This article was downloaded by: [Nanyang Technological University] On: 16 February 2014, At: 19:22 Publisher: Routledge Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK Applied Financial Economics Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/rafe20 Extreme returns in emerging stock markets: evidence of a MAX effect in South Korea Gilbert V. Nartea a , Ji Wu b & Hong Tao Liu c a Department of Accounting, Economics, and Finance, Faculty of Commerce, Lincoln University, Lincoln, New Zealand b Institute for Financial & Accounting Studies (IFAS), Xiamen University, Xiamen, Fujian 361005, PR China c Inland Revenue Department of New Zealand, Papanui, Christchurch, New Zealand Published online: 12 Feb 2014. To cite this article: Gilbert V. Nartea, Ji Wu & Hong Tao Liu (2014) Extreme returns in emerging stock markets: evidence of a MAX effect in South Korea, Applied Financial Economics, 24:6, 425-435 To link to this article: http://dx.doi.org/10.1080/09603107.2014.884696 PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http:// www.tandfonline.com/page/terms-and-conditions
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This article was downloaded by: [Nanyang Technological University]On: 16 February 2014, At: 19:22Publisher: RoutledgeInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House,37-41 Mortimer Street, London W1T 3JH, UK
Applied Financial EconomicsPublication details, including instructions for authors and subscription information:http://www.tandfonline.com/loi/rafe20
Extreme returns in emerging stock markets: evidenceof a MAX effect in South KoreaGilbert V. Narteaa, Ji Wub & Hong Tao Liuc
a Department of Accounting, Economics, and Finance, Faculty of Commerce, LincolnUniversity, Lincoln, New Zealandb Institute for Financial & Accounting Studies (IFAS), Xiamen University, Xiamen, Fujian361005, PR Chinac Inland Revenue Department of New Zealand, Papanui, Christchurch, New ZealandPublished online: 12 Feb 2014.
To cite this article: Gilbert V. Nartea, Ji Wu & Hong Tao Liu (2014) Extreme returns in emerging stock markets: evidence of aMAX effect in South Korea, Applied Financial Economics, 24:6, 425-435
To link to this article: http://dx.doi.org/10.1080/09603107.2014.884696
PLEASE SCROLL DOWN FOR ARTICLE
Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) containedin the publications on our platform. However, Taylor & Francis, our agents, and our licensors make norepresentations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of theContent. Any opinions and views expressed in this publication are the opinions and views of the authors, andare not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon andshould be independently verified with primary sources of information. Taylor and Francis shall not be liable forany losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoeveror howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use ofthe Content.
This article may be used for research, teaching, and private study purposes. Any substantial or systematicreproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in anyform to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions
aDepartment of Accounting, Economics, and Finance, Faculty of Commerce,Lincoln University, Lincoln, New ZealandbInstitute for Financial & Accounting Studies (IFAS), Xiamen University,Xiamen, Fujian 361005, PR ChinacInland Revenue Department of New Zealand, Papanui, Christchurch, NewZealand
We investigate the significance of extreme positive returns (MAX) in the cross-sectional pricing of stocks in South Korea. Our results provide important out-of-sample evidence of a strong negative MAX effect similar to that documented byBali et al. (2011) in the US stock market. For equal-weighted portfolios, thedifference between returns on the portfolios with the highest and lowest max-imum daily returns is −1.87% per month. The corresponding difference in alpha is−1.41% per month. The results are robust to controls for size, value, skewness,momentum, short-term reversal and idiosyncratic volatility. We also sort theportfolios by the average of the five highest daily returns within the month andreport return and alpha spreads of −2.21% and −2.01% per month, respectively.However, unlike in Bali et al. (2011), the MAX effect cannot reverse theidiosyncratic volatility effect in the South Korean stock market. Our resultsimply investor preference for high-MAX stocks, consistent with cumulativeprospect theory (CPT) where investors sub-optimally overweight the possibilitythat extreme returns will persist. The MAX effect is also consistent with theoptimal expectations framework where investors derive utility from overestimat-ing the probabilities of events in which their investments pay off well.
