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A nonparametric test of market timing

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In this paper, we proposea nonparametric test for market timing ability and apply the analysis to a large sample of mutual funds that have different benchmark indices. The test statistic is formed to proxy the probability thatamanager loads on more market risk when the market return is relatively high. The test (i) only requires the ex post returns of funds and their benchmark portfolios; (ii) separates the quality of timing informationa money manager possesses from the aggressiveness with which she reacts to such information; and (iii) is robust to different information and incentive structures, as well as to underlying distributions. Overall, we do not find superior timing ability among actively managed domestic equity funds for the period of 1980-1999. Further, it is difficult to predict funds'timing performance from their observable characteristics.
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Content Preview
Journal of Empirical Finance 10 (2003) 399 – 425
www.elsevier.com/locate/econbase
A nonparametric test of market timing
Wei Jiang*
Finance and Economics Division, Columbia Business School, 3022 Broadway, New York, NY 10027, USA
Abstract
In this paper, we propose a nonparametric test for market timing ability and apply the analysis to
a large sample of mutual funds that have different benchmark indices. The test statistic is formed to
proxy the probability that a manager loads on more market risk when the market return is relatively
high. The test (i) only requires the ex post returns of funds and their benchmark portfolios; (ii)
separates the quality of timing information a money manager possesses from the aggressiveness with
which she reacts to such information; and (iii) is robust to different information and incentive
structures, as well as to underlying distributions. Overall, we do not find superior timing ability
among actively managed domestic equity funds for the period of 1980 – 1999. Further, it is difficult
to predict funds’ timing performance from their observable characteristics.
D 2003 Elsevier Science B.V. All rights reserved.
JEL classification: G1; C1
Keywords: Mutual funds; Market timing; Nonparametric test; U-statistics
1. Introduction
Based on the theory of market efficiency with costly information, there has been ample
research work on measuring professional money managers’ performance. The emphasis
has been on one of the two basic abilities: securities selectivity and market timing. The
former tests whether a fund manager’s portfolio outperforms the benchmark portfolio in
risk-adjusted terms (Jensen, 1972; Gruber, 1996; Ferson and Schadt, 1996; Kothari and
Warner, in press). The latter tests whether a fund manager can out-guess the market by
moving in and out of the market (Treynor and Mazuy, 1966; Henriksson and Merton,
1981; Admati et al., 1986; Bollen and Busse, 2001).
* Tel.: +1-212-854-9679; fax: +1-212-316-9180.
E-mail address: wj2006@columbia.edu (W. Jiang).
0927-5398/03/$ - see front matter D 2003 Elsevier Science B.V. All rights reserved.
doi:10.1016/S0927-5398(02)00065-8

400
W. Jiang / Journal of Empirical Finance 10 (2003) 399–425
Measures of market timing have fallen into one of the two categories: portfolio- and
return-based methods. The former tests whether money managers successfully allocate
monies among different classes of assets (e.g., equity versus cash) to capitalize on market
ascendancy and/or to avoid downturns. If we could observe the portfolio composition of
mutual funds at the same frequency as we observe the returns, we could infer funds’
market timing by testing whether the portfolio holdings anticipate market moves. Graham
and Harvey (1996) empirically test market timing using investment newsletters’ asset
allocation recommendations.
Holdings, however, are often not available (especially in academic studies), which
limits the market timing analysis to the returns of funds and benchmark portfolios only.
The return-based method, on the other hand, only requires data on the ex post returns of
funds and the relevant market indices. The two most popular methods along this line 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 CAPM or
multi-factor analysis of securities and portfolios to mutual funds. There has been
controversy over using such a metric to evaluate mutual fund performance. The static
a – b analysis misses the diversified and dynamic aspects of managed portfolios (Admati et
al., 1986; Ferson and Schadt, 1996; Becker et al., 1999; Ferson and Khang, 2001). A fund
manager may vary her portfolio’s exposure to the market or other risk factors, or alter the
fund’s correlation to the benchmark index in response to the incentive she faces (Chevalier
and Ellison, 1997). Consequently, the systematic part of the fund’s risk can be mis-
estimated when its manager is trying to time the market, and existing measures may
incorrectly attribute performance to funds, or fail to attribute superior returns to an
informed manager (Grinblatt and Titman, 1989). To address these issues, there has been a
great deal of study on capturing the effect of conditioning information on timing
performance measures (Ferson and Schadt, 1996; Becker et al., 1999; Ferson and Khang,
2001), controlling for spurious timing arising from not holding the benchmark
(Jagannathan and Korazjczyk, 1986; Breen et al., 1986), decomposing abnormal perform-
ance into selectivity and timing (Admati et al., 1986; Grinblatt and Titman, 1989), and
minimizing 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 a’s or b’s. The test is based on
the simple idea that a successful market timer’s fund rises significantly when the market
rises and falls slightly when the market drops. The nonparametric test has the following
properties. First, it is easy to implement because it only requires the ex post returns of
funds and their benchmark portfolios. Second, the test statistic is not affected by the
manager’s risk aversion because it separates the quality of timing information a fund
manager possesses from the aggressiveness of the reaction to such information. Third, the
test is more robust to different information and incentive structures, as well as to timing
frequencies and underlying distributions, than existing timing measures. Finally, the
method developed in this paper is 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).

