Master Thesis MSc Finance
International Momentum Strategies and the Currency Effect
by Andreas Iten
JEL classification:F3, G10, G11, G14, G15,
Keywords: International Momentum, Common Currency, Currency Effect, Author: Andreas Iten
Mail: andreas.iten1@gmail.com Phone: +31621880956
Student number: S2258994
Place and date: Groningen, 10. January, 2014 Supervisor: Dr. J.O. Mierau
2nd supervisor:
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Table of Contents
Abstract ... 3
1. Introduction ... 3
2. Literature Review ... 6
3. Data and Methodology ... 10
3.1 Data ... 10
3.2 Methodology ... 12
3.2.1 Creating Momentum Portfolios ... 12
3.2.2 Assessing the Currency Effect ... 13
4 Empirical Results ... 15
4.1 Summary Statistics ... 15
4.2 Results for the 4 week Holding Period ... 15
4.3 Robustness Testing ... 18
5 Conclusions ... 20
5.1 Limitations and Propositions for Further Research ... 21
5.2 Acknowledgements ... 22
6 References ... 23
7 Appendix ... 25
International Momentum Strategies and the Currency Effect
ANDREAS ITEN
Abstract
In this paper I investigate the currency effect in the context of international momentum research by examining whether the outcomes of international momentum strategies depend on the choice of using common currency rather than local currency denominated data. To this end, four different variations of the momentum strategy used by Chan, Hameed and Tong (1999) are derived and applied on an international investment universe of 23 stock indices for the time period of 1980 to 1995. The strategies fully or interchangeably use either US Dollar or local currency data for both the construction of the portfolios as well as for the measurement of the returns subsequently earned on these portfolios.
Returns in the common currency sample are apparently driven not only by the asset component but also by a currency component. My results indicate that this additional return component leads to significant differences in outcomes. I thus conclude that it is more accurate to use local currency data rather than common currency data in the context of international momentum research. When investigating international momentum, return continuation in the respective assets should be the sole interest and not developments in the involved currency exchange rates. I further observe that both the portfolio compositions as well as the measured returns are subject to the spurious effect induced by the currency component.
1. Introduction
Over the past thirty years the field of stock market anomalies has attracted vast attention among researchers and practitioners alike. Momentum and reversal effects have become some of the most thoroughly investigated phenomena of modern Finance. Behaviourists extrapolated from the field of psychology the observation that people tend to overreact to new information and suggested that stock markets exhibit similar patterns. They advocate that stock prices tend to overreact to news, which initially leads to an over-proportional reaction that later reverses itself. Based on this notion momentum and contrarian investment strategies were devised, which seek to exploit these effects.
Momentum focuses on profiting from short-term to medium-term return continuation effects, whereas contrarian strategies seek to capture long-term reversal effects. Having examined these strategies, De Bondt and Thaler (1985) find that stocks, which performed poorly over a 3-5 year period subsequently reversed their performance, leading them to outperform in the following 3-5 year period. Similarly, Jegadeesh and Titman (1993) find momentum effects in the stock market of the United States, observing that the “winner” and “loser” stocks of a given 3 to 12 month period exhibit a return-
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continuation effect which leads them continue their out- or respectively underperformance during the subsequent 3 to 12-month period.
One reason for the fascination of academia with these momentum and reversal effects may stem from the fact that their mere existence violates the assumption of efficient markets, which is a cornerstone notion of modern Finance theory. The theory of efficient markets by Fama (1965) proposes financial markets to be informationally efficient. If however markets were efficient, it would not be possible for investors who consider all past and presently available information to systematically earn abnormal returns without acquiring greater risk as well. The continuing profitability of momentum and contrarian investment strategies directly contradicts even the weak form of market efficiency, which is based on the idea that stock prices already incorporate all past information and thus no excess returns are to be earned purely from analysing past stock prices.
Research into the momentum effect progressed and demonstrated that the initial findings were not merely a result of data snooping as was suggested by critics. Momentum was found in US stock market data samples covering virtually all available time periods. Looking for further evidence, researchers found that the momentum effect is not restricted to the US stock market, but that it occurs internationally. In the quest for international momentum Rouwenhorst (1998) applied the momentum strategy deviced by Jegadeesh and Titman (1993) to individual stocks from twelve European markets.
He finds price momentum in all tested European markets and in a follow up study, Rouwenhorst, (1999), also in emerging markets. A plethora of further research exhibits the momentum anomaly to exist across developed and emerging markets alike, with the notable exception of Japan. Chan, Hameed and Tong, (1999) added to the literature by examining the profitability of international momentum strategies implemented not on individual stocks, as was practice before, but on stock market indices. Also for this asset class, they find statistically significant evidence for international momentum profits.
While investigating the momentum effect in international stock markets, all of the above mentioned studies use stock market data in a common currency e.g. US Dollars as in Chan, Hameed and Tong (1999), Fama and French (2011), or Deutsche Mark in Rouwenhorst (1998). Many authors motivate the use of data that had been converted from local currencies into a common currency with the practical implications their findings have when a specific “investor’s perspective” is adopted. Others refer to earlier research that had been done using common currencies. Doing so, the existing literature on international momentum disregards that there are two effects at play when international momentum strategies are researched using data in a common currency. On the one hand, this is the momentum effect itself and on the other, the currency effect.