Keywords: extreme returns; asset pricing; idiosyncratic volatility; South Korea
JEL Classification: G12; G11
I. Introduction
In a recent study, Kumar (2009) suggests that individualinvestors exhibit a preference for stocks with lottery-likefeatures. These are low-priced stocks that are highly vola-tile and offer the possibility of huge returns albeit with alow probability. Stocks that exhibit extreme positivereturns can also be considered as lottery-like. Adopting
this definition, Bali et al. (2011) investigate the role ofextreme positive returns (MAX) in the cross-sectionalstock pricing of the US stock market in the period fromJuly 1962 to December 2005. Consistent with investorpreference for lottery-like stocks, they found that stockswith the lowest MAX outperform stocks with the highestMAX by as much as 1.03% per month. They also reportthat the negative MAX effect persists even after
controlling for size, value, momentum, short-term reversaland illiquidity. As a further robustness test, they also sortstocks on the average of two, three, four and five highestdaily returns within the month with similar results. Theyexplain the negative MAX effect as a result of investors’biased preference for stocks with extreme positive returns,paying too much for these stocks, resulting in underper-formance in the following month. Following Bali et al.’s(2011) study, Annaert et al. (2013) find a negative MAXeffect in 13 European stock markets from 1979 to 2011.However, Annaert et al. (2013) show that the negativeMAX effect only exists in equal-weighted portfolios, butnot in value-weighted portfolios; the results suggest thatthe negative MAX effect may be only a small-firm phe-nomenon. Such investor behaviour is consistent with twodescriptive models of decision making under uncertainty –Tversky and Kahneman’s (1992) cumulative prospecttheory (CPT), as recently extended by Barberis andHuang (2008) and Kothiyal et al. (2011),1 and the optimalexpectations framework of Brunnermeier and Parker(2005) and Brunnermeier et al. (2007).Cumulative pro-spect theory is a nonexpected utility model where decisionmakers evaluate risk using a value function that is concaveover gains and convex over losses, and where the functionis steeper for losses than for gains.2 Instead of objectiveprobabilities, the model uses transformed probabilities,which are obtained by applying a weighting function toobjective probabilities. This weighting function over-weights small probabilities and underweights moderateand high probabilities, which means overweighting tailsof distributions it is applied to. Such overweighting of tailsdoes not represent a bias in beliefs but is simply a model-ling device that captures the common preference for lot-tery-like, or positively skewed, wealth distributions(Barberis and Huang, 2008).
The optimal expectations framework of Brunnermeierand Parker (2005) and Brunnermeier et al. (2007) is aformulation of the expected utility framework that usessubjective probabilities. In this framework, decisionmakers choose to distort their beliefs about future prob-abilities in order to maximize their current utility.Investors maximize their expected present discountedvalue of utility flows and are happy to overestimate theprobabilities of events in which their investments pay offwell. However, these distorted beliefs necessarily lead tosuboptimal decision making and lower levels of utilityon average ex post. This in turn tempers investors’tendency to be too optimistic. Optimal subjective andobjective probabilities differ in this model because thecosts of small deviations from optimal behaviour arelower than the benefits of optimism. Brunnermeier
et al. (2005) show that this model leads to three stylizedfacts. First, portfolios are not optimally diversified.Second, investors exhibit preference for lottery-likeassets, i.e. assets with positive skewness. Third, theselottery-like assets (positively skewed returns) tend tohave lower returns.
Kumar (2009) defines stocks with lottery-like featuresas those with a low price, high idiosyncratic skewness, andhigh idiosyncratic volatility. Indeed, studies show thatskewness and volatility of returns play an important rolein gambling decisions. Golec and Tamarkin (1998) findthat gamblers exhibit a preference for positive skewnessrather than risk as normally measured by variance. Mittonand Vorkink (2007) find that the portfolio returns of under-diversified investors are significantly more positivelyskewed than those of diversified investors and the under-diversification of investors does not seem to be coinciden-tally related to skewness. It could therefore be argued thatthe apparent preference of investors for stocks with highMAX could simply be an expression of preference forpositive skewness. However, Bali et al. (2011) do notfind MAX to be a proxy for skewness in their samplebecause even after controlling for skewness, the MAXeffect persists.
It is also suggested that MAX could just be a proxy foridiosyncratic volatility. Bali et al. (2011) report that stockswith high idiosyncratic volatility also appear to haveextreme returns in the same period. Since Ang et al.(2006, 2009) find that stocks with high idiosyncratic vola-tility generate low future average returns, one could arguethat the negativeMAX effect reported by Bali et al. (2011)could be due to the negative idiosyncratic volatility effect.Related to this, Petrovic et al. (2009) report a negativerelationship between current earnings volatility and futureperformance. However, Bali et al. (2011) show that MAXis not proxying for idiosyncratic volatility. They showinstead that the MAX effect is not only robust to controlsfor idiosyncratic volatility, but also reverses the negativeidiosyncratic volatility effect found by Ang et al. (2006,2009). Bali et al. (2011) argue that poorly diversifiedinvestors dislike idiosyncratic volatility, which naturallyimplies a positive idiosyncratic volatility effect. However,Bali et al. (2011) also conjecture that both IV and MAXeffects could independently exist in stock markets. Otherfirm characteristics that have been shown in the literatureto be related to returns include firm size (Banz, 1981),value (Rosenberg et al. 1985), momentum (Jegadeesh andTitman, 1993) and one-month past return (Jegadeesh,1990; Lehman, 1990). Bali et al. (2011) control for thesevariables through bi-variate sorts and still report a MAXeffect.
1 Cumulative prospect theory is a modified version of the original prospect theory of Kahneman and Tversky (1979).2 Gazioglu and Caliskan (2011) have generalized the Kahneman–Tversky value function, suggesting that a piecewise quadratic is a betterapproximation of the Kahneman–Tversky value function than the piecewise power or exponential value functions.
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Empirical evidence on the MAX effect in other marketsis understandably sparse given its novelty. As far as weknow, our study is the first to investigate the existence ofthe MAX effect in the Asian region. Asia is one of themost economically dynamic regions in the world withmany of its markets experiencing tremendous growthand development. It is also one of the most diverse interms of culture and stage of development. Inasmuch asthe global investment community looks towards Asia tospearhead the global economic recovery, it is imperativefor investors to gain a thorough understanding of its variedfinancial markets.
