
sectors of the equity market.
The
portfolios of these
be well diversified, or take meaningful sector/factor bets relative
who
managers may
to the
market
toward both growth and value over time. Market-Oriented managers are typically 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. In general,
these managers focus on securities with low valuations relative to the broad market.
23
4.
Small Capitalization: Small Capitalization managers focus on small capitalization stocks.
These companies may be unseasoned and rapidly growing but sometimes are simply
small businesses with long histories.
Typical characteristics of small capitalization
portfolios are below-market dividend yields, above-market betas,
relative to
B.
and high residual risk
broad market indices.
Description of Russell Indices
(Note: All Russell indices are capitalization-weighted)
Benchmarks
for Aggregate Portfolios
The
RusseU 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
S&P 500
Index.
500 spans only 75% of the investable U.S. equity market. As such,
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
is
it is
excludes
some
large
not strictiy a U.S.
in the
index for cross-
overweighting of certain companies. Since
does not reflect many of the long-term bets
managers make away from the index.
24
no adjustment
it
it
(2)
The
all
Russell 3000 covers
98%
market sectors according
of the investable U.S. equity market.
to their
investment opportunities, and
U.S. companies and hence has no foreign exposure.
It is
is
weights
It
confined to
adjusted for cross-
ownership, thereby reflecting true investment opportunities; and spans nearly
of the stocks in which a manager
is likely
to invest.
Hence, the index
all
is
relatively unbiased.
Style Indices
Broad equity market benchmarks
suitable for evaluating pension
like the
S«&P 500 and the Russell 3000 are
Many
managers who use the whole market as a base.
U.S. equity pension managers specialize in subsets of the market.
As
such, a finer set
of performance benchmarks that more closely match the investment styles of individual
managers
is
needed to ensure identification of elements attributable to investment
The Frank Russell Company maintains
The key fundamental
-
one for each investment
style.
characteristics of each style index are similar to the equity profile
of a typical manager of that
comprise the
four style indices
styles.
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:
25
1.
The
Russell 1000 Index:
Russell 1000
Market-Oriented style managers.
Russell
3000 Index ranked by
It is
benchmark recommended
the
is
composed of the top 1000 stocks
capitalization.
Hence,
it
for
in the
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.
Russell
2000 Index: The Russell 2000
is
the small cap
for evaluating small capitalization style managers.
2000 stocks
in the Russell
3000 Index ranked by
It is
benchmark and
composed of the
capitalization.
Of
the total U.S. equity market comprised of small stocks, the Russell
covers about
3.
useful
smallest
the
10% of
2000 Index
8%.
Earnings Growth Index: Earnings Growth Index
style
is
managers, and
is
composed of those
is
an index for Earnings Growth
securities in the Russell
1000 Index
that
have above-average growth prospects,
4.
Price Driven Index:
managers.
It is
low valuations
composed of those
is
ratios such as the
and the price/sales
ratio.
26
an index for Price Driven
securities in the Russell
relative to the broad market.
examining financial
ratio,
Price Driven Index
P/E
"Low
ratio,
1000 Index
valuation"
is
that
style
have
defined by
dividend yield, the price/book
Appendix
The Meta-Analysis
n
of Regression Values
Theoretical Meta-Analysis Parameters
A.
This Appendix
(1993). Meta-analysis
is
taken from a more detailed presentation given in Coggin and Hunter
was developed
as a parametric statistical technique to cumulate results
across studies or units of analysis. In this appendix,
and "portfolio" interchangeably.
analyzed
is
large
enough
We
we can
that
and concentrate on sampling error
assume
that the specification
initially
we
will use the
assume
that the
words "study," "manager,"
number of managers
ignore sampling error due to a finite
in regression estimates for individual
of each regression equation
is
number of managers,
managers.
identical across
We
e
or b
=
The average observed value
b
= ^
/3-l-e
by
we
(A-2)
b.
=
e, will
be zero;
are comparing the portfolios of pension fund managers,
the subscript
/3i
we
thus b=/3.
denote each manager
Then:
i.
-f-
Across portfolios,
and
is:
Across a large number of managers, the average error,
Since
j3,
(A-1)
e
-H
We
Thus:
e.
