a nonparametric test of market timing1
TRANSCRIPT
1
A Nonparametric Test of Market Timing1
Wei Jiang2
August 2001
1 I Thank Jason Abrevaya, Gene Amromin, Brad Barber, Terry Odean, Douglas Diamond, Lars Hansen, Milton Harris, two anonymous referees, and workshop participants at the University of Chicago and the University of California, Davis for their helpful comments and suggestions. All errors are mine. 2 Finance and Economics Division, Columbia Business School, New York, NY 10027. E-mail:
2
______________________________________________________________________________
Abstract
In this paper we propose a nonparametric test for money managers’ market timing ability and
apply the analysis to a large sample of mutual funds that have different benchmark indices. The
test (i) only requires the ex post returns of the funds and the benchmark portfolios; (ii) isolates
timing from selectivity; (iii) separates the quality of timing information a money manager
possesses from the aggressiveness with which she reacts to such information; and (iv) is robust
to different information and incentive structures as well as underlying distributions. Theta—the
parameter for timing ability—is on average below the neutral level (indexation) among actively
managed domestic equity funds, and is very difficult to predict from observable fund
characteristics. Overall, actively managed funds aiming at “timing the market” in general fall
short of just “riding with the market.”
JEL classification: G1; C1
Keywords: Market timing; Nonparametric test; U-statistics
______________________________________________________________________________
1. Introduction
“My money was in mutual funds. Several of them. They worked like this:
When the market went down, my funds went down a lot; when the market went
up, my funds went up a little…I thought I could do better.”
—Confessions of a day trader, to the Time magazine.
The confessions of the do-it-yourself investor speak out the doubts concerning active portfolio
management: Do and can professional money managers time the market? Investors who put
their money in actively managed mutual funds when index funds are available at a much lower
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cost hope to “beat the market” instead of merely to “ride with the market.” These investors, not
all of whom are aware of the theory of market efficiency in its strong and weak forms, expect
professional money managers to be better informed than common people about individual
securities or about the general market movements. If this is true, the superior information
possessed by a money manager will show up as one or both of the abilities: securities selectivity
and market timing. The first ability concerns identifying, and investing disproportionately in,
securities that have the potential to outperform the market in risk-adjusted terms. And the
second ability is about predicting the overall market movement and adjusting the portfolio’s
exposure to systematic risk accordingly. This is why mutual funds sometimes distinguishably
market themselves as either “stock pickers” or “market timers.” The aim of this paper is to
develop a test examining whether actively managed mutual funds—with an average annual
turnover rate around 100%3—deserve the second title.
Based on the theory of market efficiency with costly information, there has been ample
research work on measuring the performance of professional money managers with emphasis on
one of the two basic abilities. The selectivity test answers the question whether the portfolio
composed by a fund manager outperforms the benchmark portfolio in risk-adjusted terms
(Jensen, 1972; Gruber, 1996; Ferson and Schadt, 1996; Kothari and Warner, 2001). The timing
test deals with whether a fund manager can outguess the market by moving in and out of the
“time portfolios”—portfolio proxies for factors (Treynor and Mazuy, 1966; Henriksson and
Merton, 1981; Admati, et al., 1986). Measures of market timing have fallen into two categories.
The first one directly tests whether money managers successfully allocate funds among different
classes of assets (e.g., equity versus cash) to catch the market ascendancy and/or to avoid the
downturns. Theoretical work includes those by Merton (1981) and Cumby and Modest (1987).
Graham and Harvey (1996) run an empirical test on investment newsletters’ asset allocation
recommendations. Methods in this category require the knowledge of managers’ asset positions
at a reasonably high frequency, and have thus been constrained in practice. The second category,
on the other hand, requires only data on the ex post returns of the funds and the relevant markets.
3 Averaged over all actively managed domestic equity funds that were listed in the Morningstar mutual fund database for the 1980-1999 period.
4
The two most popular methods so far are those proposed by Treynor and Mazuy (1966)
(henceforth “TM”) and Henriksson and Merton (1981) (henceforth “HM”).
Most of the work on mutual fund performance measurement extends the alpha-beta analysis
of securities and portfolios to mutual funds. There has been controversy over using such a
metric to evaluate mutual fund performance. The static alpha-beta analysis misses the
diversified and dynamic aspects of managed portfolios (Admati, et al., 1985; Ferson and Schadt,
1996; Becker, et al., 1999; Ferson and Khang, 2000). In efforts to beat the market, fund
managers vary their portfolios’ exposure to market or other risk factors from time to time based
on the information they receive. Further, fund managers can alter their funds’ correlation to the
benchmark index in order to make best out of the incentives they face (Chevalier and Ellison,
1997). Consequently, the systematic part of the fund risk can be misestimated when the market
timing effect is present, and existing measures may fail to attribute superior returns to informed
investors if risk aversion varies (Grinblatt and Titman, 1990). To address these issues, there has
been a lot of work on the extension of the TM and HM measures in order to capture the effect of
conditioning information in timing performance (Ferson and Schadt, 1996; Becker, et al., 1999;
Ferson and Khang, 2000), to control for spurious timing arising from not holding the benchmark
(Jagannathan and Korazjczyk 1986; Breen and Jagannathan, 1986), to decompose abnormal
performance into selectivity and timing (Admati, et al., 1986; Grinblatt and Titman, 1990), and
to minimize the loss of test power due to sampling frequencies (Goetzmann, et al., 2000; Bollen
and Busse, 2001).
In this paper we develop an independent test to measure the market timing ability of portfolio
managers without resorting to the estimation of alpha or beta. The test is based on the simple
idea, as stated in the confession of the day trader at the start of the paper, that a successful timer
should have the fund go up a lot when the market rises and dip down a little when the market
heads south. The non-regression based nonparametric test has the following desirable properties.
First, it only requires the ex post returns of the funds and the benchmark portfolios, and is thus
easy to implement. Second, under the condition that a fund manager’s timing information is
independent from her selectivity information, the test can isolate timing from selectivity. Third,
the test separates the quality of timing information a fund manager possesses from the
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aggressiveness with which she reacts to such information. The test statistic is not affected by the
manager’s risk aversion. Finally, the test is robust to different information and incentive
structures as well as timing frequency and underlying distributions. The method that we develop
in this paper is also readily applicable to analyzing the market timing ability of financial advisors
or newsletters (Graham and Harvey, 1996), or the timing behavior of individual investors
(Odean, 1998; Barber and Odean, 2000).
The rest of the paper is organized as follows: Section 2 starts with a review of market timing
measures, and then presents the model of the nonparametric test of market timing that allows
flexibility in information and incentive structures as well as in the underlying distributions. We
demonstrate the effectiveness of the test and compare it with the TM and HM methods in a
simulation. Section 3 applies the method to a data set of mutual funds with different benchmark
indices. We show that the average actively managed fund underperforms the respective index
fund in terms of market timing. Section 4 concludes.
2. Model
2.1. Preliminaries
If we could observe the portfolio composition of mutual funds at the same frequency as we
observe the returns, we can infer funds’ market timing by testing whether the portfolio’s
exposure to the relevant market is pro-trend on average (Merton, 1981; Cumby and Modest,
1987; Ferson and Khang, 2000). But in more practical situations we tie our hands to the returns
of funds and benchmark portfolios only. The method we propose needs only ex post returns of
funds and their benchmark returns, and can be applied to funds that do not have derivatives in
their portfolios.4
4 Buying call options, for example, can induce spurious timing ability, as analyzed in Jagannanthan and Korajczk (1986). Koski and Pontiff (1999) find that 21 percent of the 679 domestic equity funds in their sample use derivative securities, but detailed information about their derivative usage is not available. To minimize spurious timing due to derivatives, we do not include funds that invest in convertible bonds in our empirical test.
6
We interpret selectivity as the manager’s ability to pick up securities that have positive risk-
adjusted excess returns, and timing as the manager’s ability to move the fund’s exposure to the
relevant market according to her forecast about future market returns. We assume that
manager’s timing information is independent of her selectivity information, a fairly standard
assumption in the performance literature (e.g., see Admati, et al. (1986) and Grinblatt and
Titman (1990)).5 Combining the selectivity and timing, we have the following equation for fund
i (all returns are expressed in excess of the riskfree rate):
,1,1,,1, +++ ++= titmtiiti rr εβα (1)
where ti ,β is a random variable adapted to the information available to the manager at time t. rm
represents the return of the relevant market (which is usually a subset of the total market) that the
mutual fund invests in. Alternatively, we can take rm to be the benchmark portfolio return
against which the fund is evaluated.
Note that equation (1) is not an equation for asset pricing, but is designed for measuring
market timing of mutual funds. We omit in the equation other factors that might affect the
expected returns of the portfolios, such as size or book-to-market factors. We justify such
abstraction as follows. First, for large diversified portfolios of securities, unlike individual
securities, the (relevant) market return is the dominant factor in the return equation. Second, the
market return in the equation is not the total market return, but the return of a narrower market
defined by the mutual fund’s investment policy, for example, small-cap growth stocks. In the
absence of security selectivity, we can think of market timing as moving in and out of the
relevant market portfolio. In the simplest case, a market timer decides on βt at date t and during
the next period t+1 she invests βt percent in the relevant market portfolio and the rest in bond.
Then equation (1) represents the return profile from such a timing strategy.
Finally, if there are other factors affecting the expected return of funds, αi may contain return
to omitted risk factors, but the method remains valid if we are only interested in testing whether
fund managers successfully time the market they are in. Our method does not require or rely on
5 Correlated timing and selectivity information would in general cause technical difficulties in separating abnormal performance from timing and that from selectivity. See detailed discussion in Grinblatt and Titman (1990).
7
the correct estimation of αi or βi,t. We will show later that we use the same measure to check
that the omitted factors (size and book-to-market) do not display “timing” property against the
benchmark indices we use in the analysis. Therefore, abnormal timing performance is due to
managers’ market timing instead of to their holding a particular class of assets that exhibit
“timing” characteristics.
