Does market timing ability exist in the U.S market?

Does market timing ability exist in

the U.S market?

Xianming Li

S2308517

TeL: 0646396102

Graduation Thesis for MSc Finance

EBM866B20

Faculty of Economics and Business, University of Groningen

26

th

of June. 2014----Final Version

Supervised by Dr. Henk von Eije

Abstract

This research paper studies the existence of market timing ability of U.S mutual fund

managers. 1344 actively managed mutual funds during the period 1999 to 2012 are

investigated in order to test whether their fund managers are able to adjust their

portfolios based on the future movements of the market. The result reveals that the

fund managers do not possess an ability to forecast future market returns but they are

indeed able to time the future market volatility.

JEL Classification: G10, G11

2

1 Introduction

With the growing number of mutual funds in which an increasing amount of wealth has

been invested1, identifying successful fund managers comes to public interest. This is

even more important because tremendous evidence show that the returns of actively

managed funds are lower than those of index funds2. Therefore, the performance of

mutual funds has been of great concern to both practitioners and academia, and has

turned out to become a source of considerable research. It has been universally

acknowledged that the aggregate performance of mutual funds is mainly determined by managers’ selection ability and marketing timing ability (Andreu, Alvarez, Ortiz and Sarto, 2014). On the one hand, the selection ability refers to whether or not the funds’ portfolios include undervalued and exclude overvalued stocks with the purpose of

outperforming the risk-adjusted benchmark returns. On the other hand, the market timing ability addresses whether fund managers are able to adjust their portfolios’ market risk exposure based on forecasts of future directions of market movements

and thus profit from such adjustments.

But are mutual fund managers indeed able to successfully anticipate market

movement? Are fund managers able to protect themselves from an allegation that

they should have predicted future market movement? Broadly speaking, what can we,

as shareholders, expect from mutual fund managers? Are the fund managers

speculating even if they make an attempt to forecast the market? At one time or

another, a quite large number of mutual funds, with the purpose of promoting their

services, have asserted that they are capable of foreseeing major turns in the stock

market. The true answers to the questions have a vital bearing on responsibilities

which mutual fund managers are expected to take. Nowadays, almost all of us are

aware that the market was terribly high in early 1926 and in 2007, and that the market

1

Especially in the U.S market, mutual fund industry is well developed in recent decades. According to Investment Company Institute, over 49% U.S household invest in mutual funds. Until the end of 2011, more than 14,000 mutual funds were in operation in the U.S with a value of $13 trillion under their management, accounting for 54.6% of total managed mutual fund asset worldwide which is $23.8 trillion.

2

was extremely low around 1950. In hindsight, the average people who have no

knowledge of financial theory tend to think that such extremes should have been

predicted by the investment management, and that stocks should have been sold and

purchased accordingly. However, the truth is that such actions were not really always

observed. Provided that investment managers are not qualified to predict the market,

revision of certain conception regarding the responsibilities of the management may

be necessary.

The debate as to the existence of the market timing ability has been a heated topic for

a long while. One strand of finance literature argues that aggregate market returns

might be predictable, and thus the performance of mutual funds can be influenced

through a derivation of optimal asset allocation based on the superior market timing ability. Many research papers that examine the returns of investors’ portfolios, however, find little evidence to support such an argument. It is probably because, as

one argues, the prediction of the best time to enter or exit the market is complicated.

The high speed at which the market reacts to newly published information indicates

that stock prices may have already incorporated the impact of new developments. In

other words, when the market turns, it turns so fast that those attempting to time the

market might miss the true rebounding time, and thus are less likely to compensate

the concomitant information and transaction costs caused by frequent asset turnover.

The pioneers of market timing studies are Treynor and Mazuy (1966) who argue that

the market exposure is supposed to be high when the market is expected to move

upward and low when the market is forecasted to move downward and that the

change in market exposure leads to a convex or nonlinear relationship (the derivation

of such relationship is displayed in following section) between individual funds returns

and market excess returns. Therefore, Treynor and Mazuy (1966) include a quadratic

term (representative of the nonlinearity) in capital asset-pricing regression model

(hereafter TM model) and test the existence of such quadratic term and they, however,

4

Merton (1981) follow the steps of the two pioneers and introduce an alternative

approach (hereafter HM model) which directly test put-option-like features since they

believe that fund managers with the market timing abilities are capable of maintaining

a certain level of portfolio value even when the market declines as if they have

acquired free put options in their portfolios. Their findings are much similar to those of

Treynor and Mazuy (1966) and only find 3 funds with significant positive market timing

abilities out of 116 in their sample. Following Treynor and Mazuy (1966) and

Henriksson and Merton (1981), Kon(1983), Lee and Rahman (1990),Andreu, Alvarez,

Ortiz and Sarto (2014), Bollen and Busse (2001), Chang and Lewellen (1984), Jiang

(2003) and Becker, Ferson, Myers and Schill (1999) again find no significant evidence

to support the market timing ability and some of them even find the negative market

timing ability.

In this paper, rather than using original TM models, I adopt an extended model

proposed Goetzmann, Ingersoll and Ivkovic (2000) to test the market timing ability.

The extended TM model, on the one hand, similar to the original one, tests the

existence of the quadric term. On the other hand, unlike the original TM model, it

takes Fama-French factors (1993) into consideration. While the original TM model is

derived based on the market model which only considers market risk (to be explained

in the following section), the revised version is based on Fama-French (1993) asset

pricing model which incorporate small-cap risk and book-to market risk. The extended

model should be more appropriate to test market timing abilities because the two

added risks are widely acknowledged in the recent development of finance theory.

However, even the extended TM model, which employs market timing measures based on the nonlinear relationship between the realized funds’ returns and the simultaneous market returns, suffer from some biases. First of all, Bollen and Busse

monthly returns under the null hypothesis of no market timing ability and use these simulated returns to estimate the TM and HM models. Their findings are that in the test using monthly data, the results are biased because 55.6% and 58.3% coefficients of the quadratic term are positive in each model, and that in daily data test the number of positive and negative coefficient are almost half-half. Thus, they conclude that increased data frequency increases the test power. Many researchers, such as

Treynor and Mazuy (1966) and Henriksson and Merton (1981) conduct their tests with

monthly data, which may lead to unreliable results. In this context, I adopt the

extended model using daily data to overcome this bias.