The South Korean stock exchange (SKE) was estab-lished on 3 May 1963 as a government-run nonprofitcorporation. By the end of 2008, there were 763 stockslisted in the exchange with total market capitalization of440 billion USD (KRX, 2008). It is ranked as the fourthlargest stock market in Asia by market capitalization. Itis also reported to have the most liquid stock marketamong emerging markets (McDonald and Richardson,2006). Trading hours for the SKE are from 9 am to 3pm, Monday to Friday with off-hour sessions of 1.5hours before and around 3 hours after the opening andclosing bells, respectively. Thus, there are nonoverlap-ping trading hours between the US stock markets andSKE (Park and Yi, 2011). The transaction cost in theSKE is 0.3% of sales proceeds. Compared to the USstock markets, the SKE has some unique trading rulesand regulations (Cumming et al. 2011). First, there iscurrently a price limit for all listed stocks. FromDecember 1998, all stocks had a daily price limit of15% upper or lower bound. The price limits stop stockprices from following a random walk process and soresults in the SKE being inefficient (Ryoo and Smith,2002). Second, short-sales are not allowed in the SKE.Third, the insider trading rules in the SKE are not asstrict compared to the US stock markets. Finally, it issuggested that stock prices in the SKE are more easilymanipulated by investors than in the US stock markets(Cumming et al. 2011). All of the above cause the SKEto be less efficient than the US stock markets. Moreimportantly, the SKE is highly dominated by individualinvestors rather than institutional investors. For example,in 2008 alone more than 80% of total numbers of tradeswere done by either domestic or foreign individualinvestors. Finally, the trading value contributed by insti-tutional investors is only 18.2% of the total trading valuein 2008 (KRX.com, 2013). Furthermore, Park and Yi,(2011) suggest that South Korean individual investorsare still immature and prone to irrational behaviour (Parkand Yi, 2011). Inasmuch as there are important differ-ences between South Korean and US stock markets, it isinteresting to examine if the MAX effect first documen-ted in the US markets also exist in the emerging mar-kets. Since stocks with lottery-like features tend to
attract retail investors with strong gambling propensity(Han and Kumar, 2013), we expect an even strongernegative MAX effect in the South Korean stock market.
Our results provide strong evidence of the existence of anegative MAX effect in the South Korean stock marketmuch like the one documented by Bali et al. (2011) in theUS and Annaert et al. (2013) in 13 European countries.This demonstrates that the MAX effect is not solely adeveloped market phenomenon. Our results imply inves-tor preference for high-MAX stocks in the South Koreanstock market, a behaviour that is consistent with bothcumulative prospect theory and the optimal expectationsframework. Inasmuch as the MAX effect is driven byinvestor preference towards lottery-type stocks, we sug-gest that investors in the South Korean market are subjectto the same behavioural bias as investors in the US andEuropean countries.
We report a return spread of −1.87% per month forequal-weighted portfolios and a corresponding alphaspread of −1.41% between high- and low-MAX portfo-lios, higher than those reported in the US even thoughwe use a smaller dispersion of MAX by sorting stocksinto only three portfolios instead of the 10 portfoliosemployed by Bali et al. (2011). These results suggestthat investors can systematically increase portfolioreturns with a MAX strategy of going long stocks withlow MAX and short stocks with high MAX. This resultis robust to controls for size, value, skewness, momen-tum, short-term reversal and idiosyncratic volatility indi-cating that the negative MAX effect is not driven bythese well-known effects.
The rest of the article is organized as follows. Section IIdescribes our data and methods and defines our variables.Section III presents our main empirical results as well asthose of robustness tests and Section IV concludes thearticle.
II. Data and Methods
Daily and monthly stock market data for the period fromJanuary 1993 to December 2008 were obtained fromDatastream. We rank stocks at the beginning of eachmonth t according to MAX, defined as the maximumdaily return in the past month, t − 1. We then form threeportfolios with cut-off points at the top 33.33% and thebottom 33.33%. We determine raw and risk-adjustedreturns (FF-3 alpha) of each portfolio at the end ofmonth t, reforming portfolios every month. The FF-3alphas (henceforth just alpha) are computed relative tothe Fama–French three-factor model (1) (Fama andFrench, 1993), which is estimated using the full sampleof monthly value- or equal-weighted returns for eachportfolio:
Evidence of a MAX effect in South Korea 427
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Ri; t�1 � Rf ; t�1 ¼ αi þ bi Rm; t�1 � Rf ; t�1
� �
þ siSMBt�1 þ hiHMLt�1 þ εi(1)
where Ri, t − 1 is the return of stock i at time t − 1, Rm, t − 1 isthe market return that is the value-weighted return of allstocks in the sample at time t − 1, Rf, t − 1 is the risk-freerate at time t − 1 and is defined as negotiable certificate ofdeposit (NCD) 91-day rate, SMBt − 1 is the differencebetween the returns on small- and big-stock portfolios attime t − 1, HMLt − 1is the difference between returns onhigh and low book-to-market ratio (BM) stock portfoliosat time t − 1 and εi is the error term. Excess market returns,SMB and HML were all constructed using South Koreanstock market data. We generate daily values of SMB bysorting stocks at the beginning of every month t into threegroups according to size (Small, Medium, Big). SMB isthe difference in daily returns between the small- andlarge-stock portfolios. Similarly, we generate daily valuesof HML by sorting stocks into three groups according totheir BM in month t − 6 (High-, Medium- and Low-BM).HML is the difference in daily returns between the high-and low-BM stock portfolios.