W. Jiang / Journal of Empirical Finance 10 (2003) 399–425
401
The rest of the paper is organized as follows: Section 2 presents the nonparametric
statistic of market timing and compares it with the TM and HM methods. Section 3 applies
the method to a data set of mutual funds with different benchmark indices. Section 4
concludes.
2. Model
2.1. Market timing test statistics
We assume that a money manager’s timing information is independent of her
information about individual securities. This is a fairly standard assumption in the
performance measurement literature (e.g., see Admati et al., 1986; Grinblatt and Titman,
1989).1 With independent selectivity and timing, we have the following market model of
fund returns (all returns are expressed in excess of the risk-free rate):
ri;tþ1 ¼ ai þ bi;trm;tþ1 þ ei;tþ1;
ð1Þ
where i is the subscript for individual funds throughout this paper. bi,t is a random variable
adapted to the information available to the manager at time t and rm represents the return of
the relevant market (which can be a subset of the total market) in which the mutual fund
invests. It is the benchmark portfolio return against which the fund is evaluated. In the
simplest case, a market timer decides on bt at date t and invests bt percent in the market
portfolio and the rest in bonds until date t + 1. Eq. (1) represents the return process from
such a timing strategy.
For a triplet {rm,t , rm,t , rm,t } sampled from any three periods such that rm,t < rm,t <
1
2
3
1
2
rm,t , an informed manager should, on average, maintain a higher average b in the trm,t ,
3
2
rm,t b range than in the trm,t , rm,t b range. The b estimates for both ranges (given two
3
1
2
observations for each range) are (ri,t À ri,t )/(rm,t À rm,t ) and (ri,t À ri,t )/(rm,t À rm,t ),
2
1
2
1
3
2
3
2
respectively. Accordingly, we propose using the probability


r
À r
r
À r
h ¼
i;t
i;t
i;t
i;t
2Pr
3
2
>
2
1
À 1;
ð2Þ
rm;t À r
r
À r
3
m;t2
m;t2
m;t1
as a statistic of market timing ability. We motivate this market timing measure as follows.
A manager’s timing ability is determined by the relevance and accuracy of her
information. Let rˆm,t + 1 = E(rm,t + 1 | It) be the manager’s prediction about the next-period
market return based on It, her information set (both public and private) at time t. If It is not
informative at all, then the conditional distribution equals the unconditional one, that is,
f(rm,t + 1jrˆm,t + 1) = f(rˆm,t + 1), where f(Á) stands for the probability density function. In this
case, the conditional forecast equals the unconditional one and the manager would not be
able to tell when the market will enjoy relatively high returns. More specifically, for two
1
Correlated timing and selectivity information would in general cause technical difficulties in separating
abnormal performance due to timing from that due to selectivity. For a detailed discussion, see Grinblatt and
Titman (1989).