Treynor and Mazuy (1966) suggest the following quadratic regression:
[ ] ,1,2
1,1,,1, ++++ +++= titmitmtiiti rrr εγβα (2)
for the ith fund. Assume the manager observes a private signal yt which equals the future market
return plus an independent noise term:
.1, ttmt ry η+= + (3)
Superior timing ability corresponds to that the variance of the noise term is finite, or ∞<<2ησ .
The manager with constant absolute risk aversion (CARA) preference will respond to the signal
by making the portfolio beta a linear function of the signal (Admati, el al., 1986), which in turn
makes the portfolio return a quadratic function of the market return as in equation (2). Thus a
significantly positive coefficient iγ represents superior market timing performance.
Henriksson and Merton (1981) define the manager’s timing ability as
( ) ( ) 10|0ˆPr0|0ˆPr 1,1,1,1, −<<+>>=∆ ++++ tmtmtmtm rrrr (4)
where 1,ˆ +tmr is the manager’s forecast about 1, +tmr . Superior ability corresponds to ∆ being
greater than zero. The HM model assumes that the manager sets a higher target beta in an up
market (when the excess return on the market portfolio is greater than one) forecast than that in a
down market one. Given the aggressiveness of the manager’s reaction (expressed as the
difference between the two betas), the contribution of ∆ to the fund return can be inferred by the
following regression:
[ ] ,1,1,1,,1, ++
+++ +++= titmitmtiiti rrr εγβα (5)
8
where [ ] ),0max( 1,1, ++
+ = tmtm rr . The coefficient on [ ]++1,tmr becomes the value added by effective
timing that is equivalent to a call option on the market portfolio where the exercise price equals
the riskfree rate. As we can see, the γ coefficients in both the TM and HM models cannot
disentangle pure market timing (expressed as 2ησ in the TM model and ∆ in the HM model)
from the manager’s aggressiveness (expressed as the linear reaction coefficient in TM and the
difference between the high and low betas in HM).
2.2. A Nonparametric Test Statistic
In this section we propose a nonparametric measure to identify the market timing aspect of fund
performance. As specified in (1), a manager who times the market would move ti ,β
endogenously. Let ( )1,, ˆ += tmti rφβ , where )|(ˆ 1,1, ttmtm ZrEr ++ = is the manager’s prediction
about the next period market return based on tZ , the set of information available to her at time t,
both public and private. It is reasonable to assume that the manager does not make systematic
mistake, therefore the predictions should be unbiased. We do not put any parametric restrictions,
such as linearity, on the response function ( )⋅φ except requiring it to be a non-decreasing
function of 1,ˆ +tmr . If the manager does not possess valuable information or does not react to her
information, (1) collapses to the standard CAPM equation. Let ( )tii E ,ββ = be the unconditional
expectation of the fund’s beta, which should be commensurate with the fund’s stated investment
policy.
The manager’s timing ability relies on the relevance and accuracy of the signal tZ .
Suppose tZ is not informative at all. Then the conditional distribution of the forecast equals the
unconditional one, that is, ( ) ( )1,1,1, ˆ|ˆ +++ = tmtmtm rfrrf , where ( )⋅f stands for the probability density
function. In that case the probability of a right prediction in excess of that of a wrong one should
be zero, that is, the following parameter:
9
( ) ( )( ) ,1|ˆˆPr2
|ˆˆPr|ˆˆPr
1,1,1,1,
1,1,1,1,1,1,1,1,
2121
21212121
−>>=
><−>>=
++++
++++++++
tmtmtmtm
tmtmtmtmtmtmtmtm
rrrrrrrrrrrrν
(6)
takes the value of zero for two periods 21 tt ≠ in the absence of timing ability. In the other
extreme, if the forecast is always perfect, that is, 1,1,ˆ ++ ≡ tmtm rr , then ν attains its upper bound of
one. Symmetrically, ν equal to –1 represents perfect perverse market timing. Therefore, the
value of ]1,1[−∈ν can be a measure of the fund manager’s market timing ability. The more
accurate the information tZ is, the higher the value of ν .
Now we can put the information structure and the reaction function together. Grinblatt
and Titman (1990) prove that an investor who has independent timing and selectivity
information and nondecreasing absolute risk aversion6 always increases her beta as her
information about the market becomes more favorable, or, 0ˆ 1,
>∂∂
+tm
t
rβ
. We will discuss in more
detail about this specification in the next section. Combining this result with (6), the following
probability
( ) ( )( ) 1|Pr2
|Pr|Pr
1,1,
1,1,1,1,
2121
21212121
−>>=
><−>>
++
++++
tmtmtt
tmtmtttmtmtt
rrrrrr
ββββββ
(7)
is greater than zero if and only if the manager possesses superior information. At any range of
market return, the fund return should on average rise more when the market return is higher
and/or lose less when the market is lower if the manager times the market successfully. If so, the
probability that the fund returns bear a convex relation with the relevant market returns should be
higher than that of a concave relation, but the convexity or concavity needs not be global nor be
restricted to the parametric forms as specified in the TM and HM models. Based on (7), we
construct the following nonparametric test statistic.
6 Nonincreasing absolute risk aversion requires that the investor’s risk aversion measured by
)(')(''
wuwu− be
nonincreasing in the wealth level w. Commonly used utility functions, such as exponential, power, and log utilities, all meet this criterion.
10
For a triplet { }31,, ,=jtmti jj
rr sampled from any three periods such that 321 ,,, tmtmtm rrr << , a
manager with superior information should, on average, maintains a higher average beta in the
[ ]32 ,, , tmtm rr range than in the [ ]
21 ,, , tmtm rr range. Since beta at any point is the slope of the fund
return against the market return, the parameter
−−
<−−
−
−−
>−−
=12
12
23
23
12
12
23
23
,,
,,
,,
,,
,,
,,
,,
,, PrPrtmtm
titi
tmtm
titi
tmtm
titi
tmtm
titi
rrrr
rrrr
rrrr
rrrr
θ (8)
is an indicator for the manager’s market timing ability. We will drop the fund subscript i where
there is no confusion. Under the null hypothesis of no timing ability, the beta has no correlation
with the market return in which case the statistic θ assumes the neutral value of zero. Without
superior information, a manager would move the portfolio exposure to the market in the right
direction as often as she would in the wrong direction if she tries to time the market.
The sample analogue to θ becomes a natural candidate as a statistic. It is a U-statistic with
kernel of order three:
∑
=<<
−
−<
−
−−
−
−>
−
−−
kmrjmrimrn
imrjmrirjr
jmrkmrjrkr
imrjmrirjr
jmrkmrjrkrnU
,,, ,,,,1
,,,,1
1
3, (9)
where n is the sample size and ( )⋅1 is the indicator function. By the property of U statistics, nU
is a n -consistent and asymptotically normal estimator for θ (Serfling, 1980; Abrevaya and
Jiang, 2000), that is,
( ) ),0( 2nU
dn NUn σθ →− .
Further it is the least variance estimator among the unbiased estimators for the same parameter
θ , the probability in favor for the manager to form a correct prediction about the next-period
market return.
11
Abrevaya and Jiang (2000) provide detailed discussions about the asymptotic distribution of
the nU statistic and the simulation results of its limited sample properties. Let ( )jjj tmtt rrz ,,≡
and denote the kernel function of nU by
( )
.|1
|1,,
,,,,,,,
,,,,,,,
<<
−−
<−−
−
<<
−−
>−−
=
kmjmimimjm
ij
jmkm
jk
kmjmimimjm
ij
jmkm
jkkji
rrrrrrr
rrrr
rrrrrrr
rrrr
zzzh
The sample analogue to the asymptotic standard error of nU is derived in Abrevaya and Jiang
(2000) using the jackknife method:
( )∑ ∑=
−
−
=
n
i kjnkjiU Uzzzh
nnn
1
2
,
12 ,,
29σ̂ . (10)
For small samples (below 50) the nonparametric bootstrap by resampling the triplets offers a
better approximation. Simulation results in Abrevaya and Jiang (2000) show that the size of the
test is very accurate7 if we use bootstrap method in standard error estimation for sample sizes
below 50 and use the asymptotic formula for larger sample sizes.
2.3. Properties
Now we have a new measure of market timing. We will call it theta (θ). It has a ready
interpretation of the probability (with a neutral value of zero) that a fund manager loads on more
systematic risk in a higher return period than in a low return one in excess of the probability that
she does the perverse. Since the seminal work by Treynor and Mazuy (1966) and Henriksson
and Merton (1981), there has been a lot of work on the extension of these measures in order to
relax the restrictive behavioral and distribution assumption, while retaining their intuitive appeal,
7 For 1,000 simulations, rejection rates at 5% significance level are between 4.5% and 5.5% for all error specifications.
12
ease of implementation, and minimal data requirements.8 In this section we discuss how theta as
a measure of market timing represents a significant contribution on these grounds, and point out
its limitations.
2.3.1. Information Structure and Behavioral Assumptions
The measure ν in (6) puts weaker restrictions on the information structure than the TM and HM
measures. The TM measure assumes noise additive signals with normal distributions as
expressed in (3). The manager is considered possessing valuable information if and only if
∞<<2ησ . This criterion is built on the grounds of Blackwell informativeness (Blackwell, 1951).
Comparing a manager with superior information ( ∞<<2ησ ) with one without ( ∞→2
'ησ ), it is
known that the first manager’s signal y is Blackwell more informative than the latter one’s y’ if
and only if 'η has the same distribution as ζη + for some ζ that is independently distributed
from η . This criterion can only order information structures where all random variables are
from the same distribution family, such as the normal distribution.
In our model, a manager is considered possessing valuable information if and only if the
probability ν specified in (6) is greater than zero. A sufficient condition for this result is that the
conditional distribution ( )11 ,, |ˆ tmtm rrF first-order stochastically dominates ( )
22 ,, |ˆ tmtm rrF
whenever 21 ,, tmtm rr > . That is, for any possible value of *
mr , the two distributions satisfy
( ) ( )2211 ,
*,,
*, |ˆPr|ˆPr tmmtmtmmtm rrrrrr <<< ,
whenever 21 ,, tmtm rr > . Dewatripont, et al. (1999) show that the first-order stochastic dominance
(FOSD) criterion about informativeness is compatible, but weaker than, the Blackwell
informativeness. To see this, take the TM specification of private signals as in (3), where 1tη
8 Goetamann, et al. (2000) had an excellent review on the research work that addresses the limitation of the TM and HM timing measures.