Returns obtained from stock market prices in local currencies are driven by the change in the price of an asset over the considered time period, as given by the forces of supply and demand in a national stock market. Contrarily, returns in a common currency are not only driven by the change in price of an asset but also by changes in the corresponding currency exchange rate.
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A simple example displays the potential impact the currency effect may have with regards to international momentum research. Consider an investor who buys one share at the NYSE Euronext Amsterdam for 100 Euros and sells it again for 100 Euros one month later. Disregarding transaction costs, his trade results in a return of 0%. Let us now assume that over the considered month, the Euro/US Dollars exchange rate appreciates from 1.20 US Dollars to 1.25 US Dollars. Adopting a US investors perspective, the exact same trade now results in a different outcome. The US Investor buys the share for 120 US Dollars and sells it for 125 US Dollars on month later, yielding him a profit of 4,17%. Adopting the perspective of a US investor, the trade yields a very attractive return which might induces him to set up a position in the stock in order to profit from the potential momentum effect, whereas the local currency outcome does not deliver any indication to do so at all.
It thus might be possible that momentum studies which adopt the perspective of a US investor attribute international returns to return continuation in particular national stock markets, whereas in truth the returns actually stem from developments in the corresponding currency exchange rates. Focusing on the currency issue in the context of a related topic, Mink (2012) aptly states, “whether or not contagion occurred is not a matter of perspective.” The same holds for the occurrence of international stock market momentum.
Research Question
These above observations raise the question how to measure international stock market momentum accurately. Does it matter empirically whether local or common currency data is used? Does the currency effect have a significant impact on momentum returns? Here, I find the momentum literature to be incomplete.
The present paper contributes to the momentum literature by analysing the impact of the currency effect in the context of international momentum research. In order to do so, I implement the momentum strategy used by Chan, Hameed and Tong (1999) in four different versions on a dataset in US Dollars as well as in local currencies, consisting of 23 national stock indices over the period of 1980 to 1990. I show that the choice of using either a local currency or a common currency dataset matters. The results show that the currency component, which partly drives common currency returns, leads to significantly different outcomes. The findings furthermore highlight that this spurious effect impacts not only the measurement of returns but also the composition process of the momentum portfolios. Based on the notion that international momentum research should solely measure actual return continuation in the considered stock markets, these observations lead to the conclusion that it is more accurate to use local currency data rather than US Dollar data for the analysis.
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My findings are relevant for the discussion on international momentum, since conclusions regarding the magnitude, significance and even presence of momentum in specific countries drawn in earlier studies, which worked with common currency data, might be incorrect.
Some of the earlier found international momentum returns may in fact be due to currency exchange- rate developments. On the other hand some actually occurring momentum profits might have been omitted due to currency effects.
The results furthermore, convey potential practical implications regarding style based global asset allocation decisions. My findings suggest that the analysis for asset allocation to specific national markets based on the momentum style factor should always be conducted with data in local currencies.
The spurious effect of common currency returns can significantly influence the process of capturing momentum.
The remainder of this paper is structured as follows. Section two provides an overview of the existing literature relevant to this paper. Section three describes the data and methodology used in the research process. The fourth section describes and critically evaluates the empirical results. The final section holds conclusions and discusses limitations and further research propositions.
2. Literature Review
The following section provides an overview of the relevant literature for this paper. The first subsection provides a short review of the efficient markets theory. The following subsection concerning momentum refers to price momentum in stock markets or stock market indices only and focuses on three studies and their follow-up papers. These selected studies are either central to the momentum literature in general or specifically focus on international momentum strategies. The review explicitly focuses on the used strategies and actually found momentum returns rather than the research into the origins or causes of the momentum phenomenon. For a more comprehensive overview of the existing vast momentum literature, including more recent findings, I refer the interested reader to the paper “Momentum” by Jegadeesh and Titman (2011). A further subsection of this literature review presents works related to the currency effect.
Efficient Markets
The efficient market hypothesis by Eugene Fama (1965, 1970) is a key element of finance theory. In its core principles the theory proposes financial markets to be informationally efficient. The theory suggests that, given the consideration of all information available at the time of the investment decision, it is not possible to consistently earn returns in excess of the market average, without acquiring greater risk. In an efficient market, systematic abnormal returns do not occur, since utility
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maximizing market participants with rational expectations immediately arbitrage away any arising profit opportunities from incorrectly priced assets.
Strong-form efficiency, assumes that asset prices incorporate all past, current, new and inside information instantaneously. Less rigorously, prices in semi strong efficient markets are assumed to reflect all past and new information at all times. Whereas strong and semi-strong form market efficiency has regularly been challenged by evidence from empirical research as well as by behavioral arguments, it is the assumption of weak-form market efficiency that proves resilient. The assumption that stock prices incorporate all past information and thus no excess returns can be earned purely from analyzing past stock prices, is however persistently violated by the occurrence of momentum and reversal effects.