Secondly, since I employ daily data to conduct the test, a bias induced by

autocorrelation and heteroskedasticity of the funds’ daily returns might be an issue to

be considered. Breen, Jagannathan and Ofer (1986) suggest that heteroskedasticity and autocorrelation of fund returns may bias the standard error of the quadratic term coefficients in the TM model, thus affecting the significance of the test results. To completely remove such bias, in the first robustness test, I adopt a bootstrap approach similar to the one used by Bollen and Busse (2001) to resample all residuals and recalculate the t-statistics of the timing coefficients.

Thirdly, rather than by the fund managers’ timing abilities, the nonlinearity (quadratic term) might be induced by artificial timing effects which are related to particular

trading strategies. Jagannathan and Korajczyk (1986) show that the trading based on

realized returns may distort a linear relationship into a nonlinear one. To illustrate,

assume a mutual fund manager who is not able to time the market but adjusts his portfolio’s market exposure in the second period in line with the realized performance of the market in the first period. Such a strategy would induce a correlation between the market return in the first period and the portfolio’s beta in the second period, thus leading to a contemporaneous nonlinear relation between the realized market and

fund returns. The fund managers adopting a momentum strategy which exposes their

6

positive market timing abilities and in contrast, others adopting a mean-reversion

strategy would be considered to have negative timing abilities even though such

abilities are non-existent. In short, some usually adopted strategies which are

seemingly innocent could induce a nonlinear relation between the market returns and

the fund returns. Jagannathan and Korajczyk (1986) further point out that if the fund

managers passively invest (buy and hold) in some stocks whose return structures

have option-like characteristics, the relation between the fund returns and the market

returns of the funds, which should have been linear without the market timing ability,

might be distorted to a convex relationship too. Jiang, Yao and Yu (2007) attempt to

circumvent such artificial timing effects by developing a new approach named “holding-based measure”. More specifically, they firstly estimate market betas of stocks in fund portfolios based on past market returns and past stocks’ returns and then fund portfolios’ betas are estimated as the weighted average of the betas of all stocks included in the portfolios. Compared to traditional models which use realized fund’s returns and contemporaneous market returns as mentioned in previous paragraph, this new approach only requires ex ante portfolio information---the

portfolio beta at the beginning of first period and makes a comparison between the ex

ante portfolio beta and the market returns in the second period, thus suffering no bias

caused by the trading strategies during the holding period. Nonetheless, one problem

embedded in the method is that it needs a complicated process to estimate betas of each stock. Since a fund’s portfolio may include hundreds of stocks, the beta estimations are likely to induce errors. Additionally, because data on funds’ portfolio composition are only available for each quarter, their sample size is limited. In the

second robustness test, I adopt a modified version of Jiang, Yao and Yu (2007) with a

dynamic perspective, that is, I study whether the change in market exposure in the

first period is correlated with the change in market returns in the second period. The

main advantage of this model is to avoid problems regarding the nonlinear

relationship induced by artificial timing effects.

other factors. Busse (1999) finds that omission of important explanatory variables in the timing formula would bias the timing coefficients’ standard errors and thus the inference of market timing ability. In the third robustness test, I incorporate other

related market factors into the dynamic model. Busse (1999) and Cao, Simin and

Wang (2011) suggest that market volatility and market liquidity may be two potential

candidates.

Market volatility is a potential factor that should be taken into consideration when the

fund managers attempt to build up an optimal asset allocation. In previous studies,

few of them analyze the predictability of future market volatility (volatility timing ability). Busse (1999) finds that in order to protect their portfolios’ value from a highly unstable market, mutual fund managers are reluctant to expose their portfolios to a highly

volatile situation. Thus, it might be interesting to add volatility indicators in the

dynamic model. But there appears to be a problem if market returns and market

volatility are correlated. Statistically, if two explanatory variables are not correlated,

the loading of one variable should not change when the other is added to the model.

In this context, if market returns is not correlated to market volatility, market timing

measures are not biased even with presence of volatility timing ability. Otherwise market returns’ timing measures, due to multicollinearity, are biased downward if the both factors (two explanatory variables) are highly and positively correlated. Glosten, Jagannathan and Runkle (1993) find a low correlation using both conditional and unconditional models. Busse (1999) examines the MSCI Spain and give similar conclusion.

Compared to the market volatility timing ability, even fewer studies pay attention to

market liquidity timing which should have considerable impact on the asset allocation.

Cao et al (2011) list several reasons why market liquidity is an important factor to be

considered. Firstly, there is a relationship between market liquidity and fund

performance. For instance during the period of 2008 financial crisis, the aggregate

8

If fund managers are able to accurately time future market liquidity, they would adjust

their risk exposure accordingly to reduce losses and enhance performance. As the

amount of money inflow to funds and the remuneration of fund managers are usually

determined by fund performance evaluation, the fund managers are quite motivated

to adjust their portfolio based on expected liquidity risk. Secondly, if market returns are

not persistently predictable, market liquidity, like market volatility, might be more

persistent. Thus, it might be more straightforward for fund managers to time market

liquidity rather than market returns. Finally, the asset pricing literature has identified

market-wide liquidity as a necessary variable that is vital for pricing assets. Cao et al

(2011) examine the market timing ability of fund managers from an aggregate liquidity

perspective and suggest that the adjustment of market exposure should be a positive

function of the aggregate level of market liquidity. Their findings significantly support

the hypothesis that mutual fund managers do decrease their market exposure when

aggregate liquidity is low. Someone may wonder whether a correlation between

market volatility and market liquidity exists, which generate the comparable statistical

bias as pointed out in previous paragraph. Chang and Wu (2012) find that this is not

the case. For these reasons, I add liquidity timing to the dynamic model together with

market return timing and volatility timing.

This research, in the first place, enriches the market return timing literature and confirms the previous findings by others. Secondly, it studies the fund managers’ market volatility timing and market liquidity timing abilities to which has been paid less attention. Thirdly, based on common characteristics, it may be relevant and useful to the individual and institutional investors who want to identify better-than-average mutual funds that are able to time the market. For instance, the retirement savings investors whose investment objective is to maintain the value of their money may select funds which invest less in stocks because the findings of this paper show that a mutual fund with a larger fraction of investment in stocks may signal that such a fund is more likely to be involved in a highly unstable market.

The structure of this paper is further as follows: section 2 presents the methodology

and gives a description of each econometric model to be adopted while section 3 lists

sources of the data and the selection criteria. The main results of the extended TM

model are exhibited in section 4 and robustness tests are displayed in section 5.

Section 6 documents results of common characteristics analysis and section 7

concludes.

2 Methodology

2.1 Review of the TM Model and Its Extension

The TM model is widely adopted. See, for instance, studies by Treynor and

Mazuy(1966), Jiang (2003),Cumby and Glen (1990), Ferson and Schadt (1996),

Kryzanowski, Lalancette, and To (1996), Becker, Ferson, Myers, and Schill (1999),

and Kon (1983). The derivation of the TM model follows the three steps listed below.

