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Market states and disposition effect: evidence fromTaiwan mutual fund investorsJen-Sin Lee a , Pi-Hsia Yen b & Kam C. Chan ca Department of Finance , I-Shou University , No.1, Sec. 1, Syuecheng Rd., Dashu District,Kaohsiung City, 84001 , Taiwanb Department of Finance , Vanung University , No. 1, Van-Nung Rd., Chung-Li, Tao-Yuan,32061 , Taiwanc Department of Finance , Western Kentucky University , 1 Big Red Way, Bowling Green , KY42101 , USAPublished online: 09 Dec 2011.
To cite this article: Jen-Sin Lee , Pi-Hsia Yen & Kam C. Chan (2013) Market states and disposition effect: evidence fromTaiwan mutual fund investors, Applied Economics, 45:10, 1331-1342, DOI: 10.1080/00036846.2011.617696
To link to this article: http://dx.doi.org/10.1080/00036846.2011.617696
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Applied Economics, 2013, 45, 1331–1342
Market states and disposition effect:
evidence from Taiwan mutual fund
investors
Jen-Sin Leea,*, Pi-Hsia Yenb and Kam C. Chanc
aDepartment of Finance, I-Shou University, No.1, Sec. 1, Syuecheng Rd.,
Dashu District, Kaohsiung City, 84001, TaiwanbDepartment of Finance, Vanung University, No. 1, Van-Nung Rd., Chung-
Li, Tao-Yuan, 32061, TaiwancDepartment of Finance, Western Kentucky University, 1 Big Red Way,
Bowling Green, KY 42101, USA
We study the disposition effect across market states in the context of mutual
fund investors in Taiwan. Usingmutual fund data at the fund and individual
levels during July 2001 to October 2008, we find that the disposition effect
varies across market states. Our results suggest that investors redeem their
mutual fund units more under a bear market than a bull market when they
have extreme capital losses. When investors have moderate capital gains,
they are less active in redeeming their mutual fund units under a bull market
relative to a bear market. Under a neutral market, investors actively redeem
mutual fund units in both winner and loser mutual funds except when they
have extreme capital losses. Thus, disposition effect is not uniform; it varies
by market condition. In addition, the disposition effect phenomenon also
exists for Taiwan mutual fund investors as well. Our findings are robust to
aggregate and individual investor levels.
Keywords: market states; disposition effect; mutual funds;
behavioural finance
JEL Classification: G15; G10
I. Introduction
In the context of behavioural finance, the disposition
effect refers to a phenomenon that investors sell
winners too early and ride losers too long (Shefrin
and Statman, 1985). Shefrin and Statman (1985) and
Frazzini (2006) suggest that the disposition effect of
investors is a result of the prospect theory and mental
accounting. When investors have unrealized invest-
ment gains, they are ‘risk-averse’ so they tend to sell
their investments too early to lock in their
investment gains. However, they become ‘risk-see-
kers’ when they have unrealized investment losses
because they tend to keep holding the money-losing
investments for too long. Previous behavioural
finance studies primarily document the existence of
the disposition effect without addressing the impact
of different market states on investors’ disposition
effect. We argue that market states (bear, bull or
neutral market) affect investors’ expectations of the
future market trend, and hence, intertwine with the
disposition effect.
*Corresponding author. E-mail: [email protected]
Applied Economics ISSN 0003–6846 print/ISSN 1466–4283 online � 2013 Taylor & Francis 1331http://www.tandfonline.com
http://dx.doi.org/10.1080/00036846.2011.617696
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The objective of this study is two-fold. First, westudy the disposition effect across market states.Since market state affects investor psychology regard-ing the future market trend, we contend that thedisposition effect varies by market states. In addition,the general investment literature on market statesusually limits the examination of the impact ofdifferent market states to various research issues tobull and bear markets only. Instead, we also study aneutral market state. Our findings offer new perspec-tives of the disposition effect. Second, we examine thedisposition effect with respect to mutual fund inves-tors in Taiwan. Barber et al. (2007) document thatTaiwan individual stock investors, as a group, exhibitthe disposition effect. More specifically, Barber et al.find that the aggregate Taiwan individual stockinvestor is about twice as likely to sell a stock ifthey are holding that stock for a gain rather than aloss. Our results in mutual funds enable us to examinewhether the disposition effect is also present formutual fund investors.
Our findings suggest that investors redeem theirmutual fund units more under a bear market than abull market when they have extreme capital losses.When investors have moderate capital gains, they areless active in redeeming their mutual fund units undera bull market relative to a bear market. Under aneutral market, investors actively redeem mutualfund units in both winner and loser mutual fundsexcept when they have extreme capital losses. Thus,the disposition effect is not uniform; it varies withrespect to different market conditions. Our findingsare robust to aggregate and individual levels.
The remainder of this article is organized asfollows: Section II describes the background andtestable hypotheses. Section III presents the data andresearch method. Section IV presents our findingsand discussion. Section V concludes the article.
II. Background and Testable Hypotheses
There is a voluminous literature on behaviouralfinance. To conserve space, we confine our discussionto the disposition effect and different market states.
