Currency Momentum Strategies

Transcription

1 Currency Momentum Strategies Christophe El Harake Julien Faure Emmanuelle Oesterlé Adélaïde De Touchet Abstract The literature review in this paper will present evidence of previously published momentum articles. Over the last of few years, this field has grown enormously after Jegadeesh & Titman published their famous article Return to Buying Winners and Selling Loser: Implication for stock market efficiency. In this article, the authors state that a simple trading strategy based on buying stocks that have performed relatively well in the past and selling stocks that have performed relatively bad in the past realize positive returns over medium-term horizon. Although, early research was mostly conducted on US equity market there is now a vast amount of literature covering other asset classes such as bonds, commodities and currency in non-us markets. In this way, the aim of this paper is to provide the main evidence from some of previously published momentum articles. Our literature review will focus on data sample, the methodology, the ranking criteria and their main results. 1

2 SUMMARY 1 Academic Papers Jegadeesh and Titman (1993) Return to Buying Winners and Selling Loser: Implication for stock Market Efficiency Conrad and Kaul (1998) An anatomy of Trading Strategies Jegadeesh and Titman (2001) Profitability of Momentum Strategies: An Evaluation of Alternative Explanations John M. Griffin, Xiuqing Ji, and J. Spencer Martin (2003) Momentum Investing and Business Cycle Risk: Evidence from Pole to Pole Lukas Menkhoffa, Lucio Sarnob, Maik Schmelinga, (2012) Andreas Schrimpfe, Currency momentum strategies Pedro BARROSO, Pedro SANTA-CLARA, (2015) Momentum has its moments Klaus Grobys, Jesper Haga, (June 2016) Are momentum crashes pervasive regardless of strategy? Evidence from the foreign exchange market Klaus Grobys, Jari-Pekka Heinonen, and James Kolari, (July 2016) Is currency momentum driven by global economic risk? Data Data sample Return calculation Data processing Creating the portfolios Momentum Results Conclusion References

3 The literature review in this paper will present evidence of previously published momentum articles. Over the last of few years, this field has grown enormously after Jegadeesh & Titman published their famous article Return to Buying Winners and Selling Loser: Implication for stock market efficiency. In this article, the authors state that a simple trading strategy based on buying stocks that have performed relatively well in the past and selling stocks that have performed relatively bad in the past realize positive returns over medium-term horizon. Although, early research was mostly conducted on US equity market there is now a vast amount of literature covering other asset classes such as bonds, commodities and currency in non-us markets. In this way, the aim of this paper is to provide the main evidence from some of previously published momentum articles. Our literature review will focus on data sample, the methodology, the ranking criteria and their main results. 1 Academic Papers In this part of the paper, we have summarized some of previously published momentum articles in order to bring to light the main finding within the field. 1.1 Jegadeesh and Titman (1993) Return to Buying Winners and Selling Loser: Implication for stock Market Efficiency trading strategies that select stocks based on their past returns will exist. To test the momentum effect, they constructed J-month/K-month strategies where stocks are selected based upon their return over the past 3, 6, 9, 12 months (J = 3,6,9,12) and the holding period is also 3, 6, 9 or 12 months long (K=3,6,8,12). In total they test 16 strategies. As the single most descriptive figure, the article focused largely on the zero cost portfolios. Their zero cost portfolios are representing the difference in performance between the winners (highest past returns) and losers (lowest past returns) deciles. For their data, all 16 analyzed zero cost strategies yielded positive returns. Their 6 month look-back / 6 month investment portfolio generating annualized returns of 12,01% per annum, and their most successful zero cost strategy has a formation period of 12 months and a holding period of 3 months. The (12,3) strategy yielded a monthly zero cost return of 1,31% or 16,9% annually. One may note that these portfolios would theoretically require no capital to implement and has no market exposure. So, the results are very impressive. Document 1: The most successful zero sssssssssssssssscost strategy One of groundbreaking works in this area was undertaken Jegadeesh and Titman from the Anderson Graduate School of Management at UCLA, and published in the Journal of Finance in March Their paper investigate stock market efficiency. Their study, which include daily returns of NYSE and AMEX stocks from 1965 to 1989, states that if prices either overreact or underreact to information consistently then profitable 3