= b-i8
also
managers.
denote observed regression values (including the intercept) as b, population values as
sampling error as
be
to
/3
(A-3)
ej
and e will be uncorrelated, so
that the variance
of observed values, a^, will
be larger than the variance of population values, o^, by the amount of sampling error, a^:
27
c,'
From
=
V+
<^'
(A-4)
equation (A-4), the variance of the population regression values can be written as:
a/=
The key
known
(A-5)
a,'-a^'
to meta-analysis is the fact that the
statistical
sampling error variance,
Thus equation (A-5) becomes a formula
theory.
<r^,
to
can be computed using
compute the population
variance, a/.
Estimating Meta-Analysis Parameters
B.
In the previous section,
we assumed
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 wiU differ by chance from the theoretical sampling error variance. Hence
we
use the notation "s^" for the estimated variances below.
If a population value is
that the best estimate
b
where
b; is
=
assumed be constant across
of that value
E[Ni bj/
E
is its
studies,
Hunter and Schmidt (1990) show
frequency-weighted average:
(A-6)
Ni
the observed value in study
i
and N;
is
the
number of observations
corresponding observed variance estimate across studies
is
in study
i.
The
the frequency-weighted average
squared deviation:
s,^
=
E[N.(b.
-
b)^/ E N.
The observed variance
in population values (if
estimate,
(A-7)
s,,^,
is
a confounding of two sources of variation: variation
any) and variation in observed values due to sampling error.
28
Thus an
estimate of the variation in population values can only be obtained by correcting the observed
variance estimate,
s^^,
Hunter and Schmidt (1990) show that sampling error
for sampling error.
across studies behaves like error of measurement, and the resulting formulas are comparable to
the standard formulas in classic psychometric measurement theory or reliability theory.
From
psychometiic theory (Thomdike (1982)),
classic
=
Observed value
true value
+
we
have:
error of measurement
(A-8)
where the true value and error of measurement are uncorrelated. Hence:
=
Observed variance
In meta-analysis,
sampling error,
e,
s,'
is
=
population variance
=
s/
The sampling
s,^
=
(A-9)
error variance
similarly true that the population regression values, ft
+
+
Therefore
we
,
and the
can write:
(A- 10)
sampling error variance
(A-11)
s,2
The observed variance estimate,
above.
+
are uncorrelated across studies.
,
Observed variance
it
true variance
Sb^, is
the frequency-weighted average squared deviation defined
error variance estimate required by meta-analysis is then:
E[Ni(standard error hf]/
E Ni
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).
Consider a special case where a/=0;
i.e.,
the
homogeneous case where
value across studies and a^ = a^. The observed variance,
29
Sb',
/3
has the same
has a sampling error variance that
depends on the number of studies. With probability approximately .50,
negative (as in
negative,
For such a sample of
less than <x^.
and hence
it
means
where variance
the model
ANOVA
is
is
when
the sample
is less
less than
of
/3
<r^^;
will
be
than one). If the variance estimate
ANOVA),
is
In a statistical model
is zero.
a negative value does not imply that
inconsistent or that the computations are incorrect.
the population variance,
negative or zero, the inference
is that
attributed to sampling error.
That
corrected variance across studies
A
value
estimated by subtraction (as in
be
studies, the estimated variance
of the population variance
that the best estimate
The estimate of
C.
F
will
Sb^
s^',
there is
is,
all
can thus be positive, negative or zero. If
no variation
in
observed values that cannot be
variance in observed values
is positive, it
may
still
be
it is
is artifactual.
If the
trivial in size.
Significance Test for Real Variation Across Studies
The hypothesis
ratio of the
that there is
no
real variation in observed values has
a
statistical test.
The
observed variance estimate to 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)
ks,Vs,2
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 large, it
amount of
(Hedges and Olkin (1985), Cohen (1988), and Hunter and Schmidt (1990)).
square value
studies.
is
not significant, there
However,
if
the
k
is
strong evidence that there
studies are not independent, then the
30
is
no
power of
has high
real variation
Thus
if the chi-
real variation across
the chi-square test
is
reduced as discussed in the next section.
Independence
D.
Given a
set
of regression estimates, there
the preceding discussion,
would
it
was assumed
is
a corresponding
that the variance
set
of sampling errors.