402
W. Jiang / Journal of Empirical Finance 10 (2003) 399–425
periods, t1 p t2, the following parameter takes the value of zero in the absence of timing
information2:
m ¼ Prðˆrm;t1þ1 > ˆrm;t2þ1 j rm;t1þ1 > rm;t2þ1Þ À Prðˆrm;t1þ1 < ˆrm;t2þ1 j rm;t1þ1 > rm;t2þ1Þ
¼ 2Prðˆrm;t1þ1 > ˆrm;t2þ1 j rm;t1þ1 > rm;t2þ1Þ À 1:
ð3Þ
At the other extreme, if the forecast is always perfect, that is, rˆm,t + 1 u rm,t + 1, then m attains
its upper bound of one. Symmetrically, m = À 1 represents perfectly perverse market
timing. Therefore, the value of ma[ À 1,1] indicates the fund manager’s market timing
ability: the more accurate the information It the higher the value of m. The next step is to
find a relationship between the manager’s forecast (rˆm,t + 1) and her action (bt) so that h
defined in Eq. (2) is a valid proxy of m.
Suppose the manager receives a favorable signal that leads to a high rˆm,t + 1. How
much market exposure (bt) the manager would like to take apparently depends on two
factors: the precision of the forecast and the aggressiveness with which she uses her own
information. The first part concerns natural ability, while the latter can be affected by the
manager’s risk aversion. Grinblatt and Titman (1989) show that an investor who has
independent timing and selectivity information and non-increasing absolute risk aver-
sion3 would increase bt in Eq. (1) as information about the market becomes more
favorable, or
Bbt
B
> 0. Combining
Bbt > 0 with Eq. (3), we see that the following
ˆ
rm;tþ1
Bˆrm;tþ1
probability is greater than zero if and only if the manager possesses superior timing
information:
2Prðbt > b Arm;t
1
t2
1 þ1 > rm;t2 þ1 Þ À 1:
ð4Þ
From the analysis above, therefore, superior timing ability m>0 (defined in Eq. (2))
translates into h>0 (defined in Eq. (2)) if a manager loads on more market risk when signals
about future market returns are more favorable. Eq. (2) is testable because the sample
analogue of h can be formed. Under the null hypothesis of no timing ability, the b has no
correlation with the market return, in which case the statistic h assumes the neutral value of
zero. Intuitively, an uninformed manager would move the market exposure of her portfolio
in the right direction as often as she would do in the wrong direction. Note that a triplet {ri,t ,1
ri,t , ri,t } is convex vis-a`-vis the market return if and only if (ri,t À ri,t )/(rm,t À rm,t )>
2
3
3
2
3
2
(ri,t À ri,t )/(rm,t À rm,t ). Therefore, h measures the probability that the fund returns bear a
2
1
2
1
convex relation with the market returns in excess of that of a concave relation.
2
The HM method tests whether the probability Prðˆrm;tþ1 > 0 j rm;tþ1 > 0Þ þ Prðˆrm;tþ1 < 0 j rm;tþ1 < 0Þis
greater than one. When the HM model is the correct specification, our measure picks up the manager’s timing
ability among a subset of triplets where at least two observations of market returns are of opposite signs. In
general, our measure allows the manager to make finer forecasts and uses more information in the return data by
looking at all triplets frm;t1þ1; rm;t2þ1; rm;t3þ1g for t1 6¼ t2 6¼ t3:
3
Non-increasing absolute risk aversion requires that the investor’s risk aversion measured byÀ u00ðwÞ be non-
u0ðwÞ
increasing in the wealth level w. Commonly used utility functions, such as the exponential, power, and log
utilities, all meet this criterion.