Momentum
Jegadeesh and Titman (1993) show that trading strategies, which buy the best performing and sell the worst performing stocks of a past period earn significant abnormal returns. In a setup that has since become one of the standard methodologies in momentum research, they form portfolios of winner and loser stocks measured over periods of three to twelve months. In their method, returns of individual stocks are being evaluated on their performance over a period of j months and subsequently ranked in ascending order. They arranged stocks form equally weighted decile portfolios where the highest and lowest return deciles become winner and loser portfolios. The portfolios are then held for a subsequent period of K months. Jegadeesh and Titman apply this strategy on a dataset of US stcoks over the 1965 to 1989 period. They show that these strategies yield significant positive returns, even more so when short-term reversals are accounted for by a one week lagging period between formation period j and holding period k. The most successful strategy they find is the one using a 12 month formation period and a 3 month holding period. The strategy yields a return of 1.48% per month. Their results deliver evidence that the described relative strength profits cannot be attributed to their systematic risk. The findings also exclude the possibility that the momentum profits are due to lead-lag effects that result from delayed stock price reactions to common market factors. However, their findings suggest that the found momentum may be due to delayed price reactions to company-specific news. The authors furthermore observe that the momentum returns to the zero cost winners and losers portfolios are positive for all but the first of the 12 months following the portfolio formation period. This positive performance however reverses in the second and third year after portfolio initiation.
A further observation of this study is that especially the stocks of the winner decile portfolios exhibit significantly higher returns than the stocks of the loser decile portfolios during the time of the quarterly earnings announcements. In line with the theory on the reversal effect, the results also show that returns in the 8 to 20 months after the portfolio formation are significantly higher for the stocks in the loser decile portfolios than for the stocks in the winner decile portfolios. The follow up study by
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Jegadeesh and Titman (2001) confirms their findings as their strategies remain profitable in the nineteen nineties.
In 2011, Jegadeesh and Titman (2011) conducted a further updated analysis on momentum for the 1990 to 2009 period. They document that the 6 month j, 6 month k strategy continues to yield significant positive returns in 16 out of 20 years with average annual profits of 13.5%, with a t-statistic of 2.9. However, in 2009 the momentum strategies incur an extraordinary large loss of -36.5%. The authors find that the stock market pattern preceding the loss is very similar to the year 1933 where momentum strategies also yielded a heavy loss causing the decade of the 1930’s to be the only decade of the twentieth century in which momentum strategies produced negative returns. One or more years of negative market performance as experienced after the stock market crash of 1929, as well as more recently in the years after the market crash of 2007, is followed by a sharp recovery in the subsequent period. Jegadeesh and Titman argue that in such circumstances low beta stocks emerge as winners stocks from a period of heavily declining markets, whereas high beta stocks will be seen as loser stocks due to their over proportionate down movement with the market. Basing the momentum portfolio weights according to these results will lead to heavy losses if in the succeeding period a steep market recovery follows. This has happened in 1933 as well as in 2009. Jegadeesh and Titman find that more than half of the losses of 2009 can be attributed to these beta values of the stocks in the respective loser decile momentum portfolios and winner decile momentum portfolios.
Rouwenhorst (1998) shows that the momentum anomaly exists also outside of the US stock markets.
The author implements the momentum strategy used by Jegadeesh and Titman (1993) on a dataset consisting of 2190 individual stocks from 12 European stock markets, for the 1980 to 1995 period.
Previous to the analysis all market data is converted to deutsche marks. Rouwenhorst finds that also internationally applied strategies that buy past winner stocks and sell past loser stocks earn significant positive returns. The results for the zero cost arbitrage portfolios are very similar to the findings of Jegadeesh and Titman (1993) with the most successful strategy being the 12 month formation period, 3 month holding period which delivers an average monthly return of 1.35%. All strategies yield an average monthly return of around 1% that is significant at a 5% level. The results imply that irrespective of the length of the formation period, longer holding periods lead to lower returns. The study further finds that momentum returns are independent of market size. Return continuation in all company specific size deciles and is thus not limited to small stocks, as was suggested by critics.
Furthermore the relative strength portfolios continuously contain stocks from all 12 countries that comprise the dataset, ruling out the possibility that the found momentum returns stem from a few selected countries. In a follow up study, Rouwenhorst (1999) implemented the same framework as in his previous study on a dataset of 2200 stocks from 31 emerging markets. Returns for this study are computed in US Dollars. The author documents evidence for the presence of the momentum anomaly in emerging markets.
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In their paper on the profitability of international momentum strategies, Chan, Hameed and Tong (1999) use a different strategy than the one used by Jegadeesh and Titman (1993) or Rouwenhorst (1998,1999). They form momentum portfolios based on the performance of an asset over a formation period of 1-26 weeks relative to the cross-sectional average return of all assets. The strategy buys thus past winners and sells past losers proportionally to their out- or underperformance. The authors implement this strategy on a data set consisting of 23 national stock market indices for the period of 1980 to 1995, thereby expanding the momentum literature by the inclusion of the asset class of stock market indices. For their analysis the authors use stock market price data converted into US Dollars.
