# Time-series momentum trading strategies in the global stock market.

In recent years, the presence of abnormal profits in stock markets
has been empirically validated, thereby putting the Efficient Market
Hypothesis on trial; and the assertion that the market knows everything
or the market cannot be beaten has been proven to be a myth. With the
presence of profitable trading rules in stock markets, speculation
becomes a common phenomenon making the financial system intrinsically
instable, vulnerable to shocks, and prone to crashes. This study, while
exploring the presence of profitable trading rules in the global market
in recent years, finds that developed countries' submarkets are
more vulnerable to speculating activities Business Economics (2015) 50,
80-90. doi: 10.1057/be.2015.16

Keywords: time-series trading strategies, global stock market, momentum trading

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Ever since the introduction of the Efficient Market Hypothesis [Fama 1970], stock markets are presumed to be efficient in the sense that stock prices are perceived to incorporate and reflect all publicly and privately available information. This suggests that asset prices cannot be predicted from their own past returns. Therefore, markets are unlikely to offer opportunities to earn so-called abnormal profit that cannot be justified by the relevant underlying fundamentals. This implies that no investor can beat the market or fool his fellow investors consistently. However, available literature in the area documents significant presence of asset-pricing anomalies. Thus, the assertion of the lack of predictability in asset returns is seriously challenged, and substantial abnormal profit in stock markets has often been empirically validated.

With the denial of the Efficient Market Hypothesis, predictability becomes a critical element of financial markets, which now might offer enough prospects for speculators to be rewarded. In an intrinsically predictable financial market, it is indeed possible to design successful and profitable trading rules. Speculators are better positioned and more inclined to trade with such rules and appear to profit at the expense of hedgers. As speculation becomes a common phenomenon, the financial system becomes intrinsically instable, vulnerable to shocks, and prone to crashes. The waves of crises that have hit the global financial markets over the past years and their ultimate devastating impact on the rest of the economy have led researchers in the field to explore the possible presence of abnormal return and possibilities of speculation in financial markets. The present study explores the possible presence of a particular profitable trading rule in the global stock market in recent years, especially around the financial melt-down of 2007-08. Specifically, it inquires into the possible presence of time-series momentum trading strategies and their potential to fetch abnormal returns in the global stock market. (1)

Time-series momentum, which is by nature an asset pricing anomaly, has drawn the attention of researchers in recent years. The available literature on momentum trading distinguishes between cross-section and time-series momentum trading strategies. Although cross-section momentum trading involves playing in relative terms, time-series momentum trading in an asset is based on its historical return. Abnormal cross-section profit exists if a stock could perform consistently better than its peers, whereas designing a successful and profitable time-series momentum trading rule in the stock market depends largely on the predictability of the market. Hence, time-series momentum trading strategies challenge the "random walk" hypothesis--which rules out the predictability of future prices from the present prices--thereby invalidating the Efficient Market Hypothesis, at least in its weak form. Opportunities open up for speculators, making the financial system inherently fragile. This study explores the presence of time-series momentum trading strategies in the global stock market in order to comment on the possible intrinsic fragility of the system.

1. Earlier Literature in the Field

Traditional literature on cross-section momentum trading implemented simpler methods and indicators, such as the-market-to-book value of a stock. Studies made by Rosenberg, Reid, and Lanstein [1985], Chan, Hamao, and Lakonishok [1991], Brennan, Chordia, and Subrahmanyam [1998], and Lakonishok, Shleifer, and Vishny [1994] emphasized the presence of cross-section momentum trading strategies.

It was perhaps Brock, Lakonishock, and LeBaron [1992] who first explored the possible presence of a moving average-based momentum in stock markets. Using a 100-year data series preceding 1987, the study found significant evidence of stock return predictability. Their study was critically analysed by a number of studies that were conducted later on. Hudson, Dempsey, and Keasey [1996] found that the result obtained by the earlier study did not hold when transaction costs are incorporated in the model. Ready [2002] found the results did not hold when applied to the United States intraday stock market. The study did not find the trading strategies to earn abnormal returns over a simple buying and selling strategy. However, Bessembinder and Chan [1995], following the Brock, Lakonishock, and LeBaron [1992] method, found significant evidence of profitable trading strategies in the Asian markets. Moving average methods were used by many other studies in determining profitable trading rules. Ratner and Leal [1999] used different moving average methods to test for profitable trading strategies in 10 selected Latin American and Asian markets during 1982-95. However, the findings were mixed. The result found profitable technical trading strategies in only three out of 10 markets.

More recent literature on momentum trading uses more sophisticated and complex techniques. Lo, Mamaysky, and Wang [2000], using a technical pattern recognition model, found profitable trading strategies to be present in the stock market of the United States. Potvin, Soriano, and Vallee [2004] used genetic programming to explore the presence of profitable trading strategies in the Toronto stock exchange. The study found that trading rules thus constructed win over simple buy-and-hold strategies during recession and stable periods. However, during recovery, the trading strategies are significantly beaten by the simple buy-and hold strategies. O'Neill and others [2001] used "Grammatical Evolution," an automatic programming technique, to construct profitable trading strategies in FTSE100.

In a more recent study by Moskowitz, Ooi, and Pedersen [2012], which used 58 liquid instruments, a strong positive predictability of future asset returns was traced based on the past returns. Therefore, it supported the existence of a diversified portfolio of time-series momentum across all asset classes, which outperform the standard buy-and-hold strategies. They concluded that having a momentum strategy will profit the speculators at the expense of the hedgers. Moreover, they argued that time-series momentum trading strategies are in line with the predictions of some of the significant behavioural and rational asset pricing theories. They pointed out that the studies by Barberis, Shleifer, and Vishny [1998], Daniel, Hirshleifer, and Subrahmanyam [1998], and Hong and Stein [1999] emphasized a single risky asset. Hence, they considered time-series momentum strategies to be of greater importance than the cross-section momentums. Similarly, the literature on rational theories of momentum considers a single risky asset [Berk, Green, and Naik 1999; Johnson 2002; Ahn, Conrad, and Dittmar 2003; Sagi and Sesholes 2007; Liu and Zhang 2008]. Baker and Wurgler [2007] and Qiu and Welch [2006] found a direct link between time-series momentum and measures of investor sentiment. Lo and Mackinlay [1988] and Lewellen [2002] analysed the relationship between time-series and cross-sectional momentum, the factors driving such strategies, and their relationship with the existing theory. Baltas and Kosowski [2012] extend the work of Moskowitz, Ooi, and Pedersen [2012] and conclude that commodity trading advisors seem to follow a time-series momentum strategy. More recently, Chakrabarti and Sen [2014] explored momentum trading rules in the context of the Indian stock market and green stocks in India and the global market. The present study will closely follow the time-series momentum methodology prescribed by Moskowitz, Ooi, and Pedersen [2012].

2. The Analysis

This study seeks to explore the possible presence and profitability of time-series momentum trading strategies in the global stock market over a period of January 2004 to March 2015. The period covers a cycle around the financial melt-down of 2007-08--the precrisis period of 2004-07, the crisis period of 2007-09, and its aftermath. The study uses monthly data, where the global stock market is represented by market indices from three regions of the world: the United States, the European region, and the Asia-Pacific region. One benchmark stock index is selected for each of these three regions from the set of STOXX Total Market Indices.