W. Jiang / Journal of Empirical Finance 10 (2003) 399–425
403
The sample analogue to h becomes a natural candidate as a statistic. It is a U-statistic
with kernel of order three:
 À1
X


ˆ
n
r
À r
r
À r
h
i;t3
i;t2
i;t2
i;t1
n ¼
sign
>
;
ð5Þ
3
r
À r
r
À r
r
m;t
m;t
m;t
m;t
m;t <r
<r
3
2
2
1
1
m;t2
m;t3
where n is the sample size and sign(Á) is the sign function that assumes value 1 ( À 1) if the
argument is positive (negative) and equals zero if the argument is zero. By the property of
pffiffiffi
U-statistics, hˆn is a
n-consistent and asymptotically normal estimator for h (Serfling,
pffiffiffi
d
1980; Abrevaya and Jiang, 2001). That is,
nð ˆ
hn À hÞ ! N ð0; r2ˆ Þ when n ! l. Further
hn
hˆn, as defined in Eq. (5), is the least variance estimator among all unbiased estimators for
the population coefficient h.
Abrevaya and Jiang (2001) provide the asymptotic distribution of the hˆn statistic. Let
zt u (rt , rm,t ), j={1, 2, 3}, and denote the kernel function of hˆn by
j
j
j


ri;t À ri;t
rt À ri;t
hðz
3
2
2
1
t ; z ; z Þ ¼ sign
>
j r
< r
< r
:
1
t2
t3
m;t
m;t
m;t
r
1
2
3
m;t À r
r
À r
3
m;t2
m;t2
m;t1
A consistent estimator of the standard error of hˆn is derived in Abrevaya and Jiang (2001):
 
!2
9 X
n
À1
n
X
ˆ
r2ˆ ¼
hðz ; z ; z Þ À ˆ
h
:
ð6Þ
h
t1
t2
t3
n
n
n
2
t1¼1
t2;t3
Simulation results in Abrevaya and Jiang (2001) show that the size of the test is very
accurate4 if we use the bootstrap method in standard error estimation for sample sizes
below 50 and use the asymptotic formula for larger sample sizes.
2.2. Properties
The new market timing measure (h) has a ready interpretation as the probability that a
fund manager takes relatively more systematic risk in a higher return period than in a low
return one. Since the seminal work of Treynor and Mazuy (1966) and Henriksson and
Merton (1981), there has been much work extending these measures in order to relax their
restrictive behavioral and distribution assumptions while retaining their intuitive appeal,
ease of implementation, and minimal data requirements.5 In this subsection, we discuss the
4
Using 1000 simulations, rejection rates at 5% significance level are between 4.5% and 5.5% for all error
specifications.
5
Goetzmann et al. (2000) had an excellent review of the research that addresses the limitation of the TM and
HM timing measures.

404
W. Jiang / Journal of Empirical Finance 10 (2003) 399–425
contribution of the nonparametric timing measure on these grounds and point out its
limitations. The fund subscript i will henceforth be omitted where there is no confusion.
2.2.1. Information structure and behavioral assumptions
The nonparametric measure allows a more flexible specification of a fund manager’s
response to information. We require bt to be a non-decreasing function of rˆm,t + 1, that is,
the manager sets a higher b for the fund when her forecast of the next-period market return
is more favorable. Grinblatt and Titman (1989) show that sufficient conditions for this to
hold are i.i.d. random noise in market returns, independent selectivity and timing
information, and non-increasing absolute risk aversion. This requirement is less stringent
than those of the TM and HM measures, which require linear or binary response function
by the manager. The i.i.d. assumption, however, rules out heteroscedasticity in returns and
hence volatility timing by money managers. We will relax this assumption and discuss the
possible impact of volatility timing in a later section.
In general, a fund manager’s reaction to information depends on her risk aversion
(which could be affected by the incentive she faces) as well as her natural ability. The
functional form of such a response is difficult to specify without being somewhat arbitrary.
For example, the TM measure uses the following quadratic regression of a fund’s returns:
rtþ1 ¼ a þ brm;tþ1 þ c½rm;tþ1Š2 þ etþ1;
ð7Þ
where superior timing shows up in a positive coefficient ci. As analyzed in Admati et al.
(1986), the return process of Eq. (7) comes out of a linear response by the fund manager in
the form of:
bt ¼ ¯b þ k½ˆrm;tþ1 À EðrmÞŠ:
ð8Þ
The linear response function 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 she faces instead of the fund’s 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 (Admati and Pfleiderer, 1997), option
compensation (Carpenter, 2000), or non-linear flow-to-performance responses by fund
investors (Chevalier and Ellison, 1997).
The HM measure, on the other hand, assumes that a manager takes only two b values—
a high b when she expects the market return to exceed the risk-free rate and a low b when
otherwise. The binary-b strategy results in the following return model:
rtþ1 ¼ a þ brm;tþ1 þ c½rm;tþ1Šþ þ etþ1;
ð9Þ
where [rm,t + 1]+ = max(0, rm,t + 1). The coefficient on [rm,t + 1]+ represents the value added
by effective timing that is equivalent to a call option on the market portfolio where the
exercise price equals the risk-free rate. Such a specification, while intuitive, is highly
restrictive as well. After all, there is no reason to expect a uniform reaction to information
by all fund managers. In comparison, the nonparametric measure offers more flexibility. It