Treynor and Mazuy (1966) firstly assume that the market model holds:

R_i,t= α_i+ β_i,tR_mt + ε_i,t (1)

10

α_i captures the security selection ability, β_i,t represents market risk and ε_i,t is an error term. Secondly, testing market timing, in nature, is equivalent to testing equation

(2) which is shown as follows:

β_i,t= β_i,t−1+ δ_iR_mt + ω_i,t (2)

where βi,t−1 is market exposure of fund i during the period t-1. It is because the beta at time t-1 should be adjusted to the beta at the time t based on market return at the

time t. In other words, the covariance (could be measured by δi) between market return and time-varying market exposure plays an essential role. Therefore, δ_i is expected to be significantly positive if fund managers do possess market returns

timing ability because positive δ_i implies that the managers increase their portfolios’ market exposure as market returns move upward. The final step is to substitute

equation (2) into equation (1) for β_i,t, leading to TM model as equation (3) shows:

R_i,t= α_i+ β_i,t−1R_mt + δ_iR2_mt + μ_i,t (3)

where the quadratic term captures the market timing ability. The model, adopted in

this research and firstly proposed by Goetzmann, Ingersoll and Ivkovic(2000),

extends the TM model (equation 3) by introducing Fama and French factors.

Goetzmann et al. (2000) argue that such an equation reduces measurement bias in

the market timing specification. The extended model is as follows:

R_i,t= α_i+ β_1,tR_mt + β_2,tHML_t+ β_3,tSMB_t+ δ_iR_mt2 +ε_i,t (4)

where HML represents the difference between the returns of high book-to-market

portfolios and the returns of low book-to-market portfolios and SMB stands for the

difference between the returns of small-cap portfolios and the returns of large-cap

2.2 Bootstrap Approach

As mentioned earlier, Breen, Jagannathan and Ofer (1986) argue that

heteroscedasticity and temporary autocorrelation, which causes standard errors to be biased, may affect the significance of coefficients in the return-based models (for instance, TM model). Since standard corrections of standard error in software (for example, the HAC standard error correction) may not completely correct the

misspecification of standard errors, to overcome that problem, I adopt a bootstrap

technique similar to the one used by Bollen and Busse (2001). There are three steps

to be followed in this procedure. In the first place, I estimate the coefficients of the

extended TM model on fund-by-fund basis based on daily data from 1999 to 2012 and

store the coefficients and residuals. Secondly, I use bootstrap methods to generate

fund returns in the following way. For each date and each fund, a residual is randomly

chosen with replacement (i.e. the same residual can be chosen more than one time) from the stored residuals of that fund and then added to that date’s fitted value of that fund. I bootstrap the residual for every day in the sample period. Such a procedure is

repeated for each fund 100 times and thus I obtain 100 sets of bootstrap returns for

each fund. The third step is to estimate the timing coefficients from 100 sets of

bootstrap returns for each fund based on the extended TM model. Thus, I generate

100 timing coefficients for each fund and then calculate the standard error of the 100 coefficients. Under the null hypothesis that no market timing ability exists (δ = 0). t-statistics of the timing coefficient for each fund can be calculated as follows:

t = δ(orignal )

σ( bootstrap δ) (5)

where σ( bootstrap δ) is standard error of the 100 timing coefficients. The t-statistics can be compared to 1.96 in order to assess the coefficients’ significance. The merit of such a bootstrap approach is that it distinguishes luck from true market skills while the

12 2.3 Dynamic Approach

Jagannathan and Korajczyk(1986) indicate particular trading strategies may also

induce a nonlinear relationship between fund returns and market returns. To

circumvent the problem, inspired by Jiang, Yao and Yu (2007), besides adopting the

extended TM model, I use the following model

βi,t= βi,t−1+ nm=1δi,m(MFm,t+1− MFm,t) + εi,t (6)

or alternatively

∆β_i,t= n_m=1δ_i,m∆MF_m,t+1+ ε_i,t (7)

where ∆MF_m,t+1 represents changes in market factors from time t to time t+1 (the second period) and ∆β_i,t is changes in market beta of fund i from time t-1 to time t (the first period). To calculate the market beta of fund i at the beginning of time t,

Capital Asset Pricing Model (CAPM) is applied to the daily excess returns of the fund i

and daily market excess returns during the period t. In this context, to be more specific,

the market beta for each month in the sample period is obtained using subsequent

daily returns of one month. For example, the beta of fund i at the beginning of January, 2000, can be calculated by applying fund i’ daily returns during January, 2000 and market excess returns during January, 2000 to CAPM. Once the beta for each month

is obtained, the change between the betas in adjacent months can be calculated (∆β_i,t). Finally, I panel regress the equation (7) using the obtained changes in the market betas and changes in market factors. The main idea of this approach is to see

the relationship between adjustment of the market exposure in the first period and the

market change in the second period. For example, if the market returns in the second

period move upward, if market timing ability exists, the market exposure should be

adjusted upward in the first period. The advantage of this model is to avoid testing the

2.4 Common Characteristic Analysis

No matter what the overall timing performance of mutual funds is, there is always a

variation of timing performance across funds. Thus, it is tempting to identify fund

managers who are armed with superior market timing abilities. In order to do so, we

can test whether there are common characteristics among better market timers. For

instance, are mutual funds of larger size (or small size) may be superior timers? Is a

higher management fee a signal for better timing performance? Do better timers

result in more frequent trading and thus high turnovers? To answer these questions,

I consider six fund characteristics which are total asset value, turnover rate,

management fee, dividend per share and fraction of investment in stocks. Then I

conduct a cross-sectional analysis using the six characteristics as the following

equation shows:

Timing Ability_i = γ_0,i+ γ_j,iCharateristics_j,i+ε_i,t (8)

where Timing Ability_i is timing performance of fund i and Charateristics_j,i is the level of jth characteristics of fund i.

3 Data

3.1Returns and Characteristics of Mutual Funds

Data of returns for U.S mutual funds are retrieved from CRSP database. Firstly, I

search and download the entire mutual fund database, 59833 funds in total. Since

market timing usually refers to actively managed equity funds, three types fund are

chosen based on their objective codes which are growth funds (G), growth and

income funds (GI) and balanced funds (BA). I manually remove passive funds (index

funds), non-U.S funds and international funds, reducing to total of 2394 U.S domestic

14

Since the daily data for U.S mutual fund returns are only available from 1999, I use a sample period from Jan 04 in 1999 to Dec 31, 2012. Among 2394 funds, because 649 funds do not have available daily returns, the sample is further reduced to 1745. Finally, I only remove funds whose returns are available for less than 3 years in order to minimize survivorship bias. As shown in Table 1, there are 1344 funds left in the sample.

