Momentum effect: empirical evidence from Karachi stock exchange.
Habib-Ur-Rahman ; Mohsin, Hasan M.
1. INTRODUCTION
Capital market efficiency and the prediction of future stock prices
are the most thought-provoking and ferociously debated areas in finance.
The followers of traditional financial theory strongly believe that the
markets are efficient in pricing the financial instruments. This view
became popular after Fama's work on the Efficient Market
Hypothesis. But before 1990s, wide-ranging financial literature
documented that stock prices, to some extent, are predictable. Many
psychologists, economist and the journalists are of the view that
general tendency of individuals is to overreact to the information. De
Bondt and Thaler (1985) studies this view of experimental psychology
that whether such behaviour matters at the market level or not. They
found out that stock prices will overreact to information, and suggested
that contrarian strategies buy the past losers and sell the past
winners, earn abnormal returns. They extended the holding period from 3
to 5 years and provide the evidence of long term returns reversal.
Jegadeesh (1990) and Lehmann (1990) supported the evidence of return
reversal in short term, i.e. from one week to one month. They suggested
that the contrarian strategies having holding period of one week to one
month earned the significant abnormal return. Lo and Mac Kinalay (1990)
objected on the ground that a major portion of this abnormal return,
reported by Jegadeesh (1990) and Lehmann (1990), is due to the delayed
reaction of stock prices to common factors rather than to overreaction.
Some other researchers pointed out some other reasons of this abnormal
stock returns i.e. short-term pressure on stock prices and absence of
liquidity in the market rather than overreaction.
Despite of this literature on contrarian strategies, the early
literature on market efficiency emphasised on the relative strength
strategy, buy past winner and sell past looser. Levy (1967) worked on
relative strength strategy and reported that the stock with its current
price substantially higher than average prices of last twenty seven
weeks will earns abnormal returns. As concern to the practice, a large
number of practitioners still apply relative strength rule for stock
trading. Grinblat (1989) and Titman (1991) analysed the sample of mutual
fund and found that mutual funds have a tendency to buy the stock that
has shown an increase in its price over last quarter. Copeland and
Mayers (1982) and Stikle (1985) also suggested the abnormal returns
realised by the relative strength strategy. Jegadeesh and Titman (1993)
analysed this contradiction between practitioners and academic
literature and pointed out some possibilities. One possibility is that
the abnormal returns earned by practitioners are fake or un-correlated
to their tendency towards the buying past winners. Second possibility is
the difference of time period used in both analyses. Contrarian
strategies used the trading strategies either based on very long holding
period, 3 to 5 years, or very short period, one week to one month.
However, time period used in the case of abnormal return realised by
practitioners is three months to twelve months. Then Jegadeesh and
Titman (1993) documented this strategy and found momentum effect in
American Financial Markets by considering 16 medium temporal horizons.
As this was a very serious question on the market efficiency hypothesis.
Some researchers objected this empirical statement of momentum effect
and refer it to snooping data. Schwert (2002) reported the momentum
effect as temporary phenomena and it should disappear as it becomes
visible to the investor's community.
As 1 tested the momentum effect on the stock returns of companies
listed on Karachi Stock Exchange, cultural and institutional differences
were expected to affect the results as compared to the western
countries. Hofstede (1999) analysed that Asians tend to score low in
"individualism" test as compared to the western countries test
takers. Individualism hasn't any direct relationship with the
momentum effect but it relates to "overconfidence" and
"conservatism". Danial and Subrahmanyam (1998) and Barbris,
Shlifer, and Vishny (1998) suggested that the "overconfidence"
and "conservatism" are the determinants of relative
strength/momentum strategies.
In 2000, Chui, Titman, and Wei were the first to analyse the
momentum effect on the Eight Asian Stock market's return from 1976
to 2000. They constructed 6-6 months value weighted strategy, in which
winners and losers stocks were ranked as top and bottom 30 percent
respectively. They reported very low momentum effect in Asian markets
(Sig only in Hong Kong), except Indonesia and Korea. I expected no
momentum effect or very low, if and statistically insignificant.