In
of the sampling errors across studies
only by sampling error from the hypothetical error variance across
itself differ
independent replications. This
is
true for
most applications of meta-analysis and follows
immediately from the independence of the estimates across studies. However,
this is
not always
true.
In this study the impact of the market proxy
equity pension fund managers
common
may
overlap.
is
controlled.
Hence
However, the
the securities the
will contribute their particular returns to both portfolio return sequences.
It
two portfolios will have time
two
two portfolios have
of those securities will thus contribute to the residuals of the two portfolios.
the
portfolios of
in
The residuals
This means that
series regression residuals that are not entirely independent.
can be shown that the sampling errors for the two portfolio regressions will also be
nonindependent and positively correlated. The strength of the correlation largely depends on the
degree of fund overlap, and possibly on additional unmeasured
Consider the
residuals
r)Se^.
is r,
The
set
common
of regression residuals for two portfolios.
then the error variance across portfolios will not be
factors.
If the correlation
s^^,
between
but rather the product [(1-
adjusted formulas for meta-analysis are therefore:
s,^
=
s/
s,'
=
s,' - (l-r)s,'
+
(A-15)
(l-r)s.^
(A-16)
31
s,^
=
(s,^ -
s,^
+
r
s^
(A-17)
Thus, standard meta-analysis formulas will underestimate the variance of
/3.
estimated variances for selectivity and timing will be too low by the amount
In particular, the
rSe^.
The
adjusted
formula for chi-square would thus be:
X^
= k
J^
=
(A-18)
s,V(l-r)s,^
Hence, the standard chi-square
in equation (A- 14)
power
(A-19)
[l/(l-r)](k s,Vs,2)
homogeneity of regression values given
earlier
would be an underestimate and thus would have somewhat lower than optimal
to detect departures
a conservative
test statistic for
test for
from homogeneity. Therefore the standard chi-square
test
would be
heterogeneity. All meta-analysis results presented in this study use the
adjusted formulas for the variances and the chi-square
32
test.
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A
Direct
Table
Summary
This table presents summary
Statistics for
statistics for the
I
Pension Manager Performance (1983-90)
71 managers for the entire sample period.
The number of
positive and negative
selectivity and timing values are given for each model for each benchmark portfolio. Only those values which are significant at the
.05 level or less are counted. The numbers in parentheses indicate the percent of the total sample.
Russell 30GG
Positive
Bhattacharva and Pfleiderer Model
Selectivity
Negative
Stvle Index
Positive
Negative
S&P
Positive
500
Negative
Table
Mean
II
Values of Performance Measures Across Models and Benchmarks
This table presents the mean values of the selectivity and timing values across models and benchmarks for the entire sample period.
in parentheses indicate the rank among investment styles for each measure,
The numbers
Russell
3000
Timing
Selectivity
S&P 500
Style Index
Selectivity
Timing
Selectivity
Timing
.0016**
-.0100
.0003
-.0008*
-.0470**
Bhattacharya and Pfleiderer Model
All
Managers
.0008**
Earnings Growth
-.0003
Market Oriented
Price Driven
SmaU
Capitalization
-.0092
(3)
.0538**(1)
.0007* (4)
.0217 (2)
.0020**(2) -.0274 (3)
.0022**(1)
.0012
(2)
.0015**(2)
-.0234
(3)
.0009* (3)
-.0765**(4)
.0031**(1)
-.0005
(4)
-.0843**(4)
.0586*
(1)
!o072 (1)
.0017**(1) -.0451
(2)
.0009* (2) -.0539**(3)
-.0007
(4)
(3)
-.1024**(4)
Trevnor and Mazuy Model
All
Managers
.0008**
Earnings Growth
-.0003
-.0828
(3)
.2014**(1)
.0016**
-.0706
.0008*
-.0011
(2)
(3)
(4)
Market Oriented
.0021**(1)
-.0278
(2)
.0019**(2) -.1261
Price Driven
.0016**(2)
-.0877
(3)
.0009* (3) -.3286* *(4)
.0032**(1) .2074* (1)
Small Capitalization
•* Significant
-.0004
(4)
-.4625**(4)
at the .05 level
* Significant at the
.