Table 1 Fund selection process

This table the list criteria for mutual fund selection in sample. All funds are retrieved from CRSP database. Then based on each criteria, the total number of mutual funds are filtered step by step. This results in US actively managed funds with daily data available from 1999 for more than 3 years

Total available funds

59833

US active domestic funds

2394

Daily data available from 1999

1745

Daily data available for more than 3 years

1344

In addition to daily returns, characteristics (annual) for each fund, namely total net asset (TNA), dividend per share, turnover ratio, management fee, expense ratio and fraction invested in stocks are also retrieved from the CRSP database. Table 2 reports summary statistics of our fund sample during the period from 1999 to 2012. Among 1344 samples, 605 are growth funds, 499 are growth and income funds and 240 are balanced funds. For each characteristic, I first average the annual numbers for each fund and then calculate cross-section average across all funds. The following characteristics are obtained: the average total asset value across all funds is $1296.09 million coupled with an average dividend per share of $0.16, a management fee per share of $0.56, an annual turnover of 101% and annual expense ratio of 1.25%. In addition, the average fraction of wealth invested in common stocks is 83.28%.

3.2 Market Wide Indicators

There are five market-wide data which should be retrieved, namely market returns,

market-wide liquidity, market-wide volatility and two Fama-French factors. Market

French3. The 3-month treasury bill rate is used as risk-free rate. I find market liquidity

by the following method proposed by Pastor and Stambaugh (2003) through the

following equation:

r_i,t+1e = φ_i,t+ θi,tri,t+ Li,tsign ri,te ∗ vi,t+ πi,t+1 (9)

where r_i,te is excess return of each stock in S&P 500 at day t, r_i,t is the return of each stock at day t, and v_i,t is the volume for that stock at time t. L_i,t is an indicator of liquidity for each stock. Then, I average Li,t to obtain Lt for each day as following equation shows:

L_t= 1

N Li,t N

i=1 (10)

Table 2 Summary statistics of fund characteristics

This table shows the characteristics of mutual funds in the sample categorized into three types based on investment objectives, which are growth fund, growth and income fund and balanced fund, respectively. All characteristics, total net asset (TNA), dividend per share, annual turnover, management fee per share, expense ratio and investment in stocks are calculated in the same way by first averaging over time for each fund and then across funds.

3

http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/

All funds Growth

funds

Growth and

income funds Balanced funds

Number of Funds

1344 605 499 240

TNA (millions)

1296.09 1311.24 1388.48 1065.79

Dividend per Share

0.16 0.08 0.17 0.12

Annual Turnover

1.01 1.29 0.63 1.05

Management Fee per Share

0.56 0.62 0.54 0.47

Expense Ratio (%)

1.25 1.29 1.20 1.22

16

where N is the number of stocks in the stock index. The idea of this liquidity model (equation 9) is that order flow, which is constructed as a stock’s volume signed by contemporaneous excess return on this stock, should be accompanied by a return that one expects to be partially reversed in the future if the stock’s liquidity is not perfect. The model is performed under an assumption that the greater the expected reversal for a given volume, the lower the stock’s liquidity. Thus, one should expect Li,t is negative in general and higher in absolute magnitude when liquidity is lower (Pastor and Stambaugh, 2003).

Finally, I apply GARCH (1,1) model to 20-year market returns series from 1992 to

2012 which are retrieved from website of Kenneth R. French and then obtain the

conditional variance of market returns for each month as an indicator of market-wide

volatility. Table 3 shows the mean, median, standard deviation, max and min of each

of the 5 market-wide factors.

Table 3 Summary statistics for five monthly market factors in percentages

This table reports summary statistic for market returns, returns of high B/P portfolio minus low B/P portfolio (HML), returns of small-cap portfolios minus high-cap portfolios (SMB), market volatility and market liquidity. For market volatility, Garch (1,1) model is applied to market returns for 20 years. Equation (9) ri,t+1e = φi,t+

θi,tri,t+ Li,tsign ri,te ∗ vi,t+ πi,t+1 is adopted to derive market liquidity indicators.

Mean Median Std Max Min

Market Return 0.41 1.15 4.72 11.34 -17.15

HML 0.32 0.24 3.61 13.87 -12.68

SMB 0.47 0.19 3.73 22.02 -16.39

Market Volatility 0.24 0.20 0.18 1.05 0.05

Market Liquidity -3.12 -2.55 7.91 20.1 -33.36

4 Results of the Extended TM Model

I firstly study the mutual fund market timing abilities using the extended TM model with

Fama-French factors. Column (1) - column (5) of Table 4 displays, for the extended

Table 4 TM model

This table reports the results of δ of the extended TM model with equation (4) Ri,t= αi+ β1,tRmt+ β2,tHMLt+

β_3,tSMBt+ δiRmt2 +εi,t on fund-by-fund basis. The number (No.) and fraction (percentage) of funds with positive (P), negative (N), significantly positive (PP) and significantly negative (NN) coefficients are displayed based on 5% significance level. Timing coefficient represents the average of the coefficients in each category. Cross-section statistics in column (1) is calculated as the average of timing coefficients divided by the S/ n where S is cross-section standard deviation and n is the number of the coefficients.

The Extended TM (1) (2) (3) (4) (5) Total P N PP NN All Funds No. 1344 658 686 103 240 Percentage (%) 100 48.95 51.05 7.66 17.71 Timing coefficient (δ) -0.0508 0.2055 -0.2966 0.2201 -0.4521 Cross-section t-statistic -2.2823 - - - - Growth funds No. 605 279 326 43 75 Percentage (%) 100 46.12 53.88 7.11 12.39 Timing coefficient (δ) -0.0408 0.2154 -0.2600 0.2331 -0.5615 Cross-section t-statistic -1.3943 - - - -

Growth and income funds

No. 499 326 173 59 84 Percentage (%) 100 65.33 34.66 11.82 16.83 Timing coefficient (δ) 0.0182 0.2010 -0.3261 0.2498 -0.4596 Cross-section t-statistic 0.5233 - - - - Balanced funds No. 240 53 187 1 81 Percentage (%) 100 22.08 77.91 0.42 33.75 Timing coefficient -0.2196 0.1810 -0.3331 0.1468 -0.3681 Cross-section t-statistic -3.2068 - - - -

coefficients and also filters the number and fraction of funds which show significantly

positive and negative timing coefficients in four categories based on fund objective: all

funds, growth funds, growth and income funds and balanced funds. For all categories

except growth and income funds, the number of funds with positive coefficients is

smaller than that of funds with negative coefficients. But for all cases, the funds with

significantly positive coefficients are less than the funds with significantly negative

coefficients. Especially for balanced funds, there is only one fund with a significantly

18

compared to the fraction of funds of significantly negative timing (17.71%, 12.39%,

16.83% and 33.75%), respectively for each category, the fraction of funds with

significantly positive coefficients is much smaller relative to the sample (7.66%, 7.11%,

11.82% and 0.42%, respectively for each category). The average timing coefficients

are displayed in the third row for each subdivision. Except growth and income funds

(0.0182, insignificant), all other groups show negative average timing coefficients.