2. LITERATURE REVIEW
Jegadeesh and Titman (1993) conducted the study by analysing the
AMEX and NYSE stocks from 1965 to 1989. They formed 32 strategies with
the formation and holding period from 3 months to 12 months (with and
without one week gap in formation and holding periods). They reported
the positive returns against each 32 zero-cost momentum portfolio. All
of these returns were statistically significant except 3/3 months
strategy (the strategy with 3 months formation period as well as 3
months holding period). They reported the momentum effect in American
Stock's markets with average monthly return of 1 percent. Further,
they reported that these average returns of these portfolios are not due
to their idiosyncratic risk or delayed reaction of stock prices to
common factors. They reported average monthly returns of 0.095
(t-statistics .0307) in 6/6 strategy.
Conrad and Kaul (1998) changed the time period and investigated the
momentum effect in American Stock's markets from 1962 to 1989.
Further, they decreased the strategies from 3-12 months to 1-36 weeks
(where one week is the formation period and 36 weeks were the holding
period). They reported the positive returns of zero-cost momentum
portfolio with statistically significance, except 1-1 week. So, they
confirmed the momentum effect documented by Jegadeesh and Titman (1993).
Chan, Jegadeesh, and Lakonishok (1996) used the primarily listed
stock on the NYSE, NASDAQ, and AMEX but they used only 6-month/6-months
strategy, the most representative strategy. They reported the zero-cost
momentum return of 0.088 over the first two quarters and the return was
not less than 0.154 over the first four quarters. But, these returns
were -0.06 and 0.012 respectively in the year two and three, following
the date of formation. These results are consistent with the above
discussion by JT (1993) on the contradiction between practitioners and
the proponents of contrarian strategy.
Lee and Swaminathan (2000) objected on the study conducted by Chan,
Jegadeesh, and Lakonishok (1996, 1999) keeping in view the Fama and
French three factor model. They were of the view that NASDAQ should be
excluded from the analysis because NASDAQ firm are smaller and it is
more difficult to involve in the trading of relative strength
strategies. Then, they conducted the study on the data from 1965 to 1995
using all listed firms of NYSE and AMEX. They constructed 16 different
strategies, i.e. 3-3, 3-6, 3-9, 3-12; 6-3, 6-6, 6-9, 6-12; 9-3, 9-6,
9-9, 9-12; 12-3, 12-6, 129, 12-12; and reported positive and
statistically significant returns for all of the constructed strategies.
Korajczyk and Sadka (2004) also reported the momentum effect after
incorporating the risk and transaction cost.
Rouwenhort objected that all of the studies to support the momentum
effect were conducted on the same data set and this effect may be due to
the snoopy data. Then Rouwenhorst (1998) decided to conduct the study in
an international context. He selected 2190 European companies and used
the sample data ranging 1980-1995. He constructed 32 different
strategies; 16 strategies without one month gap between formation period
and holding period and 16 strategies with one month gap between
formation period and holding period, and reported the positive and
statistically significant returns from momentum portfolio. One
interesting aspect of their study was that the worst and best performing
portfolios were same as reported by Jagedeesh and Titman (1993). Results
of remaining 16 strategies, with a gap of one month after formation
period were also same as reported by the Jegadeesh and Titman (1993) in
their original study on American Stock Market's returns. Further,
he extended the analysis on individual countries and found a strong
momentum effect in Holland, Denmark, Belguim and Spain. At the end, he
also analysed the momentum effect even after incorporating the
firm's size. He also reported the reversal in second year as by JT
(1993). De Bondt and Weber (1998) reported the momentum effect in
Frankfurt Stock Exchange (FSE) with the sample from 1961 to 1991, but
they used a different methodology. They supported momentum effect by
reporting the cumulative excess returns of all zero-cost momentum
portfolios, where the excess return is the difference between zero-cost
momentum portfolio and the index return. Dijk and Huibers (2002)
examined 15 European countries by taking the sample from 1987 to 1999.