The find significant momentum returns to their zero cost arbitrage strategies for all but the 12-week holding period. The strategies earn average weekly returns of 0.2615% and even 0.5018% for the 1- week and 2-week holding periods correspondingly. For the 4-week, 12-week and 26-week holding periods the returns respectively are 0.2708%, 0.0968% and 0.1545% where only the 12-week momentum returns is not significant at a 5% or 10% level. With a series of regressions, the study exhibits that the major source of momentum profits arises from price continuations in individual stocks. While momentum profits could be improved by including previous period currency exchange rate performance, the returns attributed to this source appear comparatively irrelevant to the past stock price component. The authors highlight the practical implications of their findings for global asset allocation decisions based on this style factor.
The Currency Effect
As there is no previous work regarding the impacts of the use of a common currency in the context of international momentum strategies, the following section refers to work that is examining or discussing the topic in related literature.
In a note on the accurate measurement of stock market contagion, Mink (2012) poses the question whether or not it empirically matters if contagion analyses are conducted with return data denominated in local currencies or with data that had been converted to a common currency. Mink argues that contagion either does or does not exist in a market and thus cannot occur when measured in one currency but not when measured in another. The author elaborates on the fact that returns computed from common currency data measure both changes in stock prices as well as changes in the respective currency exchange rate that is applicable to the conversion. He argues that only returns in local currency properly reflect the supply and demand conditions on a national stock market purely.
Using the expressions in Appendix 4, Mink illustrates the different components which drive the local currency and common currency returns. Mink moves on to demonstrate the potentially grave impact of the currency effect on the outcomes of internationally implemented contagion tests. By conducting the identical tests using once US Dollar data and once local currency data, he disproves the occurrence of stock market contagion during the 2008 financial crisis in nine out of ten cases. The seminal contagion
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test, conducted with data in US Dollars, finds stock market contagion in ten out of 28 national stock markets. The same test yields only one case of contamination when conducted with return data in local currencies.
In research on international financial topics, the use of converted currency data is rarely explicitly motivated. If any motivation for the use of common currencies is given at all, then the authors mainly stress two arguments. On the one hand there is the adoption of the perspective of a specific investor e.g. a US investor or a German investor. On the other lies the argument that most previous research had been done in a common currency.
In an early case where currency converted data is used, Grubel (1968) states to be adopting the perspective of a US investor in his analysis of the benefits of international diversification. Most of the following work on international diversification continued went on to use data converted to US Dollar, motivating this choice by the following the premises of earlier work e.g. Ley and Sarnat (1970). The paper on diversification by Longin and Solnik (1995) stands out as an exception. The authors claim to use local currency returns in order to analyse correlations across markets rather than across currencies, displaying awareness of the issue.
In the field of international momentum research, Chan, Hameed and Tong (1999) dissect the components of the momentum returns and exhibit awareness of the presence of a currency component in their US Dollar based data. However, they do not account for the influence of this currency component in their international momentum framework, but rather examine whether past currency developments predicted future momentum returns. Likewise, Rouwenhorst in his landmark paper on international momentum strategies does not mention nor account the currency effect that is present in the common currency returns used for his analysis.
The momentum cornerstone paper by Jegadeesh and Titman (1993) solely consider US stocks, thereby avoiding the currency question. The vast majority of subsequent studies, especially with focus on international applications of momentum strategies, base their research methodology on a common currency approach.
3. Data and Methodology 3.1 Data
Price data from 23 different equity indices was retrieved using Datastream. Focusing on a global investment universe, the sample contains nine countries from the Asia-Pacific region, eleven countries from Europe, two from North-America and one from Africa. These countries are Australia, Austria, Belgium, Canada, Denmark, France, Germany, Hong Kong, South Korea, Italy, Japan, the Netherlands, Norway, South Africa, Spain, Singapore, Switzerland, the United Kingdom, the United States, Thailand, Taiwan, Malaysia, and Indonesia. For a comprehensive list of the specific indices used, please refer to table 1. For each index I obtain market data denominated in each corresponding
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country’s local currency as well as in US Dollars. The sample period is identical to the one used in Chan Hameed and Tong (1999) and spans from 01/01/1980 until 30/06/1995 with exception of South Africa, Taiwan and Indonesia. Due to unavailability of earlier records, data for these countries starts at a later point in time.
Since many of the stock markets contained in the sample operate in different time zones, their daily returns represent realized returns over different periods. In order to account for this difference, returns are sampled in weekly intervals, which moderate the non-synchronous data bias. Additionally, weekly intervals for the formation period returns and holding period returns start at different days of the week.
For the determination of the formation period returns, weeks begin and end on Wednesdays, whereas for the holding period returns, weeks start and end on Thursdays. Applying different start and end days for formation and holding period weeks, assures that no price information from any country’s holding period is used in the portfolio formation process. The indices used in this paper differ from those used in Chan, Hameed and Tong (1999) in several cases due to the unavailability of the particular data.