Based on cross-section t-statistics compared to plus and minus 1.96, all funds

(t=-2.2823) shows a significant negative market timing ability. Among the other groups,

balanced fund managers shows extremely insufficient timing ability with significantly

negative average timing coefficients of -0.2196 (t=-3.0268).

The results of the extended TM model reveal that mutual fund managers do not

possess market return timing and these findings are comparable those of other

researchers who adopt the original TM model (See example, Treynor and

Mazuy(1966), Jiang (2003), Cumby and Glen (1990), Ferson and Schadt (1996),

Kryzanowski, Lalancette, and To (1996), Becker, Ferson, Myers, and Schill (1999),

Jiang, Yao and Yu (2007) and Kon (1983))

5 Robustness Tests

5.1 Heteroscedasticity and Autocorrelation

decrease that much. For balanced funds, such fraction even increases by 0.83%. Therefore, heteroscedasticity and autocorrelation are not the issues here.

Table 5 The TM model with bootstrap approach

This table reports the results of δ of the extended TM model with equation (4) Ri,t= αi+ β1,tRmt+ β2,tHMLt+

β_3,tSMBt+ δiRmt2 +εi,t on fund-by-fund basis with a bootstrap approach that corrects for heteroscedasticity and

autocorrelation. Firstly I save the coefficients and residuals from the original TM model and then bootstrap residual each day for each fund and add that residuals to fitted value of that day to obtain generated returns. I bootstrap for every day for each fund and the process for each fund is repeated 100 times. Thus I generate 100 sets of new generated returns for each fund afterwards and then re-estimate the equation with the new returns, thus providing me with 100 new timing coefficients for each fund. Finally, t-statistics are calculated through equation (5) t = δ(orignal)/σ( bootstrap δ) to determine the significance of the coefficients. The number (No.) and fraction (percentage) of funds with significantly positive (PP) and significantly negative (NN) coefficients are displayed based on 5% significance level in each category. In addition, column (1) and (2) in this table replicate column (4) and (5) from Table 4 in order to make a comparison between the extended TM model and the bootstrap TM model.

The Extended TM Bootstrap TM

(1) (2) (3) (4) PP NN PP NN All Funds No. 103 240 119 217 Percentage (%) 7.66 17.71 8.85 16.15 Timing coefficient (δ) 0.2201 -0.4521 0.3670 -0.6202 Growth funds No. 43 75 51 72 Percentage (%) 7.11 12.39 9.11 11.90 Timing coefficient (δ) 0.2331 -0.5615 0.3622 -0.7076

Growth and income funds

No. 59 84 66 62 Percentage (%) 11.82 16.83 13.23 12.42 Timing coefficient (δ) 0.2498 -0.4596 0.3773 -0.6234 Balanced funds No. 1 81 2 83 Percentage (%) 0.42 33.75 0.83 34.58 Timing coefficient 0.1468 -0.3681 0.1510 -0.5420

5.2 Artificial Timing Effects

Jagannathan and Korajczyk (1986) point out that there may be artificial timing effects

20

strategy effect refers to particular trading strategies resulting in a correlation between the market return in the first period and the portfolio’s beta in the second period, thus inducing a contemporaneous nonlinear relation between the realized market and fund

returns of two periods. The passive investing effect means the fund managers buy

and hold the option-like securities in the fund portfolios. Since such option-like

securities have nonlinear relationship between their returns and the market returns,

including such securities in the portfolios may make the relationship between the

portfolio returns and market returns nonlinear, even though the fund managers are not

market timers. To remove the bias induced by those two artificial timing effects,

instead of testing the nonlinearity, I adopt the following dynamic model, inspired by

Jiang, Yao and Yu (2007), to directly see the relationship between the change in

market exposure in the first period and the change in market returns in the second

period:

∆β_i,t= δ_i∆R_{mt +1}+ ε_i,t (11)

where ∆R_{mt +1} is the change in market excess return during the second period and ∆β_i,t is the market exposure change in the first period. As described in the methodology section, the market beta of fund i at the beginning of each month, is

calculated by applying CAPM to daily fund returns and market returns during that month. Then the change in the betas (∆β_i,t) between adjacent months can be generated. Then I define that first period is 1 month and the second periods (timing

horizon) could be 3 months, 6 months, 9 months, 12 months and 24 months. In other

words, the change in market exposure last one month is regressed, based on

equation (10), against the subsequent change in market returns of subsequent 3

month, 6 months, 9 months, 12 months and 24 months, respectively. For each timing

horizon, I obtain a timing coefficient. Rollover techniques are adopted. It means, for

example, if I test for 3-month horizon market returns, the first pair of dependent and

independent variables are the changes in market beta from January 1999 to February

1999 and the changes in market returns from February 1999 to May 1999. Then the

from February 1999 to March 1999 and the changes in market returns from March

1999 to June 1999, etc. The market timing measure δ_i is expected to be significantly positive if the fund managers are able to time the market. If the artificial effects exist,

the significant negative timing ability (based on the nonlinearity) as found in the last

section should be alleviated more or less in the dynamic model. As expected, none of

coefficients (0.1019, 0.1015, 0.1433, 0.1020 and 0.1423: not tabulated) obtained for

each timing horizon are statistically significant. In terms of no existence of positive

market returns timing ability, the results of this dynamic test are robust to those of the

extended TM test in the previous section.

5.3 Market Volatility and Liquidity Timing

Busse (1999) finds that misspecification of timing function would bias the timing coefficients’ standard errors and thus the estimation of market timing ability. They therefore suggest to include market volatility when testing market returns timing ability

because fund managers might change market exposure in terms of changes of

market volatility. Cao et al (2011), furthermore, indicates that market liquidity is

another important factor that fund managers should keep in their minds. Therefore,

besides adopting equation (10), I use the following dynamic model, which is firstly

proposed by Bodson, Cavenaile and Sougne (2013), to test market timing abilities of

all three kinds in a single analysis.