13
and 2tη are i.i.d. for 21 tt ≠ , and the manager’s ability determines 2
ησ . In their setting, we can
calculate our ν as follows:
[ ],1
22
1|Pr2
1,1,
1,1,1,1,
21
212112
−
−Φ=
−>−<−=
++
++++
ησ
ηην
tmtm
tmtmtmtmtt
rr
rrrr
where ( )⋅Φ stands for the cumulative probability function of the standard normal distribution. It
is easy to see that ν in monotonically increasing in ησ
1 , the precision of the private signal.
∞=ησ leads to 0=ν (no timing) and 0=ησ implies 1=ν (perfect timing).
The HM method characterizes a valuable forecast as the sum of two conditional probabilities
of a correct forecast about the sign of the market excess return exceeding one, as specified in (4).
Suppose a pure HM market timer gives only two possible predictions about 1, +tmr , positive or
negative. Then the ν measure of our model picks up the manager’s timing ability among a
subset of pairs of data where 01,1, 21<++ tmtm rr . On the other hand, our measure uses more
information in the return data by looking at all pairs of { }1,1, 21, ++ tmtm rr for 21 tt ≠ .
The theta measure also allows flexible specification of fund managers’ response functions to
the information. We only require that ( )1,ˆ += tmt rφβ is a nondecreasing function of 1,ˆ +tmr , that is,
the manager sets a higher beta for the fund when her forecast of the next period market return is
more favorable. Grinblatt and Titman (1990) prove that this is true when the manager has
independent timing and selectivity information and has nonincreasing absolute risk aversion.
The first assumption is required by all performance measures in order to separate timing from
selectivity, and the second assumption is satisfied by commonly adopted utility functions in
research. The flexibility on the response part is particularly appealing because a fund manager’s
reaction to the acquired information depends on her risk aversion as well as the incentive she
faces. The functional form of her response is difficult to specify without being somewhat
arbitrary. For example, a linear response by the fund manager:
14
( )[ ]mtmt rEr −+= +1,ˆλββ (11)
(Treynor and Mazuy, 1966; Admati, et al., 1986) is consistent with the manager’s acting as if she
were maximizing the expected utility of a CARA preference. However such an assumption is
questionable if the fund manager maximizes the utility related to her own payoff under the
incentive instead of the total return. The deviation from maximizing a CARA preference is large
when there is non-linearity in the incentive, explicitly or implicitly, in the forms of benchmark
evaluation, option compensation, or non-linear flow-to-performance responses by fund investors.
After all, there is no reason to expect a uniform reaction to information among all fund
managers. Comparatively, the theta measure imposes less stringent restrictions on the manager’s
reaction function.
2.3.2. Ability versus Response and Conditional Information
Theoretically there is a distinction between performance and ability. A fund manager’s market
timing performance relies on both the quality of her private information (ability) and the
aggressiveness with which the manager reacts to her information (response). This constitutes a
dichotomy that is difficult to decompose. Ability possessed by the manager is more important to
the investors because investors can essentially “undo” the aggressiveness of the manager by
investing more or less of their wealth in the fund or by trading in other accounts.
Regressions like (2) and (5) basically cater for the response aspect of market timing. We see
that the estimated TMγ̂ in the TM regression will pick up the coefficient in the linear reaction
function, that is, the λ term in (10). Hence more aggressive funds can show up as better market
timers with higher TMγ̂ . The HMγ̂ coefficient in the HM model is an unbiased estimate for
)( LH ββ −∆ where ∆ is the probability defined in equation (4) and Hβ ( Lβ ) is the manger’s
target beta when the predicted market excess return is positive (negative). Both ability (the ∆
term) and aggressiveness (the LH ββ − term) are reflected in the estimated timing. The
nonparametric statistic theta, on the other hand, measures how often a manager correctly ranks a
15
market movement and appropriately acts on it, instead of measuring how aggressively she acts
on it. We see that in the linear response case,
1|ˆˆˆˆ
Pr2321
12
1122
23
2233,,,
,,
,,,,
,,
,,,, −
<<
−−
>−−
= tmtmtmtmtm
tmtmtmtm
tmtm
tmtmtmtm rrrrr
rrrrrr
rrrrλλθ ,
where λ cancels out. The probability of a correct signal is closely related to the signal quality,
while the magnitude has more to do with the fund manager’s risk aversion. Thus our measure
largely reflects quality, and offers a way to estimate timing ability without a simultaneous
estimation of risk aversion which has been a difficult task in empirical studies.9 For the same
reason, there is great complementarity between the nonparametric method and the two other
methods. Used together in empirical work they can offer a more complete picture of market
timing performance of fund managers.
The theta statistic can also be extended to the context of conditional market timing. The
literature on conditional performance evaluation stresses the importance of distinguishing
abnormal performance that merely reflects publicly available information (as captured by a set of
lagged instrumental variables) from performance attributed to better information. In the context
of market timing, work by Ferson and Schadt (1996), Harvey and Graham (1996), Becker, et al.
(1999), and Ferson and Khang (2000) are all in this line. The conditional market timing
approach assumes that investors can time the market on their own using readily available public
information, or they can undo any perverse timing that is predicted from the public information
by trading on other accounts. Under such circumstances, the real contribution of a fund manager
would be her successful timing on the residual part of market returns that is not predictable from
public information.
Let tmr ,~ be the residuals of market returns that cannot be explained by lagged instrumental
variables. Then a conditional version of our measure is to test whether a fund manager, on
average, maintains a relatively high tβ when the unexplained part of the return 1,~
+tmr is
relatively high. Accordingly, we can use a variation of the statistic defined in (9) to capture 9 Becker, et al. (1999) estimate signal precision and funds’ risk aversion simultaneously, but the estimated risk aversion coefficients are largely out of reasonable range (and being negative in some cases).
16
funds’ conditional performance on market timing. Specifically, the test statistics is computed on
all triplets such that kmjmim rrr ,,,~~~ << :
∑
=
−
−<
−
−−
−
−>
−
−−
<< imrjmrirjr
jmrkmrjrkr
imrjmrirjr
jmrkmrjrkrn
kmrjmrimrnU
,,,,1
,,,,1
1
3 ,~
,~
,~
~ . (12)
The standard error of nU~ can be estimated using (10) with ( )kji zzzh ,, replaced by
<<−
−<
−
−−
<<−
−>
−
−
kmrjmrimrimrjmr
irjr
jmrkmrjrkr
kmrjmrimrimrjmr
irjr
jmrkmrjrkr
,~
,~
,~|
,,,,1,
~,
~,
~|,,,,
1 .
2.3.4. Model Specification and Potential Bias
Theoretically superior performance of managed portfolios can be decomposed into selectivity
and timing components (Admati, et al., 1986; Griblatt and Titman, 1990), but such
decomposition has been proved difficult empirically (Coggin, et al., 1993; Kothari and Warner,
2001). Like other timing measures, our measure relies on two assumptions to avoid detecting
spurious timing because of selectivity issues. The first assumption is that a portfolio manager’s
information on the selectivity side (individual securities) is independent of her information on
the timing side (market movement). Practically this requires that each individual security
constitutes only a small portion of a diversified portfolio and has a negligible impact on the
whole market,10 or the fund manager acts on selectivity at a much lower frequency than on
market timing (so that the manager keeps roughly constant the composition of her risky portfolio
for most of the times when she tries to time the market frequently). The second assumption is
that the portfolio does not consist of derivatives, such as options, whose returns bear a convex
(concave) relationship with the market in the absence of market timing.
For most timing measures, bias in estimation would arise when econometricians observe
return data at a frequency different from the frequency at which the manager times the market.
Goetzmann, et al. (2000) show that monthly evaluation of daily timers using the HM measure is
10 This may not be a reasonable assumption for large companies and industry bellwethers.
17
biased downward. At the same time, a big component of timing skill would show up as
selectivity. Bollen and Busse (2001) show that the results of standard timing tests are sensitive
to the frequency of data used. The major source of the bias is the mis-specification of the
regressor [ ]+mr in the HM equation which should take different values depending on the actual
timing frequency, while the regressions use returns at uniform frequencies (such as monthly).
Goetzmann, et al. (2000) suggest replacing the monthly option value [ ]+mr with accumulated
daily option value when daily data are not readily available. Our simulation (more details at the
end of this section) show that the theta measure is more robust to the difference between timing
frequency and sampling frequency because it does not rely on a regression involving a
potentially unknown regressor, that is, [ ]+mr measured on the “right” frequency.
Another problem is the negative correlation between estimated selectivity and timing in the
context of TM or HM type regression models (Jagannathan and Korajczyk, 1986; Coggin, 1993).
The negative correlation may well arise as an artifact because of the negatively correlated
sampling errors from the two estimates. Our simulation shows that a significant negative
correlation between the two estimated abilities would occur in the TM or HM models (or
between the selectivity measure from one model and the timing measure from the other) even
when the correlation is non-existent. Goetzmann, et al. (2000) and Coggin, et al. (1993) have
similar results. On the other hand, the correlation between theta and the selectivity measures
from standard regression models is close to the truth (which is zero by the construction of the
simulation). Therefore, if one is interested in testing whether the information about individual
securities and overall market movement are largely independent, or whether good stock pickers
tend to be bad timer, it would be a good idea to compose the two measures from two statistical
procedures that have little correlated sampling errors. This can be done, for example, by
calculating the correlation between the theta measure and the alpha measure from other
regression-based models. However, such a method to isolate timing from selectivity still
depends on a reliable estimation of selectivity,11 an issue that falls out of the scope of this paper.
11 Several papers, e.g., Goetzmann, et al. (2000) and Kothari and Warner (2001), point out the difficulty of measuring accurately selectivity using multifactor regression models.