Table 1: Overview of the Sample Countries, the specific Stock Market Indices and the respective Local Currencies as well as the Sample Periods
Country Index Name Currency Sample Period
Australia ASX ALL ORDINARIES INDEX Australian Dollar 01.01.80 30.06.95 Austria MSCI AUSTRIA INDEX Austrian Schilling 01.01.80 30.06.95
Belgium MSCI BELGIUM INDEX Belgium Franc 01.01.80 30.06.95
Canada S&P/TSX COMPOSITE INDEX Canadian Dollar 01.01.80 30.06.95 Denmark COPENHAGEN SE GENERAL INDEX Danish Kroner 01.01.80 30.06.95 France FRANCE-DS MARKET INDEX French Franc 01.01.80 30.06.95
Germany FAZ GENERAL INDEX Deutsche Mark 01.01.80 30.06.95
Hong Kong HANG SENG INDEX Hong Kong Dollar 01.01.80 30.06.95 Indonesia IDX COMPOSITE INDEX Indonesian Rupiah 01.01.83 30.06.95 Italy MILAN COMIT GLOBAL INDEX Italian Lire 01.01.80 30.06.95 Japan NIKKEI 225 STOCK AVERAGE INDEX Japanese Yen 01.01.80 30.06.95 Korea (South) KOREA SE COMPOSITE INDEX Korean Won 01.01.80 30.06.95 Malaysia FTSE BURSA MALAYSIA KLCI INDEX Malaysian Ringgit 01.01.80 30.06.95 Netherlands CBS ALL SHARE GENERAL INDEX Dutch Guilder 01.01.80 30.06.95
Norway OSLO SE INDEX Norwegian Kroner 01.01.80 30.06.95
Singapore SINGAPORE STRAITS T. INDEX Singapore Dollar 01.01.80 30.06.95 South Africa MSCI SOUTH AFRICA INDEX S. African Rand 01.01.93 30.06.95 Spain MADRID SE GENERAL INDEX Spanish Peseta 01.01.80 30.06.95 Switzerland CREDIT SUISSE GENERAL INDEX Swiss Franc 01.01.80 30.06.95 Tawian TAIWAN SE WEIGHED TAIEX INDEX Taiwan Dollar 01.01.85 30.06.95 Thailand BANGKOK S.E.T. INDEX Thailand Baht 01.01.80 30.06.95 United Kingdom FT 30 ORDINARY SHARE INDEX Sterling Pound 01.01.80 30.06.95 United States DOW JONES INDUSTRIALS INDEX U.S. Dollar 01.01.80 30.06.95
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In this paper I investigate whether the currency denomination of the data sample matters in the context of international momentum research. Examining a potentially present currency effect thus amounts to studying the differences in momentum returns that arise from the use of local or common currency data. To this end, I determine a methodology to create momentum portfolios and implement it using data in both local currencies and US Dollars. I then move on to analyze and compare the outcomes. A difference in resulting returns would indicate the presence of a currency effect.
3.2.1 Creating Momentum Portfolios
By replicating the momentum strategy used by Chan, Hameed and Tong (1999) on an investment universe consisting of 23 national stock market indices, I determine the performance of all stock market indices over a formation period of (j) weeks. At the end of the formation period a momentum portfolio is created based on the performance evaluation and subsequently held for a holding period of (k) weeks. The duration of the portfolio formation period (j) is always equal to that of the holding period (k). For example a portfolio whose weights are determined based on a 4-week formation period would subsequently be held for a holding period of 4 weeks.
The return to the momentum strategy 𝜋𝑡 for holding period (k) is given by expression (1). 𝑤𝑖𝑡 stands for the portfolio weight assigned to index i in period t, whereas 𝑅𝑖𝑡 stands for the return of the respective index i earned in period t. I calculate the return to the momentum strategy in period t, by multiplying the portfolio weight 𝑤𝑖𝑡 of each index with the return the index 𝑅𝑖𝑡 earns in period t.
(1)
𝜋𝑡(𝑘) = ∑ 𝑤𝑖𝑡(𝑘)𝑅𝑖𝑡(𝑘)
𝑁
𝑖=1
For the momentum portfolio held in period t, the weight 𝑤𝑖𝑡 assigned to each index is determined by the relative performance of each index in period t-1 compared to the cross sectional average return 𝑅𝑚𝑡−11 of the previous period t-1.
Hence, in a next step, the (j) week formation period return of each index is calculated, allowing then to determine the cross-sectional average of the formation period returns. I subtract the cross-sectional average return from each individual formation period return to attain the return deviation of each index. The actual deviation from the cross sectional average return in period t-1, positive or negative,
1 The cross-sectional average return Rmt−1 is given by expression: Rmt−1=1
N ∑Ni=1Rit−1
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corresponds to the long or short position taken in the respective index during period t. It follows that indices that have underperformed relative to the cross sectional average return in period t-1 become
“short” positions in the momentum portfolio, whereas outperforming indices become “long” positions.
The momentum portfolios resulting from this strategy always contain all of the available indices N at each point in time. The magnitude of under- or outperformance is proportionally reflected in each index’s portfolio weight.
(2)
𝑤𝑖𝑡(𝑘) = 1
𝑁(𝑅𝑖𝑡−1− 𝑅𝑚𝑡−1)
The above portfolio weighing function (2) implements the above described “momentum concept” by yielding a positive value i.e. a long position for stock indices that performed well in the previous period and a negative value i.e. a short position for stock indices that performed poorly relative to the cross-sectional average in period t-1.
The weight 𝑤𝑖𝑡(𝑘) assigned to each country’s stock index is proportional to the degree of deviation of its return from the cross-sectional average return. It follows that countries whose returns deviated more strongly in the previous period t-1 consequently attain greater weights in the momentum portfolio held in period t.