∆β_i,t= δ_i,1∆R_{mt +1}+ δ_i,2∆L_t+1+ δ_i,3∆V_t+1+ ε_i,t (12)

where ∆L_t is the change in market-wide liquidity, ∆V_t is market-wide volatility and ∆β_1,i,t is change in market exposure. The timing horizons are also 3 months, 6 months, 9 months, 12 months and 24 months and the rollover technique is applied in

the same way as explained in the previous section.

A statistical problem may appear if two of the factors in equation (11) are correlated. If

22 Table 6 Dynamic model

This table shows panel regression results of equation (12) ∆β_i,t= δi,1∆Rmt +1+ δi,2∆Lt+1+ δi,3∆Vt+1+ εi,t.,

where ∆β_i,t is the changes in the market betas of fund I in the first period, ∆Rmt +1, ∆Lt+1, and ∆Vt+1 are the

change in the market returns, the market liquidity and the market volatility in the second period. As robustness test to artificial timing effect, it is testing changes in exposure on the forecasts of future market movement instead of quadratic term. For each fund, beta for each month is obtained by regressing one subsequent month fund excess returns against market excess returns. For 3-month horizontal test, the first period is 1 month and second period is 3 months and 1-month change in beta is regressed against 3-month change in market-wide factors. For 6-month horizontal test, the first period is 1month and second period is 6 months and 1-month change in beta is regressed against 6-month change in market-wide factors, etc. Change in each factor will use rollover technique. The coefficients for each market factors are provided and the numbers in parentheses are p-values for the coefficients.

Fund Objective Timing Horizon ∆R_{mt +1} ∆L_t+1 ∆V_t+1

All funds 3-month horizon 0.0855 -6.1095*** 0.0475 (0.3365) (0.0009) (0.3806) 6-month horizon 0.0819 -7.4681*** 0.0612 (0.3538) (0.0013) (0.2690) 9-month horizon 0.1414 -7.8457*** 0.0122 (0.1118) (0.0007) (0.8268) 12-month horizon 0.1167 -7.3834*** -0.0330 (0.1956) (0.0017) (0.5628) 24 month horizon 0.1431 -4.1289* 0.0089 (0.1454) (0.0850) (0.8878) Growth funds 3-month horizon 0.0299 -8.4033*** 0.0621 (0.6570) (0.0000) (0.1313) 6-month horizon 0.0374 -8.7497*** 0.0689 (0.5770) (0.0000) (0.1025) 9-month horizon 0.0112 -7.904*** 0.056 (0.8698) (0.0000) (0.1972) 12-month horizon 0.1026 -6.2893*** -0.0369 (0.1514) (0.0008) (0.4147) 24-month horizon 0.0471 -3.1001 -0.1546*** (0.5429) (0.1015) (0.0022)

Growth and Income funds

3-month horizon 0.1574 -1.5148 0.0264 (0.3131) (0.7085) (0.7807) 6-month horizon 0.138 -3.9573 0.0547 (0.3778) (0.3304) (0.5773) 9-month horizon 0.2929* -6.0509 -0.0299 (0.0949) (0.1359) (0.7631) 12-month horizon 0.1255 -6.5117 -0.0324 (0.4299) (0.1122) (0.7471) 24-month horizon 0.2568 -5.4113 0.1819* (0.1252) (0.1843) (0.914)

Table 6 (continued)

Fund Objective Timing Horizon ∆R_{mt +1} ∆L_t+1 ∆V_t+1

Balanced funds 3-month horizon 0.075 -10.0223*** 0.0547 (0.4934) (0.0005) (0.4119) 6-month horizon 0.0764 -11.6748*** 0.0554 (0.4828) (0.0001) (0.4166) 9-month horizon 0.2176 -11.5832*** -0.0106 (0.496) (0.0001) (0.897) 12-month horizon 0.1344 -12.0774*** -0.0241 (0.229) (0.000) (0.7325) 24-month horizon 0.1475 -4.0399 0.0605 (0.2438) (0.1904) (0.4565)

Note:*, **, *** represent significance level at 10%, 5% and 1%.

three factors and find that none of them are highly correlated with another (market

returns vs market liquidity: 8.84*10-4, market returns vs market volatility: 8.08*10-7,

market volatility vs market liquidity: -2.62*10-5). Therefore, the correlation problem

does not exist.

It can be expected that manager are supposed to increase the market exposure when

market returns and market liquidity are forecasted to increase and decrease the

market exposure when the market volatility are predicted to be higher next period.

Thus, if fund managers are capable of timing the market factors of all three kind, δ₁ and δ2 are expected to be significantly positive and δ3 to be significantly negative. Table 6 lists the results of such a test. As is shown, for all timing horizons, none of the

loadings for the change in market returns are at least 5% significantly positive, which

indicates that market returns timing ability does not exist. The results coincide with

those of the previous tests.

However, the fund managers are found to possess strong skills at timing the market

volatility in the short term, especially growth fund and balanced fund managers. Other

interesting findings are that the absolute values of coefficients for the changes in

24

12-month horizon, the coefficients are increased from 6.1095 to 7.3834 for all funds,

from 1.5148 to 6.5147 for growth and income funds and from 10.0223 to 12.0774 for

balanced funds. This can be interpreted as a strengthening market-timing ability along

the short timing horizon, which means that within a year, the longer the timing horizon,

the stronger the volatility timing skills. In other words, mutual fund managers are

better at predicting longer future market stability than nearby future. However, when

the timing horizon is stretched to 24 month, the market-volatility timing capability

disappears. A possible ad hoc explanation for such results is that the average market

volatility for a longer period is easily estimated than that for a shorter period. To

illustrate, if fund managers are about to time the market volatility in 6 months, they are

likely to choose substantial historical 6-month data as a guide. Since data of 6-month

period is more reliable than those of 3 month-period (because the past 6-month

period has a larger sample size of data), the managers are better at predicting the

longer period. However, there are more uncontrolled and unpredictable variables that

may affect the estimation in the longer period. This explains why the volatility timing

skill vanishes after 2 years.

In terms of market liquidity timing, no evidence is shown to supports its existence

because none of the coefficients for the change in market liquidity are significantly

positive and some of them are even negative. In addition, to avoid underestimating

the fund managers, I test whether the fund managers possess timing ability of the

market return per unit of risk, that is, sharp ratio timing ability. The results show a

significantly negative ability of this kind (details of such test are in Appendix).