The disposition effect
There are two strands of literature in dispositioneffect. The first strand of literature discusses thepresence of a disposition effect among investors.According to Shefrin and Statman (1985) and Chenet al. (2007), investors have pride and they avoidregrets. Chen et al. point out that ‘. . . investors often
sell stocks that have performed well so that they can
feel good about themselves. At the same time,
investors tend not to sell their poorly performing
stocks because they are not ready to acknowledge
that they made a mistake and because they are afraid
that the stocks may recovery’ (p. 427). Shefrin and
Statman (1984) suggest that investors refer to selling
appreciated stocks to realize investment gains and not
as liquidating their personal property. Therefore,
investors prefer to sell the winners to lock in the
unrealized gains quickly. However, investors prefer to
keep holding onto the losers as long as possible
because they refer to selling money-losing invest-
ments as selling their own personal property, which
they are reluctant to do. Many studies document the
presence of the disposition effect (e.g. Odean, 1998;
Frazzini, 2006; Barber et al., 2007). In general,
behavioural finance studies suggest that there exists
a disposition effect among investors.The second strand of literature offers extensions
on disposition effect research. Grinblatt and
Keloharju (2001) separate the investment losses
into extreme and moderate losses and characterize
the functional form of the disposition effect by
including dummy variables for extreme losses
(greater than 30%) and for moderate losses (less
than or equal to 30%), with a baseline of either
capital gains or no losses. They find that while both
moderate and extreme losses decrease investor pro-
pensity to sell their investments, there is a larger
effect when investors experience extreme losses over
moderate losses. Hung and Yu (2006) develop a
heterogeneous model of disposition effect. Hung and
Yu show that higher cognitive reference and less
risk-aversion attitude make the disposition effect
stronger. Da Costa et al. (2008) study relation
between gender and the disposition effect in an
experiment. They find that female participants do
not keep losing stocks and sell winners because their
reference points shifts. Lee et al. (2010), in a study
of mutual fund investors in Taiwan, examine the
herding behaviour of investors and the disposition
effect. Lee et al. document that during periods of
herding, investors actively redeem mutual fund units
when the funds experience moderate losses.
Investors, however, are more reluctant to redeem
the mutual funds with extreme capital losses.
Overall, the literature on the disposition effectsuggests that the disposition effect is not uniform.
The extent of the disposition effect depends on
investors’ characteristics as well as across different
levels of losses. The impact of different market states
(up or down market) on the disposition effect is not
clear. Our study fills this void.
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Market states and hypotheses development
Many studies find that investor investment behaviouris affected by market states (e.g. Lee et al., 2002;Cooper et al., 2004; Huang, 2006; Tetlock, 2007). Leeet al. (2002) argue that investor sentiment is associ-ated with different market states. Therefore, marketstate affects the investor’s investment decision. Theystate that ‘. . . bullish (bearish) shifts in sentiment leadto downward (upward) revisions in the volatility ofreturns and are associated with higher (lower) futureexcess returns’ (p. 2281).
Following Lee et al. (2002), we argue that thepatterns of investor disposition of funds vary acrossmarket states. Specifically, under a bull (bear)market, investors expect that the probability ofreversing losses into gains or limiting losses ishigher (lower). Thus, investors prefer to less (more)actively redeem the loser mutual funds units under abull (bear) market. Our first hypothesis is
H1: Mutual fund investors more actively redeemtheir mutual fund units when the mutual funds havelosses under a bear market than under a bull market.
When themarket is neutral, the market trend is hardto predict. Therefore, investors are likely to becautious. Thus, investors lock in the unrealized gainsand stop their losses quickly. We expect that investorsactively redeem their winner and loser mutual fundunits under a neutral market. Our second hypothesis is
H2: Investors actively redeem both winner and losermutual fund units under a neutral market.
Shefrin and Statman (1985) and Chen et al. (2007)suggest that investors often sell stocks that haveperformed well to feel good about themselves. Undera bull (bear) market, we expect investors to be moreoptimistic (pessimistic) about the future markettrend. Hence, investors are likely (less likely) tohold onto their mutual fund units if the mutual fundsonly provide moderate gains under a bull (bear)market. Our third hypothesis is
H3: Mutual fund investors are more (less) activelyto redeem their funds units when mutual funds havemoderate gains under a bear (bull) market.
III. Data and Methods
Data
We study the disposition effect of mutual fundinvestors in Taiwan. The data are obtained from
the Taiwan Securities Investment Trust and
Consulting Association. The sample is from July
2001 to October 2008. There are a total of 110 mutual
funds with monthly returns and other necessary data
such as redemption rate, market adjusted return, size,
turnover rate and management fees. Using mutual
fund monthly data, we investigate the disposition
effect in an aggregate basis. Many mutual studies use
the aggregate approach (e.g. Sirri and Tufano, 1998;
Shu et al., 2002; Lee et al., 2010). To get robust
results, we also obtain the individual-level data from
three mutual funds in a well-known local fund house.
The individual data cover August 2000 to October
2008, with 15 428 individuals and 663 288 records of
mutual fund redemption.