Furthermore, since portfolio weights are proportionate to the individual deviations from the cross- sectional average return, it must always be true that the sum of all weights is zero ∑N𝑖=1𝑤𝑖𝑡(𝑘)= 0.
Proportionally, the strategy buys and sells offsetting positions. Thus, the strategy leads to a zero cost arbitrage portfolio. I further assume no restrictions on short selling and make no adjustments for trading costs.
3.2.2 Assessing the Currency Effect
In order to examine the currency effect in respect to the profitability of momentum strategies, I apply the strategy given by equation i using both US Dollar and local currency denominated data. To this end, I derive four different variations of the above described momentum strategy. Since the portfolio weights as well as the holding period returns can be computed from either US Dollar data or local currency data, four different possible strategies emerge. Expression (5) presents the four variations of the strategy, where components marked with the $ symbol stem from the dataset in US Dollars.
(3)
𝜋𝑡1(𝑘) = ∑ 𝑤𝑖𝑡$(𝑘)𝑅𝑖𝑡$(𝑘)
𝑁
𝑖=1
𝜋𝑡3(𝑘) = ∑ 𝑤𝑖𝑡(𝑘)𝑅𝑖𝑡$(𝑘)
𝑁
𝑖=1
14 𝜋𝑡2(𝑘) = ∑ 𝑤𝑖𝑡(𝑘)𝑅𝑖𝑡(𝑘)
𝑁
𝑖=1
𝜋𝑡4(𝑘) = ∑ 𝑤𝑖𝑡$(𝑘)𝑅𝑖𝑡(𝑘)
𝑁
𝑖=1
In strategy 𝜋𝑡1(𝑘) I determine both the portfolio composition, as well as the subsequently earned returns on the positions using US Dollar market data. This strategy is identical to the strategy used by Chan, Hameed and Tong (1999) and adopts the perspective of a US investor.
For strategy πt2(k) I compute both the weights and the subsequently earned returns using local currency data. Since no currency conversion is involved, this strategy captures the pure international momentum returns. Such a strategy either assumes no particular investors perspective at all, or adopts that of a global investor with assets and liabilities across all considered markets. This strategy also exemplifies the merely theoretical results for a “representative global investor”.
In strategy πt3(k) I determine the portfolio weights using local currency data, returns are measured in US Dollars. This strategy again adopts the perspective of an US investor who incurs the returns in his reference currency but implements the momentum portfolio based on local currency data. This approach is motivated by the notion that the portfolio weights computed from local currencies capture existing momentum more effectively since the formation period performance is unaffected by currency exchange rate movements.
In strategy πt4(k) I compute the portfolio weights using US Dollar data while measuring the resulting momentum returns in local currencies. Regarding the returns again, either no particular investor’s perspective is adopted, or that of a representative international investor.
For a more illustrative account of the strategy I refer the interested reader to appendix 9.
In the spirit of Chan, Hameed and Tong (1999) I compute the weekly returns to all four strategies.
This return measure is calculated by dividing the t-period returns by the product of the long/short margin, the length of the holding period and the amount of investment in long or short positions;
𝜋𝑡(𝑘) (0.5 ∗ 𝑘 ∗ 𝐼⁄ 𝑡(𝑘)). The returns can be interpreted as the weekly profit from the zero cost arbitrage momentum strategies.
I examine the magnitude and significance of the weekly average returns to all strategies and report t- values for the returns of all strategies. Furthermore, I assess whether the mean returns of the four strategies are significantly different from each other by conducting a paired sample t-test for all strategy pairs. A t-value above the critical value indicates that a currency effect leads to significantly different outcome.
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4 Empirical Results
This section reports the main results from the analysis and is structured as follows: First, general summary statistics are provided, followed by a commented overview of the strategies’ outcome for the four-week holding period. The remainder of the section concludes by reporting the findings from the robustness tests.
4.1 Summary Statistics
Appendix 2 contains table 2 presenting summary statistics of the weekly return data from the 23 indices used in this study. The table shows for both US Dollar and local currency data the weekly mean returns as well as weekly maximum returns, minimum returns, standard deviation. Furthermore the table shows the correlation statistics and p-values for a two sample t-test of the identical index data in both currencies. Examining the correlations between weekly US Dollar and local currency based return series averaging at 0.78, immediately makes the gravity extent of the currency effect apparent.
4.2 Results for the 4 week Holding Period
I implement the four different strategies as described in the previous section on an investment universe consisting of 23 stock market indices, using a holding period of 4 weeks. The fifteen-year sample period spans from January 1980 until July 1995. In period t, the portfolios contain long positions in the winner indices and short positions in the loser indices of the previous period t-1. Table 3 displays the outcomes of the 4-week holding period.
Table 3: Average Weekly Profits to all four Momentum Strategies implemented in 23 Countries over the full Sample Period and a 4-week Holding Period. (1980-1995)
πt1(k), πt2(k) πt3(k) πt4(k)
(k) = 4-weeks 0.2225 0.2150 0.2529 0.1635
(4.73)*** (4.76)*** (5.29)*** (3.68)***
This table displays the average weekly profits in percentages to the momentum strategies 1-4 for the 4-week holding period. The numbers in parentheses are the t-statistics. Significance levels of 10% 5% and 1 % are indicated with
*,**,*** correspondingly.