6 Common Characteristics Analysis

Since the timing performance varies across funds, it is interesting to identify common

characteristics in mutual funds with superior timing abilities from the three

perspectives---the market returns, the market volatility and the market liquidity. In

Table 7 This table shows the results of three cross-section analysis using equation (13) Si= γ0,i+ γ1,iTNA +

γ_2,iExp + γ_3,iTR + γ_4,iMF + γ_5,iDiv + γ_6,iStock +εi,t. S (δi,1, δi,2, and δi,3 ) are the coefficients of re-estimating

equation (11) ∆β_i,t= δi,1∆Rmt +1+ δi,2∆Lt+1+ δi,3∆Vt+1+ ϵi,t on fund-by-fund basis with a 3-month timing

horizon, where ∆β_i,t is the changes in the market betas of fund i in the last one month, ∆Rmt +1, ∆Lt+1, and

∆Vt+1 are the change in the market returns, the market liquidity and the market volatility in the subsequent 3

months. Total net asset (TNA), expense ratio (Exp), Turnover Ratio (TR), management fee (MF), dividend (Div) and the fraction of stocks in portfolio (Stock) are averaged for fund i during the sample period from 1999 to 2012.

TNA Exp R Turnover

R

Management Fee

Dividend % in stock

Market Returns Timing -8.93E-07 1.8545 -0.0002 0.0370 0.0806* 0.0014***

(0.4849) (0.2643) (0.4924) (0.1257) (0.0513) (0.0001)

Market Volatility Timing 4.99E-07 -11.9457 0.3322 -0.6248 -1.8562 -0.1098***

(0.9459) (0.9004) (0.1321) (0.6533) (0.4346) (0.0000)

Market Liquidity Timing 7.14E-07 0.8404 -0.0045** 0.0180 -0.0473* -0.004**

(0.3501) (0.3976) (0.0486) (0.2134) (0.0557) (0.0375)

Note:*, **, *** represent significance level at 10%, 5% and 1%.

time on fund-by-fund basis and store the coefficients of ∆R_{mt +1}, ∆V_t+1, and ∆L_t+1 as indicators for the valence of the three skills of the fund managers (timing ability).

Secondly, I average the characteristics for each fund (annual total asset value, annual

expense ratio, annual turnover rate, annual management fee per share, annual

dividend and the fraction invested in stocks) from the sample period 1999 to 2012.

Finally, I perform three cross-sectional analysis based on the following equation

(which is extended from equation 8):

Si = γ0,i+ γ1,iTNAi+ γ2,iExpi+ γ3,iTRi + γ4,iMFi + γ5,iDivi + γ6,iStocki+ εi,t (13)

where Si represents coefficients of the three timing abilities for fund i, TNA is average total asset value, TR is average turnover rate, MF is average management fee, Div is

average dividend and Stock is average fraction of investment in stocks. Because

26

those characteristics are all positive as shown in Table 2, the characteristics with

significantly positive coefficients are the ones which enhance the timing abilities of

three kinds. Table 7 demonstrates that the mutual funds which possess better market

return timing abilities invest in more stocks and pay relative higher dividends.

However, a larger fraction of investment in stocks seems to be a detrimental

characteristic for the funds with better volatility and liquidity timing abilities. In addition,

highly paid dividends and higher turnover ratios may be a warning signal that the

mutual funds are not able to predict future market liquidity. Investors, when choosing a

mutual fund, should keep their investment objective in minds. For instance, retirement

saving investors may be reluctant to be involved in highly unstable market and thus

should pick up a mutual fund which invests less in stocks.

7 Conclusion

This paper firstly adopts the extended TM model with Fama-French (1993) factors to

test whether or not mutual fund managers in the U.S market possess market timing

abilities. During the process, the biases which are induced by artificial timing effects

and heteroscedasticity and autocorrelation and which may distort the results are removed by adopting a dynamic model and a bootstrap approach. The results lead to the following conclusion.

Firstly, consistent with the conclusions of Treynor and Mazuy (1966), Henriksson and Merton (1981), Kon(1983), Lee and Rahman (1990), Bollen, Andreu, Alvarez, Ortiz

and Sarto (2014), Busse (2001), Chang and Lewellen (1984), Jiang (2003) and

Becker, Ferson, Myers and Schill (1999), there is no evidence to support the

existence of positive market return timing ability because only of a few funds show

significantly positive coefficients out of a large sample. Secondly, I employ a dynamic

model, removing biases induced by artificial timing, to directly see the relationship

between the change in market exposure of fund portfolios in the first period and the

return timing abilities. In addition, evidence in favor of market liquidity timing ability is

not strong, either. However, there is evidence to support the existence of market

volatility timing abilities. I find that within a year the volatility timing ability is

strengthened along the timing horizon meaning that the longer the horizon, the better

the skill. But from the mediate-term perspective of two years, this kind of ability vanishes. Thirdly, in fear of underestimating the fund managers’ expertise, I test their prediction ability of future market returns per unit of risk. Surprisingly, they show a

significantly negative timing ability. Finally, I use three cross-sectional analyses to find

common characteristics of the funds with better timing abilities. The mutual funds with

superior market returns timing abilities seem to include more stocks in their portfolios.

However, a larger fraction in stock investment may also signal that the mutual funds

are more likely to be involved in a highly unstable market.

To end this paper, I would suggest two directions for the further research. Firstly,

because in the dynamic model, the estimated beta at the beginning of each month

using one-month daily returns may be not so accurate, I recommend the further

research using daily data of portfolio composition if applicable. Thus, daily betas for

the funds can be obtained by averaging (weighted) the betas of stocks included in the

portfolios, which increases the test power of the dynamic model. Secondly, I would

recommend the further research to make questionnaires to ask fund managers what

other objective factors (besides market returns, market volatility and market liquidity)

they may consider when they adjust their portfolios because incorporating more

28

Reference

Becker, C., Ferson, W., Myers, D.H., Schill, M.J., 1999. Conditional market timing with

benchmark investors. Journal of Financial Economics, 52: 119–148.

Bodson, L., Cavenaile, L., and Sougne, D. 2013. A global approach to mutual funds

market timing ability. Journal of Empirical Finance, 20: 96-101

Busse JA (1999) Volatility timing in mutual funds: evidence from daily returns. Review

of Financial Study, 12:1009–41

Bollen, N., Busse, J., 2001. On the timing ability of mutual fund managers. Journal of

Finance, 56 (3): 1075–1094.