We control for various known cross-sectional effectsincluding size (Banz, 1981), value (Rosenberg et al.1985), skewness (Harvey and Siddique, 2000), momen-tum (Jegadeesh and Titman, 1993), one-month past return(Jegadeesh, 1990; Lehman, 1990) and idiosyncratic vola-tility (Ang et al. 2006, 2009) using a 3 × 3 double-sortingmethodology similar to that employed by Bali et al.(2011). First we sort on the control factor (i.e., size,value, momentum and so on) into three groups. Withineach group we sort further into three more groups based onMAX. Then we average within each MAX categoryresulting in three portfolios with variation in MAX butsimilar levels in the control variable. The size variable atthe beginning of month t is defined as the firm’s marketcapitalization at the end of month t − 1, value is the firm’sBM six months prior, i.e. at the end of t − 6. Skewness ofstock i at the beginning of month t is computed using dailyreturns in the past 22 trading days. Following Jegadeeshand Titman (1993), the momentum variable at time t is the
stock’s 11-month past return lagged one month, i.e. returnfrom month t − 12 to month t − 2. The short-term reversalvariable is defined following Jegadeesh (1990) as thestock’s one month past return, i.e. return in month t − 1.Idiosyncratic volatility (IV) of stock i in at the beginningof month t is defined as the SD of daily residuals from theFama–French three-factor model (1) estimated using dailyreturns in month t − 1.
III. Empirical Results
Univariate sorting
Table 1 shows the average monthly returns and FF-3 alphaof equal-weighted (EW) and value-weighted (VW) port-folios sorted according to MAX. Table 1 shows that theequal-weighted high-MAX portfolio provides a lowerreturn than the low-MAX portfolio indicating a negativeMAX effect. The return difference at −1.87% per monthon average is statistically significant at 10% level. Thisresult is qualitatively the same as Bali et al.’s (2011)findings in the United States where they report a returnspread of −0.65% per month that is also statistically sig-nificant at the 10% level. The results become more inter-esting when we turn our attention to the alpha values. Thealpha spread is a better indicator of the MAX effect since itcontrols for the standard set of systematic risk factors. Wedocument a negative alpha spread of −1.41% per month,which is significant at the 1% level. In contrast, Bali et al.(2011) report an equal-weighted alpha spread of only–0.66% per month. In spite of the narrower range inMAX afforded by our three-portfolio sorting procedure,we report wider return and alpha spreads compared withthose documented by Bali et al. (2011) for the UnitedStates. However, unlike Bali et al. (2011), we do not finda significant MAX effect in value-weighted portfolios.The value-weighted return and alpha spreads are negative,but they are not significant at conventional levels. Henceour results suggest that the strong negative MAX effect inthe South Korean stock market is a small-firm
Table 1. Returns and FF-3 alpha of portfolios sorted on MAX
EW portfolios VW portfolios
Average return FF-3 alpha Average return FF-3 alpha
Notes: At the beginning of each month t over the test period, stocks are sorted into three portfolios based on MAX. MAX is the stock’shighest return in month t − 1. LMAX, MMAX, and HMAX refer to low-, medium- and high-MAX portfolios, respectively. Average rawreturns and FF-3 alpha of equal- and value-weighted portfolios over the test period are reported with t-stats in parentheses. FF-3 alpharefers to the Fama–French three-factor model alpha (α coefficient) using the full sample of monthly returns for each portfolio.
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phenomenon, which is consistent with Annaert et al.’s(2013) findings in European countries. We suggest thatthe strong negative MAX effect in the SKE is largelydriven by individual investors with a strong preferencefor stocks with lottery-like features considering that theSouth Korean stock market is highly dominated by indi-vidual investors. This is plausible, as Kumar (2009) finds,that individual investors exhibit a stronger preference forstocks with lottery-like features than institutional inves-tors. Second, the fact that the MAX effect in the SKE isstronger in equal-weighted portfolios than in value-weighted portfolios is consistent with lottery-type stocksbeing small-cap stocks as documented in Kumar (2009).Kumar (2009) also finds that Asian investors invest morein lottery stocks compared with US investors, thus theMAX effect in the South Korean stock market couldconceivably be stronger than in the US stock market.Finally, Han and Kumar (2013) suggest that since lot-tery-type stocks attract retail investors, they tend to beoverpriced and earn significant negative alpha. Thisappears to be the case in the South Korean stock market.
In Table 2 we report the characteristics of the MAX-sorted portfolios. We report average values of portfoliocharacteristics related to MAX, size (market capitaliza-tion), value, skewness, momentum, short-term reversaland idiosyncratic volatility as of the portfolio formationdate. These variables are as defined previously. We reportportfolio MAX values not only in the portfolio formationmonth (t = 0) but also in the followingmonth (t = 1) as wellto test for the persistence of MAX. The MAX valuesillustrate the persistence of MAX, with high-MAX port-folios in the previous month continuing to exhibit highermaximum daily returns than low-MAX portfolios in thefollowing month consistent with Bali et al.’s (2011) find-ings for the US market. Establishing this tendency forMAX to persist is crucial in relating the MAX effectwith cumulative prospect theory (CPT) as we will see inthe next section.