The STOXX Total Market Index for a country represents the relevant country as a whole, covering approximately 95 percent of the free float market capitalization of companies in the represented country, with a variable number of components. For the United States, the study uses the STOXX U.S.A. Total Market Index. The Asian region is represented by the STOXX Asia Total Market Index, which covers the Asian region as a whole. It includes approximately 95 percent of the free float market capitalization of Asian companies with a variable number of components. The European region is represented by the STOXX Europe Total Market Index. Specifically, it covers 95 percent of the free float market capitalization across 18 European countries: Austria, Belgium, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Luxembourg, the Netherlands, Norway, Portugal, Spain, Sweden, Switzerland, and the United Kingdom.

Monthly return series are computed using the formula ([P.sub.t]/[P.sub.t-1]).

The time-series momentum trading strategy

In addition to Moskowitz, Ooi, and Pedersen [2012], the methodology employed here has been followed by Chakrabarti and Sen [2015] in the context of green stocks in the global market. The study starts by an analysis of descriptive statistics and exploration into the possible presence of autocorrelation in the return series. The presence of profitable time-series momentum trading strategy depends on the predictability of present returns from past returns. Therefore, an analysis of autocorrelation might be taken as the starting point of the paper. From the descriptive statistics shown in Table 1, all the series are found to be nonnormal (given by the Jarque-Bera statistic), having skewness and fat tails. The series thus exhibit almost all the stylized facts that a financial time-series is said to exhibit in the literature.

The probabilities for testing the null hypothesis of no autocorrelation up to order 36 (based on the Q statistic) are shown in Table 2. As the successful designing and implementation of a profitable time-series momentum trading strategy is based on predictability of price, the presence of autocorrelation in price return hints toward possibility of designing successful trading strategies. The presence of autocorrelation in the market index is evident in the European market at all lags. The United States market is also characterized by the presence of autocorrelation beyond the eighth lag. The Asian market index, however, is characterized by absence of autocorrelation.

With a simple analysis of the descriptive statistics, we now move on to the formation of time-series momentum (TSM) trading strategies. The analysis is conducted in terms of risk-adjusted return as risk-averse investors in a financial market usually take decisions on the basis of the risk-adjusted returns. Moreover, it would be easier to compare different asset returns if they are adjusted by their volatilities or risk. A monthly "excess return" series, [r.sup.i.sub.t], is constructed for each regional market index using appropriate risk-free rates. The Asian Templeton Bond indices available for the three regions selected have been used as the risk-free asset for purposes of adjustment.

In order to define the risk-adjusted return series for each index, the study has estimated conditional volatility given by the conditional standard deviation for each index return. The conditional standard deviation series are constructed by estimating a suitable GARCH family model that models the return and volatility simultaneously by taking into account the stylized facts of any financial time series. In all three cases, the relevant model has been an EGARCH model of order (1, 1, 1) that incorporates asymmetric responses of volatility toward good and bad news. The risk-adjusted return, for asset i in month t, hence is defined as ([r.sup.i.sub.t]-[r.sup.f.sub.t])/ ([[sigma].sup.i.sub.t-1]), where [r.sup.i.sub.t] is the return in month t, [r.sup.f.sub.t] is the risk-free rate in month t and [[sigma].sup.i.sub.t-1] is the conditional standard deviation of the return series in month t-1. The risk-adjusted returns defined in this way are very similar to the Sharpe Indices.

The construction of time-series momentum trading strategies requires the concept of a look-back period and a holding period. The look-back period is defined as the period in time that an investor looks backward in order to define his strategy on any given asset. Once the decision on the asset is taken and the portfolio is formed, it will be held for a period of a chosen length--the holding period. It is the cumulative return on the asset over a chosen look-back period that provides a signal to the investors to take their desired position on the asset over a given holding period. Specifically, an investor would buy an asset if the cumulative return over a given look-back period L is positive and the position will be held over the holding period H. The investor will hold a selling position in the reverse case. Hence, following Moskowitz, Ooi, and Pedersen [2012], the time-series momentum return series for any given market index i, with look-back period L and holding period H, would be given by:

[r.sup.TS,i.sub.t:t+H] = sign([r.sup.i.sub.t-L:t]) [r.sup.i.sub.t:t + H/[[sigma].sup.i.sub.t]]. (1)

Sign ([r.sup.i.sub.t-L:t]) is the signal determined by the cumulative return over the look-back period (from t-L to t). If such returns are positive (negative), the return from holding the asset over the holding period (from t to t+H) will be (+1) (-1) times the cumulative return over the holding period. Each time-series momentum return is then adjusted for varying volatility. The study has constructed 49 (7x7) trading strategies ([L.sub.i], [H.sub.j], i, j = 1, 2, 6, 12, 24, 36, 48) for each of the three market indices chosen.

Can the trading strategies "beat the marker"?

The study now is extended to explore the ability of the time-series momentum trading strategies to offer abnormal return over the respective market. Alternatively, it seeks to explore whether the trading strategy defined for a particular market could beat the market on which it is defined. For that, the study estimates equation (2).

[R.sup.TS(L, H).sub.t] = [alpha]+[beta][(Market).sub.t] + [gamma][(Market).sup.2.sub.t] + [[epsilon].sub.t] (2)

for each of the three market indices.

In this model, [R.sup.TS(L, H)] is monthly time-series momentum return on a market index with look-back period L and holding period H. In this model, if [alpha] (alpha) is significantly positive, the trading strategy could beat the market in the sense that it overperforms the market. A significantly negative [alpha] would imply that the trading strategy would underperform the market. The interpretation of [alpha] is similar to Jensen's Alpha [Jensen 1968].

The coefficient of Market that is [beta] (beta) measures the sensitivity of the trading strategy with respect to market movement. The interpretation is similar to that of beta in a Capital Asset Pricing Model. A time-series momentum trading strategy with a [beta]>1 implies over-sensitivity of the strategy with respect to market movement. Similarly, a time-series momentum trading strategy with a [beta]<1 would be defensive and under-sensitive to the market movement.

The coefficient of [(Market).sup.2] is interpreted as the ability of the strategy to act as a hedging instrument. A positive value of [gamma] (gamma) would imply that the time-series momentum trading strategy gives positive return even when the market return is positive or negative. Hence, the strategy gives positive market return under extreme market conditions and might act as a hedging instrument. With these interpretations, equation (2) is estimated separately for the three regional markets. The results are summarized in Tables 3-5.

Time-series momentum strategies in the European region

The performance of the time-series momentum trading strategies in the European region is shown in Table 3.

Out of the 49 estimated alpha values, 22 are statistically significant either at 1 percent or at 5 percent level of significance. Out of these, only eight are positive and the remaining 14 are negative. However, for look-back periods of 6, 2, and 1 months and for holding periods of 1, 2, 6, and 12 months the alpha values are found to be significantly positive. Hence, the short-term time-series momentum trading strategies can, to some extent, beat the market.

The picture is different for look-back and holding periods of 12, 24, 36, and 48 months. These are characterized by negative alpha values, implying that time-series momentum trading strategies are not profitable for longer periods.

None of these trading strategies are sensitive to the market movements. This is evident from the insignificant beta coefficients reported in Table 3. The time-series trading strategies cannot act as hedging instruments either. The insignificant gamma coefficients obtained in the estimation process imply that the time-series trading strategy returns are not at all related to the best or worst conditions in the market in which they are defined. Hence, time-series trading strategies cannot be said to be profitable in the European region except in the short run, are not sensitive to market movements, and cannot act as hedging instruments.

Time-series momentum strategies in the United States

The performance of the time-series momentum trading strategies in the United States is shown in Table 4.

The results have some differences with those obtained for the European region. Out of the 49 alphas, 21 are statistically significant of which 14 are significantly positive. Positive alphas are obtained for short to medium look-back periods (2, 6, and 12 months) and holding periods (1, 2, 6, 12, and 24 months).