W. Jiang / Journal of Empirical Finance 10 (2003) 399–425
405
only requires the reaction function to be non-decreasing in the manager’s forecast of
market return.
When a linear reaction function is the correct specification, the nonparametric measure
gives the same result as the TM measure. In the TM model, the manager’s private signal,
yt, is generated according to
yt ¼ rm;tþ1 þ gt;
ð10Þ
where gt is a normal random variable that is independent of rm,t + 1 and is i.i.d. across time.
Timing ability is represented by the inverse of the variance of the noise term. For any two
gt and gt from two periods t1p t2, we can calculate Eq. (3) as follows:
1
2
m ¼ 2Prðgt À g < rm;t
2
t1
1 þ1 À rm;t2 þ1 j rm;t1 þ1 > rm;t2 þ1 Š À 1

!
Ar
¼
m;t
2U
1 þ1 À rm;t2 þ1 A
pffiffiffi
À 1;
ð11Þ
2rg
where U(Á) stands for the cumulative probability function of the standard normal
distribution. It is easy to see that m is monotonically increasing in 1/rg, the precision of
the private signal. An infinitely noisy signal (rg = l) leads to m = 0 (no timing) and a
perfect signal (rg = 0) implies m = 1 (perfect timing). Therefore, the nonparametric measure
will identify a good timer who adopts the TM timing strategy.
2.2.2. Ability versus response
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.
Except for special cases, existing performance measures are not able to extract the
information-related component of performance. As Grinblatt and Titman (1989) point
out, it would be better if performance measures (in addition to detecting abnormal
performance) could ‘‘also select the more informed of two [managers]’’. An investor
should be more concerned with the quality of the manager’s information than with the
manager’s aggressiveness because the investor can choose the proportion of her wealth
invested in the fund in response to the manager’s ability.
The TM and HM measures reflect both aspects of market timing. We see that the
estimated cˆTM in the TM regression will pick up the coefficient in the linear reaction
function (the k term in Eq. (8)). Hence, more aggressive funds can show up with
higher cˆTM. The cˆTM coefficient in the HM model is an unbiased estimate for the
product D(bH À bL), where D is the probability defined in footnote 4, and bH(bL) is the
manager’s target b when the predicted market excess return is positive (negative).
Thus, both ability (the D term) and aggressiveness (the bH À bL term) are reflected in
the estimated timing. The nonparametric statistic, on the other hand, measures how
often a manager correctly ranks a market movement and appropriately acts on it,
instead of measuring how aggressively she acts on it. We see that, in the linear

406
W. Jiang / Journal of Empirical Finance 10 (2003) 399–425
response case (as in Eq. (8)), the k coefficient cancels out in the nonparametric
measure because


ˆ
r
r
À ˆr
r
ˆ
r
r
À ˆr
r
h ¼
m;t
m;t
m;t
m;t
m;t
m;t
m;t
m;t
2Pr k
3
3
2
2 > k
2
2
1
1 j rm;t < rm;t < rm;t
À 1
r
1
2
3
m;t À r
r
À r
3
m;t2
m;t2
m;t1