They changed the formation and holding periods; formation period was
fixed by 12 months and holding period was of 1, 3, 6 and 12 months. They
observed the momentum in all of the constructed strategies by reporting
the positive and statistically significant results of all zero-cost
momentum portfolios. Risk adjusted returns, reported by Dijk and Huibers
(2002) were also positive. Rouwenhorst (1999) was against the first to
investigate the emerging markets with respect to momentum effect. He
examined the sample of 1705 companies from 20 emerging countries from
1982 to 1997. He reported the momentum effect in 17 out of 20 countries
with a slightly change in methodology, i.e. ranking the stock
portfolios; top 30 percent, middle 40 percent, and bottom 30 percent.
The momentum was lower in emerging markets as compared to developed
markets [Rouwenhorst (1999); Jigadeesh and Titmann (1993)].
Momentum effect was studied in American Stock Market's
returns, European Stock Market's returns and in the Emerging Stock
Market's returns, as discussed in above mentioned literature. Then,
in 2000, Chui, Titman, and Wei were the first to analyse the momentum
effect on the Eight Asian Stock market's return from 1976 to 2000.
They constructed 6-6 months value weighted strategy, in which winners
and losers stocks were ranked as top and bottom 30 percent respectively.
They reported very low momentum effect in Asian markets (Sig only in
Hong Kong), except Indonesia and Korea. However, a strong reversal
effect was observed in the Asian Stock Market's returns. Griffin,
Ji, and Martin (2003) analysed the worldwide momentum effect by
constructing 6-6 strategy and collected the data from following regions:
Africa, Asia, Europe, and the United States. They found momentum effect
in almost all of the studied countries of the world except the Asian
countries having the weakest momentum effect. Faten (2011) studies
almost 100 companies listed on the Tunisian stock markets. He
constructed 16 relative strength strategies and reported the average
monthly return of 0.0243 in zero-cost momentum portfolio. Further he
reported the effect of size and market factors on momentum profits.
As Asian markets were studied with only one strategy and the sample
was upto 2000 [Chui, Titman, and Wei (2000)], 1 intended to focus on
Karachi Stock Exchange. So, I will take a sample from Karachi Stock
Exchange from 1999 to 2008. Rest of the paper is as follows; Section 3
represents the methodology, Section 4 presents the data analysis and
discussion, and Section 5 will show the conclusion of the study.
3. METHODOLOGY
In the first section, I constructed the momentum strategies and for
the selection of momentum strategies, 1 analysed the following
techniques;
(1) Weighted Relative Strength Strategy versus Decile,
(2) Full versus Partial Rebalancing,
(3) Equally-Weighted versus Value-Weighted Portfolio.
Further, I will discuss about the formation and holding periods,
and the methods of calculating average monthly returns in all of the
constructed strategies for our analysis, in last part of this section.
3.1. Momentum Effect Strategies Construction
To test the momentum effect in Pakistani Stock Market's
returns, 16 momentum strategies (3-3, 3-6, 3-9, 3-12; 6-3, 6-6, 6-9,
6-12; 9-3, 9-6, 9-9, 9-12; 12-3, 12-6, 12-9, 12-12) were constructed
with some special following considerations;
3.1.1. Weighted Relative Strength Strategy versus Decile
For ranking stock in each portfolio (winner's portfolio,
losers' portfolio and momentum portfolio), literature suggested two
methods i.e. WRSS and Decile Strategy. In WRSS, stock is ranked by
comparing its performance with average sample performance. Momentum
Portfolio is constructed by;
Momentum Portfolio
* Long position in the stock that has performed above sample
average;
* Short position in the stock that has performed below sample
average;
Weight of asset i is calculated as;
Wi = [+ or -] 1/N (Ri - AR)
Where: AR = the average (arithmetic mean) of returns of all of the
sample,
[R.sub.i] = Return of the evaluated asset,
N = the number of stock in entire sample.
While in Decile strategy, stocks are ranked on the basis of their
historical performance as follows;
Momentum Portfolio
* Long position in top portfolio (in descending order of all
portfolios);
* Short position in bottom portfolio (in descending order of all
portfolios);
I selected the "Decile Strategy" due to one severe
problem in WRSS, i.e. weighting scheme.