Long-term trading strategies, however, underperform the market, which is evident from the negative alpha values obtained for longer look-back and holding periods. Moreover, the positive alpha values obtained for the United States time-series momentum trading strategies are much smaller than what we obtained for the European region. Hence, the time-series momentum trading strategies in the European market, when they could beat the market, would give much more return than the time-series momentum trading strategies in the United States.

Fifteen of these United States time-series momentum trading strategies (that is in 31 percent cases) are sensitive to market movements. These are evident by significant beta values all of which are significantly greater than one in absolute terms. Of these significant beta values, only seven are positive--five of which are for one-month look-back periods, where the time-series momentum trading strategies may be said to be aggressive or oversensitive to markets. In almost all other cases, significant beta values are negative and somewhat insensitive to market returns.

For short to medium look-back and holding periods, gamma values are found to be significantly negative. This shows the inefficacy of the trading strategies as hedging instruments. Rather, they provide negative returns in extreme market conditions. There is only one case, where gamma is significantly positive.

All things considered, time-series momentum trading strategies cannot be said to be very profitable in the United States. However, they can beat the market in more cases than in Europe.

Time-series momentum strategies in the Asian region

The performance of the time-series momentum trading strategies in the Asian region is shown in Table 5.

Compared with the two other regions, the estimated values of alpha, beta, and gamma have been significantly lower for the trading strategies defined for the Asian region. Out of the 49 alphas, 16 are statistically significant, of which only three are significantly positive. Positive alphas are obtained for short look-back period (2 months) and short to medium holding periods (2, 6, and 12 months). Negative alphas are obtained for long-term time-series momentum trading strategies. There are 24 statistically significant beta values, but only five are positive. The remaining 19 significant beta values are negative. All the beta values are, however, less than one in absolute values. Hence, the Asian time-series momentum trading strategies cannot significantly beat the market and are not over-sensitive to the market movements. Moreover, the Asian time-series momentum trading strategies cannot serve as hedging instruments. Although 31 gamma coefficients--out of a total of 49--are statistically significant, these are all negative and are of very small values compared with those obtained for the other markets. Hence, in extreme market conditions, Asian time-series momentum trading strategies offer negative returns. The time-series momentum trading strategies in the Asian market are least effective and less profitable compared with the time series momentum trading strategies defined over the two other markets.

Thus, the two developed markets offer better opportunities of making profit through suitable trading strategies. This might raise further question as to whether the developed markets as a whole could offer higher momentum profits compared with the emerging markets. In the final section, the study explores this area by comparing the profitability of time-series momentum trading strategies in the developed and the emerging markets.

Time-series momentum strategies: Developed vs. emerging markets

In order to design time-series momentum trading strategies for the developed and emerging markets, the study selects two benchmark indices available for the developed and emerging markets as a whole. To represent the emerging market, the study uses the STOXX Emerging Markets Total Market Index. This index represents the world's emerging markets as a whole, covering approximately 95 percent of the free float market capitalization of the investable stock universe with a variable number of components. The developed markets are represented by the STOXX Developed Total Market Index. It represents the world's developed markets as a whole, covering approximately 95 percent of the free float market capitalization of the investable stock universe with a variable number of components.

The descriptive statistics for the returns in these two markets are shown in Table 6.

The returns for both markets are negatively skewed, have excessive kurtosis, and are nonnormal. The probabilities for accepting the null of no autocorrelation up to order 36 are reported in Table 7.

The returns for both markets are characterized by significant presence of autocorrelation. This suggests the possibility of designing successful momentum trading strategies.

The 49 time-series momentum trading strategies as described earlier are constructed on these two markets' indices over the study period of January 2004 to February 2015. The study then explores the three aspects that have been introduced in the earlier subsection, namely:

* whether these trading strategies could beat the respective markets;

* how sensitive they are to the market movements; and

* how profitable they are in extreme market conditions.

The results are summarized in Tables 8 and 9.

As is evident from Table 8, which presents the results for the emerging markets, only six out of the 49 alpha values are statistically significant. Out of these, only one is positive. Hence, the trading strategies cannot be said to beat the market. Similarly, the strategies are not very sensitive to the market movements. Only five of the estimated betas are statistically significant. Moreover, the negative values of these betas suggest that the trading strategies move in the opposite direction of the market movements. Gamma values are significant for only six cases, out of which four are positive. Thus, in only four cases-for longer look-back and holding period do the trading strategies give more returns in the extreme market conditions--do the trading strategies act as a hedging instrument.

The results obtained for the developed markets are shown in Table 9.

In the developed countries market, 15 out of the total 49 estimated alpha values are statistically significant. Out of these only five, defined over medium-term look-back (6 and 12 months) and short to medium holding period (1, 2, 6, and 12 months), are positive. For long-term look-back (24, 36, and 48 months) and for medium to long-term holding periods (12,24,36, and 48 months) the alphas are significantly negative.

Hence, in the developed markets, short-to-medium-term time-series momentum trading strategies can beat the market sometimes, while the long-term time-series momentum strategies are likely to significantly underperform the market.

The time-series momentum trading strategies, however, are not significantly sensitive to the market movements. In only two cases are the beta values significantly negative. Hence, when the time-series momentum trading strategies are sensitive to market movement, the returns are negatively related to the market movements. Moreover, the time-series momentum trading strategies cannot act as hedging instruments. The estimated gamma value turns out to be significantly positive in only one case.

3. Conclusion

The study has explored the efficacy of time-series momentum trading strategies in the global market during the period 2004-15. This period covers a significant stock market cycle in the global economy, from the precrisis period from 2004 to late 2007, through the crisis period of 2008-09, and the aftermath of the crisis when the markets are characterized by fluctuations but without a significant crisis. The exploration into the presence of profitable time-series momentum trading strategies started from the three major markets in the world, namely, the Asian region, European region, and the United States. The results obtained for the European region and for the United States have been somewhat similar. Significant and profitable time-series momentum trading strategies might be isolated for short-to-medium-term look-back and holding periods. Moreover, the European time-series momentum trading strategies are more profitable than the United States time-series momentum trading strategies. Long-term time-series momentum trading strategies, defined for long-term look-back and holding periods, however, are not profitable for these two markets.

The time-series momentum trading strategies in the Asian market are less effective and less profitable compared with the time-series momentum trading strategies defined over the two other markets. This led us further to explore the profitability of the time-series momentum trading strategies defined over the developed markets and the emerging markets as a whole. The results were that almost no profitable time-series momentum trading strategies exist for the emerging markets as a whole. However, in the developed markets, short-to-medium-term time-series momentum trading strategies can beat the market sometimes, while the long-term strategies significantly underperform the market.

The time-series momentum trading strategies however are not attractive to the hedgers in either the emerging or developed markets. As these cannot offer positive returns in extreme market conditions, the strategies are likely to be least preferred by the hedgers or a risk-averse person. Hence, the market remains for the speculators. And, as suggested by the empirical findings, the developed markets remain more vulnerable to speculating activities compared with the emerging markets around the financial crisis of 2007-08.

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(1) The phrase "global stock market" is used to generalize for stock markets all over the world. In fact, of course, stock markets are individual exchanges in individual countries.

GAGARI CHAKRABARTI *

* Gagari Chakrabarti is an assistant professor of Economics at Presidency University, Kolkata, India. Her primary areas of research are financial economics, quantitative finance, and financial markets as complex systems. She obtained her M.Sc., M.Phil. and Ph.D. degrees in Economics from the University of Calcutta.