4 Whilst the returns over the 3 to 12 month investment horizon were universally positive, with positive average returns for the zero cost portfolio in all but the first month in year 1, average return in year 2 are negative in every month. This suggest that the momentum strategy has not enabled the selection of stocks generating higher long term returns, but instead the momentum over this 3 to 12 month time horizon appears to be a temporary effect. 1.2 Conrad and Kaul (1998) An anatomy of Trading Strategies In 1998, Conrad and Kaul use a single unifying frameword in order to analyze the sources of profits to a wide spectrum of return-based trading strategies implemented. The authors investigated a 63 years long data sample, which including all available securities on NYSE and AMEX form 1926 to To do so, they examine the causes of momentum profits by decomposing them according to the model of Lo and Mckinlay (1990). Their methodology differs from Jegadeesh and Titman (1993). Indeed, they show that actual trading strategies implemented based on past performance are completely unpredictable and follow random walk. They suggest that higher returns of winners in the holding period represent their unconditional expected rates of return, and thus predict that the returns of the momentum portfolio will be positive on average in any post-ranking period. Their decomposition of trading profits is based on the assumption of mean stationary of the returns of individual securities during the period in with the strategies are implemented. They find that the momentum effect is due to the crosssectional dispersion variation in mean returns. They argue that as long as there is dispersion in mean return there will be a momentum profit. It is arguable that the momentum effect can co-exist with the hypothesis of random walk, which the supporters of time-series predictability would reject. In addition, their zero cost portfolios consist of a long position in the stocks that performed above the mean and a short position in the stocks that performed below the mean. To do the analyze, they examine eight different strategies with equal formation and holding periods ranging between 1 week and 36 months. From the 36 strategies implemented there is an equally amount of positive and negative average returns. 21 of them are statistically significant profitable. They show that the momentum strategies are statistically significant profitable from 3 to 12 months, which corresponds well to the results of Jegadeesh and Titman (1993). The best performing strategy is 9x9 in the period with a monthly average return of 0.71 percent followed by 12x12 and 6x6 with monthly average return of 0.7 and 0,36 percent respectively. 1.3 Jegadeesh and Titman (2001) Profitability of Momentum Strategies: An Evaluation of Alternative Explanations The second article of Jegadeesh and Titman reexamine the momentum profits that were documented in their 1993 article. The study sample is different from their previous work. In fact, it includes all NASDAQ stocks to firms listed on the NYSE and AMEX and sample period is from In addition, they also exclude low priced stocks and stocks with low market capitalization. However, the methodology they follow is identical to Jegadeesh & Titman (1993). From they explain that past winners outperform past losers by approximately 1.39 percent per month, which is close to the corresponding returns in the original Jegadeesh & Titman (1993). The results are statistically significant at the 1 percent level. Interestingly, these results suggest that both winners and losers contribute about equally to momentum profits. 4

5 Indeed, the authors show that the winners (P1 portfolio) outperform the equalweighted index by 0.56 percent per month, whereas the loser (P10 portfolio) underperforms the index by 0.67 percent per month. In this paper, the authors document that the momentum profits in the eight years subsequent to the Jegadeesh & Titman (1993) sample period are remarkably identical to the profits found in the earlier time period. This evidence provides some assurance that the moment profit are not entirely due to data snooping biases. 1.4 John M. Griffin, Xiuqing Ji, and J. Spencer Martin (2003) Momentum Investing and Business Cycle Risk: Evidence from Pole to Pole In this article, the authors examine whether macroeconomics risk can explain momentum profits internationally. In the same time, they address in part whether momentum returns are consistent with risk based explanation or behavior explanation. The study data consist of U.S. monthly stock return data include common share of all NYSE and AMEX from 1926 to Thus, in addition to U.S. stocks, they include data from 39 non-u.s. countries that have a minimum of 50 stocks available on DataStream International. The authors allocate the past 20% best performing stock into the winner portfolio and the bottom 20% into the loser portfolio because some countries simply do not have enough stocks. Hence, the stocks within each portfolio are equally weighted. To avoid microstructure, they report one set of result where the investment is executed immediately after the end of the ranking period and a second set of results where they skip one month between the ranking period and the holding period. First of all, the authors present the results for momentum portfolio formed with a 1- month gap between the portfolio ranking and holding period. They find that the average monthly momentum profit from a winner minus loser strategy is 1.63, 0.78, 0.32 and 0.77 in Africa, America (excluding the United States), Asia, and Europe, respectively. The profits are highly significant in all regions except for Asia. We can notice that forming the portoflios immediately after the ranking period makes the momentum profit smaller. In this case, the average monthly return is 0.7% in Europe, 0.31% in the United States, 0.5% for America (excluding the United States), 1.42% percent for Africa, and 0.13% for Asia. Still, these measurements are statistically significant in all regions except Asia. In sum, momentum profit are generally quite economically important and statistically significant around the world. Now, the authors investigate whether momentum returns are correlated across countries. To do so, they state if profits arise due to systematic risk and markets are integrated, then one ought to expect high correlations among returns to momentum strategies in various countries. They also find low intraregional and interregional correlation between momentum returns and argue that momentum profits are probably not driven by a global risk factor. To find out whether momentum strategy is robust both during good and bad economic states they look at performance growth and decline in GDP growth and aggregate stock market. They examine momentum profit in the 22 markets for which the OECD provides GDP data. Whenever available, they use seasonally adjusted real GDP. From there, they present that momentum profits are 1.18%, 0.11% and 0.28% in the America (excluding U.S.), Asia and Europe in periods of negative GDP growth and 0.61%, 0.14%, and 0,76% in periods of positif GDP growth. They states that regional momentum profits are not statistically significant in the periods of negative GDP growth, but this not 5