3.1.2. Full versus Partial Rebalancing
Second important consideration is to decide about rebalancing
technique. In full rebalancing, each portfolio is reshaped at end of
each formation/period, while partial rebalancing technique rebalances
each portfolio at beginning of each months as follows;
[FIGURE 1 OMITTED]
We used full rebalancing method because this method is more viable
to private investor because he does not follow the market on monthly
basis.
3.1.3. Equally-Weighted versus Value-Weighted Portfolio
The Next important consideration is regarding the weights assigned
to each portfolio. In equally-weighted method, portfolios are
constructed irrespective of the market capitalisation. On the other
hand, portfolios are weighted on the basis of market capitalisation in
value-weighted portfolio. By using the value-weighted portfolio method,
it becomes very difficult to conclude that either effect is in entire
sample or only in stock having large capitalisation. So, we selected
equally-weighted portfolio for our study.
3.2. Calculating the Average Monthly Returns
On the basis of these considerations, we collected monthly stock
prices of the selected companies listed on Karachi Stock Exchange. We
calculated the stock returns from stock prices by using continuous
compounding returns;
[R.sub.t] = 100% X ln([P.sub.t]/[P.sub.t-1])
We arranged the selected companies in descending order and selected
top 10 and bottom 10 companies for calculating the average monthly
returns. First portfolio with the stock having highest returns and last
portfolio with the lowest stock return are known as Winner's stock
and loser's stock in the literature as well as in our study. Next
step is to construct the momentum portfolio; that is constructed on the
basis of long position in winner's stock portfolio and short
position in the loser's stock portfolio. Momentum effect is
evaluated by calculating the average monthly returns in holding period
(period starting immediately after formation period). The following 16
strategies were constructed;
3.3. Other Issues in Strategies Construction
In order to find the momentum effect in Pakistani markets, we
collected the monthly stock prices of 300 companies listed on Karachi
Stock Exchange from Jan 1999 to December 2007. We found negative returns
of zero-cost portfolio in 15 out 16 strategies. There was a decreasing
trend in momentum losses reported from zero-cost portfolio. This was a
good indicator towards a very small momentum effect as reported by
Griffin, Ji, and Martin (2003). They analysed the worldwide momentum
effect by constructing 6-6 strategy and collected the data from
following regions: Africa, Asia, Europe, and the United States. They
found momentum effect in almost all of the studied countries of the
world except the Asian countries having the weakest momentum effect;
aligned with Chui, Titman, and Wei (2000).
By evaluating the decreasing trend and reported results of Griffin,
Ji, and Martin (2003), the study extended to "Long Period
Analysis". Finally we subdivided the sample in two groups to check
the momentum effect. We changed the sample after finding small evidence
of momentum. Another sample of monthly stock prices of 50 companies
listed on Karachi Stock Exchange was taken and analysed the effect by
taking eight most representative strategies, i.e. 6/3, 6/6, 6/9, 6/12
and 12/3, 12/6, 12/9, and 12/12.
3.4. Robustness Test
The momentum effect may be associated with the specific type of
stocks on the basis of market capitalisation, book to market value and
trading volume. We ranked the stock with respect to market
capitalisation, book to market value and trading volume in case of
strong momentum effect reported in Karachi Stock Exchange.
3.5. Risk Identification
The risk and return are associated with each other and we should
identify the risk factors if momentum strategies reported the reasonable
abnormal profit by having long position in past winners and short
position in past losers in Karachi Stock Exchange. We have used CAPM and
Fama and French 3 factor model to identify these risk factors.
4. DATA ANALYSIS AND DISCUSSION
This section presents the results of all 16 momentum strategies
calculated from the monthly stock prices of 300 companies from 1999 to
2007. Strategies were constructed on the basis of equal weights and full
re-balancing strategies. Stocks were ranked on the basis of average
monthly returns of formation period and then ten companies from the top
and ten from the bottom were selected as winners and losers stocks
respectively. Table 1 presents the results of the momentum strategies;
where no momentum effect was supported except 12/9 strategy that allowed
an average monthly return of 1.25 percent, statistically significant but
1 can observe a decreasing trend in losses reported in zero-cost
momentum portfolios (Figure 3).