Identifying market states
While several studies use an ‘eye-ball’ approach to
identify bull and bear markets, we use a statistical
approach. Following Pagan and Sossounov (2003),
we determine the peak and the trough of the stock
market and then classify the market state as a bull
market, a bear market or a neutral market. Pagan
and Sossounov (2003) and Edwards et al. (2003) only
classify the market states into a bull and a bear
market. In our study, we extend their bull and bear
market conditions to include a neutral market defi-
nition. The specific procedures for identifying differ-
ent market states are as follows:
Step 1: Confirm locations of peak and trough –
According to Pagan and Sossounov, the peak and
trough represent relatively high and low points of a
stock index series during a period of time. Pagan and
Sossounov introduce the following equation:
Pt�8, . . . ,Pt�1 5Pt 4Ptþ1, . . . ,Ptþ8½ � ð1Þ
where Pt represents stock index of month t. Equation
1 suggests that if stock index, Pt, is higher than the
stock index for the previous 8 months and the
subsequent 8 months, then the corresponding loca-
tion of Pt can be regarded as one peak. Likewise, the
trough has to meet the requirements of Equation 2
Pt�8, . . . ,Pt�1 4Pt 5Ptþ1, . . . ,Ptþ8½ � ð2Þ
According to Equations 1 and 2, the peak (trough)
is higher (lower) than the stock index for the
subsequent 8 months. Edwards et al. refer to the
‘8 months’ as window width. In our study, the 8
months is the time length rather than the time width;
therefore, we refer to the 8 months as the window
length.
Market states and disposition effect 1333
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Step 2: Identify the bull and bear market state –
A bull market state is a continuous uptrend on stock
index levels and requires a large cumulative up-rangeand longer-lasting time for an uptrend. Therefore, a
bull market state has to meet three requirements.
First, from trough to peak, the stock index must be a
confirmed uptrend. Second, there must be more thana 20% cumulative increase in stock index values.
Third, the length of time between trough and peak
should be at least 4 months.1 When the stock index
hits a peak, it is the end of the uptrend; and then thestock index will move to a downtrend. We determine
a bear market state in a similar procedure. Since
Pagan and Sossounov (2003) only suggest procedures
to determine a bull and a bear market, we extendtheir study to include a neutral market.
Step 3: Identify a neutral market state – After
identifying bull and bear markets, we classify an
unspecified duration between the bull and bearmarkets as neutral market states. For example,
during the period between August 2004 and
October 2005 (a total of 15 months) for the Taiwan
market, the stock index has a narrow fluctuation thatcannot be clearly identified as bull or bear market.
When a stock price is in this type of a narrow
fluctuation, Katsenelson (2007) defines it as a ‘range-
bound market’. We follow Katsenelson and simplycall it a ‘neutral market’.
We identify the market states and conduct windowlength sensitivity analysis during the sample period
in Table 1. To obtain robust results, we vary thewindow length specified in Equations 1 and 2. Theclassification of a bull, bear and neutral market arerobust with a window length of 8 to 10months.We usea window length of 8 months to conduct our study.
Table 2 presents the stock market summary statis-tics of the specific bull, bear and neutral markets inTaiwan for our sample. In Panel A (the bull market)of Table 2, there are three sample periods that meetPagan and Sossounov’s definition of bull markets:October 2001 to March 2002, May 2003 to February2004, and November 2005 to October 2007. Each ofthe three periods has at least a 63% cumulativereturn. The bear market are shown in Table 2,Panel B. Each of the bear market periods has at leasta �20% cumulative return.2 The neutral market(Table 2, Panel C) lasts for 15 months, starting on theTaiwan stock index at 5420.57 points and closing at5764.30 points, a small increase of 6%. We plot thethree market states in Fig. 1. The bull, bear andneutral market states are consistent with the trend ofthe market in Taiwan.
Basic statistical models
Following the literature,3 we use the following basicmodel to examine the behaviour of mutual fundinvestors’ redemption in the full, bull, bear andneutral market samples as follows:
REDi,t¼ �þ�1MARi,t�1þ�2LNSIZEi,t�1þ�3TORi,t�1
þ�4FEEMi,t�1þ�5MASTDi,t�1þ �i,t ð3Þ
Table 1. Window length sensitivity analysis
Window length Bull market Bear market Neutral market
10 months Number of cumulative months 40 21 15Percentage of sample 52.63% 27.63% 19.74%
9 months Number of cumulative months 40 21 15Percentage of sample 52.63% 27.63% 19.74%
8 months Number of cumulative months 40 21 15Percentage of sample 52.63% 27.63% 19.74%
Notes: We classify the Taiwan stock market into bull, bear and neutral market states according to Pagan and Sossounov(2003). Because Pagan and Sossounov only suggest procedures to determine bull and bear markets, we extend their study toinclude a neutral market. While Pagan and Sossounov recommend using 8 months in their procedure, we also provide theresults in 9- and 10-month windows. The classification of market states is robust to three window lengths.
1 Pagan and Sossounov (2003) propose using a minimum of 4 months between the peak and the trough. The 4-month windowis also supported by Hamilton (1919) and Edwards et al. (2003).2 The actual periods of the first bull market was from April 2000 to September 2001 with a cumulative return of �63%. Inorder to meet our sample (July 2001 to October 2008) to match the mutual fund individual data, we cut apart of the first bullmarket periods from our sample beginning date July 2001 to the ending date of first bull market periods September 2001.3Other research is on the following: RED is used in O’Neal (2004) and Lee et al. (2010); MAR is cited from Garvey andMurphy (2004) and Frazzini (2006); LNSIZE andMASTD are cited from Sirri and Tufano (1998) and Shu et al. (2002); TORand FEE_M are cited from Cici (2005), Chevalier and Ellison (1997) and Jain and Wu (2000).