Table 2 presents the average weekly momentum returns to all four strategies for the holding period of four weeks. All strategies exhibit positive average weekly momentum returns, which are highly significant. The entirely US Dollar based strategy 𝜋𝑡1(𝑘) yields a weekly average return of 0.2225%, which is slightly greater than the 0.2150% attained in strategy 𝜋𝑡2(𝑘) which is entirely local currencies
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based. Strategy 𝜋𝑡3(𝑘) for which the portfolio weights stem from local currency data, but returns are incurred in US Dollars, exhibits with 0.2529% the largest average weekly profit of the four strategies.
Contrarily strategy 𝜋𝑡4(𝑘) where portfolio weights are computed from US Dollar data, but profits incur in local currencies yields the smallest weekly average return of 0.1635%.
To assess whether the average weekly mean returns of the four strategies are significantly different from each other, I conduct a paired sample t-test. Table 4 shows the t-statistics of the paired two- sample t-tests of all strategy pairs.
Table 4: Overview of the Outcomes of the Paired Two-Sample T-tests of all Strategy Pairs for the 4-week Holding Period.
(k) = 4-weeks 𝜋𝑡1(𝑘) 𝜋𝑡2(𝑘) 𝜋𝑡3(𝑘) 𝜋𝑡4(𝑘)
𝜋𝑡1(𝑘)
𝜋𝑡2(𝑘) (0.42)
𝜋𝑡3(𝑘) (2.06)** (2.84)***
𝜋𝑡4(𝑘) (-4.32)*** (-4.34)*** (-5.12)***
The values in parentheses are the t-values from the paired two-sample T-test of the strategy pairs given by the strategy in the vertical column and the strategy in the horizontal row. A value greater than a corresponding critical value signals that the difference in mean returns of the two considered strategies is significant.
Significance levels of 10% 5% and 1 % are indicated with *,**,*** correspondingly.
The t-value of 0.4162for the two-sample t-test implies that the mean returns of the entirely US Dollar based strategy 𝜋𝑡1(𝑘) and entirely local currency based strategy 𝜋𝑡2(𝑘) are not significantly different from each other. The mean returns of strategy pairs 𝜋𝑡1(𝑘) and 𝜋𝑡4(𝑘) as well as 𝜋𝑡2(𝑘) and 𝜋𝑡3(𝑘) in which the strategies share identical portfolio weights but earn their returns in US Dollars and local currencies respectively, are significantly different from each other with corresponding t-values of (-) 4.3227 and 2.8394. Strategy pairs 𝜋𝑡1(𝑘)and 𝜋𝑡3(𝑘) as well as 𝜋𝑡2(𝑘) and 𝜋𝑡4(𝑘) in which portfolio weights stem from different data-sets but returns incur in the same currency set-up – either US Dollars or local currencies – exhibit significantly different mean returns too. With the exception of strategy pair 𝜋𝑡1(𝑘)and 𝜋𝑡3(𝑘) all values imply significance at 1% level.
Interpretation and Comparison of Strategies
Examining the difference in outcomes of strategy 𝜋𝑡1(𝑘) and 𝜋𝑡2(𝑘) highlights the implications of the currency effect in general. The weights and the incurred returns of strategy 𝜋𝑡1(𝑘) stem from the US Dollar data set, whereas the weights and returns from strategy 𝜋𝑡2(𝑘) originate from the local currencies data set. Therefore, the two strategies do not only have different portfolio compositions but they also measure their returns in different currencies. Comparing the two strategies thus exhibits the full range of implications attributable to the currency effect. A difference can originate from both the different weights as well as the different returns.
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I find that both strategies earn highly significant and positive weekly mean returns which differ only slightly in magnitude. Furthermore the outcome of the paired sample t-test implies that the mean returns of the two strategies are not significantly different from each other. These findings indicate, that for the four-week holding period the choice of the currency does not matter, as there is no evidence for a currency effect.
In a next step, the differences in outcomes of strategy pairs 𝜋𝑡1(𝑘) and πt4(k) as well as πt2(k) and πt3(k) are examined. Since the portfolio composition within each strategy pair is identical, the disparities in returns must stem from the differences in the measurement of the returns and thus from the currency effect. Keeping portfolio weights constant stresses the implications of the currency effect under adaption of different investor perspectives. I compared strategy pairs 𝜋𝑡1(𝑘) and πt4(k) as well as πt2(k) and πt3(k), where each pair shares identical portfolio weights stemming from the same data set. I find that the identical portfolios indeed yield different results. In strategy 𝜋𝑡1(𝑘) the portfolio weights based on US Dollars lead to an average weekly momentum profit in US Dollars of 0.2225%.
However, measured in local currencies the same portfolio yields an average weekly profit of only 0.1635%. The paired sample t-test indicates that the returns of the two strategies are significantly different from each other. Similarly in strategy πt3(k) the portfolio weights formed from local currency data lead to an average weekly return of 0.2529% when measured in US Dollars, and merely 0.2150%
when measured in local currencies. The paired sample t-test again indicates that the two outcomes are significantly different from each other.