18
2.3.5. Statistical Robustness
Breen, et al. (1986) point out that heteroscedasticity can significantly affect the conclusion of the
HM tests. Jagannathan and Korajczyk (1986) and Goetzmann, et al. (2000) demonstrate the bias
of the HM measure due to skewness. The theta measure, on the other hand, is asymptotically
distribution free. Abrevaya and Jiang (2000) prove that the asymptotic distribution of the U-
statistic is unaffected by heteroscedasticity or skewness. Finally, statistically nU in (9) is the
least variance estimator among all unbiased estimators of θ in (8). The simulation results shown
in Abrevaya and Jiang (2000) demonstrate that the nonparametric test has accurate size even for
small samples and is robust (both the value of the statistic and its standard error) to outliers, non-
normality, and heteroscedasticity which are common in financial data.12
2.4. Simulations
In this section we compare the effectiveness of all three methods using simulations. We simulate
on two sample sizes, 60 and 120 monthly returns. The market returns tmr , are the last five or ten
years of the S&P500 monthly returns as of December 1999. The first two unconditional
moments are calculated from the data to calibrate ( )mrE and ( )mrσ . Assume that both ( )mrE
and ( )mrσ are public knowledge. The fund return data are generated according to (1). Assume
that the manager receives a private signal in the noise-additive form of (3). Her response to the
signal is making the portfolio beta a linear function of the signal as specified in (10).
The quality of the manager’s private information is characterized by ησ , the standard
deviation of tη . We classify the quality of information into three groups: precise ( ( )mrσση 2= ),
medium ( ( )mrσση 4= ), and coarse ( ( )mrσση 8= ). They correspond to the correlation between
12 For example, Bollen and Busse (2001) test the hypothesis that fund returns are normally distributed, and reject normality at the one percent level. They also conjecture that the relative skewness of market and fund returns is driven by the crash of 1987 and other smaller crashes in the sample.
19
the signal and the actual market return ( )1,, +tmt ryρ being 0.44, 0.24, and 0.12 respectively.13
Similarly, we divide the response intensity into three groups: aggressive ( 20.0=λ ), medium
( 10.0=λ ), and conservative ( 05.0=λ ). For each information/response combination we apply
the three methods: the TM method, the HM method and the nonparametric method. We run
1,000 simulations for each design. At medium information quality and ten-year horizon, the
correlation between the nonparametric measure and the TM measure ranges from 0.42 to 0.44;
the same for the nonparametric measure and the HM measure ranges from 0.57 to 0.60. Both
correlations are lower when the manager reacts more aggressively to the signals. The correlation
between the TM and HM measures is high and stable at around 0.98. Quantitative results are
posted in Table 1 from which we can infer the following qualitative features.
First, Panel A of Table 1 reports the nonparametric measure θ̂ and the two γ̂ coefficients
from the TM and HM models. The θ̂ estimates are roughly invariant across different degrees of
responsiveness (aggressiveness) but vary significantly across different levels of information
quality (ability). Further, the standard errors of θ̂ are very robust to different specifications, too.
The two other methods are just the opposite. Both parametric γ̂ coefficients are basically
adjusted to the manager’s aggressiveness, and display little variation with the quality of
information. The intuition behind this separation is as follows:14 the TM and HM coefficients
essentially measure the expected convexity in the funds’ relation to the market return. That
reflects both the probability (related to signal quality) and the magnitude (related to risk
aversion). The nonparametric measure is just the probability, not the magnitude; thus it largely
reflects quality, not risk aversion.
[Table 1 Panel A here]
In Panel B of Table 1, we examine the spurious correlation between the estimated selectivity
ability and timing ability when the true correlation is non-existent ( 0=α by the construction of
the simulation). Since we design the simulation according to the TM model, the correctly
13 Farnsworth, et al. (2001) find that the best performing mutual funds (those in the upper 5%) have performance similar to artificial mutual funds that have the correlation values ranging from 0.24 to 0.32. 14 I am grateful to an anonymous referee for suggesting this interpretation.
20
specified TM regression produces unbiased estimation for selectivity, TMα̂ . We show the
correlation between TMα̂ and the timing measures from the three models. There is a significant
negative relationship between the selectivity and the timing measures from both the TM and HM
models. Coggin, et al. (1993) point out that such a negative correlation is largely an artifact of
negatively correlated sampling errors for the two estimates. The spurious part of the correlation
is difficult to be detached if one uses both selectivity and timing measures from one statistical
procedure or similar procedures (such as TM and HM). If we use θ̂ and TMα̂ as proxies for
timing and selectivity, the spurious correlation largely vanishes, especially at large samples.
[Table 1 Panel B here]
Next we examine the issue of using uniform measuring frequency (such as monthly) when
the timing frequency is unknown (can be daily or weekly). Simulations in Goetamann, et al.
(2000) show that the HM monthly measure severely underestimates the performance of daily
timers. Bollen and Busse (2001) show that standard tests of timing are very sensitive to data
frequency. We obtain the S&P 500 daily data from January 1990 to December 1999 from the
Center for Research in Securities Prices (CRSP). We simulate the daily returns of a daily timer
according to (11) using nine possible combinations of information quality and manager
responsiveness as before. Then we compound the daily return data into monthly returns and
proceed on the estimation with the monthly data only. Results are displayed in Table 1 Panel C.
Comparing them to those in Panel A, we see that the nonparametric test slightly underestimates
the daily timer’s ability when the information quality is high. At medium and low information
quality, the nonparametric test delivers quite accurate results. On the other hand, the magnitude
of timing is reduced by about two-thirds for the TM and the HM methods. The latter result is
consistent with what obtained by Goetamann, et al. (2000) using data simulated from the HM
model. At medium information quality and medium responsiveness, the average θ̂ for monthly
and daily timer are 0.124 and 0.123 respectively, the average TMγ̂ changes from 0.101 to 0.031,
and the average HMγ̂ from 2.093 to 0.572. As we discussed before, the TM and HM measures
largely pick up the magnitude of convexity of fund returns against the market. Linear
regressions produce downward (in magnitude) biased estimates when the regressor is measured
21
with error. On the other hand, the nonparametric measure is about the probability of convexity,
which is less affected by the measurement frequency.
[Table 1 Panel C here]
3. Testing Market Timing of Mutual Funds
3.1. Data
Data in this paper are retrieved from Morningstar Principai Pro Plus for Mutual Funds (1980-
1999) published by Morningstar Incorporated in January 2000 and the CRSP Bias-Free Mutual
Funds Data. Morningstar offers quality data on surviving funds of all categories on the monthly
frequency. To overcome the survivorship bias, we supplemented the data set with the perished
funds from the CRSP data.
For the purpose of this research, we focused on diversified equity funds and domestic sector
funds that specialize in technology. The latter was included because those funds invest heavily
in a sector that had been high-flying and much more volatile than the overall stock market. It
would be interesting to see how well these funds perform in a sector where market timing can be
highly rewarding. Morningstar records separately multiple classes of shares issued by the same
fund out of basically the same portfolio. We use one series of return data (the one that has the
longest record) for each unique portfolio, but add together assets under management for that
fund. We exclude index funds and enhanced index funds whose managers are not expected to
time the market. We also exclude funds that have R2 greater than 0.95 from a regression on a
best-fitted index because these funds are highly suspicious of being “closet indexers.” Finally,
for estimation of meaningful accuracy, we only use funds (survived or perished) that have at
least two full years’ monthly return data within the 1980-1999 window. Altogether there are
1,827 surviving funds and 110 dead funds in the sample. The sample of dead funds are under-
represented because CRSP does not have data at monthly frequency for about half the dead funds
that perished during the 1980s. However, this does not affect the conclusion of our results. If
managers of perished funds do not have better market timing ability than those of live funds,
22
then evidence of no significant market timing ability is likely to hold up in a sample with full
information about perished funds.
All returns are expressed in percentage terms. Morningstar reports monthly returns that are
computed each month by taking the change in monthly net asset value (NAV), reinvesting all
income and capital gains during the month, and dividing by the starting NAV. Unless otherwise
noted, we do not adjust total returns for sales charges (such as front-end or deferred loads and
redemption fees), preferring to give a clearer picture of fund manager’s ability and strategy.
However, the returns do account for management, administrative, 12b-1 fees, and other costs that
are automatically taken out of fund assets. We use the monthly return of three-month T-bills as
the proxy for the riskfree rate fr . To find the proper benchmark for each funds, we regress its
returns on four representative indices: S&P 500 (benchmark for large-cap funds); S&P 400 (for
mid-cap funds); Russell 2000 (for small-cap funds); and NASDAQ Composite (for technology
funds). The index that gives the largest R2 of regression is selected as the benchmark for
measuring the fund’s market timing ability. The average R2 on a best-fitted index is 82.2%, and
the average R2 on the next best-fitted index is 72.4%.
The summary statistics of the mutual funds are reported in Table 2. We classify funds into
different groups according to their stated prospectus objective and best fitted indices. The seven
objective groups are: Small Company, Growth, Equity Income, Growth and Income, Asset
Allocation, Balanced, Specialty—Technology, and Aggressive Growth. We report the number
of funds in each group, the median assets under management, the mean monthly return and the
standard deviation, the mean alpha values from one-factor regressions and the standard
deviation, and the mean alpha values from Fama-French (1993) three-factor regressions and the
standard deviation. All together 26.1% of the live funds and 18.2% of the dead funds beat their
respective indices before taking out their sales charges.
[Table 2 here]
23
3.2. Do Funds Outguess the Market?
Using the nonparametric theta method introduced in the previous section, we are ready to test the
market timing ability of mutual funds. We assume that a fund manager sets a target average beta
according to the fund’s investment objective and policy. This is the unconditional expected beta
of the fund. In an attempt to time the market, the manager will vary the fund’s beta according to
her prediction about future market movement. The theta method lets us see how often the
manager sets a higher beta in a high market return period than in a low market return period. In
Table 3, we report the average market timing θ̂ estimation for all groups of funds, together with
the number of funds that have positive and negative θ̂ , and the number of funds whose θ̂ values
are significantly positive or negative (at 5% and 2.5% significance levels). In computing the
average θ̂ , we use both equal weighting and standard error weighting, that is, assigning a weight
to each fund’s θ̂ that is inversely proportional to its standard error.