Keywords: time-series trading strategies, global stock market, momentum trading

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Ever since the introduction of the Efficient Market Hypothesis [Fama 1970], stock markets are presumed to be efficient in the sense that stock prices are perceived to incorporate and reflect all publicly and privately available information. This suggests that asset prices cannot be predicted from their own past returns. Therefore, markets are unlikely to offer opportunities to earn so-called abnormal profit that cannot be justified by the relevant underlying fundamentals. This implies that no investor can beat the market or fool his fellow investors consistently. However, available literature in the area documents significant presence of asset-pricing anomalies. Thus, the assertion of the lack of predictability in asset returns is seriously challenged, and substantial abnormal profit in stock markets has often been empirically validated.

With the denial of the Efficient Market Hypothesis, predictability becomes a critical element of financial markets, which now might offer enough prospects for speculators to be rewarded. In an intrinsically predictable financial market, it is indeed possible to design successful and profitable trading rules. Speculators are better positioned and more inclined to trade with such rules and appear to profit at the expense of hedgers. As speculation becomes a common phenomenon, the financial system becomes intrinsically instable, vulnerable to shocks, and prone to crashes. The waves of crises that have hit the global financial markets over the past years and their ultimate devastating impact on the rest of the economy have led researchers in the field to explore the possible presence of abnormal return and possibilities of speculation in financial markets. The present study explores the possible presence of a particular profitable trading rule in the global stock market in recent years, especially around the financial melt-down of 2007-08. Specifically, it inquires into the possible presence of time-series momentum trading strategies and their potential to fetch abnormal returns in the global stock market. (1)

Time-series momentum, which is by nature an asset pricing anomaly, has drawn the attention of researchers in recent years. The available literature on momentum trading distinguishes between cross-section and time-series momentum trading strategies. Although cross-section momentum trading involves playing in relative terms, time-series momentum trading in an asset is based on its historical return. Abnormal cross-section profit exists if a stock could perform consistently better than its peers, whereas designing a successful and profitable time-series momentum trading rule in the stock market depends largely on the predictability of the market. Hence, time-series momentum trading strategies challenge the "random walk" hypothesis--which rules out the predictability of future prices from the present prices--thereby invalidating the Efficient Market Hypothesis, at least in its weak form. Opportunities open up for speculators, making the financial system inherently fragile. This study explores the presence of time-series momentum trading strategies in the global stock market in order to comment on the possible intrinsic fragility of the system.

1. Earlier Literature in the Field

Traditional literature on cross-section momentum trading implemented simpler methods and indicators, such as the-market-to-book value of a stock. Studies made by Rosenberg, Reid, and Lanstein [1985], Chan, Hamao, and Lakonishok [1991], Brennan, Chordia, and Subrahmanyam [1998], and Lakonishok, Shleifer, and Vishny [1994] emphasized the presence of cross-section momentum trading strategies.

It was perhaps Brock, Lakonishock, and LeBaron [1992] who first explored the possible presence of a moving average-based momentum in stock markets. Using a 100-year data series preceding 1987, the study found significant evidence of stock return predictability. Their study was critically analysed by a number of studies that were conducted later on. Hudson, Dempsey, and Keasey [1996] found that the result obtained by the earlier study did not hold when transaction costs are incorporated in the model. Ready [2002] found the results did not hold when applied to the United States intraday stock market. The study did not find the trading strategies to earn abnormal returns over a simple buying and selling strategy. However, Bessembinder and Chan [1995], following the Brock, Lakonishock, and LeBaron [1992] method, found significant evidence of profitable trading strategies in the Asian markets. Moving average methods were used by many other studies in determining profitable trading rules. Ratner and Leal [1999] used different moving average methods to test for profitable trading strategies in 10 selected Latin American and Asian markets during 1982-95. However, the findings were mixed. The result found profitable technical trading strategies in only three out of 10 markets.

More recent literature on momentum trading uses more sophisticated and complex techniques. Lo, Mamaysky, and Wang [2000], using a technical pattern recognition model, found profitable trading strategies to be present in the stock market of the United States. Potvin, Soriano, and Vallee [2004] used genetic programming to explore the presence of profitable trading strategies in the Toronto stock exchange. The study found that trading rules thus constructed win over simple buy-and-hold strategies during recession and stable periods. However, during recovery, the trading strategies are significantly beaten by the simple buy-and hold strategies. O'Neill and others [2001] used "Grammatical Evolution," an automatic programming technique, to construct profitable trading strategies in FTSE100.

In a more recent study by Moskowitz, Ooi, and Pedersen [2012], which used 58 liquid instruments, a strong positive predictability of future asset returns was traced based on the past returns. Therefore, it supported the existence of a diversified portfolio of time-series momentum across all asset classes, which outperform the standard buy-and-hold strategies. They concluded that having a momentum strategy will profit the speculators at the expense of the hedgers. Moreover, they argued that time-series momentum trading strategies are in line with the predictions of some of the significant behavioural and rational asset pricing theories. They pointed out that the studies by Barberis, Shleifer, and Vishny [1998], Daniel, Hirshleifer, and Subrahmanyam [1998], and Hong and Stein [1999] emphasized a single risky asset. Hence, they considered time-series momentum strategies to be of greater importance than the cross-section momentums. Similarly, the literature on rational theories of momentum considers a single risky asset [Berk, Green, and Naik 1999; Johnson 2002; Ahn, Conrad, and Dittmar 2003; Sagi and Sesholes 2007; Liu and Zhang 2008]. Baker and Wurgler [2007] and Qiu and Welch [2006] found a direct link between time-series momentum and measures of investor sentiment. Lo and Mackinlay [1988] and Lewellen [2002] analysed the relationship between time-series and cross-sectional momentum, the factors driving such strategies, and their relationship with the existing theory. Baltas and Kosowski [2012] extend the work of Moskowitz, Ooi, and Pedersen [2012] and conclude that commodity trading advisors seem to follow a time-series momentum strategy. More recently, Chakrabarti and Sen [2014] explored momentum trading rules in the context of the Indian stock market and green stocks in India and the global market. The present study will closely follow the time-series momentum methodology prescribed by Moskowitz, Ooi, and Pedersen [2012].

2. The Analysis

This study seeks to explore the possible presence and profitability of time-series momentum trading strategies in the global stock market over a period of January 2004 to March 2015. The period covers a cycle around the financial melt-down of 2007-08--the precrisis period of 2004-07, the crisis period of 2007-09, and its aftermath. The study uses monthly data, where the global stock market is represented by market indices from three regions of the world: the United States, the European region, and the Asia-Pacific region. One benchmark stock index is selected for each of these three regions from the set of STOXX Total Market Indices.

The STOXX Total Market Index for a country represents the relevant country as a whole, covering approximately 95 percent of the free float market capitalization of companies in the represented country, with a variable number of components. For the United States, the study uses the STOXX U.S.A. Total Market Index. The Asian region is represented by the STOXX Asia Total Market Index, which covers the Asian region as a whole. It includes approximately 95 percent of the free float market capitalization of Asian companies with a variable number of components. The European region is represented by the STOXX Europe Total Market Index. Specifically, it covers 95 percent of the free float market capitalization across 18 European countries: Austria, Belgium, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Luxembourg, the Netherlands, Norway, Portugal, Spain, Sweden, Switzerland, and the United Kingdom.

Monthly return series are computed using the formula ([P.sub.t]/[P.sub.t-1]).

The time-series momentum trading strategy

In addition to Moskowitz, Ooi, and Pedersen [2012], the methodology employed here has been followed by Chakrabarti and Sen [2015] in the context of green stocks in the global market. The study starts by an analysis of descriptive statistics and exploration into the possible presence of autocorrelation in the return series. The presence of profitable time-series momentum trading strategy depends on the predictability of present returns from past returns. Therefore, an analysis of autocorrelation might be taken as the starting point of the paper. From the descriptive statistics shown in Table 1, all the series are found to be nonnormal (given by the Jarque-Bera statistic), having skewness and fat tails. The series thus exhibit almost all the stylized facts that a financial time-series is said to exhibit in the literature.