ˆ
r
r
À ˆr
r
ˆr
r
À ˆr
r
¼
m;t
m;t
m;t
m;t
m;t
m;t
m;t
m;t
2Pr
3
3
2
2 >
2
2
1
1 j rm;t < rm;t < rm;t
À 1:
r
1
2
3
m;t À r
r
À r
3
m;t2
m;t2
m;t1
Thus, our measure largely reflects the information quality component of performance.
Based on this analysis, we also see that 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 the market timing performance of fund
managers.
2.2.3. Conditional information
The nonparametric measure can be extended to the context of conditional market
timing. The literature on conditional performance evaluation stresses the importance of
distinguishing performance that merely reflects publicly available information (as captured
by a set of instrumental variables) from performance that can be attributed to better
information. The conditional market timing approach (see, e.g., Ferson and Schadt, 1996;
Graham and Harvey, 1996; Becker et al., 1999; Ferson and Khang, 2001) assumes that
investors can time the market on their own using readily available public information, or
that by trading on other accounts they can undo any perverse timing that is predicted from
the public information. Under such circumstances, the real contribution of a fund manager
would be successful timing on the residual part of market returns that is not predictable
from public information.
Let r˜m,t and r˜i,t , j = 1, 2, 3, be the residuals of market returns and the fund return that
j
cannot be explained by lagged instrumental variables. The following statistic then proxies
the probability that a fund manager loads on more market risk when the market return is
higher, controlled for public information in both market and fund returns:
 À1
X


˜
n
˜
r
À ˜r
˜
r
À ˜r
h
i;t3
i;t2
i;t2
i;t1
n ¼
sign
>
:
ð12Þ
3
˜r
À ˜r
˜
r
À ˜r
˜
r
m;t3
m;t2
m;t2
m;t1
m;t <˜
r
<˜r
1
m;t2
m;t3
Theoretically, h in Eq. (2) and h˜ in Eq. (12) can have different magnitudes or even
different signs because the probabilities are conditional on different states. That is, a
manager who successfully times the unpredicted part of the market return can show up as a
mis-timer on the gross market return if we do not control for public information. Both
public and private information can be used to enhance portfolio returns, but a truly
informed manager should have superior market timing based on information beyond that
which is readily available to the public.

W. Jiang / Journal of Empirical Finance 10 (2003) 399–425
407
2.2.4. Statistical robustness
Breen et al. (1986) point out that heteroscedasticity can significantly affect the
conclusions of the HM tests. Jagannathan and Korajczyk (1986) and Goetzmann et al.
(2000) demonstrate the bias of the HM measure due to skewness. The asymptotic
distribution of the hˆn statistic, on the other hand, is unaffected by heteroscedasticity or
skewness. Further, hˆn in Eq. (5) is the least variance estimator among all unbiased
estimators of h in Eq. (2). The simulation results shown in Abrevaya and Jiang (2001)
demonstrate that the nonparametric test has accurate size even for small samples and is
robust (in terms of both the value of the statistic and its standard error) to outliers, non-
normality, and heteroscedasticity that are common in financial data.6 However, we do
require the errors in Eq. (1) to be serially uncorrelated. As we will be using monthly return
data for our empirical test, this assumption is not a serious concern. However, the statistic
can be biased when applied to high-frequency data.7
The nonparametric method also offers a timing measure that has little correlation with the
estimation error in the standard selectivity measures. TM or HM type regression models
would produce a spurious negative correlation between estimated selectivity and timing
because of the negatively correlated sampling errors between the two estimates (Jagannathan
and Korajczyk, 1986; Coggin, 1993; Kothari and Warner, in press). Our simulation shows
that a significant negative correlation between the two estimated abilities will 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. Coggin et al. (1993) and
Goetzmann et al. (2000) have similar results. On the other hand, the correlation between hˆn
and the selectivity measures from standard regression models is close to the truth.
2.2.5. Model specification and potential bias
In this section, we discuss three specification issues that can affect the consistency and
power of market timing tests: the separability of timing from selectivity; the difference
between the frequencies at which data are sampled and at which the manager times the
market; the relationship between market timing and volatility timing. The nonparametric
measure is more robust to model specifications than the TM and HM measures, though it
does not overcome all the biases.
A manager can enhance portfolio returns by selecting securities and by timing the
market. Decomposing returns in this fashion, however, is empirically difficult (Admati et
al., 1986; Grinblatt and Titman, 1989; Coggin et al., 1993; Kothari and Warner, in press).
Our measure relies on two common assumptions to avoid detecting spurious timing
because of selectivity issues. The first assumption is that a portfolio manager’s information
on the selectivity side (movement of individual securities) is independent of her
6
For example, Bollen and Busse (2001) test the hypothesis that fund returns are normally distributed and
reject normality at the 1% 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.
7
When applying the measure to high-frequency data, we would recommend the following modification in
forming hˆn: use only triplet observations {rm,t + 1, rm,t + 1, rm,t + 1} that are at least k periods apart, where k is the
1
2
3
lag of possible serial correlation, and rescale the statistics by the number of triplets actually used, denote it m. For
 À1
n
any finite k, m !
when n ! l.
3