Chang, E., Lewellen, W., 1984. Impact of size and flows on performance for funds of hedge funds. Journal of Business, 57 (1): 57–72.

Lee, C., Rahman, S., 1990. Market timing, selectivity, and mutual fund performance: an empirical investigation. Journal of Business, 63 (2): 261–278

Chang, Matthew., 2012, Who offer Liquidity on Options Markets when Volatility is

High? Review of Pacific Basin Financial Markets and Policies, 15(4): 1-24

Cao, C., Simin, T., Wang, Y.2013. Do mutual fund managers time market liquidity?

Journal of Financial Markets, 16(2):279-207

Cumby, R., Glen, J., 1990. Evaluating the performance of international mutual funds.

Journal of Finance, 45: 497–521.

Do V, Faff R and Veeraraghavan M. 2009. Do Australian hedge fund managers possess timing abilities? Applied Financial Economics, 19: 27–38.

Fama, E., French, K., 1992. The cross-section of expected stock returns. Journal of

Finance, 47 (2): 427–465.

Glosten LR, Jagannathan R, Runkle DE (1993) On the relation between the expected value and the volatility of the nominal excess return on stocks. Journal of Finance,

48:1779–801

Goetzmann WN, Ingersoll J and Ivkovic Z (2000) Monthly measurement of daily timers. Journal of Financial and Quantitative Analysis, 35: 257–290.

Henriksson, R.D., Merton, R.C., 1981. On market timing and investment performance

II: statistical procedures for evaluating forecasting skills. Journal of Business, 54: 513–534.

Holmes K and Faff R (2004) Stability, asymmetry and seasonality of fund

performance: An analysis of Australian multi-sector managed funds. Journal of

Business Finance Accounting, 31: 539–578.

Jagannathan, R., Korajczyk, R., 1986. Assessing the market timing performance of managed portfolios. Journal of Business, 59: 217–236.

Jiang, G.J., Yao, T. and Yu, T., 2007 Do mutual funds time the market? Evidence

30

José Alvarez, Laura Andreu, Cristina Ortiz & José Luis Sarto,2014 A nonparametric approach to market timing: evidence from Spanish mutual funds, Journal of

economic and finance, 38: 119-132

Kon, S.J., 1983. The market timing performance of mutual fund managers. Journal of

Business, 56: 323–347.

Kosowski, R., Timmermann, A., White, H., Wermers, R., 2005. Can mutual fund stars

really pick stocks? New evidence from a bootstrap analysis. Journal of Finance,

61(6): 2551-2595

Ln, F., Kim, S., and Ji, P. 2014. On timing ability in Australian managed funds.

Australian Journal of Management, 39(1): 93-107.

Pastor, L., Stambaugh, R., 2003. Liquidity risk and expected stock returns. Journal of

Politics and Economics, 111 (3): 642–685

Treynor, J., Mazuy, K., 1966. Can mutual funds outguess the market? Harvard

Appendix: Joint market timing ability

Because the fund managers have shown strong skills at timing the market volatility,

we may underestimate fund managers’ expertise if we only separately look at their individual market factors timing ability, which means they may not adjust the market

exposure based on predicted market returns alone, but instead based on the joint

forecast of the market returns and market volatility. It indicates that even if the

managers forecast higher future market returns, they might not raise their portfolio

betas with concomitant higher sensitivity to future market volatility since they need to

protect their portfolio value from a highly unstable environment. Ln, Kim and Ji (2013)

also argue that industry practices are normally constrained by fund mandates which

comply managers to conservative behavior and force them to stay away from highly

volatile markets. The following model including Fama-French factors, which is an

extension of that adopted by Chen and Liang (2007), is adopted to test the fund managers’ timing ability of future market returns per unit of risk:

Ri,t = αi+ β_1,i,Rmt + β_2,i,HMLt+ β_3,i,SMBt+ δi(R_σmt) 2+ ε_i,t (14)

where σ is market wide volatility and δ measures joint timing ability. Chen and Liang (2007) suggest that when fund managers execute a buy-and-hold strategy, β₁ captures market exposure and δ, the joint timing coefficient for the return and risk, is 0. However, if mutual funds possess the joint timing ability, the coefficient is expected

to be significantly positive. As can be observed from Table 8, the coefficients from

squared ratio are -6.32*10-7, -3.30*10-7, -7.76*10-7 and -1.05*10-6 for each category

respectively and all of the coefficients of the joint timing ability for all categories are

significantly negative with p-values equal to 0 (even though the coefficients are very

small). It means the fund managers are also not adequate in terms of forecasting

32 Table 8 Result of joint timing ability

This table shows the results of equation (14) Ri,t= αi+ β1,i,Rmt+ β2,i,HMLt+ β3,i,SMBt+ δi(Rmt/ζt) 2+ εi,t

and lists the coefficients for all factors in the equation (12). The coefficients of (M/V)^2 indicates the ability of the fund managers’ joint timing ability. The loadings of HML and SML displays’ mutual fund investment styles and constant capture the selection ability. The numbers in parentheses are p-values for each coefficient.

Constant Rmt HML SML (Rmt/σ_t)^2

All funds 0.0006*** 0.8975*** 0.0782*** -0.0198*** -6.32E-07***

(0.000) (0.000) (0.000) (0.000) (0.000)

Growth funds 0.0003*** 0.9953*** -0.0421*** 0.9953*** -3.30E-07***

(0.000) (0.000) (0.000) (0.000) (0.000)

Growth and income funds 0.0006*** 0.9172*** 0.2066*** -0.0820*** -7.76E-07***

(0.000) (0.000) (0.000) (0.000) (0.000)

Balanced funds 0.0012*** 0.0692*** 0.1038*** -0.0347*** -1.05E-06***

(0.000) (0.000) (0.000) (0.000) (0.000)

Note:*, **, *** represent significance level at 10%, 5% and 1%.

Until now, all results lead to the conclusion that market returns timing ability does not

exist. In spite of such a fact, the results do show a strong skill at stock selection

because constant for all categories are significantly positive, which are 0.0006,

0.0003, 0.0006 and 0.00012 respectively. This test also provides us another

interesting findings on investment style. Since the mean of HML and SMB shown in

the Table 3 are positive, positive loadings of the two factors have positive effects on

the fund returns. The growth funds did invest in growth stocks and this is confirmed by

the significantly negative coefficient for HML (-0.0421). Moreover, they invest much

more in small-cap stocks, which is confirmed by a significantly positive coefficient for

SMB (0.9953). Growth and income funds primarily invest more in value stocks

(significantly positive coefficient for HML, 0.2066) and large-cap companies