[Table 3 Panel A here]
Overall there is no evidence that mutual fund managers possess superior market timing
abilities. The average θ̂ value of all live funds is –1.33, that of the dead funds is –2.62. As
expected, dead funds underperform live funds in market timing performance. According to the
interpretation of theta as defined in (8), the probability that the manager of an average live fund
moves the fund’s exposure to the market in the correct direction is 1.34 percentage points lower
than the probability of a move in the wrong direction. The total numbers of funds with positive
and negative θ̂ values are 719 to 1,108. Out of eight fund groups by stated prospectus
objectives, only the smallest fund group (special-technology) shows up an average θ̂ parameter
above the neutral level zero. All other seven groups have negative average timing coefficients,
and have more funds with θ̂ values significantly (at both 5% and 2.5% significance levels)
different from zero on the negative side than on the positive side. All fund groups by best-fitted
indices have average θ̂ values below zero. Further, the group of funds that is most expected to
time the market—Asset Allocation funds—has an average theta value of –1.8, which is not
indicative of their possessing superior market timing ability. These results are consistent with
24
those in Ferson and Schadt (1996), Becker, et al. (1999), Edelen (1999), and Goetzmann, et al.
(2000) on the tendency for perverse market timing estimates among mutual funds.
The top five percent market timers have θ̂ values above 8.47. Recall from (6) that in
probability terms, θ is equal to ( ) ( )1,1,1,1,1,1,1,1, 21212121|ˆˆPr|ˆˆPr ++++++++ ><−>> tmtmtmtmtmtmtmtm rrrrrrrr ,
the probability that a fund manager makes a right prediction about future market returns in
excess of the probability of a wrong one. Suppose the manager’s private signal takes the noise
additive form of (3). We find by simulation using the empirical distribution of the S&P 500
monthly returns during the sampling period (similar to the one we have done in Section 2.4) that
θ̂ equal to 8.47 corresponds the correlation between the manager’s signal and the future market
return being around 0.20. By the nature of the theta method, this estimation is not affected by
the manger’s risk aversion or the intensity of her reaction to her private signals. It is interesting
that Farnsworth, et al. (2001), through a completely different statistical procedure, find that the
best performing mutual funds (those in the upper 5%) have performance similar to artificial
mutual funds that have correlation values ranging from 0.24 to 0.32.
Since θ̂ is a random variable, with the large sample of mutual funds, we are bound to find
funds with significantly positive or negative θ̂ values even when the truth is 0=θ . Hence we
would like to see whether superior ability exists among fund managers beyond the statistical tail
probability. We plotted in Figure 1 and Figure 2 the cumulative empirical distribution of θ̂ of
all live and dead funds against normal distributions with the same standard deviation but
centered on the neutral value of zero (no ability). The empirical distributions lie mostly above
the reference normal distributions, suggesting that the empirical distributions are first-order
stochastically dominated by their respective reference normal distributions based on the
hypothesis of no ability. We applied the Kleacan-McFadden-McFadden (1991) robust test for
stochastic dominance15 on both empirical distributions of θ̂ and their respective normal
15 The test is based on the following idea: if F does not first-order stochastically dominate G, then
[ ] 0)()(maxmax >−= xGxFd , for all values of x within the support. The test statistic is built on the empirical
analogue d̂ by constructing )(ˆmax xd of F against G at fine grids. The resulting statistic follows a non-standard distribution and its standard error is obtained through an algorithm provided in Kleacan, et al. (1991).
25
distributions with equal variances. The test rejects the hypothesis that the normal distribution
does not first-order stochastically dominate the empirical distribution of live funds at 1%
significance level, and that of dead funds at 5% significance level (the significance level is
higher due to a smaller sample size). This result implies that the distribution of timing ability of
actively managed funds is first-order stochastically dominated by a normal distribution that
would prevail if no superior ability exists on average and manager’s abilities are similarly
dispersed. If an investor does not have superior knowledge about individual managers’ ability,
she would be better off timing wise by choosing an index fund (no timing) than randomly
choosing a fund from the pool of actively managed funds.
[Figure 1 here]
[Figure 2 here]
As a comparison, we list in Table 3 Panel B the TM and HM estimation of market timing for
the same sample. The correlations between the TM and the HM estimates are above 0.90 for all
groups. The correlations between the nonparametric and the TM estimates vary from 0.29 to
0.62, those between the nonparametric and the HM measures range from 0.44 to 0.73. The latter
correlation is higher because, as we discuss in Section 2, the HM measure caters more on the
information quality side of the market timing while the TM measure basically reflects the
intensity of manager’s reaction. The group of Special-Technology funds has positive average
market timing using all three methods. All other fund groups except the Asset Allocation group
have negative average timing parameters using all three methods. The average TMγ̂ value of
Asset Allocation funds is positive but is very close to zero (in a magnitude of 0.13 of its standard
error). The aggregate picture of mutual funds’ market timing performance is similar across
different methods. For the purpose of individual fund evaluation, however, the three methods
contain different information.
[Table 3 Panel B]
It is hard to see why equity fund managers as a whole end up mistiming the market when no
timing can be done easily by passive management. One hypothesis is that the real contribution
of market timing concerns private information, not publicly available information. The
26
conditional performance evaluation literature says that investors will not pay managers to use
readily available public information, nor would they penalize managers for mistiming that is
predictable from the public information. According to the view taken in this literature, any effect
of timing or mistiming stemming from the public information component is spurious timing.
Work by Ferson and Schadt (1996), Ferson and Warther (1996), and Becker, et al. (1999) show
that fund managers do vary beta according to publicly available information, such as past returns,
dividend yields, and term structure. More importantly, their results indicate that conditioning
beta on such public information removes part of the negative value of the TMγ̂ coefficient in a
TM type regression.
We use (12) to analyze mutual funds’ market timing on information that is more
sophisticated than those readily implied by publicly available indicators and lagged variables.
To represent public information, we use a collection of variables that are adopted by previous
studies on conditional market timing (Becker, et al., 1999; Ferson and Khang, 2000). The
variables are: (1) the lagged level of the one-month Treasury bill yield, less its 12-month lagged
moving average; (2) the lagged dividend-to-price ratio for the CRSP value-weighted NYSE and
Amex stock index; (3) the lagged slope of the U.S. Treasury yield curve measured as the
difference between four-year and one-year fixed-maturity bond yields from the CRSP Fama-
Bliss files, and (4) a dummy variable for the month of January. We use four months’ lagged
values for the first three variables. The results are reported in Table 3 Panel C. Comparing it
with Panel A we see that funds’ timing on the unpredicted part of the market returns is almost
identical to their timing on the aggregate market returns, and the overall performance is on the
negative side. Therefore after controlling for the public information, we find no evidence that
mutual funds have market timing ability based on superior information. This result is not
surprising since the lagged variables only explain less than four percent of the variations in
market returns, and the overall picture of timing on gross returns should not be much different
from timing on residual returns. The empirical work by Edelen (1999) attributes the poor timing
performance to the cost of liquidity motivated trading caused by the random in and out flows of
funds, an issue we will also address in the next section. Another explanation is human
27
psychology, if traders are more prone to taking profits than taking losses (Odean, 1998), the mis-
timing phenomenon can result.
[Table 3 Panel C here]
Finally, we want to check that the deviation of the theta values from the neutral level zero is
mainly due to timing instead of to holding particular classes of assets that exhibit timing
characteristics. Jagannathan and Korajczyk (1986) predict that funds investing in small stocks
can show up spurious timing against a market benchmark that consists mainly of big stocks. For
example, they find that an equally weighted stock index shows “timing” relative to a value-
weighted index. This is because small stocks have payoffs resembling that of a call option
related to its underlying assets. This is why we classify mutual funds into groups by best-fitted
indices (from the large-cap S&P 500 to the small-cap Russell 2000) and test market timing of
funds relative their own benchmarks, instead of relative to a uniform market portfolio. To check
whether common factors (such as book-to-market ratio) may interfere with our timing test
results, we apply the same nonparametric test on the Fama-French (1993) factor portfolios
against the market indices that we use for the same sampling period. Altogether there are six
factor-mimicking portfolios sorted by size (small and big) and book-to-market equity (low,
medium, and high). We find none of the six portfolios exhibits timing characteristics relative to
the indices we use at less than 10% significance level. Therefore, our results on market timing
should not be driven by the characteristics of the portfolios that mutual funds hold. However, the
TM and HM regressions show that the small size portfolios sorted by book-to-market show some
spurious timing effect relative to the small-cap index Russell 2000. Both regressions produce
positive and significant (at 5% level) timing coefficients for the Small/Low portfolio, and
negative and significant (at 5% level) timing coefficients for the Small/Medium and Small/High
portfolios. This points out that performance measurement can be sensitive to benchmark
specification.
The overall mis-timing phenomenon is related to the puzzle that the Jensen’s alpha is
predominantly negative among actively managed funds (Jensen, 1972; Gruber, 1996). Work by
Grinblatt and Titman (1989), and Goetzmann, et al. (2000) address the bias that time-varying
28
betas introduce into performance evaluation measures. In the HM model, for example, the
manger sets a higher target beta in an up market than in a down market. Suppose the manager
does not possess any selectivity information, i.e., alpha is zero, but she can perfectly predict the
general market movement. Then the portfolio return as a function of the market return will be a
piece-wise linear function convexly kinked at the origin. Regressions without control for timing
would pick up a positive alpha under such circumstances. That is, timing ability shows up as
selectivity. Symmetrically, negative alpha can be partially attributed to market mis-timing.
3.3. Some Related Questions
In this section we analyze some related questions about market timing by focusing on the live
funds. The issues of interest are: (1) Do experienced managers do better in timing the market?
(2) Is it easier for small funds to time the market? (3) Can the high turnover ratio of actively
managed funds be justified as successful attempts to time the market? And (4) does funds’
market timing impaired by the in- and out-flows of investment money? We report the results in
Table 4. Overall the relationship between the average timing performance and fund
characteristics is weak. It is difficult to predict market timing ability of fund managers from
observable characteristics.