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where the following apply:
REDi,t the mutual fund redemption
rate. REDi,t¼Redeemi,t/
(Sizei,t�1), where Redeemi,t is
the volume of the redemption
of fund i in time t and Sizei,t�1represents the assets of fund i in
time t� 1.MARi,t�1 the market adjusted return of
the mutual fund. MARi,t�1¼
Ri,t�1�Rm,t�1, Ri,t�1 is the raw
return of fund i in time
t� 1. Ri,t�1¼(Netvaluei,t�1�
Netvaluei,t�2)/Netvaluei,t�2,
where Netvaluei,t�1 and
Netvaluei,t�2 are the total net
asset values of fund i in times
t� 1 and t� 2. Rm,t�1 is the
market performance of the
stock index in time t� 1.
Rm,t�1¼(Indext�1� Indext�2)/
Indext�2, where Indext�1 and
Indext�2 are the market indexes
of fund i in times t� 1 and t� 2.LNSIZEi,t�1 the natural logarithm of total
net assets. LNSIZEi,t�1 is the
natural logarithm of total net
assets of fund i in time t� 1.TORi,t�1 the turnover rate. TORi,t�1 is
the turnover rate of fund i in
Table 2. Summary statistics of Taiwan market index under different market states
Beginning date Ending dateChanges inmarket index
Length ofmarket state(months) Total months
% share ofsample period
Panel A: Bull marketFirst period 2001/10 2002/3 70% 6 40 52.63%
(3636.94) (6167.47)Second period 2003/5 2004/2 63% 10
(4148.07) (6750.54)Third period 2005/11 2007/10 68% 24
(5764.30) (9711.37)
Panel B: Bear marketFirst period 2001/7 2001/9 �16%a 3 21 27.63%
(4352.98) (3636.94)Second period 2002/4 2003/4 �33% 13
(6167.47) (4148.07)Third period 2004/3 2004/7 �20% 5
(6750.54) (5420.57)
Panel C: Neutral marketFirst period 2004/8 2005/10 6% 15 15 19.74%
(5420.57) (5764.30)
Notes: This table summarizes the movement of the Taiwan market index during July 2001 to October 2007. We use Pagan andSossounov’s (2003) definition to classify the Taiwan market into bull, bear and neutral markets in Taiwan in our sample. Theactual periods of the first bear market is April 2000 to September 2001, with a �63% cumulative return, but in order to meetour sample (July 2001 to October 2008), we cut apart of the first bull market periods from our sample begin of July 2001 toSeptember 2001.
Fig. 1. Distribution of market statesNotes: This figure plots the movement of the Taiwanmarket index during July 2001 to October 2007. We usePagan and Sossounov’s (2003) definition to classify theTaiwan market into bull, bear and neutral markets inTaiwan in our sample. Horizontal axis represents time, andvertical axis represents stock index. Dark gray shadow,white and light gray shadow areas are bull market, bearmarket and neutral market states, respectively.
Market states and disposition effect 1335
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time t� 1 and is the turnover/
total net assets.FEEMi,t�1 the management fees ratio.
FEEMi,t�1 is the managementfee ratio of fund i in time t� 1and is the management fees/total net assets.
MASTDi,t�1 the mutual fund risk.MASTDi,t�1 is the SD of fundi in time t� 1, MASTDi,t�1¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiP12
k¼1 ðMARi,t�k�MARiÞ2=11
q,
where MARi,t�k is the market-adjusted return of fund i in timet� k and MARi is the mean ofthe market-adjusted return offund i from times t� 1 to t� 12.
�i,t a random error term.
To examine the testable hypotheses, we modify
Equation 3 to include various levels of mutual fund
gains and losses. We also follow Lee et al. (2010) to
classify the mutual fund gains and losses in five
different categories. Because there are 110 different
mutual funds, we include dummy variables to
account for the fixed effect from each mutual fund.
Hence, the empirical model is as follows:
REDi,t ¼X110
i¼1
�iDi þ �1EXTREWINi,t�1
þ �2MODERWINi,t�1
þ �3TIEi,t�1 þ �4MODERLOSi,t�1
þ �5EXTRELOSi,t�1
þ �6LNSIZEi,t�1 þ �7TORi,t�1
þ �8FEE Mi,t�1
þ �9MASTDi,t�1 þ "i,t ð4Þ
where the following apply:
EXTREWINi,t�1 an extreme capital gains for a
mutual fund at t� 1,MODERWINi,t�1 a moderate capital gains for a
mutual fund at t� 1,TIEi,t�1 ineligible capital gains or losses
for a mutual fund at t� 1,EXTRELOSi,t�1 an extreme losses for a mutual
fund at t� 1,
MODERLOSi,t�1 a moderate losses for a mutualfund at t� 1,
Di dummy variables for the ithmutual fund, and
"i,t a random error term.
Other variables are defined earlier. We estimateEquation 4 four times: the full sample and the bull,bear and neutral markets. For the five performanceindicators in Equation 4, we classify the mutual fundperformance into five indicators, namely, an extremecapital gain (EXTREWIN), a moderate capital gain(MODERWIN), ineligible capital gains or losses(TIE), a moderate capital loss (MODERLOS), andan extreme capital loss (EXTRELOS). TIE is therange that MAR falls into �10%. The remainingpositive 90% is further divided into two parts, whereEXTREWIN and MODERWIN fall within therange of the top 45% and the middle 45% ofMAR, respectively. Similar definitions apply toEXTRELOS and MODERLOS for the remainingnegative 90% of MAR.