6 surprising given that GDP growth is positive over most available sample periods. The authors conclude that momentum strategies are robust both during good economic states and bad economics states and therefore momentum strategies are not related to risk arising from macroeconomics states. 1.5 Lukas Menkhoffa, Lucio Sarnob, Maik Schmelinga, (2012) Andreas Schrimpfe, Currency momentum strategies The authors try to explain the origin of momentum returns, since the literature until December 2012 had not settled on a commonly accepted explanation for momentum returns. The study is based on the study of the foreign exchange markets. This paper studies the economic anatomy of momentum profits in FX markets. To do so, the authors started by creating portfolios with high past excess returns, on which investors have a long position, and portfolios with low past excess returns, on which investors have a short position. The data they use are from January 1976 to January 2010, and the study is based on 48 currencies. At the end of each month, they formed six portfolios based on lagged returns over the previous 1,3,6,9,12 months and these portfolios are held for 1,3,6,9,12 months. The first portfolio is the one with the lowest returns, and the sixth is the one with the highest returns. They work with the pure spot rate changes, because they want to see if currency momentum occurs in spot rates, or if it is mostly driven by interest rate differentials (forward discount). Momentum strategies have excess returns of 6-10% for holding periods of one month. When the holding period increases, then the profits of the strategy are decreasing. Moreover, the profitability of currency momentum strategies occurs in spot rate changes, so currency momentum strategies are not only driven by interest rate differential. Their sharp ratio for the 1month-1month strategy is 0.95, which is very high. Also, the number of currencies in the portfolio can determine the profitability of the strategy: increasing the size of the tradable currency universe reduces the gains. Excess returns in momentum strategies and carry trades are not correlated in foreign exchange markets. At the end of their research, they find that currency momentum strategies lead to important excess returns (up to 10% per annum). They also conclude that the returns provided by currency momentum strategies are not related with the carry trade returns. Another contribution of this paper is the fact that momentum returns are sensitive to transaction costs. The authors show that momentum strategies lead to portfolios composed of currencies with high transaction costs. Indeed, they explain that turnover can be extremely high, especially with a one-month formation and holding period. Also, the winner and the loser currencies have higher transactions costs. As a result, trading in the winner and loser currencies is more costly. They notice that the effects of transactions costs on the average spot rate changes of portfolios are relatively less affected. However, it can only partially explain momentum returns, and transaction costs are going to decrease more and more. Also, the profitability of currency momentum strategies varies a lot over time (which reduces arbitrage opportunities), and momentum returns are related to currency characteristics. Indeed, the higher is the volatility, the more profitable is the currency, and if the risk rating in the country is high, then the positive excess returns are more important. Momentum effects are strong and momentum strategies allow high excess returns and sharp ratios, even more in FX markets than in stock markets. 6