[FIGURE 3 OMITTED]
Figure 3 documented a decreasing trend except one 3/3 strategy.
Very short formation with very short holding period strategies have
documented abnormal results in momentum literature, i.e. one of the
possibilities explained by Jegadeesh and Titman (1993) for the
contrarian strategies suggested and supported by De Bondt and Thaler
(1985).
This was a strong indicator towards a very slight momentum effect
as reported by Griffin, Ji, and Martin (2003). They analysed the
worldwide momentum effect by constructing 6-6 strategy and collected the
data from following regions: Africa, Asia, Europe, and the United
States. They found momentum effect in almost all of the studied
countries of the world except the Asian countries having the weakest
momentum effect; aligned with Chui, Titman, and Wei (2000). So, 1
extended our analysis to "Long Period Holding Analysis" after
observing this trend where returns tendency toward profits with long
holding period.
4.1. Long Holding Period Analysis
By considering contrarian strategies [De Bondt and Thaler (1985)
and Chui, Titman, and Wei (2000)], I extended our analysis by increasing
the holding period by 24, 36 and 48 months with the formation period of
6 and 12 months as momentum was reported only in 1 out of 16 momentum
strategies, i.e. 12/9. Table 2 presents the results of long in
winners' stock, short in loser's stock and zero cost portfolio
returns respectively.
Again all of the zero-cost momentum portfolio returns were negative
and statistically insignificant (except one where negative returns were
statistically significant in formation period of 6 months with holding
period of 36 months). By increasing holding period there is decreasing
trend in losses observed in zero-cost momentum portfolios, so it is
serviceable to compare the returns in short term and long term holding
periods.
4.2. Short Term vs. Long-term Holding Period Analysis
I analysed zero-cost portfolio return differences between short
term and long term horizon among the following strategies;
(1) 6/24 vs 6/3,
(2) 6/36 vs 6/6,
(3) 6/48 vs 6/9,
(4) 12/24 vs 12/3,
(5) 12/36 vs 12/6,
(6) 12/48 vs 12/9,
Table 3 shows the positive differences in all of the 6 selected
strategies, which shows decreasing trends in losses as I increased the
holding period but yet no evidence of momentum effect has been reported
from Karachi Stock Exchange.
4.3. Sub Sample Period Analysis
During our analysis of stock prices of 300 companies listed on
Karachi Stock Exchange, I have yet analysed momentum effect in only 1
out 16 strategies. This may be due to long sample period and literature
suggests to sub divide the sample period in such a scenario to properly
evaluate the momentum effect. So, 1 sub divided the sample period into
two group based on the time horizon. I analysed the data from Jan 1999
to June 2003 in the 1st sub sample period and then from July 2003 to Dec
2007 in 2nd sub sample period as follows;
Returns of zero-cost portfolios are negative in all of 8
constructed strategies from -0.03159 to -1.03755 (Table 4). So, there is
no evidence of momentum from the period of 1999 to 2003 in Karachi Stock
Exchange.
Table 5 also shows the negative returns of zero-cost portfolios in
all of the 8 constructed strategies ranging from -0.00646 to -0.31532.
Consistency in decreasing trend is obvious from both sub sample periods
(Tables 4 and 5).
Then I changed the sample and selected another 50 companies listed
on the Karachi Stock Exchange. Here, I limited our analysis by taking
eight most representative strategies, i.e. 6/3, 6/6, 6/9, 6/12 and 12/3,
12/6, 12/9, and 12/12.
Table 6 presents that monthly average return of zero-cost momentum
portfolios are (0.0523, -0.0085, 0.0064, 0.0059, 0.0289, 0.0200, 0.0102,
and 0.0012). These returns are positive in 7 out of 8 strategies. To
find out the average momentum effect value in Karachi Stock Exchange on
the basis of these 8 constructed strategies, 3/3 should not be included
in average value with reference to the discussion on the contradiction
between practitioners and the proponents of contrarian strategy by
Jegadeesh and Titman (1993) and 6/6 should also be excluded due to Jan
effect. So, I calculated the average monthly return from 6 out of 8
strategies as 0.012 and significant only in 12/3, 12/6 and 12/9
strategy. I conclude our analysis as there is very low momentum effect
in Karachi Stock Exchange and these results are aligned with Griffin,
Ji, and Martin (2003), Chui, Titman, and Wei (2000) and Rouwenhorst
(1999).