To investigate the disposition effect, we setEXTREWIN, MODERWIN, MODERLOS,EXTRELOS and TIE in each model at the sametime. Therefore, the five performance indicators arenot only dummy variables, but they are dummyvariables series times the real value of the perfor-mance value series. For example, EXTREWIN is adummy variable series times the real value of theperformance value series (MAR). This approach canmitigate the collinear problem because of too manydummy variables.
In addition, our estimation could suffer fromendogeneity because the explanatory variable, fundsize (LNSIZE ), can be influenced by the redemptionrate (RED).4 Therefore, we mitigate endogeneity byusing an instrumental variable approach to replacethe fund size variable. We follow the proceduresin Kasanen et al. (2001), Khorana et al. (2005),and Lee et al. (2010) to indentify an instrumentalvariable to proxy the fund size variable. Essentially,we choose one set of explanatory variables, thosewhich have the lowest correlation with the redemp-tion rate and the highest correlation with the fundsize variable, to be the instrumental variable for theLNSIZE. As a result, we use the lags of the fiveperformance indicator variables and turnover rate toget a predicted value of the fund size variable. Thatis, we conduct the following multiple regressionanalysis to obtain the predicted LNSIZEt�1 as the
4When mutual fund investors redeem their units, the fund size drops or vice versa.
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instrument for LNSIZEt�1:
LNSIZEi,t�1 ¼ �0 þ �1EXTREWINi,t�2
þ �2MODERWINi,t�2 þ �3TIEi,t�2
þ �4MODERLOSi,t�2
þ �5EXTRELOSi,t�2
þ �6TORi,t�2 þ �i,t�1 ð5Þ
Then our empirical model becomes
REDi,t ¼X110i¼1
�iDi þ �1EXTREWINi,t�1
þ �2MODERWINi,t�1
þ �3TIEi,t�1 þ �4MODERLOSi,t�1
þ �5EXTRELOSi,t�1
þ �6LNSIZEi,t�1 þ �7TORi,t�1
þ �8FEE Mi,t�1
þ �9MASTDi,t�1 þ "i,t ð6Þ
The model coefficients and hypotheses
First, the hypothesis H1 is supported in Equation 6when the coefficient of MODERLOS (�4) under abear market is smaller than the same coefficient undera bull market.5 Similarly, H1 is supported if thecoefficient of EXTRELOS (�5) under a bear market issmaller than the same coefficient under a bull market.
Second, H2 is supported when the coefficient ofEXTREWIN (�1) and MODERWIN (�2) are allsignificantly positive in Equation 6 and the coeffi-cients of MODERLO (�4) and EXTRELOS (�5) aresignificantly negative under a neutral market.
Third, H3 is supported when the coefficient ofMODERWIN (�2) under a bull market is smallerthan the same coefficient under a bear market inEquation 6.
IV. Results and Discussions
Descriptive statistics
In Table 3, Panels A to D present the summarystatistics for the full sample and the bull, bear andneutral markets, respectively. The number of obser-vations for the aggregate mutual fund data rangesfrom 1650 in the neutral market to 4400 in the bullmarket with a total of 8360 in the full sample. We also
find that the mean of the mutual fund marketadjusted return (MAR) is 0.82% and �0.50% undera bear and a bull market, respectively. Thus, onaverage, fund investors in aggregate basis receivebetter (worse) market performance under a bull(bear) market.
The means of the redemption rate under eachmarket state are given in Table 4. The redemptionrates under each market state are different, suggestingthat mutual fund investor aggregate redemptionbehaviour is different across market states. Forexample, the mean redemption rate when mutualfunds have extreme capital gains (EXTREWIN)under bull, bear and neutral markets are 11.04%,5.32% and 8.13%, respectively. Hence, it would beinteresting to examine the disposition effect acrossmarket states.
Hypotheses
Table 5 presents the results of Equation 6 for theaggregate redemption behaviour across market states.We present the full sample and the bull, bear andneutral markets in columns (2) to (5). However, weneed to be cautious when we interpret the coefficientsfor the extreme and moderate capital losses coeffi-cients. Because the two variables are negative innature, positive estimated coefficients actually meanless redemption or vice versa.
For the full sample, the mutual size, fee and riskare positive and significant at the 1% level. Hence,mutual redemption rate is positively associated withsize, fee and risk. The estimated coefficients for bothextreme capital gains and capital losses are positiveand significant at the 1% level. The findings suggestthat when a mutual fund has extreme capital gains,the mutual fund investors redeem more of their units(estimated coefficient of 0.33). On the contrary, whena mutual fund has an extreme capital loss, the mutualfund investors redeem less of their units (estimatedcoefficient of 0.18). Therefore, in general, Taiwaninvestors exhibit the disposition effect because theyredeem more when their investments have good gainsand they redeem less when their investments havelosses.
For the subsamples under bull, bear and neutralmarkets, the findings are similar with respect tocontrol variables of size, fee and risk. These controlvariables continue to be positive and significant,suggesting that they relate to the mutual fundaggregate redemption behaviour irrespective to themarket state. However, the relation between mutual
5 The significantly positive coefficient of loser mutual funds (�4 and �5) stands for that investors redeem their mutual fundunits less in relative to the insignificantly coefficient of loser mutual funds.