The rest of the columns in Table 2 show that high-MAXstocks tend to be small stocks with low value (BM), havepositively skewed returns, tend to be winners in the pre-vious month and have high idiosyncratic volatility. Thesecharacteristics are generally consistent with those reportedby Bali et al. (2011) for their sample of US stocks exceptfor the high-MAX portfolios in the United States havinghigher value than low-MAX stocks. It is interesting to notethat high-MAX stocks also tend to be stocks that havepositively skewed returns over the past month since Golecand Tamarkin (1998) show that gamblers are attracted bypositive skewness. We therefore expect high-MAX stocksto be specially favoured by speculators.
In summary, we find empirical evidence of a highlysignificant negative MAX effect for equal-weighted port-folios in the South Korean stock market though the sameappears absent in value-weighted stock portfolios, T
able2.
Characteristicsof
portfoliossorted
onMAX
MAX(t=0)
MAX(t=1)
Size
Value
Skewness
Mom
entum
REV
IV
HMAX
0.1118
(54.52
61)
0.08
40(52.58
78)
2003
71.0
(17.10
67)
1.26
44(22.08
73)
0.53
41(26.51
76)
−0.00
74(−0.22
20)
0.05
79(6.421
5)0.03
86(51.85
17)
MMAX
0.06
87(39.28
83)
0.07
23(45.40
72)
4127
47.6
(18.02
56)
1.34
94(20.89
98)
0.17
92(9.580
1)0.03
39(1.133
0)−0.01
02(−1.34
42)
0.02
66(39.81
21)
LMAX
0.03
93(36.89
18)
0.06
38(42.22
32)
4978
85.8
(20.56
05)
1.62
31(23.91
80)
−0.21
58(−11.100
3)0.02
93(1.267
0)−0.05
23(−9.10
76)
0.01
87(38.77
07)
HMAX-LMAX
0.07
24(31.34
36)
0.02
01(9.146
2)−2
9751
4.9(−11.060
2)−0.35
86(−4.03
93)
0.74
99(26.78
77)
−0.03
67(−0.90
71)
0.1102
(10.30
90)
0.01
99(22.44
92)
Notes:A
tthe
beginn
ingof
each
mon
thto
verthetestperiod
,stocksaresorted
into
threepo
rtfolio
sbasedon
MAX.M
AXisthestock’shigh
estreturninmon
tht−
1.LMAX,M
MAX,and
HMAXreferto
low-,medium-andhigh
-MAXpo
rtfolio
s,respectiv
ely.MAX(t=0)
istheMAXin
mon
tht−
1,on
emon
thprevious
totheform
ationmon
tht;MAX(t=1)
istheMAX
during
theform
ationmon
tht.Sizeistheaveragepo
rtfolio
marketcapitalizationas
ofthebeginn
ingof
theform
ationmon
thtand
expressedin
Log
ofmillionKoreanWon;V
alue
isthe
book
-to-marketratioof
thepo
rtfolio
int−
6;Skewnessisthetotalskewnessof
returnsinmon
tht−
1;Mom
entumattim
etisthestock’s11-m
onthpastreturn
lagg
edon
emon
th,i.e.return
from
mon
tht−
12to
mon
tht−
2;REVisthepo
rtfolio
return
inmon
tht−
1;IV
istheaverageidiosyncratic
volatility
ofreturnsin
t−1;
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consistent with Annaert et al.’s (2013) findings in 13European countries. Our results indicate that investors inthe South Korean stock market could systematicallyincrease their returns by short-selling stocks with highMAX and buying stocks with lowMAX. Next we conductrobustness tests by way of bivariate sorts to examine if thenegative MAX effect in equally weighted portfolios couldbe explained by certain control variables.
Bivariate sorting
As we show in Table 2, stocks with high MAX maynot be representative of the full universe of the stocksas they tend to be small, low-value stocks that are
previous winners and have high idiosyncratic volatility.Well-known cross-sectional effects such as the BMeffect, short-term reversals and the IV effect postulatethat low-value stocks, previous month’s winners andthose with high idiosyncratic volatility tend to under-perform. Therefore, the negative MAX effect couldpossibly be due to these cross-sectional effects. Hencewe conduct a battery of bivariate sorts to control forcross-sectional effects related to size, value, skewness,momentum, short-term reversal and idiosyncratic vola-tility. As in Ang et al. (2006, 2009), we focus ourattention on alpha spreads since they control for thestandard set of systematic risk factors and report theresults in Table 3.