5. CONCLUSION
Objective of this paper is to analyse the momentum effect in
Karachi Stock Exchange. 1 constructed 16 momentum strategies (3-3, 3-6,
3-9, 3-12; 6-3, 6-6, 6-9, 6-12; 9-3, 9-6, 9-9, 9-12; 12-3, 12-6, 12-9,
and 12-12) by following equal weighted, full rebalancing and Decile
techniques. I collected the data of 300 companies listed on Karachi
Stock Exchange from 1999 to 2007. Stocks were ranked on the basis of
average monthly stock returns and top ten stocks were selected as
winner's stock and bottom ten were selected as loser's stock.
Zero-cost momentum portfolio was constructed as long position in
winner's stock portfolio and short position in loser's stock
portfolio. Returns of zero-cost momentum portfolio were positive only in
1 out of 16 strategies. And a decreasing trend in losses reported in 15
strategies was observed, so I extend our analysis on "Long Period
Analysis", "Short term and Long term Holding Period
Analysis" and at the end I sub divide the sample in two groups and
check the momentum effect. Here I find very slight evidence of momentum
and I consider it better to change the sample. So, I took another sample
of monthly stock prices of 50 companies listed on Karachi Stock Exchange
and analysed the effect by taking eight most representative strategies,
i.e. 6/3, 6/6, 6/9, 6/12 and 12/3, 12/6, 12/9, and 12/12. These
strategies were also constructed on the basis of equal weighted, full
rebalancing and Decile techniques. I calculated the average monthly
return from 6 out of 8 strategies as 0.012 and significant only in 12/3,
12/6 and 12/9 strategy. I conclude our analysis as there is very low
momentum effect in Karachi Stock Exchange and these results are aligned
with Griffin, Ji, and Martin (2003), Chui, Titman, and Wei (2000) and
Rouwenhorst (1999).
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Comments
The study constructed 16 momentum strategies by following equal
weighted, full rebalancing and Decile techniques. The empirical work
utilised stock prices of 300 companies listed on Karachi Stock Exchange
from 1999 to 2007. The returns of zero-cost momentum portfolio were
positive only in 1 out of 16 strategies. Also, a decreasing trend in
losses was reported in 15 strategies. Then, the authors extended their
analysis for the longer period and found some evidence of momentum
effect which remained significant even after changing the sample. In my
view, it is an excellent piece of empirical work. However, some
suggestive comments are made so that this study can further be improved.
Authors have used full rebalancing strategy, while partial rebalancing
technique is also another option for them to analyse their framework. It
involves monthly rebalancing regardless of the length of the holding
period. In the opinion of authors, the first method is more viable to a
private investor because he does not follow the market on monthly basis.
But, this argument needs further justification. Secondly, the data used
in this work is based on 300 companies. It is also possible to conduct
the same exercise while considering segments of these companies as per
the sectoral classification adopted by KSE. Then apply these momentum
strategies to analyse performance related to each sector and report any
inter-sectoral heterogeneity in terms of empirical results.
Adnan Haider
Institute of Business Administration, Islamabad.
Habib-Ur-Rahman <
[email protected]> is PhD student,
Shaheed Zulfiqar Ali Bhotto Institute of Science and Technology
(SZAB1ST), Islamabad. Hasan M. Mohsin <
[email protected]> is
Senior Research Economist, Pakistan Institute of Development Economics,
Islamabad.