The probabilities for testing the null hypothesis of no autocorrelation up to order 36 (based on the Q statistic) are shown in Table 2. As the successful designing and implementation of a profitable time-series momentum trading strategy is based on predictability of price, the presence of autocorrelation in price return hints toward possibility of designing successful trading strategies. The presence of autocorrelation in the market index is evident in the European market at all lags. The United States market is also characterized by the presence of autocorrelation beyond the eighth lag. The Asian market index, however, is characterized by absence of autocorrelation.

With a simple analysis of the descriptive statistics, we now move on to the formation of time-series momentum (TSM) trading strategies. The analysis is conducted in terms of risk-adjusted return as risk-averse investors in a financial market usually take decisions on the basis of the risk-adjusted returns. Moreover, it would be easier to compare different asset returns if they are adjusted by their volatilities or risk. A monthly "excess return" series, [r.sup.i.sub.t], is constructed for each regional market index using appropriate risk-free rates. The Asian Templeton Bond indices available for the three regions selected have been used as the risk-free asset for purposes of adjustment.

In order to define the risk-adjusted return series for each index, the study has estimated conditional volatility given by the conditional standard deviation for each index return. The conditional standard deviation series are constructed by estimating a suitable GARCH family model that models the return and volatility simultaneously by taking into account the stylized facts of any financial time series. In all three cases, the relevant model has been an EGARCH model of order (1, 1, 1) that incorporates asymmetric responses of volatility toward good and bad news. The risk-adjusted return, for asset i in month t, hence is defined as ([r.sup.i.sub.t]-[r.sup.f.sub.t])/ ([[sigma].sup.i.sub.t-1]), where [r.sup.i.sub.t] is the return in month t, [r.sup.f.sub.t] is the risk-free rate in month t and [[sigma].sup.i.sub.t-1] is the conditional standard deviation of the return series in month t-1. The risk-adjusted returns defined in this way are very similar to the Sharpe Indices.

The construction of time-series momentum trading strategies requires the concept of a look-back period and a holding period. The look-back period is defined as the period in time that an investor looks backward in order to define his strategy on any given asset. Once the decision on the asset is taken and the portfolio is formed, it will be held for a period of a chosen length--the holding period. It is the cumulative return on the asset over a chosen look-back period that provides a signal to the investors to take their desired position on the asset over a given holding period. Specifically, an investor would buy an asset if the cumulative return over a given look-back period L is positive and the position will be held over the holding period H. The investor will hold a selling position in the reverse case. Hence, following Moskowitz, Ooi, and Pedersen [2012], the time-series momentum return series for any given market index i, with look-back period L and holding period H, would be given by:

[r.sup.TS,i.sub.t:t+H] = sign([r.sup.i.sub.t-L:t]) [r.sup.i.sub.t:t + H/[[sigma].sup.i.sub.t]]. (1)

Sign ([r.sup.i.sub.t-L:t]) is the signal determined by the cumulative return over the look-back period (from t-L to t). If such returns are positive (negative), the return from holding the asset over the holding period (from t to t+H) will be (+1) (-1) times the cumulative return over the holding period. Each time-series momentum return is then adjusted for varying volatility. The study has constructed 49 (7x7) trading strategies ([L.sub.i], [H.sub.j], i, j = 1, 2, 6, 12, 24, 36, 48) for each of the three market indices chosen.

Can the trading strategies "beat the marker"?

The study now is extended to explore the ability of the time-series momentum trading strategies to offer abnormal return over the respective market. Alternatively, it seeks to explore whether the trading strategy defined for a particular market could beat the market on which it is defined. For that, the study estimates equation (2).

[R.sup.TS(L, H).sub.t] = [alpha]+[beta][(Market).sub.t] + [gamma][(Market).sup.2.sub.t] + [[epsilon].sub.t] (2)

for each of the three market indices.

In this model, [R.sup.TS(L, H)] is monthly time-series momentum return on a market index with look-back period L and holding period H. In this model, if [alpha] (alpha) is significantly positive, the trading strategy could beat the market in the sense that it overperforms the market. A significantly negative [alpha] would imply that the trading strategy would underperform the market. The interpretation of [alpha] is similar to Jensen's Alpha [Jensen 1968].

The coefficient of Market that is [beta] (beta) measures the sensitivity of the trading strategy with respect to market movement. The interpretation is similar to that of beta in a Capital Asset Pricing Model. A time-series momentum trading strategy with a [beta]>1 implies over-sensitivity of the strategy with respect to market movement. Similarly, a time-series momentum trading strategy with a [beta]<1 would be defensive and under-sensitive to the market movement.

The coefficient of [(Market).sup.2] is interpreted as the ability of the strategy to act as a hedging instrument. A positive value of [gamma] (gamma) would imply that the time-series momentum trading strategy gives positive return even when the market return is positive or negative. Hence, the strategy gives positive market return under extreme market conditions and might act as a hedging instrument. With these interpretations, equation (2) is estimated separately for the three regional markets. The results are summarized in Tables 3-5.

Time-series momentum strategies in the European region

The performance of the time-series momentum trading strategies in the European region is shown in Table 3.

Out of the 49 estimated alpha values, 22 are statistically significant either at 1 percent or at 5 percent level of significance. Out of these, only eight are positive and the remaining 14 are negative. However, for look-back periods of 6, 2, and 1 months and for holding periods of 1, 2, 6, and 12 months the alpha values are found to be significantly positive. Hence, the short-term time-series momentum trading strategies can, to some extent, beat the market.

The picture is different for look-back and holding periods of 12, 24, 36, and 48 months. These are characterized by negative alpha values, implying that time-series momentum trading strategies are not profitable for longer periods.

None of these trading strategies are sensitive to the market movements. This is evident from the insignificant beta coefficients reported in Table 3. The time-series trading strategies cannot act as hedging instruments either. The insignificant gamma coefficients obtained in the estimation process imply that the time-series trading strategy returns are not at all related to the best or worst conditions in the market in which they are defined. Hence, time-series trading strategies cannot be said to be profitable in the European region except in the short run, are not sensitive to market movements, and cannot act as hedging instruments.

Time-series momentum strategies in the United States

The performance of the time-series momentum trading strategies in the United States is shown in Table 4.

The results have some differences with those obtained for the European region. Out of the 49 alphas, 21 are statistically significant of which 14 are significantly positive. Positive alphas are obtained for short to medium look-back periods (2, 6, and 12 months) and holding periods (1, 2, 6, 12, and 24 months).

Long-term trading strategies, however, underperform the market, which is evident from the negative alpha values obtained for longer look-back and holding periods. Moreover, the positive alpha values obtained for the United States time-series momentum trading strategies are much smaller than what we obtained for the European region. Hence, the time-series momentum trading strategies in the European market, when they could beat the market, would give much more return than the time-series momentum trading strategies in the United States.

Fifteen of these United States time-series momentum trading strategies (that is in 31 percent cases) are sensitive to market movements. These are evident by significant beta values all of which are significantly greater than one in absolute terms. Of these significant beta values, only seven are positive--five of which are for one-month look-back periods, where the time-series momentum trading strategies may be said to be aggressive or oversensitive to markets. In almost all other cases, significant beta values are negative and somewhat insensitive to market returns.

For short to medium look-back and holding periods, gamma values are found to be significantly negative. This shows the inefficacy of the trading strategies as hedging instruments. Rather, they provide negative returns in extreme market conditions. There is only one case, where gamma is significantly positive.