408
W. Jiang / Journal of Empirical Finance 10 (2003) 399–425
information on the timing side (market movement). In practice, this requires that each
individual security constitutes only a small portion of a diversified portfolio and has a
negligible impact on the whole market (the manager does not select ‘‘too many’’ stocks at
one time, either); or the fund manager must act on selectivity at a much lower frequency
than on market timing (so that the manager keeps roughly constant the composition of her
risky portfolio when trying to time the market). The second assumption is that the portfolio
does not contain derivatives. Jagannanthan and Korajczk (1986) show that buying call
options, for example, can induce spurious timing ability. Kosik and Pontiff (1999) find that
21% of the 679 domestic equity funds in their sample hold derivative securities, but
detailed information about their derivative holdings is not available. Our measure, like the
TM and HM measures, cannot distinguish market timing from option-related spurious
timing.
For most timing measures, biases arise when the econometrician observes 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 biased severely downward. At the same time, a major component of timing
skill would show up as security-selection skill. Bollen and Busse (2001) show that the
results of standard timing tests are sensitive to the frequency of data used. Ferson and
Khang (2001) point out that an ‘‘interim trading bias’’ can arise when expected returns are
time varying and managers trade between return observation dates. The major source of
bias is the mis-specification of the regressor [rm]+ in the HM equation that should take
different values depending on the actual timing frequency rather than uniform frequencies
(such as monthly). Goetzmann et al. (2000) suggest replacing the monthly option value
[rm]+ with its accumulated daily option value when daily data of fund returns are not
readily available. Simulations show that the nonparametric 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 [rm]+ measured at the ‘‘right’’
frequency. Ferson and Khang (2001) use conditional portfolio weights to control for
interim trading bias as well as for trading on public information. Since our measure does
not use portfolio weights, it can potentially be subject to such bias.
The third model specification issue comes from the fact that the manager might be
timing market volatilities as well as market returns. Busse (1999) shows that funds attempt
to decrease market exposure when market volatility is high. Laplante (2001) shows that
observed mutual fund positions are not informative about future market volatility. If
volatility and expected return are uncorrelated, then our market timing measure remains
consistent in the presence of volatility timing. If the correlation is positive, the market
timing measure would underestimate the information quality of a successful volatility
timing manager.8 The opposite is true when the relation is negative. Research on the
relationship between the expected return and volatility (see, e.g., Breen et al., 1989;
Glosten et al., 1993; Busse, 1999) finds that the relation between return and volatility is
weak, both conditionally and unconditionally. If this is the case, the manager’s timing on
return and volatility likely to be weakly related.
8
If the manager tries to time the volatility, she may reduce market exposure even when the expected return is
high, if high-expected return tends to go with high volatility.

Document Outline

  • A nonparametric test of market timing
    • Introduction
    • Model
      • Market timing test statistics
      • Properties
        • Information structure and behavioral assumptions
        • Ability versus response
        • Conditional information
        • Statistical robustness
        • Model specification and potential bias
      • Simulations
    • Testing the market timing of mutual funds
      • Data
      • Do funds out-guess the market?
      • Some related questions
        • Does experience matter?
        • Do small funds fare better?
        • Is high turnover rate justified as timing?
        • Do investor flows affect market timing?
    • Conclusion
    • Acknowledgements
    • References

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