10 level
39
-.2799**
.0004
-.0008* (4)
!oi08 (1)
.0017**(1) -.1799 (2)
.0011**(2) -.2293* (3)
-.0004 (3)
-.7828**(4)
Table
m
Correlation of a Performance Measure Between Benchmarks*
Each model was estimated for all managers for the entire period using each of the three
benchmark portfolios. Panel A presents the Pearson and Spearman correlations between
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
Stvle Index
Bhattacharya
&
Pfleiderer
Model
RusseU 3000
Style Index
Treynor and Mazuy Model
Russell 3000
Style Index
Pearson
.806
Spearman
S&P
500
Spearman
Pearson
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
3000
.992
.988
.901
.923
Style Index
.991
.990
.835
.930
S&P500
.990
.985
.866
.894
Russell
*A11 correlations are significant at the .0001 level
41
Table
V
Correlation Between Selectivity and Timing
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 the
selectivity and timing values for each model for each benchmark.
Bhattacharya and Pfleiderer Model
Treynor and Mazuy Model
Benchmark
Pearson
Spearman
Pearson
Spearman
RusseU 3000
-.447
-.488
-.485
-.427*
Style Index
-.359'^
-.315'
-.399''
-.359"
S&P
-.487
-.504
.467
-.387
500
*
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
42
Table VI
Average Correlation Between Regression Residuals
This table presents the average correlations between the regression residuals for the 71 managers for the
entire period across benchmarks and models. The numbers in parentheses indicate the 95% confidence
interval for the average correlation.*
Bhattacharya and Pfleiderer Model
Trevnor and Mazuv Model
Benchmark
Russell 3000
.084 (.062, .123)
.083 (.061, .122)
Style Index
.071 (.052, .105)
.071 (.052. .105)
S&P500
.232 (.177, .330)
.226 (.173, .321)
*
The formulas for the confidence interval of the average correlation are derived in Hunter and Coggin
These formulas use the normal approximation to the chi-square distribution, and are reasonably
accurate for sample sizes greater than 30. Let N=the number of time series returns per manager, n=the
number of managers, and r = the average correlation between regression residuals. In our case, N = 96 and
n = 71. If we define XI = 1.96 *v(2/(N-1)) and X2 = (1 +(n-1)*r)/(n-1). then:
(1992).
95%
lower bound for
r
=
r -
[(XI /(I +X1)) * X2].
95% upper bound
43
for
r
=
r
+ [(XI /(I -XI)) * X2].
Table
VII
Meta-Analysis Results
This table presents the meta-analysis results for the selectivity
portfolios
and using heteroscedasticrty-consistent standard
and timing values tjased on the three benchmark
errors, for the entire period (n
Panel A: Bhattacharya and Pfleiderer Model
b
x' (df=70)
= 71 managers).
Table
80%
Probability Intervals for
This table presents the
and the
80%
Observed and Population
Selectivity
all
Panel A:
period.
and population values of sejectivrty and
The observed values are bounded by b± 1^8(^),
l.28(Sg).
Bhattacharya and Pfleiderer Model
Observed Values
Selectivity
Benchmark
Lower
S&P 500
-.003121
Russell 3000
-.002687
Style Index
-.001606
Upper
.003800
.004255
.004854
Population Values
Market Timing
Selectivity
Upper
Lower
Upper
Lower
Upper
-.181391
.087434
.136814
.148697
-.001999
.002678
.003161
.003937
.116401
-.083870
.022443
.065481
-.106131
.086126
-.155203
.168703
-.001623
-.000689
Mazuy Model
Observed Values
Selectivity
S&P 500
Style Index
Upper
Lower
-.003019
.003864
.004223
.004912
-1.092766
-.001622
Population Values
Market Timing
Lower
Russell 3000 -.002632
Market Timing
Lower
Panel B; Treynor and
Benchmark
and Market Timing Values
probability intervals for the observed
managers for the entjre
population values are bounded by b ±
market timing using
VIII
-.848546
-.830330
Upper
.532916
.683034
.689144
45
Selectivity
Lower
-.002038
-.001615
-.000822
Upper
.002883
.003206
.004112
Market Timing
Lower
-1.032817
Upper
-.786826
.472967
.621314
-.777474
.636288
/
U
(J
Date Due
MIT LIBRARIES
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