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fund gains/losses and redemption rates is different
with respect to market states. The magnitude and
significance of the mutual fund performance variables
(extreme gains, moderate gains, ineligible gains,
moderate losses and extreme losses) are not stable
across market states. Hence, it is imperative to
examine closely how market states interact with the
disposition effect.We present the results for the individual data in
Table 6. While the magnitude of the specific coeffi-
cients is different from those in Table 5, the results
are qualitatively similar. First, with the exception of
the risk variable under a bear market, the control
variables are very stable across market states in terms
of magnitude and statistical significance. Second, the
results in the full sample suggest a disposition effect
at the individual investor level. Third, the results
across market states hint that disposition effects vary
by market state.The hypothesis testing requires additional calcula-
tion. We summarize the results in Table 7.
Specifically, we conduct t-tests to examine if the
Table 3. Summary statistics for variables
RED MAR SIZE TOR FEE_M MASTD
Panel A: Full samplesMean 6.89% 0.50% 1102.36 31.51% 0.13% 17.09%Median 4.27% 0.19% 1090.85 25.48% 0.13% 4.45%Maximum 195.16% 22.98% 22 522.20 222.97% 1.41% 355.36%Minimum 0.00% �14.87% 4.53 �0.34% 0.01% 0.61%SD 0.09 0.04 0.86 0.25 0.03 0.48Observations 8360 8360 8360 8360 8360 8360
Panel B: Bull marketMean 8.48% 0.82% 1140.61 32.11% 0.13% 28.88%Median 5.78% 0.41% 1125.00 25.57% 0.13% 4.87%Maximum 195.16% 17.56% 22 522.20 222.97% 0.48% 355.36%Minimum 0.00% �14.87% 4.53 0.01% 0.03% 0.61%SD 0.10 0.04 0.89 0.26 0.02 0.63Observations 4400 4400 4400 4400 4400 4400
Panel C: Bear marketMean 4.54% �0.50% 1030.16 36.43% 0.13% 4.46%Median 2.19% �0.44% 989.00 31.16% 0.14% 4.52%Maximum 114.21% 14.15% 10 063.72 205.97% 1.41% 10.05%Minimum 0.05% �14.18% 55.19 0.00% 0.05% 0.68%SD 0.07 0.05 2.27 0.26 0.04 0.01Observations 2310 2310 2310 2310 2310 2310
Panel D: Neutral marketMean 5.92% 1.06% 1106.62 23.02% 0.13% 3.30%Median 3.62% 0.41% 1099.63 19.38% 0.13% 3.14%Maximum 59.05% 22.98% 9536.57 129.29% 0.17% 7.66%Minimum 0.12% �9.71% 75.50 �0.34% 0.01% 0.84%SD 0.07 0.04 2.34 0.18 0.02 0.01Observations 1650 1650 1650 1650 1650 1650
Notes: This table presents the summary statistics for the variables. Panels A–D present the statistics in the full samples, bullmarket, bear market and neutral market, respectively. REDi,t¼ the mutual fund redemption rate. REDi,t¼Redeemi,t/(Sizei,t�1), where Redeemi,t is the volume of redemption of fund i in time t and Sizei,t�1 represents the assets of fund i in timet� 1. MARi,t�1¼ the market adjusted return of the mutual fund. MARi,t�1¼Ri,t�1�Rm,t�1, Ri,t�1 is the raw return of fund iin time t� 1. Ri,t�1¼ (Netvaluei,t�1�Netvaluei,t�2)/Netvaluei,t�2; Netvaluei,t�1 and Netvaluei,t�2 are the total net asset valuesof fund i in times t� 1 and t� 2. Rm,t�1 is the market performance of stock index in time t� 1; Rm,t�1¼ (Indext�1� Indext�2)/Indext�2, where Indext�1 and Indext�2 is the market index of fund i in times t� 1 and t� 2. LNSIZEi,t�1¼ the naturallogarithm of total net assets; LNSIZEi,t�1 is the natural logarithm of total net assets of fund i in time t� 1. TORi,t�1¼ theturnover rate; TORi,t�1 is the turnover rate of fund i in time t� 1 and is the turnover/total net assets. FEEMi,t�1¼ themanagement fees ratio; FEEMi,t�1 is the management fee ratio of fund i in time t� 1 and is the management fees/total netassets. MASTDi,t�1¼ the mutual fund risk; MASTDi,t�1 is the SD of fund i in time t� 1; MASTDi,t�1 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiP12
k¼1 ðMARi,t�k �MARiÞ2=11
q, where MARi,t�k is the market adjusted return of fund i in time t-k; MARi is the mean of
the market adjusted return of fund i from time t� 1 to t� 12.
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coefficients are statistically significant different along
H1 and H3. We use the following t-statistics to
calculate the difference between any two estimated
coefficients, A and B
t ¼ ð�A � �BÞ=ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�2A=nA � �
2B=nB
q
where � is the SE of an estimated coefficient and n is
the number of observations. For H1 in relation to the
moderate capital losses, the estimated coefficients
under bear and bull markets are 0.31 and 0.37,
suggesting that the redemption rate in the bear
market is �0.31% for every percent of loss while
the redemption rate is �0.37% under a bull market.