All things considered, time-series momentum trading strategies cannot be said to be very profitable in the United States. However, they can beat the market in more cases than in Europe.

Time-series momentum strategies in the Asian region

The performance of the time-series momentum trading strategies in the Asian region is shown in Table 5.

Compared with the two other regions, the estimated values of alpha, beta, and gamma have been significantly lower for the trading strategies defined for the Asian region. Out of the 49 alphas, 16 are statistically significant, of which only three are significantly positive. Positive alphas are obtained for short look-back period (2 months) and short to medium holding periods (2, 6, and 12 months). Negative alphas are obtained for long-term time-series momentum trading strategies. There are 24 statistically significant beta values, but only five are positive. The remaining 19 significant beta values are negative. All the beta values are, however, less than one in absolute values. Hence, the Asian time-series momentum trading strategies cannot significantly beat the market and are not over-sensitive to the market movements. Moreover, the Asian time-series momentum trading strategies cannot serve as hedging instruments. Although 31 gamma coefficients--out of a total of 49--are statistically significant, these are all negative and are of very small values compared with those obtained for the other markets. Hence, in extreme market conditions, Asian time-series momentum trading strategies offer negative returns. The time-series momentum trading strategies in the Asian market are least effective and less profitable compared with the time series momentum trading strategies defined over the two other markets.

Thus, the two developed markets offer better opportunities of making profit through suitable trading strategies. This might raise further question as to whether the developed markets as a whole could offer higher momentum profits compared with the emerging markets. In the final section, the study explores this area by comparing the profitability of time-series momentum trading strategies in the developed and the emerging markets.

Time-series momentum strategies: Developed vs. emerging markets

In order to design time-series momentum trading strategies for the developed and emerging markets, the study selects two benchmark indices available for the developed and emerging markets as a whole. To represent the emerging market, the study uses the STOXX Emerging Markets Total Market Index. This index represents the world's emerging markets as a whole, covering approximately 95 percent of the free float market capitalization of the investable stock universe with a variable number of components. The developed markets are represented by the STOXX Developed Total Market Index. It represents the world's developed markets as a whole, covering approximately 95 percent of the free float market capitalization of the investable stock universe with a variable number of components.

The descriptive statistics for the returns in these two markets are shown in Table 6.

The returns for both markets are negatively skewed, have excessive kurtosis, and are nonnormal. The probabilities for accepting the null of no autocorrelation up to order 36 are reported in Table 7.

The returns for both markets are characterized by significant presence of autocorrelation. This suggests the possibility of designing successful momentum trading strategies.

The 49 time-series momentum trading strategies as described earlier are constructed on these two markets' indices over the study period of January 2004 to February 2015. The study then explores the three aspects that have been introduced in the earlier subsection, namely:

* whether these trading strategies could beat the respective markets;

* how sensitive they are to the market movements; and

* how profitable they are in extreme market conditions.

The results are summarized in Tables 8 and 9.

As is evident from Table 8, which presents the results for the emerging markets, only six out of the 49 alpha values are statistically significant. Out of these, only one is positive. Hence, the trading strategies cannot be said to beat the market. Similarly, the strategies are not very sensitive to the market movements. Only five of the estimated betas are statistically significant. Moreover, the negative values of these betas suggest that the trading strategies move in the opposite direction of the market movements. Gamma values are significant for only six cases, out of which four are positive. Thus, in only four cases-for longer look-back and holding period do the trading strategies give more returns in the extreme market conditions--do the trading strategies act as a hedging instrument.

The results obtained for the developed markets are shown in Table 9.

In the developed countries market, 15 out of the total 49 estimated alpha values are statistically significant. Out of these only five, defined over medium-term look-back (6 and 12 months) and short to medium holding period (1, 2, 6, and 12 months), are positive. For long-term look-back (24, 36, and 48 months) and for medium to long-term holding periods (12,24,36, and 48 months) the alphas are significantly negative.

Hence, in the developed markets, short-to-medium-term time-series momentum trading strategies can beat the market sometimes, while the long-term time-series momentum strategies are likely to significantly underperform the market.

The time-series momentum trading strategies, however, are not significantly sensitive to the market movements. In only two cases are the beta values significantly negative. Hence, when the time-series momentum trading strategies are sensitive to market movement, the returns are negatively related to the market movements. Moreover, the time-series momentum trading strategies cannot act as hedging instruments. The estimated gamma value turns out to be significantly positive in only one case.

3. Conclusion

The study has explored the efficacy of time-series momentum trading strategies in the global market during the period 2004-15. This period covers a significant stock market cycle in the global economy, from the precrisis period from 2004 to late 2007, through the crisis period of 2008-09, and the aftermath of the crisis when the markets are characterized by fluctuations but without a significant crisis. The exploration into the presence of profitable time-series momentum trading strategies started from the three major markets in the world, namely, the Asian region, European region, and the United States. The results obtained for the European region and for the United States have been somewhat similar. Significant and profitable time-series momentum trading strategies might be isolated for short-to-medium-term look-back and holding periods. Moreover, the European time-series momentum trading strategies are more profitable than the United States time-series momentum trading strategies. Long-term time-series momentum trading strategies, defined for long-term look-back and holding periods, however, are not profitable for these two markets.

The time-series momentum trading strategies in the Asian market are less effective and less profitable compared with the time-series momentum trading strategies defined over the two other markets. This led us further to explore the profitability of the time-series momentum trading strategies defined over the developed markets and the emerging markets as a whole. The results were that almost no profitable time-series momentum trading strategies exist for the emerging markets as a whole. However, in the developed markets, short-to-medium-term time-series momentum trading strategies can beat the market sometimes, while the long-term strategies significantly underperform the market.

The time-series momentum trading strategies however are not attractive to the hedgers in either the emerging or developed markets. As these cannot offer positive returns in extreme market conditions, the strategies are likely to be least preferred by the hedgers or a risk-averse person. Hence, the market remains for the speculators. And, as suggested by the empirical findings, the developed markets remain more vulnerable to speculating activities compared with the emerging markets around the financial crisis of 2007-08.

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(1) The phrase "global stock market" is used to generalize for stock markets all over the world. In fact, of course, stock markets are individual exchanges in individual countries.

GAGARI CHAKRABARTI *

* Gagari Chakrabarti is an assistant professor of Economics at Presidency University, Kolkata, India. Her primary areas of research are financial economics, quantitative finance, and financial markets as complex systems. She obtained her M.Sc., M.Phil. and Ph.D. degrees in Economics from the University of Calcutta.