7 1.6 Pedro BARROSO, Pedro SANTA- CLARA, (2015) Momentum has its moments The authors focus here on momentum s specific risk. The sharp ratio of the momentum strategy exceeds the sharp ratio of the market itself, as well as the size and value factors. However, a huge crash risk exists when investors use momentum strategies. The authors develop a method to manage the risk of momentum strategy in order to avoid the worse crashes and improve the sharp ratio when there is no crash. The authors estimate the risk of momentum by using the realized variance of daily returns. Thanks to that measure, they find that risk is highly predictable. They explain that managing the risk can lead to better economic results. In their results, they find that for a risk-managed momentum, compared to unmanaged momentum, the sharp ratio improves from 0.52 to 0.97, the excess kurtosis from to 2.68, and the left skew improves from to In their empirical results, they show that if momentum strategies provide large gains, there are a very high excess kurtosis and an important left skew. They take the examples of the crashed in 1932 and 2009 and wonder if investors could have predicted these crashes in order to manage the risk. The results of this research can help investors using momentum strategies to manage risk without forward-looking bias. Also, some investors think that momentum is dead, according to its bad results over the last ten years. However, the authors don t agree with this point of view, but only think the risk was high over those years. According to them, the risk of momentum is highly predictable and by managing the risks, investors can eliminate the exposure to crashes (it lowers the excess kurtosis and reduces the left skew) and increase the sharp ratio of their strategy. 1.7 Klaus Grobys, Jesper Haga, (June 2016) Are momentum crashes pervasive regardless of strategy? Evidence from the foreign exchange market The authors want to explore momentum crashes across strategies, by focusing on the currency market. They aim to analyze the optionality-effect across different momentum strategies in the foreign exchange market. They base their analysis on the research of Daniel and Moskowitz, published in 2013, and use a sample period from 1978 to They compare three types of momentum strategies: 12, 6, 1 month(s) formation 1 month holding period. Concerning the onemonth formation one-month holding period strategy, it is the strategy with the highest mean return, which is not the case on the equity market (this study focus on the FX market). They find that momentum strategies, either based on the cumulative return from 12 months prior to the formation date to one month prior to the formation date (12,1 strategy), or those based on the cumulative return from 6 months prior to the formation date to one month prior to the formation date (6,1 strategy), exhibit significant option-like behavior. However, it is not true for the one-month formation one-month holding strategy, which is not correlated with the dollar factor, and doesn t have any option-like behavior. 1.8 Klaus Grobys, Jari-Pekka Heinonen, and James Kolari, (July 2016) Is currency momentum driven by global economic risk? The aim of the article is to analyze the potential relation between currency return dispersion (RD), which measures the global economic risk, and currency momentum. The authors want to investigate the role of cross-sectional return dispersion in foreign exchange market and currency momentum profits. Their study is based on the fact that a 7

8 common macro risk factor exists in equity and currency markets. They link equity and currency markets in their theoretical model. They use 39 foreign exchange rates and form currency portfolios in order to compute RD across currencies. They fix RD up into high and low dispersion regimes (state of economic stress and state of economic ease). They do the assumptions that momentum payoffs are larger in states of high global economic stress. They use a momentum strategy based on a 1-month formation and 1-month holding period. Their first portfolio is composed of the lowest returns in the previous month before portfolio formation, whereas the sixth portfolio is composed of the highest returns. They are long on portfolio six and short on portfolio one. Their empirical results show an obvious link between return dispersion and momentum payoffs. Indeed, when there are tensions in global economy and when the global risk is high, currency momentum payoffs are more important than usual. In the results they present, the authors find that the spreads of the zero-cost currencies momentum strategy are significantly higher in high compared to low currency RD states. Indeed, the spread is statistically equal to zero in a regime with low RD. Thanks to robust checks, they prove their results are valid. They finally conclude that global economic risk measured by RD helps to explain currency momentum profits, since the relation between momentum payoffs and global economic risk is linearly increasing in risk. 2 Data In this second part of our report, we will first present the data sample that we used for our empirical analysis. Then, we will describe the methodology of our work in Excel and VBA in order to offer the reader a better idea of our extensive data processing work. 2.1 Data sample The data for spot exchange rates and 1- month forward exchange rates cover the sample period from January 1985 to March 2015, and are obtained via DataStream. Our total sample consists of the following 25 countries: Australia, Brazil, Bulgaria, Canada, Chile, Croatia, Czech Republic, Euro area, Hungary, India, Indonesia, Israel, Japan, Mexico, New Zealand, Norway, Philippines, Poland, Russia, Singapore, South America, Sweden, Swiss, Thailand and United Kingdom. 2.2 Return calculation There are two ways to compute the return of the currencies in our data: discrete or continuously compounded returns. Form a mathematical point of view, we decided to use continuously compounding returns as this offer some benefits. According to Campbell et al. (1997), it is common to use continuously compounded returns when studying the behavior of stock return. The natural logarithmic return for a singleperiod for a given stock I in time t is denoted R i,t and is defined as: R i,t = ln ( P i,t P i,t!! ) In our data single period returns represent the monthly returns. So, we should compute the compounded return, denoted CR i,t, is defined as : 8