The corresponding t-statistic is �7.99 suggesting that
the coefficient under a bear market is smaller than the
bull market. Hence, the finding supports H1 with
respect to moderate capital losses. With extreme
capital losses situation, H1 is not supported since the
t-statistic is positive and significant.For H2, we can simply examine the results under a
neutral market state. The results in Tables 5 and 6 for
a neutral market state show that the coefficients
associated with capital gains are positive and signif-
icant while the coefficients associated with moderate
capital losses are negative and significant. The
positive (with capital gains) and negative (with capital
losses) coefficients suggest that investors are actively
redeeming their mutual fund units under a neutral
market, which is consistent with the H2.
For H3, we conduct the t-tests based on the
coefficients under bull and bear markets when
the mutual funds have moderate capital gains. The
t-statistics are negative and significant, suggesting
Table 4. Mean of redemption rate under each market state
Fullsamples
Bullmarket
Bearmarket
Neutralmarket
EXTREWIN 9.02% 11.04% 5.32% 8.13%MODERWIN 6.23% 7.32% 4.41% 5.02%TIE 6.41% 8.33% 4.83% 4.41%MODERLOS 6.62% 8.01% 3.81% 5.70%EXTRELOS 6.30% 7.82% 4.34% 6.62%
Notes: This table presents the mean mutual fund redemp-tion rate under each market state. The numbers in the tableare the mean of the redemption rate (in %). We classify themutual fund performance into five levels, namely, extremecapital gains (EXTREWIN), moderate capital gains(MODERWIN), ineligible capital gains or losses (TIE),moderate capital losses (MODERLOS), and extreme cap-ital losses (EXTRELOS). TIE is the range that the market-adjusted return (MAR) falls into �10%. The remainingpositive 90% is further divided into two parts, whereEXTREWIN and MODERWIN fall within the range of thetop 45% and the middle 45% ofMAR, respectively. Similardefinitions apply to EXTRELOS and MODERLOS for theremaining negative 90% of MAR.
Table 5. Aggregate mutual fund redemption rate regression
equations
Dependent variable: Redemption rate (RED)
Market states
Full
samples
Bull
market
Bear
market
Neutral
market
EXTREWIN
(�1)0.33*** 0.47*** 0.13* 0.54***
(0.04) (0.06) (0.07) (0.05)
MODERWIN
(�2)
�0.24** �0.40*** 0.06 0.65***
(0.10) (0.13) (0.18) (0.20)
TIE (�3) �0.96*** �0.90** 0.03 1.22*
(0.35) (0.42) (0.41) (0.62)
MODERLOS
(�4)
0.09 0.37*** 0.31** �1.04***
(0.15) (0.27) (0.14) (0.37)
EXTRELOS
(�5)0.18*** 0.28*** 0.05 �0.16
(0.04) (0.08) (0.05) (0.12)
LNSIZE^
0.03*** 0.03*** 0.07*** 0.06***
(0.00) (0.00) (0.00) (0.01)
TOR �9.E�04 5.E�03 �2.E�03 �0.03***
(0.00) (0.01) (0.01) (0.01)
FEE_M 0.33*** 1.93*** 0.14*** 2.99***
(0.04) (0.14) (0.03) (0.16)
MASTD 0.01*** 2.E�03 �0.51*** 0.42**
(0.00) (0.00) (0.13) (0.18)
N 8360 4400 2310 1650
Adjusted R2 5.84% 8.38% 7.82% 6.83%
Notes: This table presents the results of Equation 6 for theaggregate redemption behaviour across market states. Wepresent the full sample and the bull, bear and neutralmarkets in columns (2) to (5). We are cautious when weinterpret the coefficients for the extreme and moderatecapital losses coefficients; because the two variables arenegative in nature, positive estimated coefficients mean lessredemption or vice versa. RED is redemption rate,EXTREWIN is extreme capital gains, MODERWIN ismoderate capital gains, TIE is ineligible capital gains orlosses, MODERLOS is moderate capital losses,EXTRELOS is extreme capital losses, LNSIZE
^
is theinstrumental variable for LNSIZE. The definitions of thevariables are presented in Table 3. The significantlynegative coefficient of winner mutual funds (�1 and �2)stands for that investors less active in redeeming theirmutual fund units in relative to the insignificantly coeffi-cient of winner mutual funds. The significantly positivecoefficient of loser mutual funds (�4 and �5) stands for thatinvestors redeem their mutual fund units less in relative tothe insignificantly coefficient of loser mutual funds. SEs areshown in parentheses.*, ** and *** denote significance at the 10, 5 and 1% levels,respectively.
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that investors are likely to hold on to their mutualfund units when compared with a bear market. Thefindings support H3.
V. Conclusion
We study the disposition effect of mutual fundinvestors in Taiwan. Specifically, we examine whetherfund investors have different patterns of dispositioneffect across different categories of gains and lossesunder bull, bear and neutral markets.