Notes: At the end of each month over the test period, stocks are double-sorted 3 × 3, first by the control factor (size, value, skewness,momentum, one-month past return and IV) into three portfolios and thenwithin each portfolio we sort stocks again byMAX. The alpha ofeach portfolio is presented with t-statistics in parentheses. Alpha refers to the Fama–French three-factor model alpha (αcoefficient) usingthe full sample of monthly returns for each portfolio. To control for a particular factor, we average the alpha within each MAX categoryending up with three portfolios with dispersion in MAX but containing all values of the factor being controlled. Size is the firm’s marketcapitalization at the beginning of month t; value is the book-to-market ratio in month t − 6; skewness is total skewness of returns in montht − 1; the momentum is the stock’s 11-month past return lagged one month, i.e. return from month t − 12 to month t − 2. Short-termreversal is the return in month t − 1; idiosyncratic volatility is the SD of residuals from the Fama–French three-factor model estimatedusing daily returns in month t − 1. LMAX, MMAX and HMAX refer to low-, medium- and high-MAX portfolios, respectively; BIG, bigsize;MED, medium size; SMA, small size; HBM, MBM, and LBM refer to high, medium, low book-to-market, respectively; HSK, MSK,LSK refer to high, medium, low skewness, respectively;WNR, winner;MID, middle; LSR, loser;HIV, MIVand LIV refer to high, mediumand low idiosyncratic volatility, respectively.
430 G. V. Nartea et al.
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Panel A shows the results when we double-sort onsize and MAX. The evidence in Panel A shows that thealpha spreads are negative and statistically significant atleast at the 5% level, except for the big size category.This implies that the MAX effect is weak at best for bigstocks consistent with our previous results. More impor-tantly, averaging the alpha spreads within each MAXcategory resulting in three portfolios with variation inMAX but similar levels in the control variable (size),we find a negative and highly significant alpha spreadof −1.38% per month. This indicates that the size effectis not driving the negative relationship between MAXand alpha.
Panel B of Table 3 shows the results for portfoliosdouble-sorted on value (book-to-market in month t − 6)and MAX. The alpha spreads for all Value categories arenegative and significant except for LBM, which impliesthat the negative MAX effect is also weak at best for low-value stocks. More importantly, the average alpha spreadis still significantly negative at −1.29% per month aftercontrolling for value, which indicates that the value effectis not behind the relationship between MAX and risk-adjusted returns.
Panel C shows the results for portfolios double-sortedon skewness and MAX. The alpha spreads are negativeand significant for all skewness categories. The averagealpha spread is likewise still negative and highly signifi-cant, at −1.41% per month after controlling for skewness.Therefore, the skewness effect is also not driving thenegative relationship between MAX and risk-adjustedreturn.
Panel D reports the results for portfolios double-sortedon momentum and MAX. The alpha spreads are all nega-tive and statistically significant at conventional levels. Theaverage alpha spread is also negative and highly statisti-cally significant at −1.49% per month, which implies thatthe negative MAX effect is not due to the momentumeffect.
Panel E reports the results for portfolios double-sortedon short-term reversal (REV) and MAX. The evidence inPanel E shows a highly significant alpha spread only forWNR but insignificant for MED and LSR. This indicatesthat the negative MAX effect is strongest for last month’swinners and weak at best for last month’s losers. Moreimportantly, the average alpha spread is negative andhighly significant at −1.33% per month indicating thateven after controlling for REV, the negative MAX effectpersists. Therefore, the REVeffect is not driving the nega-tive relationship between MAX and alpha.
Finally, Panel F reports the results for portfolios double-sorted on idiosyncratic volatility and MAX. Based on thealpha spreads, the negative MAX effect appears to bepresent only in high-idiosyncratic volatility portfolios.However, the average alpha spread at −1.07% per monthis highly significant, which indicates that the negative
MAX effect is not driven by the idiosyncratic volatilityeffect.
In summary, the results of the bivariate sorts indicate astrong negative MAX effect that cannot be explained bythe size, value, skewness, momentum, REV and idiosyn-cratic volatility effects. These results are similar to thefindings of Bali et al. (2011) in the US stock market andAnnaert et al. (2013) in 13 European markets. Similarly,we conjecture that the negative MAX effect in the SouthKorean stock market is driven by investors exhibiting apreference for stocks with lottery-like characteristics, inparticular those with extreme positive returns. Such apreference leads these investors to overpay for stocksthat earn extreme positive returns resulting in lowerreturns in the future. Tversky and Kahneman’s (1992)cumulative prospect theory (CPT) could potentiallyexplain investor preference for stocks with the extremepositive returns. CPT posits that investors tend to think ofpossible outcomes relative to a certain reference pointrather than to the final status, a phenomenon referred toas the framing effect. If investors take the extreme positivereturn as their reference point, they could sub-optimallyoverweight the possibility of the extreme returns persist-ing in the future and underweight average events. Indeed,we find from Table 2 that MAX is persistent, with high-MAX stocks tending to continue to have high MAX thefollowing month, a tendency that investors could poten-tially sub-optimally overweight, thereby leading to a pre-ference for high-MAX stocks.
Our results could also be interpreted according to theoptimal expectations framework of Brunnermeier andParker (2005) and Brunnermeier et al. (2007), whereagents derive utility from overestimating the probabilityof high-MAX stocks doing well in the future, which leadsto a preference for these stocks.
A further robustness test
As a further test of the robustness of the MAX effect, weemploy an alternative definition of MAX. First we collectthe five maximum daily returns for a stock, take its aver-age and call it MAX(5). Then, we use MAX(5) to sortstocks into three portfolios, high-, medium- and low-MAX portfolios. Both equal-weighted and value-weighted portfolio returns and FF-3 alpha are then com-puted the usual way.