9 CR i,t = R i,t The stocks are then ranked based on their compounded return CR i,t. The return of the portfolio consisting of equally weighted stocks T is then calculated: CR P,t = 1 T T t!! CR i,t Now the return of the momentum strategy denoted as MR is calculated by taking the return of the winner portfolio minus the return of the loser portfolio: CR MR,t = CR winner,t CR loser,t 2.4 Creating the portfolios Using a 1x1 strategy (i.e. one month formation period and one month holding period) as an example we will explain step by step our data processing work. 1. Step one: we sum up the return for each month of our sample. First, we converted each currency with respect to the dollar, by dividing the exchange rate with respect to the dollar, by the exchange rate of the dollar with respect to the British pound. Then, we created a VBA program to compute the log return: The monthly average return of the momentum strategy is calculated by taking the average of all the momentum portfolio formed throughout the sample period from 1985 to 2015 and divide it by the T. The monthly average return is: MR = 1 T 2.3 Data processing T t!! CR M,t To process the data, we use Microsoft Excel and Visual Basic programming. The data sample is quite comprehensive and it took some time to find an efficient way to do the calculations. Excel macros and some functions on excel eased the process of creating the portfolios. We are going to give a short description with illustrations of our method. This can be useful for recreation or future studies within empirical finance. Then, we created another VBA program in order to compute the return for each month: 9

10 2. Step two: we ranked all the currencies according to their returns by using the conditional formatting function in excel - that is from the highest return to the lowest return. The rank of the currencies for each period is based on the sum returns we found for the previous month (one-month formation period). It is important to notice that the lowest sum returns are the currencies we want to buy, whereas the highest sum returns are the currencies we want to sell. As a consequence, the portfolio with the highest returns is composed of the currencies we want to sell. In order to rank our currencies, we used SI and ESTNA formulas. For reasons of clarity and consistency, we decide to take nine currencies as follow: Document 2: Holding Period Document 3: Ranking 3. Step three: We affected the currencies with the highest sum returns, ranked from 1 to 5, to the first portfolio. Concerning the second portfolio, we did one more step, since we did not have the same number of currencies according to the period we were considering. Hence, we decided to look at the number of currencies ranked in our second tables by using the max function (document 3). P2 represents the five currencies we want to buy, those with the lowest sum returns. 4. Step four: We computed the total return of our portfolio by doing the sum of the returns listed. In the same time, we calculated the average by dividing the sum by 5, since we have 5 currencies in our portfolios. We also computed the cumulative returns, which will allow us to plot the graph. 5. Step five: Then, we computed the total return of the momentum strategy by computing the return of the currencies we sell (portfolio 1) minus the return of the currencies we buy (portfolio 2). The currencies we sell are those with 10

11 the highest return, meaning it represents the currencies which depreciate the most wrt the USD, so we want to sell them. The currencies we buy are those with the lowest returns: we want to buy them. By doing so, we have computed the returns of the losers (portfolio 1), minus the returns of the winners (portfolio 2). In the articles we read, the authors computed the winners minus the losers by multiplying the returns they found by -1 (since a high return means the money depreciates), which is similar to what we have done and gives the same total return. Document 4: P1 minus P2 6. Step six: we annualized the monthly return by summing the return of each month. We used a if formula, as follow: $ This formula allows to compute the annualized return only if we are in January. We then computed the average annualized monthly return by dividing the result by Step seven: We plotted the graph of the cumulative return of P1, P2 and the total cumulative return. We decided to start our period in 1995 when the 25 currencies are available, so it s more accurate. To do that, we calculated the cumulative returns from 1995, pretending there were starting at 0 in In order to plot the cumulative returns of our second portfolio, we multiplied the returns we had by -1, since our strategy consists in doing P1 P2. We then found our cumulative return. In order to calculate the total average return, we divided our total return of the strategy by 5. We also computed the cumulative average returns. We also plotted a graph with the non-cumulative total returns, in order to see when there were sharp increases or decreases. 11