[Table 4 here]
3.3.1. Does Experience Matter?
If established funds are more likely to be matched to experienced managers, we can test upon
fund age to see whether experience contributes to better timing ability. Results are posted in
Table 4 Panel A. Estimated averaged market timing ability increases monotonically with the age
of funds. Young funds (less than five years old) have a weighted average θ̂ of –1.533. The
same estimates for the medium aged funds (between five and ten years old) and old funds (more
than ten years old) are –1.315 and –1.250 respectively. Therefore, older funds are doing better
29
on average than younger funds. However, the survivorship bias, if any, would work in favor of
the older funds.
We can also use manager tenure directly as a proxy for experience. In the data set we only
have the tenure information of the current managers. Accordingly we crop out the turn data that
they are responsible for. We divide all managers into three groups depending on whether their
tenure is less than three years, between three and five years, or five years and more. The results
are shown in Panel B. The least experienced manager group (manager tenure less than three
years) has an average θ̂ of -1.550, those of more experiences groups (manager tenure between
three and five years, and five years or more) are –1.284 and –1.326. And there are
proportionately more out of experienced managers who turn out extraordinary records.
However, the length of manager tenure is endogenous to the mutual fund performance. The
manager who remains in the position for a long time is likely to have produced a reasonably
good record. Further, from the data such differences from experience are not statistically
significant. In general these results show that it is very difficult to outguess the market in the
long run.
3.3.2. Do Small Funds Fare Better?
One common sense has that small funds are in a better position to time the market since it is easy
for them to reshuffle their portfolios in a timely manner without affecting the market. This is
also consistent with the efficient market hypothesis that activities out of (costly) superior
information must be “small” relative to the market.
The size of the funds varies from less than 1 million to 99,184 million dollars in the sample.
The median is 104.75 million dollars. We divide the funds into four groups: Micro (under 20
million dollars), Small (up to 100 million), Big (up to 500 million), and Huge (500 million or
more). Results are shown in Table 4 Panel C. Estimated market timing ability deteriorates
monotonically with fund size. From the smallest to the biggest fund groups, estimated average
θ̂ are –0.629, -1.420, -1.432, and -1.635 respectively. The Micro fund group beats the Huge
fund group at 5% significance. It seems that on average small funds are doing better than their
30
larger counterparts. Especially the percentages of those with theta significantly smaller than zero
suggest a larger proportion of mis-timers among big and huge funds, who drive down their group
average results.
Chevalier and Ellison (1999) document that small mutual funds are managed often by more
experienced managers. Too see whether part of the small fund timing premium is attributed to
manager experience, we make a comparison by a two-way sort on fund size and manager tenure.
It turns out that the difference of timing performance due to fund size is similar across manager
tenure. For manager with less than three years in tenure, the timing performance of Micro/Small
funds and Big/Huge funds are -1.335 versus –1.840. For mangers with five years or more in
tenure, the corresponding estimates are –1.044 and –1.478 respectively.
3.3.3. Is High Turnover Rate Justified as Timing?
The turnover rate of a fund is a proxy for how frequently a manager trades her portfolio. The
inverse of a fund’s turnover rate is the average holding period for a security in that fund. If one
maintains a S&P 500 benchmark portfolio, the average annual turnover rate is about 4-6% for the
past ten years.16 As a comparison, the average turnover rate of actively managed funds investing
in the same market is 92.8%. Assuming turnover rate is positively correlated with the frequency
of timing-oriented trading, we would like to see to what extent does high turnover represent
successful market timing.
1,708 funds out of 1,827 report their annual turnover rates in the Morningstar database. We
divide all reporting funds into three categories according to their average annual turnover rates
during the sampling period: Low (less than 50%), Median (between 50% and 100%), and High
(100% or higher) turnover. Results are shown in Table 4 Panel D. It turns out that the highest
turnover fund group has the worst market timing record with an average theta value of –1.580.
Moderate turnover funds (-1.130) slightly outperform low turnover funds (-1.419). This result is
consistent with Morningstar’s report that mutual funds with annual turnover higher than 100%
16 Source: Vanguard 500 index fund.
31
significantly underperform their lower turnover counterparts. 17 In particular, the group of Asset
Allocation funds usually explicitly market themselves as market timers. Managers of those
funds often use a flexible combination of stocks, bonds, and cash; and shift assets frequently
based on their analyses of market trends. The average annual turnover rate of Asset Allocators is
114.4%, which is higher than the average of all funds. The relationship between average timing
and turnover rate for Asset Allocators is very similar to that of other funds. Results are shown in
Table 4 Panel B. Asset allocators with moderate turnovers have the best timing performance (-
0.878), outperforming that of low turnover asset allocators (-2.016) and high turnover ones (-
2.565).
It seems that moderate turnover represents some market timing while very high turnover
rates cannot be justified as effective timing. Dow and Gorton (1997) consider a model where
portfolio managers trade even though they have no reason to because their clients cannot
distinguish “actively doing nothing” from “simply doing nothing.” Lakonishok, et al. (1991) tell
a story that fund managers dress up their portfolios, and selling off the losers in particular, before
disclosing to the public in order to make the composition look “smart.” Haugen and Lakonishok
(1988) suggest window dressing by professional money managers as a possible explanation of
the “January Effect.” Funds engaging in such window dressing activities are selling to avoid
apologizing for and defending a losing stock’s presence to clients even though the investment
judgment may be to hold (Lakonishok, et al., 1991). As such, the high turnover rate can go with
mis-timing.
3.3.4. Do Investor Flows Affect Market Timing?
One plausible explanation about mutual funds’ unsatisfactory timing performance has been its
open nature (as opposed to closed-end funds). While fund managers try to time the market, there
are investors who attempt at timing the mutual finds. When the market fares well, new money
flows in, and the funds have a higher portion of their portfolios in cash, which results in lower
betas. When the market dips, more investors try to redeem their shares, then the cash reserve
17 Source: Morningstar report September 12, 1997.
32
runs low, which leads to higher betas. Further, without a stream of new money, big redemption
orders can force funds to liquidate shares often at inopportune times, such as selling into a falling
market. From this point of view, market mis-timing of mutual funds constitutes a price that
investors have to pay for the liquidity that they enjoy with open-end funds. Edelen (1999)
documents a negative relation between a fund’s risk-adjusted return and investor flows, and
attributed the negative return performance at open-end mutual funds to the cost of liquidity-
motivated trading.
Such logic implicitly assumes that fund investors can time the market ahead of the fund
managers. Only if investor money flows in prior to market ascendancy or flows out prior to
market descent will hit offset fund managers’ market timing endeavor. Works by Gruber (1996)
and Zheng (1999) show some evidence that funds receiving more money subsequently beat the
market—the “smart money” effect, but in the aggregate such effect is weak. Warther (1995)
documents a positive relation between flows and subsequent returns in the weekly data. Short-
term switchers in and out of funds are more likely to attack on no-load funds where they take the
advantage of the cost-free entry and exit. Hence we can look at the possible difference in timing
between load and no-load funds and infer whether fund managers’ timing ability is impaired by
investor flows. Out of the 1,827 funds, 1,012 are no-load funds. Results in Table 4 Panel E
show that load funds (with an average theta value of -1.215) slightly outperform no-load funds (-
1.467), but overall the timing performance profiles of the two groups of funds are very similar.
Further, from investors’ point of view, index funds also provide the liquidity service the cost of
which has been negligible.18
There has been evidence in the literature that retail investors and institutional investors make
their investment decisions quite differently, both with respect to the timing and to the
information content of their investment. Sias and Starks (1997) find that institutional investors
are more likely to be informed traders by comparing the return autocorrelation of securities and
portfolios dominated by institutional investors with those dominated by individual investors. In
18 Since its inception, for example, the Vanguard Total Stock Market Index Fund has lagged the index return for only 0.3%, the Vanguard 500 Index Fund about 0.2% annually, although they stand ready for investors’ purchase or redemption as open-end funds.
33
addition, if informative signals about market returns contain a marketwise component (i.e., they
are cross-sectionally correlated), then funds mainly open to institutional investors are likely to
have more difficulty timing the market because the informed in- and out-flows of investor money
can offset the funds’ attempt to time the market. To see whether this effect is reflected in data,
we divide funds into retail and institutional funds using $25,000 minimum initial investment as
the cutoff between the two. In Table 4 Panel F we compare the timing skills of the two groups of
funds. There are 1,557 retail funds and 210 institutional funds in the sample. Retail funds have
an average theta –1.330 while that of the institutional funds is –1.822. The result is consistent
with the hypothesis that funds’ market timing is impaired by informed investor money flows, but
the difference is not significant.
4. Conclusion
In this paper we propose a nonparametric test for money managers’ market timing ability and
apply the analysis to a large sample of domestic equity funds that have different benchmark
indices. Theta, the parameter for timing ability, is on average negative among actively managed
equity funds. The distribution of the estimated theta of all equity funds, both live and dead, are
first-order stochastically dominated by the equal variance normal distributions based on the null
hypothesis of no timing ability. Further, the number of funds that display extraordinary timing
ability is smaller than that implied by the right-tail probability of the reference normal
distribution.
Common wisdoms have that manager experience, small fund size and stable investment
money contribute to better timing performance. We find that average timing performance bears
a positive relationship with fund age or management tenure (proxy for manager experience), and
fund load (proxy for the stability of fund flow), and bears a negative relation with fund size.
Further, funds with moderate turnover rates outperform both low and high turnover funds.
However, overall the relation between market timing ability and fund characteristics are very
weak. The differences of the average market timing ability between different fund groups are
small to make any economic significance. Overall market timing ability is fund specific and is
34
very difficult to predict by observable characteristics. This implies that it is difficult for
investors to pick up good timers from the universe of mutual funds
With the overall negative theta values, the beta from a CAPM type regression tends to
underestimate the true systematic risk of a fund and the alpha tends to exaggerate on negative
selectivity. The negative pictures on both timing and selectivity documented by this paper and
previous studies inevitably translate into mutual funds’ total returns. Among actively managed
funds that primarily invest in domestic equities up to December 1999, only about 19.2% of the
funds beat the Vanguard S&P 500 index fund over the past 15 years , 21.8% over the past ten
years, 14.2% over the past five years, and 20.8% over the most recent three years, all before
accounting for sales charges and tax exposure. When an average actively managed fund does not
time the market successfully, investors without superior information about mutual funds would
be a better market timer by holding the relevant index portfolio. It would be imposing to expect
from an average investor the ability to select and to time mutual funds when lack of time or
ability to do so is the reason for an investor to hire a professional money manager in the first
place.