Table 4 shows that the negative MAX effect for equal-weighted portfolios is even stronger when stocks aresorted by MAX(5) compared with just sorting on MAX.The equal-weighted return spread of −2.21% per monthis statistically significant at the 5% level and is wider thanthe raw return spread of −1.87% reported in Table 1when sorting on MAX. This result is qualitatively thesame as those reported by Bali et al. (2011) for the USstock market where the raw return spread was also wider
Evidence of a MAX effect in South Korea 431
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for portfolios sorted on MAX(5) compared with thosesorted on MAX. The negative MAX effect is furtherconfirmed by a monotonic increase in alpha from high tolow MAX portfolios, i.e. −1.97% (high-MAX), −0.53%(medium-MAX), and 0.04% (low-MAX) per month andthe statistically significant negative equal-weighted alphaspread of −2.01% per month between the high and lowMAX portfolios.
The results for value-weighted portfolios confirm thosereported in Table 1, indicating the absence of a MAXeffect in value-weighted portfolios, again suggesting thatthe MAX effect is a small-firm phenomenon. On average,value-weighted raw return spread at −1.63% per month isnot statistically significant. Furthermore, the alpha spreadat −0.56% per month is also statistically insignificant.
Extreme returns and idiosyncratic volatility
Finally, since Bali et al. (2011) show that the negativeMAX effect in the US stock market reverses the IV effectreported by Ang et al. (2006, 2009), we also examine if asimilar relationship exists in the South Korean stockmarket.
At the beginning of every month, we sort stocks intothree portfolios according to idiosyncratic volatility(high-, medium-, low-IV). We then determine portfolio
returns and alpha in the usual manner and report the resultsin Table 5. Based on return spreads, our results indicatethe absence of an IVeffect. However, once we control forthe Fama–French risk factors, we find a significantlynegative IV effect. We report a highly significant equal-weighted (value-weighted) alpha spread of −1.31%(−1.29%) per month.
Could the MAX effect reverse the IVeffect as in the USmarket? We control for MAX through a bi-variate sort onMAX and IVand re-compute the alpha spreads and reportthe results in Table 6. The alpha spreads for both equal-and value-weighted portfolios are still negative and highlystatistically significant even after controlling for MAX.Evidently, the MAX effect does not drive the IV effect,much less reverse it. We conclude that these two effectsare independent of each other in the South Korean stockmarket. Hence Bali et al.’s (2011) finding that the MAXeffect reverses the IV effect could be specific only to theUS market.
The different results could be due to three anecdotalreasons. First, the South Korean stock market is highlydominated by retail investors, but the US stock marketsare dominated by institutional investors. Han and Kumar(2008) conclude that the negative IVeffect is concentratedin stocks dominated by retail investors. Therefore, it is notdifficult to image that the IV effect in the SKE could be
Table 5. Returns and FF-3 alpha of portfolios sorted on IV
EW portfolios VW portfolios
Average return FF-3 alpha Average return FF-3 alpha
Notes: At the beginning of each month t over the test period, stocks are sorted into three portfolios based on idiosyncratic volatility (IV),high IV (HIV), medium IV (MIV) and low IV (LIV). Average raw returns and FF-3 alpha of equal- and value-weighted portfolios over thetest period are reported with t-stats in parentheses. FF-3 alpha refers to the Fama–French three-factor model alpha (α coefficient) using thefull sample of monthly returns for each portfolio.
Table 4. Portfolios returns Max = 5
EW portfolios VW portfolios
Average return FF-3 alpha Average return FF-3 alpha
Notes: At the beginning of each month t over the test period, stocks are sorted into three portfolios based on MAX(5). MAX (5) is theaverage of the five highest returns of the stock in month t − 1. LMAX, MMAX, and HMAX refer to low-, medium- and high-MAXportfolios, respectively. Average raw returns and FF-3 alpha over the test period of equal- and value-weighted portfolios are reported witht-stats in parentheses. FF-3 alpha refers to the Fama–French three-factor model alpha (α coefficient) using the full sample of monthlyreturns for each portfolio.
432 G. V. Nartea et al.
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stronger than that in the US stock markets, and the MAXeffect cannot drive out the IV effect. Second, the SKEimposes a price limit to the stock market, and results inreducing the market’s efficiency and increases the marketvolatility (Kim and Rhee, 1997). Thus, a strong IV effectwould be expected in the SKE. Third, Goetzmann andKumar (2008) suggest, that the level of under-diversification is greater for unsophisticated and over-confident investors, who over-weight high volatilitystocks. This could also be the case in the South Koreanstock market, resulting in a negative IV effect that isstronger than in the US stock market. In fact, Bali et al.(2011) indicate that it is very difficult to disentangle theMAX and IVeffects and they admit that these two effectscould independently exist in stock markets. Therefore, ourresults highlight the importance of verifying empiricalrelationships found in developed markets for applicabilityin emerging markets.