Table 1
Momentum Strategies
Holding Period
J/K 3 6
Formation Period
3
Returns-Winner's Stock -0.1020 -0.0025
* -0.8977 * -0.3818
Returns-Loser's Stock 0.5861 0.0409
3.9824 4.5245
Returns-Momentum Portfolio -0.6881 -0.0435
-4.9578 -5.3333
6
Returns-Winner's Stock -0.0097 -0.0049
* -1.0123 * -0.8268
Returns-Loser's Stock 0.0540 0.0347
3.4178 3.8584
Returns-Momentum Portfolio -0.0637 -0.0396
-4.2193 -4.7817
9
Returns-Winner's Stock -0.0121 -0.0127
* -1.7845 * -1.6698
Returns-Loser's Stock 0.0838 -0.0073
4.6154 * -0.7221
Returns-Momentum Portfolio -0.0959 -0.0054
-4.8441 * -0.4212
12
Returns-Winner's Stock 0.0140 0.0068
1.1503 * 0.6581
Returns-Loser's Stock 0.0862 0.0209
4.6791 * 1.81026
Returns-Momentum Portfolio -0.0722 -0.0141
-3.6203 -1.9947
Holding Period
J/K 9 12
Formation Period
3
Returns-Winner's Stock 0.0004 0.0027
* 0.07809 * 0.5547
Returns-Loser's Stock 0.0297 0.0253
5.1255 5.3666
Returns-Momentum Portfolio -0.0293 -0.0226
-4.5974 -4.1337
6
Returns-Winner's Stock 0.0007 0.0008
* 0.1379 * 0.1689
Returns-Loser's Stock 0.0201 0.0249
4.0892 5.3828
Returns-Momentum Portfolio -0.0196 -0.0234
-3.8900 -4.7719
9
Returns-Winner's Stock -0.0094 0.0214
* -1.0758 2.785444
Returns-Loser's Stock 0.0248 0.0399
2.113? 4.1553
Returns-Momentum Portfolio -0.0342 -0.0184
-3.7094 -2.0648
12
Returns-Winner's Stock * 0.0046 -0.0080
* 0.6308 * -1.0083
Returns-Loser's Stock -0.0079 0.0125
* -1.4481 * 1.4741
Returns-Momentum Portfolio 0.0125 -0.0205
* 1.1687 -2.8684
Table 2
Momentum Strategies
Holding Period
J/K 24 36 48
Formation Period
6
Returns-Winner's Stock 0.0037 0.0091 0.0120
* 1.1911 3.5645 8.7187
Returns-Loser's Stock 0.0186 0.0156 0.0199
5.1525 3.9694 9.6452
Returns-Momentum Portfolio -0.0149 -0.0065 -0.0079
-4.6374 * -1.4275 -7.0539
Formation Period
12
Returns-Winner's Stock 0.0054 0.0082 0.0112
2.0605 3.8387 9.5768
Returns-Loser's Stock 0.0178 0.0213 0.0258
4.0147 5.3252 11.2489
Returns-Momentum Portfolio -0.0124 -0.0131 -0.0146
-3.4328 -4.6501 -6.8034
Table 3
Short-term vs. Long-term Holding Period Analysis
Holding Period
J/K 24-3 36-6 48-9
Formation 6 Returns- 0.0488 0.0331 0.0117
Period Momentum
Portfolio
12 Returns- 0.0598 0.0010 -0.0271
Momentum
Portfolio
Table 4
Momentum Strategies (Sub Period Analysis, 1999-2003)
Holding Period
J/K 3 6
Formation Period
3
Returns-Winner's Stock -0.1267 -0.0019
* -0.6963 * -0.1822
Returns-Loser's Stock 0.9108 0.0606
4.0703 4.4581
Returns-Momentum -1.0376 -0.0624
Portfolio -4.3984 -4.6230
6
Returns-Winner's Stock -0.0053 -0.0018
* -0.4069 * -0.2216
Returns-Loser's Stock 0.0810 0.0543
3.3449 4.4518
Returns-Momentum -0.0863 -0.0561
Portfolio -3.3057 -4.6817
J/K 9 12
Formation Period
3
Returns-Winner's Stock -0.0024 -0.0001
* -0.2879 * -0.0097
Returns-Loser's Stock 0.0439 0.0376
5.2492 6.6525
Returns-Momentum -0.0462 -0.0376
Portfolio -4.2629 -4.1535
6
Returns-Winner's Stock 0.0021 0.0006
* 0.2644 * 0.0920
Returns-Loser's Stock 0.0331 0.0398
5.9182 7.1006