Table 1. Descriptive Statistics for Market Return Series in the Asian region, European region, and the United States Europe Asia United States Mean 0.003 0.003 0.0003 Std. Dev. 0.042 0.052 0.002 Skewness -0.912 -0.634 -0.099 Kurtosis 4.927 5.925 9.299 Jarque-Bera 35.781 56.321 218.439 Probability 0 0 0 Table 2. Probability for Accepting the Null of No Autocorrelation up to Order 36 (Based on Q Statistic) Lag Europe Asia U.S.A. 1 0.01 0.35 0.51 2 0.02 0.36 0.77 3 0.01 0.28 0.60 4 0.00 0.29 0.62 5 0.00 0.42 0.72 6 0.00 0.22 0.13 7 0.01 0.31 0.20 8 0.01 0.41 0.12 9 0.01 0.43 0.05 10 0.01 0.52 0.07 11 0.02 0.48 0.10 12 0.03 0.51 0.10 13 0.04 0.34 0.14 14 0.05 0.38 0.09 15 0.07 0.38 0.03 16 0.09 0.41 0.04 17 0.05 0.43 0.02 18 0.03 0.49 0.03 19 0.04 0.41 0.02 20 0.04 0.45 0.03 21 0.04 0.51 0.04 22 0.05 0.55 0.01 23 0.05 0.58 0.01 24 0.05 0.61 0.01 25 0.03 0.63 0.00 26 0.01 0.39 0.00 27 0.01 0.44 0.00 28 0.01 0.49 0.00 29 0.02 0.52 0.01 30 0.02 0.44 0.01 31 0.03 0.45 0.00 32 0.03 0.50 0.00 33 0.03 0.49 0.00 34 0.03 0.53 0.00 35 0.04 0.57 0.00 36 0.05 0.62 0.00 Table 3. Profitability of Time-Series Momentum Trading Strategy in the European Region Look-Back Period Holding period L1 L2 L6 L12 Statistical Significance of Alpha H1 4.03 5.04 10.22 * 4.19 H2 7.70 10 ** 16.31 * 6.67 H6 23.44 * 29.71 * 32.42 * 15.46 H12 26.90 38.88 * 43.64 * 2.73 H24 7.20 16.19 -6.65 -42.59 ** H36 -1.08 7.76 -8.58 -41.31 ** H48 -1.59 8.55 -3.19 -55.39 ** Statistical Significance of Beta H1 -66.16 -28.00 -107.34 -30.43 H2 -53.52 13.49 -137.75 28.02 H6 -77.03 29.58 -167.05 14.32 H12 182.57 -11.17 -290.45 10.26 H24 137.53 344.51 -112.10 -147.82 H36 -307.76 -157.98 -299.17 10.72 H48 -147.10 -100.65 -497.51 -314.47 Statistical Significance of Gamma H1 -420.09 403.39 -237.42 -245.17 H2 -1121.9 191.42 -630.43 -3.60 H6 -2433.2 -2781.1 -1717.2 -74.65 H12 -538.07 -4748.1 -3143.2 50.25 H24 -1219.5 -4583.2 -3634.9 419.41 H36 -2298.7 -364.21 1407.35 5732.21 H48 1944.95 -1727.2 825.59 4148.30 Look-Back Period Holding period L24 L36 L48 Statistical Significance of Alpha H1 -2.67 -4.83 2.80 H2 -6.05 -10.10 2.95 H6 -25.90 ** -29.16 ** 3.71 H12 -62.33 * -62.48 * -7.99 H24 -81.65 * -73.61 * 0.54 H36 -76.87 * -75.64 * -31.82 * H48 -110.46 * -160.23 * -40.24 * Statistical Significance of Beta H1 54.13 20.73 1.23 H2 124.28 50.54 26.52 H6 177.40 118.94 56.06 H12 156.99 204.70 206.00 H24 -181.36 15.50 17.25 H36 51.76 235.11 21.48 H48 -81.00 -34.50 491.16 Statistical Significance of Gamma H1 376.67 86.42 -419.60 H2 990.05 -17.06 -629.05 H6 1462.69 -502.35 -1378.4 H12 1855.49 1351.38 1074.44 H24 1468.71 1555.19 2494.33 H36 7942.66 5084.64 -65.50 H48 3565.50 5480.49 4989.07 */** implies significance at 1 percent/5 percent level of significance. Table 4. Profitability of Time-Series Momentum Trading Strategy in the United States Look-Back Period Holding period L1 L2 L6 L12 Statistical Significance of Alpha H1 0.01 0.14 0.31 * 0.35 * H2 0.05 0.27 ** 0.45 * 0.58 * H6 0.33 0.64 * 1.38 * 1.44 * H12 0.60 1.30 * 2.30 * 1.91 * H24 0.02 1.15 1.42 ** 1.93 * H36 -0.38 0.34 -1.01 0.83 H48 0.09 0.20 -0.30 -0.47 Statistical Significance of Beta H1 50.23 -73.5 ** -124.8 * -118.74 * H2 90.79 -34.46 -133.2 * -111.6 ** H6 217.4 ** 90.35 -164.63 -151.95 H12 427.98 * 36.87 -92.69 -7.54 H24 904.65 * 157.70 -117.91 -196.41 H36 1304.6 * 281.02 -128.20 -225.64 H48 1566.8 * 282.03 -163.69 102.53 Statistical significance of gamma H1 237.2 -14945.1 ** -13137.4 * -14074.6 * H2 2693.9 -16961.4 ** -15439.1 * -16614.8 ** H6 -5845.5 -32487.1 ** -30634.4 ** -28592.2 ** H12 -15860.7 -46728.6 ** -52554.1 * -49431.3 ** H24 -8364.0 -40347.5 -39664.8 -41289.6 H36 2747.1 9192.9 32690.6 23265.1 H48 -5452.4 42767.4 49827.4 59447.2 Look-Back Period Holding period L24 L36 L48 Statistical Significance of Alpha H1 0.22 ** -0.03 -0.04 H2 0.17 0.0003 -0.06 H6 0.30 -0.17 -0.31 H12 0.57 -0.36 -0.64 H24 0.01 -1.33 -3.25 * H36 -1.84 ** -4.81 * -6.26 * H48 -5.96 * -7.70 * -5.64 * Statistical Significance of Beta H1 -30.10 92.66 ** 74.89 H2 -23.86 108.62 91.32 H6 74.30 222.7 ** 218.42 H12 100.75 256.96 165.70 H24 -76.21 174.73 -76.08 H36 -82.93 -14.70 -470.5 ** H48 -252.37 -453.2 ** -829.5 ** Statistical significance of gamma H1 -21238.5 * 7284.3 8733.9 H2 -22097.2 * 2131.7 4859.7 H6 -33691.7 ** -5248.3 -2806.0 H12 -40157.4 -298.6 6827.2 H24 -8811.0 -6857.8 37028.9 H36 59430.7 -11286.4 54119.3 H48 107458.1 * 4464.5 41374.8 */** implies significance at l percent/5 percent level of significance. Table 5. Profitability of Time-Series Momentum Trading Strategy in the Asian Region Look-Back Period Holding period L1 L2 L6 L12 Statistical Significance of Alpha H1 0.0008 0.00165 0.0017 0.0011 H2 0.01 0.003 ** 0.002 0.002 H6 0.011 0.007 * 0.004 0.002 H12 0.004 0.008 ** 0.002 0.0002 H24 -0.027 0.004 0.001 -0.006 H36 -0.026 0.000 -0.005 -0.008 * H48 -0.003 0.004 -0.001 -0.003 Statistical Significance of Beta H1 0.052 -0.05 -0.25 * -0.22 * H2 0.08 0.01 -0.16 * -0.18 * H6 0.25 -0.12 -0.28 * -0.18 * H12 0.84 ** -0.11 -0.08 0.04 H24 0.66 ** -0.03 0.12 -0.17 H36 0.56 -0.28 -0.31 -0.34 * H48 0.65 ** -0.13 0.05 0.002 Statistical Significance of Gamma H1 -1.57 ** -0.02572 -0.55 -0.57 H2 1.30 0.30 -0.52 -1.88 * H6 1.37 -0.74 -0.98 -4.81 * H12 -0.37 -5.36 * -7.60 * -10.89 * H24 0.52 -5.73 * -7.86 * -11.82 * H36 -0.39 -6.94 * -9.42 * -9.76 * H48 -0.54 -5.94 * -7.13 * -9.07 * Look-Back Period Holding period L24 L36 L48 Statistical Significance of Alpha H1 -0.0002 -0.002 ** 0.00 H2 -0.001 -0.003 ** -0.00026 H6 -0.006 * -0.007 * -0.00351 H12 -0.009 * -0.013 * -0.00141 H24 -0.014 * -0.013 * -0.00082 H36 -0.009 * -0.006 ** -0.00144 H48 -0.003 -0.007 * -0.0058 ** Statistical Significance of Beta H1 -0.06 0.13 -0.09 ** H2 0.09 0.12 ** 0.06 H6 0.06 0.02 0.05 H12 -0.30 ** -0.15 -0.60 * H24 -0.79 * -0.68 * -0.63 * H36 -0.45 * -0.29 * -0.65 * H48 -0.24 ** -0.24 ** -0.53 * Statistical Significance of Gamma H1 -2.16 * -0.10 -2.44 * H2 -3.91 * -1.01 ** -1.79 * H6 -7.34 * -3.15 * -3.75 * H12 -11.67 * -0.52 -3.31 * H24 -12.39 * 0.36 -1.08 H36 -8.74 * 2.72 * -1.82 ** H48 -8.92 * 1.75 -1.58 ** */**implies significance at 1 percent/5 percent level of significance. Table 6. Descriptive Statistics for Return Series in the Emerging and Developed Markets Emerging Market Developed Market Mean 0.007 0.004 Std. Dev. 0.069 0.046 Skewness -1.196 -1.250 Kurtosis 7.588 6.996 Jarque-Bera 146.14 122.20 Probability 0 0 Table 7. Probability for Accepting the Null of no Autocorrelation up to Order 36 (Based on Q Statistic): Developed vs. Emerging Markets Lag Emerging Market Developed Market 1 0.01 0.01 2 0.00 0.04 3 0.00 0.02 4 0.01 0.01 5 0.01 0.01 6 0.00 0.00 7 0.01 0.01 8 0.01 0.01 9 0.01 0.02 10 0.01 0.02 11 0.02 0.03 12 0.02 0.04 13 0.01 0.05 14 0.01 0.07 15 0.02 0.04 16 0.03 0.06 17 0.03 0.04 18 0.02 0.05 19 0.02 0.04 20 0.03 0.05 21 0.04 0.06 22 0.06 0.05 23 0.07 0.07 24 0.08 0.07 25 0.10 0.05 26 0.08 0.04 27 0.09 0.04 28 0.10 0.04 29 0.12 0.04 30 0.11 0.05 31 0.13 0.05 32 0.15 0.07 33 0.18 0.08 34 0.14 0.05 35 0.15 0.06 36 0.17 0.08 Table 8. Profitability of Time-Series Momentum Trading Strategy in the Emerging Markets Look-Back Period Holding period L1 L2 L6 L12 Statistical Significance of Alpha H1 0.11 0.10 0.04 0.05 H2 0.27 0.19 0.11 0.02 H6 0.31 0.05 0.54 -0.01 H12 0.61 0.28 0.22 0.22 H24 0.86 0.14 0.82 0.39 H36 1.16 0.63 0.69 1.01 H48 0.93 0.02 0.69 1.21 Statistical Significance of Beta H1 -2.58 -1.92 -2.46 -1.90 H2 -3.25 -2.71 -4.76 ** -2.22 H6 3.07 0.98 -9.50 ** -0.49 H12 12.29 -0.15 -7.49 -0.55 H24 6.06 4.88 -1.98 -2.43 H36 5.82 7.16 -2.77 -5.19 H48 8.64 4.64 -8.55 -1.36 Statistical Significance of Gamma H1 1.1 2.3 1.3 4.4 H2 0.1 2.2 -0.9 4.0 H6 -11.2 -7.8 -44.8 -23.6 H12 -19.6 -28.9 -79.2 -69.9 H24 -46.4 -26.7 -95.6 -96.5 ** H36 -28.8 -13.0 -56.6 -70.6 H48 -28.3 -17.8 -88.7 -90.7 ** Look-Back Period Holding period L24 L36 L48 Statistical Significance of Alpha H1 -0.15 0.00 -0.18 H2 -0.33 -0.01 -0.35 H6 -0.79 ** -0.07 -1.06 ** H12 -1.10 ** 0.06 -0.65 H24 -1.33 * 0.04 -0.82 H36 -0.90 * 0.91 * -0.55 H48 -0.48 -0.22 -0.54 Statistical Significance of Beta H1 1.03 0.94 5.13 * H2 2.47 1.61 7.19 * H6 1.67 1.62 9.68 H12 -0.70 -4.42 6.07 H24 -13.10 ** -14.13 ** 9.49 H36 -3.88 -8.88 ** 3.01 H48 -4.15 -9.05 4.81 Statistical Significance of Gamma H1 -6.8 -10.6 3.0 H2 -8.2 -14.2 10.5 H6 9.9 -0.8 53.0 H12 8.9 -11.2 60.8 ** H24 16.3 5.6 118.5 * H36 23.2 -22.1 54.6 * H48 7.3 4.7 73.7 * */** implies significance at 1 percent/5 percent level of significance. Table 9. Profitability of Time-Series Momentum Trading Strategy in the Developed Market Look-Back Period Holding period L1 L2 L6 L12 Statistical Significance of Alpha H1 0.03 0.06 0.04 0.22 ** H2 0.25 0.3 0.16 0.45 * H6 0.51 0.45 0.80 * 1.01 * H12 0.85 0.83 1.33 * 0.87 H24 0.59 -0.05 0.16 -0.23 H36 0.07 -0.63 -1.57 -0.61 H48 0.12 -0.53 -1.45 -1.20 Statistical Significance of Beta H1 -1.13 -1.55 -1.66 -4.74 H2 -3.07 -3.49 -4.01 -7.11 ** H6 -0.64 -4.93 -10.39 -15.40 ** H12 6.75 -8.21 -5.34 -3.99 H24 4.29 1.51 -14.61 -18.00 H36 -0.17 -1.59 -9.07 -27.22 H48 0.22 -4.82 -6.98 -19.35 Statistical Significance of Gamma H1 26.57 22.82 28.03 -2.70 H2 -4.06 -2.37 6.58 -23.92 H6 -17.70 -43.93 -63.41 -85.63 H12 -28.42 -122.32 -132.94 -111.22 H24 -59.58 -89.97 -170.21 -168.82 H36 -54.05 -5.81 -35.91 -83.52 H48 -51.43 -21.13 -58.76 -108.79 Look-Back Period Holding period L24 L36 L48 Statistical Significance of Alpha H1 -0.02 0.06 0.03 H2 -0.13 0.06 -0.13 H6 -0.46 -0.26 -0.67 H12 -1.02 -0.83 -1.11 ** H24 -2.41 * -1.94 * -3.10 * H36 -3.52 * -4.69 * -4.56 * H48 -5.76 * -7.60 * -4.94 * Statistical Significance of Beta H1 1.51 1.23 0.28 H2 3.55 2.28 3.26 H6 5.29 5.90 6.94 H12 14.33 13.89 12.26 H24 0.45 6.22 7.57 H36 -4.86 11.78 8.46 H48 5.24 -0.80 6.57 Statistical Significance of Gamma H1 -5.11 -28.24 -35.38 H2 -11.81 -40.93 -33.32 H6 -42.97 -81.42 -58.77 H12 -27.63 18.55 37.33 H24 -43.84 19.19 69.27 H36 40.92 121.93 102.03 H48 55.44 173.61 * 115.98 */**implies significance at 1 percent/5 percent level of significance.

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Comment: | Time-series momentum trading strategies in the global stock market. |
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Author: | Chakrabarti, Gagari |

Publication: | Business Economics |

Date: | Apr 1, 2015 |

Words: | 7724 |

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