It can be observed that in both cases returns are larger when measured in US Dollars. This indicates that parts of these returns are not due to momentum of the stock markets indices but due changes in the currency exchange rates, i.e. a weakening of the US Dollar during the sample period. The paired sample t-tests indicate the presence of a spurious effect, which results from the adoption of a US Investor perspective.
While keeping the returns constant, I compare strategy pairs, 𝜋𝑡1(𝑘) and πt3(k) as well as πt2(k) and πt4(k) . Each strategy pair measures its returns in the same currency set-up but the portfolio compositions within each pair stem from either US Dollar or local currency data. Disparities in outcomes within each pair must result from the different portfolio weights. Thus a comparison of these strategies exhibits the implications of the currency effect for the portfolio building process. The outcome of this comparison might hold suggestions for momentum based global asset allocation decisions.
Strategies 𝜋𝑡1(𝑘) and πt3(k) both adopt the perspective of a US Investor as they incur profits in US Dollars. The US Dollar based weights of Strategy 𝜋𝑡1(𝑘) lead to an average weekly return of 0.2225%, which is smaller than the 0.2529% return resulting from the local currency based weights of strategy πt3(k). The paired sample t-test indicates that the difference is significant on a 10% and 5% level but not on a 1% level. Similarly, for the returns incurred in local currencies, US Dollar portfolio weights
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lead to smaller returns than local currency weights, as Strategy πt4(k) yields 0.1635% and strategy πt2(k) 0.2150%. Again the mean returns of the strategies are highly significantly different from each other. In both cases the portfolios that were formed from local currency data lead to greater returns than those stemming from US Dollar data. This observation suggests that strategies that compute their portfolio compositions based on local currency data capture existing momentum more effectively than those who use common currency data.
My main findings exhibit that the entirely US Dollar or local currencies based strategies produce only marginally different returns, which are not significantly different from each other. However, identical portfolios lead to significantly different outcomes when their returns are measured in either US Dollars or local currencies. Notably, returns measured in US Dollars tend to be greater than returns measured in local currencies. Furthermore, both a US Dollar investor as well as a representative international investor earns significantly greater returns when they determine portfolio weights from local currencies rather than US Dollar data. I find the choice of the currency framework to be decisive for the outcomes of the momentum strategies and thus interpret these findings as evidence for a spurious effect caused by the use of a common currency rather than local currencies.
4.3 Robustness Testing
Robustness of my findings are assessed by applying the above momentum strategies for holing periods of 1, 2, 12 and 26 weeks. Table 5 presents the average weekly returns and corresponding t-values to all four strategies for all holding periods. For the corresponding tables for all holding periods containing the outcomes of the paired two sample T-tests of all strategy pairs, please refer to appendix 1 tables 6- 9. I find that the weekly average returns to all strategies remain positive for all holding periods. The large majority of returns is significant at a 1% level, with exception of strategies πt1(k) and πt4(k) in the 1-week and twelve 12-week holding period.
The significant weekly average returns of the fully US Dollar or local currency based strategies πt1(k) and πt2(k) do not suggest a clear pattern regarding which strategy yields the larger return. The outcomes of the paired sample t-tests, which are reported in the appendix to this paper, however confirm my earlier findings that the mean returns to the two strategies are not significantly different from each other, with exception of the 12-week holding period. These findings confirm the observation from the 4-week holding period returns.
full Sample Period (1980-1995)
πt1(k) πt2(k) πt3(k) πt4(k)
(k) = 1-week 0.2475 0.2877 0.3112 0.2533
(2.38)** (2.83)*** (2.92)*** (2.61)***
(k) = 2-week 0.4724 0.4501 0.5031 0.4092
(6.91)*** (6.80)*** (7.20)*** (6.37)***
(k) = 4-week 0.2225 0.2150 0.2529 0.1635
(4.73)*** (4.76)*** (5.29)*** (3.68)***
(k) = 12-week 0.1130 0.0652 0.1147 0.0343
(3.75)*** (2.43)** (3.88)*** (1.28)
(k) = 26-week 0.1227 0.1315 0.1611 0.0730
(6.01)*** (6.96)*** (7.93)*** (3.96)***
This table displays the average weekly profits in percentages to the momentum strategies 1-4 for all holding periods from 1 week to 26 weeks. The numbers in parentheses are the t-statistics. Significance levels of 10% 5%
and 1 % are indicated by *,**,***, correspondingly.
The robustness tests moreover confirm the observation that for the sample period of this paper, returns measured in US Dollars tend to be greater than returns measured in local currencies. This difference is significant for both strategy pairs 𝜋𝑡1(𝑘) and πt4(k) as well as πt2(k) and πt3(k) and all holding periods except for the 1-week holding period.
The robustness results furthermore confirm the earlier stated implications for the portfolio building process. Determining portfolio weights from a dataset in either a common or local currencies leads to significantly different momentum returns. Portfolio weights based on local currency data yield greater returns than US Dollar based weights. This is true for returns measured in US Dollars as well as for returns in local currencies. This observation further supports the notion that the use of a common currency has a spurious effect when capturing momentum in stock markets.