12 8. Step eight: We used the excel formulas to compute the kurtosis, skewness and standard deviation. We used our average annualized returns from 1995 to have all our currencies available. We also computed the sharp ratio. To do so, we used the risk-free rate of the United States over our period. It corresponds to the short-term rate of Treasury-bills. We found that rate on the OCDE website. The formula we used is the following 1 : 3 Momentum Results We chose to interpret our strategy over 20 years, from 1995, when we have all our currencies available. We find an average annual return of 8.5%, which means our strategy is profitable. Most of the previous literature on momentum strategy found a return around 10%, so the one we found seems credible. The Sharpe ratio we found is equal to It means the return is low compared to the risk taken. Since we found a high return, it means the risk taken might be high. Indeed, as we read it in the literature, when there is a crash, a momentum strategy can be very risky and investors can lose a lot of money, even if in a 1 month-formation 1 monthholding period strategy, the risk is reduced. The kurtosis is equal to It is greater than 0, which corresponds to a leptokurtic distribution. Therefore, a lot of the returns are close to the average return, and a few of them are on the extreme values. We found a positive skewness, equal to This means the distribution is asymmetric: most of the returns are around the median, and only a few are on extremely positive values. The standard deviation is It seems very high compared to the average return of It means the risk of our strategy is very high. This is consistent with the Sharpe ratio we found

13 4 Conclusion To conclude, while the anticipations based on what is observed the previous month (formation period) are globally correct, the momentum strategy is very profitable. During the end of the 1990s, the returns are particularly high (we can especially observe a sharp increase in 1997) and then increase slower until However, it is a risky strategy. Indeed, as soon as a crash appears in the economy, as it was the case in 1932 or 2008, as Pedro Barroso and Pedro Santa-Clara explained it in their article Momentum has its moments (2015), the momentum strategy becomes very risky, and investors can lose huge amounts of money. However, we observe that in 2008, the cumulated returns of our strategy are still increasing. During the crash, the momentum was very profitable, but the returns started to decline right after, during the period of recession. It is probably due to the repercussion of the crisis on the foreign exchange market. The agents were less able to make good anticipations of what was going to happen, since the market was destabilized and changing from one period to another. However, it is not the sharp decrease we could have imagined. This can be explained by the fact that we are here in a 1 month-formation 1 month-period strategy, so investors can react faster than if they were holding the currencies during a larger period. Also, in the article cited above, the authors explain that it is possible to manage the risk and to eliminate the exposure to crashes. Also, since we are in a one-month formation one-month holding period strategy, it is possible to explain these high returns by the presence of non-negligible transaction costs, as Lukas Menkhoffa, Lucio Sarno, Maik Schmelinga, Andreas Schrimpfe explained it in their article Currency momentum strategies (2012), that we developed in our literature review. 13

14 Document 5: Graphical overview of Momentum Results 14

15 References Narishman Jegadeesh, Sheridan Titman, 1995, Returns to Buying Winners and Selling Losers: Implication for Stock Market Efficiency, The Journal of Finance, Volume 48, Issue 1 (Mar., 1993), Jennifer Conrad, Gautam Kaul, 1998, An Anatomy of Trading Strategies, Review of Financial Studies, vol. 11, issue 3, Narasimhan Jegadeesh, Sheridan Titman, 2001, Profitability of Momentum Strategies: An Evaluation Of Alternative Explanations, Journal of Finance, vol. 56, No. 2, John M. Griffin, Xiuqing Ji, J. Spencer Martin, dec., 2003, Momentum Investing and Business Cycle Risk: Evidence from Pole to Pole, Journal of Finance, vol. 58, Lukas Menkhoff, Lucio Sarno, Maik Schmeling, Andreas Schrimpf, dec., 2012, Currency Momentum Strategies, Journal of Financial Economics, vol. 106, Issue 3, Pedro Barroso, Pedro Santa-Clara, 2015, Momentum Has Its Moments, Journal of Financial Economics, vol. 116, Issue 1, Klaus Grobys, Jesper Haga, June 30, 2016, Are Momentum Crashes Pervasive Regardless of Strategy? Evidence from the foreing Exchange Market Klaus Grobys, Jari-Pekka Heinonen, James W. Kolari, Is Currency Momentum Driven by Global Economic Risk?, July 14, 2016 Chopra, Navin, Josef Lakonishok, and Jay R.Ritter, 1992, Measuring abnormal performance: Do stocks overreact?, Journal of Financial Economics 31, Fama, Eugene F., and Kenneth R. French, 1992, The cross-section of expected stock returns, Journal of Finance 47, Fama, Eugene F., and James Macbeth, 1973, Risk, return and equilibrium: Empirical test, Journal of Finance 81,