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38
Table 1. Comparison of Three Measures of Market Timing Panel A. Three Market Timing Parameters: What Do They Measure
Returns are simulated according to equation (1) with sample sizes equal to 60 and 120 (months). The quality of information is classified into three groups: precise, medium, and coarse based on the magnitude of ησ . Similarly, the response intensity is sorted by λ into three groups: aggressive, medium, and conservative. The average estimated market timing parameters using the three methods are displayed and their standard deviations are shown in the parentheses.
Nonparametric Treynor-Mazuy Henriksson-Merton
Precise
mrσση 2=
Medium
mrσση 4=
Coarse
mrσση 8=
Precise
mrσση 2=
Medium
mrσση 4=
Coarse
mrσση 8=
Precise
mrσση 2=
Medium
mrσση 4=
Coarse
mrσση 8=
Sample size = 60
Aggressive
20.0=λ
0.204
(0.070)
0.122
(0.072)
0.060
(0.072)
0.204
(0.078)
0.209
(0.157)
0.208
(0.318)
4.422
(1.609)
4.529
(3.152)
4.495
(6.241)
Medium
10.0=λ
0.200
(0.068)
0.120
(0.072)
0.062
(0.072)
0.099
(0.041)
0.105
(0.084)
0.109
(0.165)
2.169
(0.779)
2.277
(1.604)
2.335
(3.138)
Conservative
05.0=λ
0.166
(0.064)
0.106
(0.070)
0.060
(0.072)
0.049
(0.022)
0.047
(0.042)
0.049
(0.078)
1.063
(0.498)
1.073
(0.804)
1.065
(1.467)
Sample size = 120
Aggressive
20.0=λ
0.234
(0.048)
0.128
(0.050)
0.066
(0.052)
0.200
(0.059)
0.198
(0.118)
0.203
(0.242)
4.151
(1.042)
4.123
(2.083)
4.189
(4.249)
Medium
10.0=λ
0.210
(0.048)
0.124
(0.050)
0.062
(0.052)
0.100
(0.029)
0.101
(0.059)
0.093
(1.119)
2.065
(0.516)
2.093
(1.043)
1.966
(2.088)
Conservative
05.0=λ
0.192
(0.044)
0.110
(0.048)
0.066
(0.050)
0.049
(0.015)
0.049
(0.030)
0.050
(0.059)
1.025
(0.268)
1.019
(0.523)
1.035
(1.038)
39
Table 1. Comparison of Three Measures of Market Timing (Continued) Panel B: Correlation between Estimated Selectivity and Timing
Use the same model specifications as in Panel A, we examine the correlation between estimated timing from different models and estimated selectivity ( TMα̂ ) from the TM model (which is unbiased). The first column (Nonparametric-HM) displays the correlation between θ̂ and TMα̂ ; the second column (TM-TM) and the third column (TM-HM) show the correlation between
TMγ̂ and TMα̂ , and that between HMγ̂ and TMα̂ .
Nonparametric-TM TM-TM HM-TM
Precise
mrσση 2=
Medium
mrσση 4=
Coarse
mrσση 8=
Precise
mrσση 2=
Medium
mrσση 4=
Coarse
mrσση 8=
Precise
mrσση 2=
Medium
mrσση 4=
Coarse
mrσση 8=
Sample size = 60
Aggressive
20.0=λ 0.033 -0.031 -0.008 -0.720 -0.688 -0.724 -0.630 -0.650 -0.649
Medium
10.0=λ -0.039 -0.019 0.028 -0.696 -0.726 -0.705 -0.596 -0.650 -0.653
Conservative
05.0=λ -0.093 -0.081 -0.017 -0.626 -0.694 -0.696 -0.595 -0.568 -0.618
Sample size = 120
Aggressive
20.0=λ 0.065 0.035 0.012 -0.721 -0.759 -0.726 -0.611 -0.653 -0.637
Medium
10.0=λ 0.013 0.002 0.024 -0.688 -0.734 -0.721 -0.630 -0.613 -0.622
Conservative
05.0=λ -0.047 -0.041 0.026 -0.639 -0.721 -0.711 -0.533 -0.625 -0.614
40
Table 1. Comparison of Three Measures of Market Timing (Continued) Panel C: Data Frequency: How Robust Is Monthly Measurement of Daily Timers?
We CRSP S&P500 daily return data for the January 1990 to December 1999 as the market return, and simulate the return data of a daily timer using the TM model as in Panel A. All return data are then compounded into monthly returns on which we perform the timing test using all three methods. For each case 1,000 simulations are tried, and the average estimated parameters are displayed in the table with their standard errors shown in the parentheses.
Nonparametric Treynor-Mazuy Henriksson-Merton
Precise
mrσση 2=
Medium
mrσση 4=
Coarse
mrσση 8=
Precise
mrσση 2=
Medium
mrσση 4=
Coarse
mrσση 8=
Precise
mrσση 2=
Medium
mrσση 4=
Coarse
mrσση 8=
Aggressive
20.0=λ
0.170
(0.039)
0.125
(0.039)
0.078
(0.039)
0.065
(0.018)
0.064
(0.021)
0.065
(0.032)
1.204
(0.320)
1.202
(0.381)
1.201
(0.578)
Medium
10.0=λ
0.169
(0.038)
0.123
(0.038)
0.073
(0.039)
0.031
(0.009)
0.031
(0.010)
0.031
(0.016)
0.577
(0.151)
0.572
(0.187)
0.569
(0.282)
Conservative
05.0=λ
0.167
(0.039)
0.124
(0.039)
0.075
(0.039)
0.015
(0.004)
0.015
(0.005)
0.015
(0.008)
0.283
(0.075)
0.283
(0.091)
0.274
(0.138)
41
Table 2. Summary Statistics of Mutual Funds
There are altogether 1,827 live funds and 110 dead ones in the sample. They are actively managed domestic equity funds that have at least two years’ monthly return data during the sampling period from January 1980 to December 1999. N is the number of funds in the group. Median Assets are expressed in term of million dollars. Mean and Std are the sample mean and standard deviation of monthly returns. 1Fα is the mean alpha value from one-factor regressions on the best-fitted indices, and Std( 1Fα ) is its sample standard deviation. 3Fα is the mean alpha value from the Fama-French (1993) three-factor regressions, and Std( 3Fα ) is its sample standard deviation.
Fund Group N Median Assets
($MM) Mean Std
1Fα Std( 1Fα ) 3Fα Std( 3Fα )
By Funds Prospectus Objective
Small company 333 139.55 1.545 6.042 0.095 0.692 0.079 0.654
Growth 722 187.60 1.744 5.291 -0.040 0.524 0.007 0.539
Equity income 94 165.40 1.200 3.625 -0.195 0.290 -0.198 0.268
Growth and income 256 212.30 1.374 4.154 -0.189 0.301 -0.184 0.281
Balanced 188 118.40 1.069 2.760 -0.118 0.327 -0.119 0.297
Asset allocation 120 108.80 1.019 2.871 -0.111 0.234 -0.108 0.202
Specialty-technology 39 724.40 3.890 9.191 0.711 1.025 1.453 1.214
Aggressive growth 75 119.15 2.063 6.758 -0.037 0.564 0.189 0.524
By Best-Fitted Indices
S&P 500 803 201.85 1.376 3.861 -0.177 0.283 -0.137 0.238
42
Fund Group N Median Assets
($MM) Mean Std
1Fα Std( 1Fα ) 3Fα Std( 3Fα )
S&P 400 240 106.90 1.178 4.431 -0.156 0.433 -0.254 0.378
Russell 2000 422 101.70 1.390 5.567 0.257 0.711 -0.014 0.619
NASDAQ Composite 362 278.90 2.469 6.776 -0.010 0.619 0.491 0.780
Dead funds 110 - 1.033 4.874 -0.392 0.532 -0.420 0.516
43
Table 3. Market Timing of Mutual Funds Panel A: The Nonparametric Method
This table reports the nonparametric estimation of mutual funds’ market timing abilities. The second column lists the equally weighted average θ̂ of all funds within the group, its standard error is reported in the parenthesis. The weighted average θ̂ (and its standard error in the parenthesis) reported in the third column uses weights that are inversely proportional to each estimation standard error. The fourth column shows the number of funds that have θ̂ above (below) zero. The fifth and sixth columns report the percentage of funds in each group that have θ̂ above (below) zero at 5% and 2.5% significance level.
Fund Group Mean θ̂ Weighted
Average θ̂
No. of θ̂ >0
(θ̂ <0)
% of θ̂ >0
(θ̂ <0) at 5%
% of θ̂ >0
(θ̂ <0) at 2.5%
By Funds Prospectus Objective
Small company -1.766
(0.356)
-1.389
(0.289)
133
(200)
2.40
(9.31)
0.60
(4.81)
Growth -0.725
(0.245)
-0.654
(0.184)
320
(402)
4.57
(5.96)
1.80
(3.46)
Equity income -2.658
(0.592)
-3.226
(0.448)
21
(73)
2.13
(18.1)
1.06
(13.8)
Growth and income -1.549 (0.357)
-1.764 (0.266)
90 (166)
3.52 (10.94)
1.95 (5.47)
Balanced -1.924
(0.442)
-2.245
(0.331)
61
(127)
1.06
(12.23)
1.06
(8.51)
Asset allocation -1.896
(0.634)
-1.775
(0.501)
45
(75)
0.83
(5.00)
0.00
(3.33)
Specialty-technology 2.633
(1.110)
2.494
(0.856)
28
(11)
7.69
(2.56)
5.13
(0.00)
Aggressive growth -2.393
(0.695)
-2.368
(0.541)
21
(54)
1.33
(10.67)
0.00
(5.33)
By Best-Fitted Indices
S&P 500 -0.163
(0.219)
-0.733
(0.159)
360
(443)
4.86
(8.22)
2.12
(5.11)
44
Fund Group Mean θ̂ Weighted
Average θ̂
No. of θ̂ >0
(θ̂ <0)
% of θ̂ >0
(θ̂ <0) at 5%
% of θ̂ >0
(θ̂ <0) at 2.5%
S&P 400 -4.368
(0.417)
-3.725
(0.313)
50
(190)
0.83
(16.3)
0.83
(10.83)
Russell 2000 -0.699
(0.319)
-0.294
(0.259)
203
(219)
2.61
(3.79)
0.47
(1.90)
NASDAQ Composite -2.624
(0.341)
-2.444
(0.270)
106
(256)
1.93
(9.94)
1.10
(4.70)
Dead funds -2.621
(0.672)
-2.932
(0.583)
41
(69)
3.63
(19.03)
1.82
(12.73)
45
Table 3. Market Timing of Mutual Funds (Continued) Panel B: The TM and HM methods
This table lists the market timing parameters from the TM and HM methods. Weighted average TMγ̂ and HMγ̂ use the inverse standard error weighting method. Their standard errors are White (1980) heteroscedasticity consistent. Corr.( θγ ˆˆ ,TM ) and Corr.( θγ ˆˆ ,HM ) are the coefficients of correlation between the TM/HM parameters and the nonparametric θ̂ values.