IV. Concluding Remarks
In a recent study, Bali et al. (2011) investigate the signifi-cance of extreme positive returns (MAX) in the cross-sectional pricing of stocks. They found that stocks withextreme positive returns subsequently underperform in thefollowing month. They refer to this as the MAX effect,which they attribute to investor preference for stocks withlottery-like characteristics. We find a similar negativeMAX effect in South Korea and thus present importantout-of-sample evidence from a major emerging stockmarket. This MAX effect cannot be explained by systema-tic risk factors, as well as well-known cross-sectionaleffects related to size, value, skewness, momentum,REV and idiosyncratic volatility. We suggest that theMAX effect is driven by investor preference for high-MAX stocks, a behaviour that is consistent with bothcumulative prospect theory and the optimal expectationsframework. This interpretation is bolstered by the persis-tence of MAX in our study, with high-MAX stocks tend-ing to continue to have high MAX the following month.The MAX effect is also consistent with the optimal expec-tations framework where investors derive utility fromoverestimating the probabilities of events in which theirinvestments pay off well. To the extent that the MAXeffect is driven by investor preference towards lottery-type stocks, we suggest that investors in the South Koreamarket are subject to the same behavioural bias as inves-tors in the US in spite of obvious differences in levels ofmarket development and sophistication. However, itappears that the MAX effect in South Korea exists onlyfor equal-weighted portfolios, which suggests that theMAX effect in South Korea is a small-firm phenomenon.Our results are consistent with the findings in 13 EuropeanT
able6.
FF-3
Alphaof
portfoliosdou
ble-sortedon
MAXan
dIV
EW
portfolio
sVW
portfolio
s
LIV
MIV
HIV
HIV-LIV
LIV
MIV
HIV
HIV-LIV
HMAX
−0.00
60(−1.42
10)
−0.01
42(−3.4115
)−0.03
24(−6.59
21)
−0.02
64(−4.09
07)
0.00
64(1.432
9)−0.01
63(−3.00
14)
−0.02
89(−3.67
89)
−0.03
53(−3.94
17)
MMAX
−0.00
30(−0.91
36)
−0.00
70(−1.81
31)
−0.00
10(−0.19
97)
0.00
20(0.324
7)0.00
07(0.214
0)−0.00
01(−0.02
96)
0.00
37(0.508
1)0.00
30(0.378
8)LMAX
−0.00
32(−1.1120
)−0.00
66(−1.82
05)
0.00
04(0.1116)
0.00
36(0.728
6)−0
.002
7(−0.72
43)
−0.00
40(−1.00
69)
0.00
16(0.354
4)0.00
43(0.738
1)AVE
−0.00
41(−2.00
73)
−0.00
93(−4.14
23)
−0.0110
(−4.03
01)
−0.00
69(−2.03
97)
0.00
15(0.663
8)−0.00
68(−2.57
30)
−0.00
79(−2.04
69)
−0.00
93(−2.10
54)
Notes:A
tthe
beginn
ingof
each
mon
thov
erthetestperiod
,stocksaredo
uble-sorted3×3,
firstb
yextrem
epo
sitiv
ereturns(M
AX)into
threepo
rtfolio
s,high
MAX(H
MAX),medium
MAX(M
MAX)andlowMAX(LMAX),andthen
with
ineach
portfolio
wesortstocks
againby
idiosyncratic
volatility
(IV),high
IV(H
IV),mediumIV
(MIV)and
lowIV
(LIV).MAXis
thestock’shigh
estreturninmon
tht−
1.Idiosyncratic
volatility
(IV)istheSDof
residu
alsfrom
theFam
a–Frenchthree-factor
mod
elestim
ated
usingdaily
returnsinmon
tht−
1.The
FF-3
alph
aof
equal-andvalue-weigh
tedpo
rtfolio
sov
erthetestperiod
arerepo
rted
with
t-statsin
parentheses.FF-3
alph
arefersto
theFam
a–Frenchthree-factor
mod
elalph
a(α
coefficient)
usingthefullsampleof
mon
thly
returnsforeach
portfolio
.
Evidence of a MAX effect in South Korea 433
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countries (Annaert et al. 2013), but it is unlike in the USmarket where the MAX effect is observed for both equal-and value-weighted portfolios. Furthermore, unlike in theUS stock market, we find that the MAX effect cannotreverse the IV effect, which implies that Bali et al.’s(2011) findings could be specific only to the US Sincethe South Korean stock market is dominated by retailinvestors, thus it exhibits a stronger significant negativeIV effect, which cannot be driven out by the MAX effect.However, our results confirm one of Bali et al.’s (2011)conjecture that both MAX and IV effects could indepen-dently exist in stock markets. This highlights the impor-tance of verifying empirical relationships found indeveloped markets for applicability in emerging markets.
We report a higher return spread of −1.87% per monthand a corresponding alpha spread of −1.41% comparedwith those reported by Bali et al. (2011). In addition,sorting stocks by the average of the five highest dailyreturns within the month instead of just the maximumdaily return generates even higher return and alphaspreads of 2.21% and 2.01% per month, respectively.Our results imply that investors in South Korea can sys-tematically increase their portfolio returns by long low-MAX stocks and short high-MAX stocks.
We suggest that investigating the role of investor beha-viour as a potential driver of the IV and MAX effects arefruitful avenues for future research.
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