Returns-Momentum -0.0316 -0.0392
Portfolio -4.0579 -4.9265
Table 5
Momentum Strategies (Sub Period Analysis, 2003-2007)
Holding Period
J/K 3 6
Formation Period
3
Returns-Winner's Stock -0.1010 -0.0027
* -0.6295 * -0.2720
Returns-Loser's Stock 0.2143 0.0204
* 1.1670 * 1.7936
Returns-Momentum -0.3153 -0.0230
Portfolio -2.6440 -2.9796
6
Returns-Winner's Stock -0.0074 -0.0046
* -0.5246 * -0.4635
Returns-Loser's Stock 0.0283 0.0122
1.3612 *0.8737
Returns-Momentum -0.0357 -0.0168
Portfolio -2.4019 *-1.4779
J/K 9 12
Formation Period
3
Returns-Winner's Stock -0.0005 0.0012
* -0.0740 * 0.1901
Returns-Loser's Stock 0.0122 0.0087
* 1.6034 * 1.4912
Returns-Momentum -0.0127 -0.0075
Portfolio -2.0326 -1.4697
6
Returns-Winner's Stock -0.0018 -0.0062
* -0.2517 * -0.9747
Returns-Loser's Stock 0.0051 0.0061
* 0.6650 * 1.005
Returns-Momentum -0.0065 -0.0123
Portfolio *-1.04156 -2.3854
Table 6
Momentum Strategies
Holding Period
J/K 3 6 9 12
Formation Period
3
Returns-Winner's 0.0445 0.0063 0.0157 0.0198
Stock 5.2500 * 0.7755 2.1159 * 1.7907
Returns-Loser's -0.0133 0.0148 0.0086 0.0129
Stock * -1.6769 * 1.4598 * 1.0179 * 0.9876
Returns-Momentum 0.0523# -0.0085# 0.0064# 0.0059#
Portfolio 6.4559 * -1.1432 * 0.6006 0.5231
6
Returns-Winner's 0.0489 0.0463 0.0296 0.0162
Stock 6.4381 4.4918 2.5752 *1.609
Returns-Loser's -0.0185 -0.0003 0.0059 0.0142
Stock -3.8817 * -0.0348 * 0.6220 * 1.0993
Returns-Momentum 0.0289# 0.0200# 0.0102# 0.0012#
Portfolio 3.6678 3.3368 2.5315 *0.3218
Italic values indicates the momentum effect.
Note: The momentum effect are indicated with #.
Fig. 2. Strategy-wise Formation and Holding Periods
Momentum Strategy Respective Formation and
Holding Periods
Strategy 1 (3/3) Where: Formation Period=3
months and Holding Period=3
months
Strategy 2 (3/6) Where: Formation Period=3
months and Holding Period=6
months
Strategy 3 (3/9) Where: Formation Period=3
months and Holding Period=9
months
Strategy 4 (3/12) Where: Formation Period=3
months and Holding Period=12
months
Strategy 5 (6/3) Where: Formation Period=6
months and Holding Period=3
months
Strategy 6 (6/6) Where: Formation Period=6
months and Holding Period=6
months
Strategy 7 (6/9) Where: Formation Period=6
months and Holding Period=9
months
Strategy 8 (6/12) Where: Formation Period=6
months and Holding Period=12
months
Strategy 9 (9/3) Where: Formation Period=9
months and Holding Period=3
months
Strategy 10 (9/6) Where: Formation Period=9
months and Holding Period=6
months
Strategy 11 (9/9) Where: Formation Period=9
months and Holding Period=9
months
Strategy 12 (9/12) Where: Formation Period=9
months and Holding Period=12
months
Strategy 13 (12/3) Where: Formation Period=12
months and Holding Period=3
months
Strategy 14 (12/6) Where: Formation Period=12
months and Holding Period=6
months
Strategy 15 (12/9) Where: Formation Period=l 2
months and Holding Period=9
months
Strategy 16(12/12) Where: Formation Period=12
months and Holding Period=12
months