TM HM
Fund Group Weighted
Average TMγ̂
(10-3)
Std. Error
(10-3) Corr.( θγ ˆˆ ,TM )
Weighted
Average HMγ̂
(10-2)
Std. Error
(10-2) Corr.( θγ ˆˆ ,HM )
By Funds Prospectus Objective
Small company -3.362 0.233 0.617 -7.473 0.940 0.746
Growth -3.496 0.138 0.465 -7.134 0.510 0.601
Equity income -3.874 0.350 0.522 -9.416 1.108 0.744
Growth and income -3.266 0.206 0.509 -7.166 0.655 0.635
Balanced -0.514 0.199 0.412 -2.371 0.622 0.557
Asset allocation 0.031 0.239 0.288 -0.550 0.776 0.438
Specialty-technology 3.374 0.664 0.545 15.568 2.892 0.679
Aggressive growth -3.182 0.429 0.429 -10.944 1.776 0.570
By Best-Fitted Indices
S&P 500 -1.515 0.118 0.334 -2.870 0.358 0.491
S&P 400 -6.322 0.237 0.459 -18.105 0.835 0.660
Russell 2000 -2.804 0.199 0.567 -4.457 0.812 0.659
46
TM HM
Fund Group Weighted
Average TMγ̂
(10-3)
Std. Error
(10-3) Corr.( θγ ˆˆ ,TM )
Weighted
Average HMγ̂
(10-2)
Std. Error
(10-2) Corr.( θγ ˆˆ ,HM )
NASDAQ Composite -2.689 0.168 0.606 -7.172 0.746 0.699
Dead funds -4.104 0.487 0.549 -9.788 1.827 0.645
47
Table 3. Market Timing of Mutual Funds (Continued) Panel C: Conditional Market Timing
In this table θ̂ is calculated using equation (12), conditional on the residual market returns instead of on market returns. The residual market returns are the residuals of each index returns from a regression on lagged instrumental variables, which include the detrended TB yield, the dividend-to-price ratio for the CRSP value-weighted NYSE and Amex stock index, the slope of the U.S. Treasury yield curve measured as the difference between four-year and one-year fixed-maturity bond yields, and a dummy variable for the month of January.
Fund Group Mean θ̂ Weighted
Average θ̂
No. of θ̂ >0
(θ̂ <0)
% of θ̂ >0
(θ̂ <0) at 5%
% of θ̂ >0
(θ̂ <0) at 2.5%
By Funds Prospectus Objective
Small company -1.740
(0.355)
-1.369
(0.289)
135
(198)
1.80
(9.61)
0.60
(4.20)
Growth -0.718
(0.246)
-0.689
(0.184)
319
(403)
4.02
(6.51)
1.94
(3.46)
Equity income -2.797
(0.599)
-3.359
(0.449)
20
(74)
1.06
(20.21)
1.06
(14.89)
Growth and income -1.653
(0.356)
-1.936
(0.265)
90
(166)
3.52
(13.28)
1.56
(5.86)
Balanced -2.070
(0.445)
-2.426
(0.332)
58
(130)
1.06
(13.83)
0.53
(10.11)
Asset allocation -1.846
(0.636)
-1.748
(0.500)
46
(74)
0.83
(5.83)
0.00
(3.33)
Specialty-technology 2.544
(1.105)
2.415
(0.850)
28
(11)
12.82
(2.56)
7.69
(2.56)
Aggressive growth -2.284
(0.689)
-2.284
(0.534)
21
(54)
1.33
(10.67)
0.00
(8.00)
By Best-Fitted Indices
S&P 500 -0.272
(0.220)
-0.887
(0.159)
353
(450)
4.11
(9.84)
1.87
(5.60)
48
Fund Group Mean θ̂ Weighted
Average θ̂
No. of θ̂ >0
(θ̂ <0)
% of θ̂ >0
(θ̂ <0) at 5%
% of θ̂ >0
(θ̂ <0) at 2.5%
S&P 400 -4.345
(0.416)
-3.708
(0.313)
53
(187)
1.25
(16.35)
0.83
(11.25)
Russell 2000 -0.653
(0.319)
-0.258
(0.259)
204
(218)
1.89
(4.50)
0.71
(1.66)
NASDAQ Composite -2.567
(0.339)
-2.441
(0.268)
107
(255)
2.76
(10.22)
1.38
(5.25)
Dead funds -2.401
(0.664)
-2.626
(0.581)
44
(66)
4.55
(19.04)
1.82
(11.82)
49
Table 4. Market Timing: Related Issues In this table we compare the timing performance of mutual funds sorted by fund characteristics. In each row we report the number of funds, the inverse standard error weighted average θ̂ and its standard error, and the percentage of funds that outperform or underperform the market at 5% and 2.5% significance level. Fund Age and Manager Tenure are proxies for manager experience. The median age and manger tenure are 5 and 4 years respectively. The median fund size is 104.75 million dollars. The turnover ratio is the average annual rate during the sampling period. The median turnover ratio is 69.0%. Load charges and minimum initial purchase are proxies for fund flow stability. Load Charges are the sum of front and deferred loads. 55.3% of the funds in the sample are no-load funds. 54.1% of the funds have minimum initial purchase of 1,000 dollars or less. 11.5% of the funds have minimum initial purchase of 25,000 dollars or more.
Fund Characteristics
No. of Funds
Weighted Average θ̂
Std. Error
% of θ̂ > 0
at 5%
% of θ̂ < 0
at 5%
% of θ̂ > 0
at 2.5%
% of θ̂ < 0
at 2.5%
Panel A: Fund Age (years since inception)
< 5 768 -1.533 0.282 2.53 11.09 0.97 7.19
≥ 5 and < 10 545 -1.315 0.206 4.77 11.38 2.20 6.97
≥ 10 514 -1.250 0.137 2.60 4.94 1.04 2.21
Panel B: Manager Tenure (years)
< 3 386 -1.550 0.251 3.89 9.84 1.81 6.73
≥ 3 and < 5 741 -1.284 0.221 2.43 6.07 0.67 2.97
≥ 5 690 -1.326 0.150 3.77 10.72 1.88 6.38
Panel C: Fund Size ($mm)
< 20 362 -0.629 0.331 4.70 5.24 2.49 3.31
≥ 20 and < 100 528 -1.420 0.239 2.27 7.95 0.95 4.92
≥ 100 and < 500 515 -1.432 0.207 3.50 9.51 1.55 5.63
≥ 500 420 -1.635 0.179 2.86 11.19 0.71 5.95
Panel D: Turnover Ratio (annual %)
All funds
< 50 522 -1.419 0.197 3.43 8.32 2.29 5.06
≥ 50 and < 100 613 -1.130 0.184 4.02 8.55 1.47 4.73
> 100 573 -1.580 0.210 2.44 10.15 0.52 6.13
50
Fund Characteristics
No. of Funds
Weighted Average θ̂
Std. Error
% of θ̂ > 0
at 5%
% of θ̂ < 0
at 5%
% of θ̂ > 0
at 2.5%
% of θ̂ < 0
at 2.5%
Asset Allocation funds only
< 50 42 -2.016 0.805 2.38 4.76 0.00 4.76
≥ 50 and < 100 26 -0.878 0.974 0.00 0.00 0.00 0.00
> 100 44 -2.565 0.868 0.00 9.09 0.00 4.55
Panel E: Load Charges
No-Load Funds 1012 -1.467 0.154 3.06 8.50 0.99 5.43
Load Funds 815 -1.215 0.166 3.44 8.71 1.84 4.54
Panel F: Minimum Initial Purchase ($ 1,000)
< 25 1557 -1.330 0.121 3.21 8.41 1.54 4.95
≥ 25 210 -1.822 0.392 2.86 10.95 0.48 7.14
51
Figure 1. Distribution of Market Timing of Live Funds
To check whether superior ability exists among fund managers beyond the statistical tail probability, we plot in this graph the empirical cumulative distribution of live funds’ θ̂ values against a reference normal distribution that has the same standard deviation but centers on zero (no ability). The empirical distribution lies all the way above the normal distribution, suggesting that the distribution of live mutual funds’ market timing ability is first-order stochastically dominated (FOSD) by a comparable distribution. The FOSD hypothesis passed the Kleacan-McFadden-McFadden (1991) test at 1% significance level.
-30 -20 -10 0 10 20 300
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
θ
cum
ulat
ive p
roba
bilit
y
normal distributionlive funds
52
Figure 2. Distribution of Market Timing of Dead Funds
In this graph we plot the empirical cumulative distribution of dead funds’ θ̂ values against a reference normal distribution that has the same standard deviation but centers on zero (no ability). The empirical distribution lies mostly above the normal distribution, suggesting that the distribution of dead mutual funds’ market timing ability is first-order stochastically dominated by a comparable distribution. The FOSD hypothesis passed the Kleacan-McFadden-McFadden (1991) test at 5% significance level.
-30 -20 -10 0 10 20 300
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
θ
cum
ulat
ive p
roba
bilit
y
normal dis tributiondead funds