We offer several interesting results. First, Taiwanmutual fund investors also exhibit a dispositioneffect, a result consistent with the results of Taiwanstock investors in Barber et al. (2007). Second,
investors redeem their mutual fund units more
under a bear market than a bull market when they
have extreme capital losses. Third, when investors
have moderate gains, they are less active in redeeming
their mutual fund units under a bull market relative
to a bear market. Fourth, under a neutral market,
investors actively redeem mutual fund units in both
winner and loser mutual funds except when they have
extreme capital losses. Thus, disposition effect is not
uniform; it varies by market condition. Our findings
are robust to aggregate and individual investor levels.Our findings offer two implications. Different
market states affect investor psychology regarding
future market trends and thus, the disposition effect
varies across bull, bear and neutral markets. Future
research in deposition effect needs to consider the
impact of different market states to disentangle the
Table 6. Individual investor mutual fund redemption rate regression equations
Dependent variable: Redemption rate (RED)
Market states
Full samples Bull market Bear market Neutral market
EXTREWIN (�1) 0.32*** 0.42*** 0.10* 0.50***(0.03) (0.03) (0.03) (0.04)
MODERWIN (�2) �0.18** �0.45*** 0.07 0.60***(0.06) (0.12) (0.12) (0.18)
TIE (�3) �0.75*** �0.88** 0.01 1.02*(0.13) (0.40) (0.33) (0.43)
MODERLOS (�4) 0.07 0.40** 0.32** �0.95***(0.10) (0.31) (0.12) (0.36)
EXTRELOS (�5) 0.12*** 0.20*** 0.05 �0.13(0.03) (0.06) (0.05) (0.11)
LNSIZE^
0.01*** 0.03*** 0.05*** 0.03***(0.00) (0.00) (0.00) (0.00)
TOR �9.E�04 5.E�03 �2.E�03 �0.02***(0.00) (0.01) (0.01) (0.01)
FEE_M 0.28*** 1.90*** 0.13*** 2.65***(0.03) (0.10) (0.03) (0.13)
MASTD 0.01*** 2.E�03 �0.34*** 0.41**(0.00) (0.00) (0.13) (0.16)
N 663 288 663 288 663 288 663 288Adjusted R2 4.38% 5.13% 6.22% 5.33%
Notes: This table presents the results of Equation 6 for the individual mutual fund investors’ redemption behaviour in threemutual funds across different market states. We present the full sample and the bull, bear and neutral markets in columns (2)to (5). We are cautious when we interpret the coefficients for the extreme and moderate capital losses coefficients; becausethese two variables are negative in nature, positive estimated coefficients mean less redemption or vice versa. RED isredemption rate, EXTREWIN is extreme capital gains, MODERWIN is moderate capital gains, TIE is the ineligi-
ble capital gains or losses, MODERLOS is moderate capital losses, EXTRELOS is extreme capital losses, LNSIZE^
is theestimated value of the natural logarithm of total net assets, TOR is turnover rate, FEE_M is management fees ratio, andMASTD is riskiness of funds. The definitions of the variables are presented in Table 3. The significantly negative coefficient ofwinner mutual funds (�1 and �2) stands for that investors less active in redeeming their mutual fund units in relative to theinsignificantly coefficient of winner mutual funds. The significantly positive coefficient of loser mutual funds (�4 and �5)stands for that investors redeem their mutual fund units less in relative to the insignificantly coefficient of loser mutual funds.SEs are shown in parentheses.*, ** and *** denote significance at the 10, 5 and 1% levels, respectively.
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Table
7.
Asummary
ofhypotheses
testingresults
Aggregate
data
Individualdata
Hypotheses
testing
Description
t-statistics
Results
t-statistics
Results
H1
ThecoefficientofMODERLOS(�4)
under
abearmarket
issm
aller
thanthesamecoefficientunder
abullmarket.
�7.99
Supported
�469.64
Supported
H1
ThecoefficientofEXTRELOS(�5)
under
abearmarket
issm
aller
thanthesamecoefficientunder
abullmarket.
144.41
Notsupported
1563.08
Notsupported
H2
ThecoefficientofEXTREWIN
(�1)
andMODERWIN
(�2)are
all
significantlypositivein
Equation4
andthecoefficientofMODERLO
(�4)andEXTRELOS(�5)are
all
significantlynegativeunder
aneu-
tralmarket.
�1and�2are
positiveand
significant;�4isnegative
andsignificant
Threeoutoffourcoeffi-
cients
supported
�1and�2are
positive
andsignificant;�4is
negativeand
significant
Threeoutoffourcoeffi-
cients
supported
H3
ThecoefficientofMODERWIN
(�2)
under
abullmarket
issm
aller
than
thesamecoefficientunder
abear
market.
�23.66
Supported
�2485.39
Supported
Notes:
This
table
summarizesthehypotheses
testing.Specifically,weconduct
t-testsbasedontheregressionresultsin
Tables5and6to
examineifthecoefficients
are
statisticallysignificantdifferentalongH1andH3.Wecalculate
t-statisticsforthedifference
inanytw
oestimatedcoefficients,A
andBast¼(�
A��B)/(�
2 A/n
A��2 B/n
B);
where�istheSE
ofanestimatedcoefficientandnisthenumber
ofobservations
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impact on disposition effect on investor behaviour.As for the mutual fund houses, they can use ourresults to help plan their cash holding to meet theanticipated mutual fund investor redemption. Forinstance, in a bull market, investors are relativelymore reluctant to redeem mutual fund shares than ina bear market for a loser mutual fund. Therefore, thecash holding requirement for a mutual fund housemay be less in a bull market than in a bear market.
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